Theoretical analysis of optical poling and frequency doubling effect based on classical model

NASA Astrophysics Data System (ADS)

Feng, Xi; Li, Fuquan; Lin, Aoxiang; Wang, Fang; Chai, Xiangxu; Wang, Zhengping; Zhu, Qihua; Sun, Xun; Zhang, Sen; Sun, Xibo

2018-03-01

Optical poling and frequency doubling effect is one of the effective manners to induce second order nonlinearity and realize frequency doubling in glass materials. The classical model believes that an internal electric field is built in glass when it's exposed by fundamental and frequency-doubled light at the same time, and second order nonlinearity appears as a result of the electric field and the orientation of poles. The process of frequency doubling in glass is quasi phase matched. In this letter, the physical process of poling and doubling process in optical poling and frequency doubling effect is deeply discussed in detail. The magnitude and direction of internal electric field, second order nonlinear coefficient and its components, strength and direction of frequency doubled output signal, quasi phase matched coupled wave equations are given in analytic expression. Model of optical poling and frequency doubling effect which can be quantitatively analyzed are constructed in theory, which set a foundation for intensive study of optical poling and frequency doubling effect.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Optical nonlinearities of excitons in monolayer MoS2

NASA Astrophysics Data System (ADS)

Soh, Daniel B. S.; Rogers, Christopher; Gray, Dodd J.; Chatterjee, Eric; Mabuchi, Hideo

2018-04-01

We calculate linear and nonlinear optical susceptibilities arising from the excitonic states of monolayer MoS2 for in-plane light polarizations, using second-quantized bound and unbound exciton operators. Optical selection rules are critical for obtaining the susceptibilities. We derive the valley-chirality rule for the second-order harmonic generation in monolayer MoS2 and find that the third-order harmonic process is efficient only for linearly polarized input light while the third-order two-photon process (optical Kerr effect) is efficient for circularly polarized light using a higher order exciton state. The absence of linear absorption due to the band gap and the unusually strong two-photon third-order nonlinearity make the monolayer MoS2 excitonic structure a promising resource for coherent nonlinear photonics.

Nonlinear optical effects on the surface of acridine yellow-doped lead-tin fluorophosphate glass

NASA Technical Reports Server (NTRS)

He, K. X.; Bryant, William; Venkateswarlu, Putcha

1991-01-01

The second- and third-order nonlinear optical properties of acridine yellow-doped lead-tin fluorophosphate (LTF) glass have been directly studied by measurement of surface enhanced second harmonic generation and third harmonic generation. The three photon excitation fluorescence is also observed. Based on these results, the large nonlinearities of the acridine LTF system which is a new nonlinear optical material are experimentally demonstrated.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Second-order processing of four-stroke apparent motion.

PubMed

Mather, G; Murdoch, L

1999-05-01

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

Retrieval of all effective susceptibilities in nonlinear metamaterials

NASA Astrophysics Data System (ADS)

Larouche, Stéphane; Radisic, Vesna

2018-04-01

Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magnetoelectric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In this work, we generalize a nonlinear transfer matrix approach to account for all nonlinear susceptibility terms and show how to use this approach to retrieve all effective nonlinear susceptibilities of metamaterial elements. The approach is demonstrated using sum frequency generation, but can be applied to other second-order or higher-order processes.

A dual-input nonlinear system analysis of autonomic modulation of heart rate

NASA Technical Reports Server (NTRS)

Chon, K. H.; Mullen, T. J.; Cohen, R. J.

1996-01-01

Linear analyses of fluctuations in heart rate and other hemodynamic variables have been used to elucidate cardiovascular regulatory mechanisms. The role of nonlinear contributions to fluctuations in hemodynamic variables has not been fully explored. This paper presents a nonlinear system analysis of the effect of fluctuations in instantaneous lung volume (ILV) and arterial blood pressure (ABP) on heart rate (HR) fluctuations. To successfully employ a nonlinear analysis based on the Laguerre expansion technique (LET), we introduce an efficient procedure for broadening the spectral content of the ILV and ABP inputs to the model by adding white noise. Results from computer simulations demonstrate the effectiveness of broadening the spectral band of input signals to obtain consistent and stable kernel estimates with the use of the LET. Without broadening the band of the ILV and ABP inputs, the LET did not provide stable kernel estimates. Moreover, we extend the LET to the case of multiple inputs in order to accommodate the analysis of the combined effect of ILV and ABP effect on heart rate. Analyzes of data based on the second-order Volterra-Wiener model reveal an important contribution of the second-order kernels to the description of the effect of lung volume and arterial blood pressure on heart rate. Furthermore, physiological effects of the autonomic blocking agents propranolol and atropine on changes in the first- and second-order kernels are also discussed.

Rigorous theory of molecular orientational nonlinear optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwak, Chong Hoon, E-mail: chkwak@ynu.ac.kr; Kim, Gun Yeup

2015-01-15

Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecularmore » hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented.« less

Effective potentials in nonlinear polycrystals and quadrature formulae

NASA Astrophysics Data System (ADS)

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Effective potentials in nonlinear polycrystals and quadrature formulae.

PubMed

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides.

PubMed

Chmielak, Bartos; Matheisen, Christopher; Ripperda, Christian; Bolten, Jens; Wahlbrink, Thorsten; Waldow, Michael; Kurz, Heinrich

2013-10-21

We present detailed investigations of the local strain distribution and the induced second-order optical nonlinearity within strained silicon waveguides cladded with a Si₃N₄ strain layer. Micro-Raman Spectroscopy mappings and electro-optic characterization of waveguides with varying width w(WG) show that strain gradients in the waveguide core and the effective second-order susceptibility χ(2)(yyz) increase with reduced w(WG). For 300 nm wide waveguides a mean effective χ(2)(yyz) of 190 pm/V is achieved, which is the highest value reported for silicon so far. To gain more insight into the origin of the extraordinary large optical second-order nonlinearity of strained silicon waveguides numerical simulations of edge induced strain gradients in these structures are presented and discussed.

Nonlinear optical properties of organic materials V; Proceedings of the 5th Meeting, San Diego, CA, July 22-24, 1992

NASA Astrophysics Data System (ADS)

Williams, David J.

The present volume on nonlinear optical properties of organic materials discusses organic nonlinear optics, polymers for nonlinear optics, characterization of nonlinear properties, photorefractive and second-order materials, harmonic generation in organic materials, and devices and applications. Particular attention is given to organic semiconductor-doped polymer glasses as novel nonlinear media, heterocyclic nonlinear optical materials, loss measurements in electrooptic polymer waveguides, the phase-matched second-harmonic generation in planar waveguides, electrooptic measurements in poled polymers, transient effects in spatial light modulation by nonlinearity-absorbing molecules, the electrooptic effects in organic single crystals, surface acoustic wave propagation in an organic nonlinear optical crystal, nonlinear optics of astaxanthin thin films; and advanced high-temperature polymers for integrated optical waveguides. (No individual items are abstracted in this volume)

Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions

NASA Astrophysics Data System (ADS)

Ma, Hui; Li, Hui; Niu, Heqiang; Song, Rongze; Wen, Bangchun

2013-11-01

The operating speed of the rotating machinery often exceeds the second or even higher order critical speeds to pursue higher efficiency. Thus, how to restrain the higher order mode instability caused by the nonlinear oil-film force and seal force at high speed as far as possible has become more and more important. In this study, a lumped mass model of a rotor-bearing-seal system considering the gyroscopic effect is established. The graphite self-lubricating bearing and the sliding bearing are simulated by a spring-damping model and a nonlinear oil-film force model based on the assumption of short bearings, respectively. The seal is simulated by Muszynska nonlinear seal force model. Effects of the seal force and oil-film force on the first and second mode instabilities are investigated under two loading conditions which are determined by API Standard 617 (Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, Seventh Edition). The research focuses on the effects of exciting force forms and their magnitudes on the first and second mode whips in a rotor-bearing-seal system by using the spectrum cascades, vibration waveforms, orbits and Poincaré maps. The first and second mode instability laws are compared by including and excluding the seal effect in a rotor system with single-diameter shaft and two same discs. Meanwhile, the instability laws are also verified in a rotor system with multi-diameter shaft and two different discs. The results show that the second loading condition (out-of-phase unbalances of two discs) and the nonlinear seal force can mainly restrain the first mode instability and have slight effects on the second mode instability. This study may contribute to a further understanding about the higher order mode instability of such a rotor system with fluid-induced forces from the oil-film bearings and seals.

Vector breather-to-soliton transitions and nonlinear wave interactions induced by higher-order effects in an erbium-doped fiber

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei; Xie, Xi-Yang

2018-06-01

Vector breather-to-soliton transitions for the higher-order nonlinear Schrödinger-Maxwell-Bloch (NLS-MB) system with sextic terms are investigated. The Lax pair and Darboux transformation (DT) of such system are constructed. With the DT, analytic vector breather solutions up to the second order are obtained. With appropriate choices of the spectra parameters, vector breather-to-soliton transitions happen. Interaction mechanisms of vector nonlinear waves (breather-soliton or soliton-soliton interactions) are displayed.

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

PubMed

Ho, Yuh-Shan

2006-01-01

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

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

PubMed

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

2017-07-01

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

Giant enhancement of second harmonic generation in nonlinear photonic crystals with distributed Bragg reflector mirrors.

PubMed

Ren, Ming-Liang; Li, Zhi-Yuan

2009-08-17

We theoretically investigate second harmonic generation (SHG) in one-dimensional multilayer nonlinear photonic crystal (NPC) structures with distributed Bragg reflector (DBR) as mirrors. The NPC structures have periodic modulation on both the linear and second-order susceptibility. Three major physical mechanisms, quasi-phase matching (QPM) effect, slow light effect at photonic band gap edges, and cavity effect induced by DBR mirrors can be harnessed to enhance SHG. Selection of appropriate structural parameters can facilitate coexistence of these mechanisms to act collectively and constructively to create very high SHG conversion efficiency with an enhancement by up to seven orders of magnitude compared with the ordinary NPC where only QPM works. (c) 2009 Optical Society of America

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

NASA Astrophysics Data System (ADS)

Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

2014-07-01

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

Non-linear effects in bunch compressor of TARLA

NASA Astrophysics Data System (ADS)

Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin

2016-03-01

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.

Quasi-phase-matching and second-harmonic generation enhancement in a semiconductor microresonator array using slow-light effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumeige, Yannick

We theoretically analyze the second-harmonic generation process in a sequence of unidirectionnaly coupled doubly resonant whispering gallery mode semiconductor resonators. By using a convenient design, it is possible to coherently sum the second-harmonic fields generated inside each resonator. We show that resonator coupling allows the bandwidth of the phase-matching curve to be increased with respect to single-resonator configurations simultaneously taking advantage of the resonant feature of the resonators. This quasi-phase-matching technique could be applied to obtain small-footprint nonlinear devices with large bandwidth and limited nonlinear losses. The results are discussed in the framework of the slow-light-effect enhancement of second-order opticalmore » nonlinearities.« less

From SHG to mid-infrared SPDC generation in strained silicon waveguides

NASA Astrophysics Data System (ADS)

Castellan, Claudio; Trenti, Alessandro; Mancinelli, Mattia; Marchesini, Alessandro; Ghulinyan, Mher; Pucker, Georg; Pavesi, Lorenzo

2017-08-01

The centrosymmetric crystalline structure of Silicon inhibits second order nonlinear optical processes in this material. We report here that, by breaking the silicon symmetry with a stressing silicon nitride over-layer, Second Harmonic Generation (SHG) is obtained in suitably designed waveguides where multi-modal phase-matching is achieved. The modeling of the generated signal provides an effective strain-induced second order nonlinear coefficient of χ(2) = (0.30 +/- 0.02) pm/V. Our work opens also interesting perspectives on the reverse process, the Spontaneous Parametric Down Conversion (SPDC), through which it is possible to generate mid-infrared entangled photon pairs.

Nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps

NASA Astrophysics Data System (ADS)

Zhang, Yu; McGilligan, Clancy; Zhou, Liang; Vig, Mark; Jiang, Jack J.

2004-05-01

Phase space reconstruction, correlation dimension, and second-order entropy, methods from nonlinear dynamics, are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps. Two conventional acoustic perturbation parameters, jitter and shimmer, are also employed to analyze voices before and after surgery. Presurgical and postsurgical analyses of jitter, shimmer, correlation dimension, and second-order entropy are statistically compared. Correlation dimension and second-order entropy show a statistically significant decrease after surgery, indicating reduced complexity and higher predictability of postsurgical voice dynamics. There is not a significant postsurgical difference in shimmer, although jitter shows a significant postsurgical decrease. The results suggest that jitter and shimmer should be applied to analyze disordered voices with caution; however, nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps.

Proceedings of the Second Annual Symposium for Nondestructive Evaluation of Bond Strength

NASA Technical Reports Server (NTRS)

Roberts, Mark J. (Compiler)

1999-01-01

Ultrasonics, microwaves, optically stimulated electron emission (OSEE), and computational chemistry approaches have shown relevance to bond strength determination. Nonlinear ultrasonic nondestructive evaluation methods, however, have shown the most effectiveness over other methods on adhesive bond analysis. Correlation to changes in higher order material properties due to microstructural changes using nonlinear ultrasonics has been shown related to bond strength. Nonlinear ultrasonic energy is an order of magnitude more sensitive than linear ultrasound to these material parameter changes and to acoustic velocity changes caused by the acoustoelastic effect when a bond is prestressed. Signal correlations between non-linear ultrasonic measurements and initialization of bond failures have been measured. This paper reviews bond strength research efforts presented by university and industry experts at the Second Annual Symposium for Nondestructive Evaluation of Bond Strength organized by the NDE Sciences Branch at NASA Langley in November 1998.

Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).

PubMed

Asaumi, K

1993-10-20

A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Efficient second harmonic generation by para-nitroaniline embedded in electro-spun polymeric nanofibres

NASA Astrophysics Data System (ADS)

Gonçalves, Hugo; Saavedra, Inês; Ferreira, Rute AS; Lopes, PE; de Matos Gomes, Etelvina; Belsley, Michael

2018-03-01

Intense well polarized second harmonic light was generated by poly(methyl methacrylate) nanofibres with embedded para-nitroaniline nanocrystals. Subwavelength diameter fibres were electro-spun using a 1:2 weight ratio of chromophore to polymer. Analysis of the generated second harmonic light indicates that the para-nitroaniline molecules, which nominally crystalize in the centrosymmetric space group, were organized into noncentrosymmetric structures leading to a second order susceptibility dominated by a single tensor element. Under the best deposition conditions, the nanofibrers display an effective nonlinear optical susceptibility approximately two orders of magnitude greater than that of potassium dihydrogen phosphate. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which nominally form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient sub-micron sized second harmonic light generators.

Observed galaxy number counts on the lightcone up to second order: I. Main result

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertacca, Daniele; Maartens, Roy; Clarkson, Chris, E-mail: daniele.bertacca@gmail.com, E-mail: roy.maartens@gmail.com, E-mail: chris.clarkson@gmail.com

2014-09-01

We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.

{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hubbard, S.F.; Petschek, R.G.; Singer, K.D.

1997-10-01

We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light formore » which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.« less

Non-linear effects in bunch compressor of TARLA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yildiz, Hüseyin, E-mail: huseyinyildiz006@gmail.com, E-mail: huseyinyildiz@gazi.edu.tr; Aksoy, Avni; Arikan, Pervin

2016-03-25

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects onmore » bunch compressor of TARLA.« less

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

Periodically poled silicon

NASA Astrophysics Data System (ADS)

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

2009-03-01

We propose a new class of photonic devices based on periodic stress fields in silicon that enable second-order nonlinearity as well as quasi-phase matching. Periodically poled silicon (PePSi) 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 second-order nonlinear effects. As an example of the utility of the PePSi technology, we present simulations showing that midwave infrared radiation can be efficiently generated through difference frequency generation from near-infrared with a conversion efficiency of 50%.

Third-Order Optical Nonlinearities of Squarylium Dyes with Benzothiazole Donor Groups Measured Using the Picosecond Z-Scan Technique

NASA Astrophysics Data System (ADS)

Li, Zhong-Yu; Xu, Song; Chen, Zi-Hui; Zhang, Fu-Shi; Kasatani, Kazuo

2011-08-01

Third-order optical nonlinearities of two squarylium dyes with benzothiazole donor groups (BSQ1 and BSQ2) in chloroform solution are measured by a picosecond Z-scan technique at 532 nm. It is found that the two compounds show the saturation absorption and nonlinear self-focus refraction effect. The molecular second hyperpolarizabilities are calculated to be 7.46 × 10-31 esu and 5.01 × 10-30 esu for BSQ1 and BSQ2, respectively. The large optical nonlinearities of squarylium dyes can be attributed to their rigid and intramolecular charge transfer structure. The difference in γ values is attributed to the chloro group of benzene rings of BSQ2 and the one-photon resonance effect. It is found that the third-order nonlinear susceptibilities of two squarylium dyes are mainly determined by the real parts of χ(3), and the large optical nonlinearities of studied squarylium dyes can be attributed to the nonlinear refraction.

Oscillation theorems for second order nonlinear forced differential equations.

PubMed

Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md

2014-01-01

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Anomalous nonlinear absorption in epsilon-near-zero materials: optical limiting and all-optical control.

PubMed

Vincenti, M A; de Ceglia, D; Scalora, Michael

2016-08-01

We investigate nonlinear absorption in films of epsilon-near-zero materials. The combination of large local electric fields at the fundamental frequency and material losses at the harmonic frequencies induce unusual intensity-dependent phenomena. We predict that the second-order nonlinearity of a low-damping, epsilon-near-zero slab produces an optical limiting effect that mimics a two-photon absorption process. Anomalous absorption profiles that depend on low permittivity values at the pump frequency are also predicted for third-order nonlinearities. These findings suggest new opportunities for all-optical light control and novel ways to design reconfigurable and tunable nonlinear devices.

Nonlinear estimation theory applied to orbit determination

NASA Technical Reports Server (NTRS)

Choe, C. Y.

1972-01-01

The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Second order nonlinear equations of motion for spinning highly flexible line-elements. [for spacecraft solar sail

NASA Technical Reports Server (NTRS)

Salama, M.; Trubert, M.

1979-01-01

A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

In situ SHG monitoring of dipolar orientation and relaxation in Disperse Red type/derivative urethane-urea copolymer

NASA Astrophysics Data System (ADS)

Samoc, A.; Holland, A.; Tsuchimori, M.; Watanabe, O.; Samoc, M.; Luther-Davies, B.; Kolev, V. Z.

2005-09-01

We investigated linear optical and second-order nonlinear optical (NLO) properties of films of urethane-urea copolymer (UU2) functionalised with a high concentration of an azobenzene chromophore. The polymer films on ITO-coated substrate were corona poled to induce a noncentrosymmetric organization of chromophore dipoles and data on the second harmonic generated with the laser beam (the fundamental wavelength 1053 nm, 6 ps/pulse, 20 Hz repetition rate) was acquired as a function of time and temperature. Second harmonic generation (SHG) was used to monitor in situ the polar alignment and relaxation of orientation of the side-chain Disperse Red-like chromophore molecules in the films poled at room temperature and high above the glass transition temperature (Tg 140-150oC). The deff coefficient was determined from the Maker-fringe method and corrected for absorption. A strong second harmonic effect with a fast relaxation was observed in "cold" (room temperature) poling experiments. A large second-order resonantly enhanced optical nonlinearity (d33 of the order of 200 pm/V) was obtained in high temperature poling. A strong and stable nonlinearity has persisted for years after the films were high-temperature poled.

Optical polarization based logic functions (XOR or XNOR) with nonlinear Gallium nitride nanoslab.

PubMed

Bovino, F A; Larciprete, M C; Giardina, M; Belardini, A; Centini, M; Sibilia, C; Bertolotti, M; Passaseo, A; Tasco, V

2009-10-26

We present a scheme of XOR/XNOR logic gate, based on non phase-matched noncollinear second harmonic generation from a medium of suitable crystalline symmetry, Gallium nitride. The polarization of the noncollinear generated beam is a function of the polarization of both pump beams, thus we experimentally investigated all possible polarization combinations, evidencing that only some of them are allowed and that the nonlinear interaction of optical signals behaves as a polarization based XOR. The experimental results show the peculiarity of the nonlinear optical response associated with noncollinear excitation, and are explained using the expression for the effective second order optical nonlinearity in noncollinear scheme.

Nonlinear identification of the total baroreflex arc: higher-order nonlinearity

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2016-01-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R2 values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R2 values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R2 values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions. PMID:27629885

Approximate analytical solutions of a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan; Öhberg, Patrik

2015-02-01

The Hamiltonian and the corresponding equations of motion involving the field operators of two quartic anharmonic oscillators indirectly coupled via a linear oscillator are constructed. The approximate analytical solutions of the coupled differential equations involving the non-commuting field operators are solved up to the second order in the anharmonic coupling. In the absence of nonlinearity these solutions are used to calculate the second order variances and hence the squeezing in pure and in mixed modes. The higher order quadrature squeezing and the amplitude squared squeezing of various field modes are also investigated where the squeezing in pure and in mixed modes are found to be suppressed. Moreover, the absence of a nonlinearity prohibits the higher order quadrature and higher ordered amplitude squeezing of the input coherent states. It is established that the mere coupling of two oscillators through a third one is unable to produce any squeezing effects of input coherent light, but the presence of a nonlinear interaction may provide squeezed states and other nonclassical phenomena.

A Second-Order Conditionally Linear Mixed Effects Model with Observed and Latent Variable Covariates

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Kohli, Nidhi; Silverman, Rebecca D.; Speece, Deborah L.

2012-01-01

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

NASA Astrophysics Data System (ADS)

Smirnova, Daria; Smirnov, Alexander I.; Kivshar, Yuri S.

2018-01-01

By combining analytical and numerical approaches, we study resonantly enhanced second-harmonic generation by individual high-index dielectric nanoparticles made of centrosymmetric materials. Considering both bulk and surface nonlinearities, we describe second-harmonic nonlinear scattering from a silicon nanoparticle optically excited in the vicinity of the magnetic and electric dipolar resonances. We discuss the contributions of different nonlinear sources and the effect of the low-order optical Mie modes on the characteristics of the generated far field. We demonstrate that the multipolar expansion of the radiated field is dominated by dipolar and quadrupolar modes (two axially symmetric electric quadrupoles, an electric dipole, and a magnetic quadrupole) and the interference of these modes can ensure directivity of the nonlinear scattering. The developed multipolar analysis can be instructive for interpreting the far-field measurements of the nonlinear scattering and it provides prospective insights into a design of complementary metal-oxide-semiconductor compatible nonlinear nanoantennas fully integrated with silicon-based photonic circuits, as well as methods of nonlinear diagnostics.

Optical nonlinearities in plasmonic metamaterials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zayats, Anatoly V.

2016-04-01

Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.

Second-harmonic generation in substoichiometric silicon nitride layers

NASA Astrophysics Data System (ADS)

Pecora, Emanuele; Capretti, Antonio; Miano, Giovanni; Dal Negro, Luca

2013-03-01

Harmonic generation in optical circuits offers the possibility to integrate wavelength converters, light amplifiers, lasers, and multiple optical signal processing devices with electronic components. Bulk silicon has a negligible second-order nonlinear optical susceptibility owing to its crystal centrosymmetry. Silicon nitride has its place in the microelectronic industry as an insulator and chemical barrier. In this work, we propose to take advantage of silicon excess in silicon nitride to increase the Second Harmonic Generation (SHG) efficiency. Thin films have been grown by reactive magnetron sputtering and their nonlinear optical properties have been studied by femtosecond pumping over a wide range of excitation wavelengths, silicon nitride stoichiometry and thermal processes. We demonstrate SHG in the visible range (375 - 450 nm) using a tunable 150 fs Ti:sapphire laser, and we optimize the SH emission at a silicon excess of 46 at.% demonstrating a maximum SHG efficiency of 4x10-6 in optimized films. Polarization properties, generation efficiency, and the second order nonlinear optical susceptibility are measured for all the investigated samples and discussed in terms of an effective theoretical model. Our findings show that the large nonlinear optical response demonstrated in optimized Si-rich silicon nitride materials can be utilized for the engineering of nonlinear optical functions and devices on a Si chip.

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

PubMed

Zhao, Haiquan; Zhang, Jiashu

2009-12-01

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

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

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

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Effets non-lineaires de second ordre dans les verres de silice

NASA Astrophysics Data System (ADS)

Godbout, Nicolas

Materials possessing inversion symmetry can not have a non-zero second-order susceptibility tensor. Since silica glasses are amorphous and isotropic, they possess this symmetry and therefore do not exhibit second-order nonlinear optical effects. However, the symmetry can be broken by several processes. The central question of this thesis is the determination of the mechanisms responsible for the second-order susceptibility in silica glasses after thermal poling. The presence of this nonlinearity arises through one of these mechanisms: the orientation of dipolar moieties possessing a second-order hyperpolarisability, or the build-up of a permanent electric field by charge motion which creates an apparent χ(2) through the already present χ (3). The dipole orientation model has a bigger potential of generating high optical nonlinearities than the built-in field model. This conclusion is based on a study of the crystalline structures of silica. The measurement of Maker fringes is the most informative technique for characterization of the optical properties of bulk poled samples. Measurements on Infrasil™ and Suprasil™ samples show an optically active layer of approximately 9 and 23 microns, with χ(2) susceptibilities of approximately 0.07 pm/V and 0.02 pm/V respectively. The analysis of Maker fringes in a similar sample suggests that the sign of the surface and bulk χ (2)-s is different, supporting the built-in field model as the origin of χ(2). Based on the results analyzed in this thesis, the second- order susceptibility of silica glasses after thermal poling results from the creation of a permanent built-in electric field caused by the movement of cations coupled to the pre-existing third-order nonlinearity. This claim is based on: the observed pump polarization dependence of Maker fringes, predictions of a steady-state ion migration model about the resulting optical properties and their confirmation by optical measurements; the presence of a bulk nonlinearity and its apparent opposite sign to the one of the surface; polarization and depolarization currents showing only signs of ion migration. (Abstract shortened by UMI.)

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

We explore the use of the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the nonlinear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

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

PubMed

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

2015-09-01

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

Electrical control of second-harmonic generation in a WSe 2 monolayer transistor

DOE PAGES

Seyler, Kyle L.; Schaibley, John R.; Gong, Pu; ...

2015-04-20

Nonlinear optical frequency conversion, in which optical fields interact with a nonlinear medium to produce new field frequencies, is ubiquitous in modern photonic systems. However, the nonlinear electric susceptibilities that give rise to such phenomena are often challenging to tune in a given material and, so far, dynamical control of optical nonlinearities remains confined to research laboratories as a spectroscopic tool. In this paper, we report a mechanism to electrically control second-order optical nonlinearities in monolayer WSe 2, an atomically thin semiconductor. We show that the intensity of second-harmonic generation at the A-exciton resonance is tunable by over an ordermore » of magnitude at low temperature and nearly a factor of four at room temperature through electrostatic doping in a field-effect transistor. Such tunability arises from the strong exciton charging effects in monolayer semiconductors, which allow for exceptional control over the oscillator strengths at the exciton and trion resonances. The exciton-enhanced second-harmonic generation is counter-circularly polarized to the excitation laser due to the combination of the two-photon and one-photon valley selection rules, which have opposite helicity in the monolayer. Finally, our study paves the way towards a new platform for chip-scale, electrically tunable nonlinear optical devices based on two-dimensional semiconductors.« less

Selectively Plasmon-Enhanced Second-Harmonic Generation from Monolayer Tungsten Diselenide on Flexible Substrates.

PubMed

Wang, Zhuo; Dong, Zhaogang; Zhu, Hai; Jin, Lei; Chiu, Ming-Hui; Li, Lain-Jong; Xu, Qing-Hua; Eda, Goki; Maier, Stefan A; Wee, Andrew T S; Qiu, Cheng-Wei; Yang, Joel K W

2018-02-27

Monolayer two-dimensional transition-metal dichalcogenides (2D TMDCs) exhibit promising characteristics in miniaturized nonlinear optical frequency converters, due to their inversion asymmetry and large second-order nonlinear susceptibility. However, these materials usually have very short light interaction lengths with the pump laser because they are atomically thin, such that second-harmonic generation (SHG) is generally inefficient. In this paper, we fabricate a judiciously structured 150 nm-thick planar surface consisting of monolayer tungsten diselenide and sub-20 nm-wide gold trenches on flexible substrates, reporting ∼7000-fold SHG enhancement without peak broadening or background in the spectra as compared to WSe 2 on as-grown sapphire substrates. Our proof-of-concept experiment yields effective second-order nonlinear susceptibility of 2.1 × 10 4 pm/V. Three orders of magnitude enhancement is maintained with pump wavelength ranging from 800 to 900 nm, breaking the limitation of narrow pump wavelength range for cavity-enhanced SHG. In addition, SHG amplitude can be dynamically controlled via selective excitation of the lateral gap plasmon by rotating the laser polarization. Such a fully open, flat, and ultrathin profile enables a great variety of functional samples with high SHG from one patterned silicon substrate, favoring scalable production of nonlinear converters. The surface accessibility also enables integration with other optical components for information processing in an ultrathin and flexible form.

Nonlinear second order evolution inclusions with noncoercive viscosity term

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles.

PubMed

Makarov, Sergey V; Petrov, Mihail I; Zywietz, Urs; Milichko, Valentin; Zuev, Dmitry; Lopanitsyna, Natalia; Kuksin, Alexey; Mukhin, Ivan; Zograf, George; Ubyivovk, Evgeniy; Smirnova, Daria A; Starikov, Sergey; Chichkov, Boris N; Kivshar, Yuri S

2017-05-10

Recent trends to employ high-index dielectric particles in nanophotonics are motivated by their reduced dissipative losses and large resonant enhancement of nonlinear effects at the nanoscale. Because silicon is a centrosymmetric material, the studies of nonlinear optical properties of silicon nanoparticles have been targeting primarily the third-harmonic generation effects. Here we demonstrate, both experimentally and theoretically, that resonantly excited nanocrystalline silicon nanoparticles fabricated by an optimized laser printing technique can exhibit strong second-harmonic generation (SHG) effects. We attribute an unexpectedly high yield of the nonlinear conversion to a nanocrystalline structure of nanoparticles supporting the Mie resonances. The demonstrated efficient SHG at green light from a single silicon nanoparticle is 2 orders of magnitude higher than that from unstructured silicon films. This efficiency is significantly higher than that of many plasmonic nanostructures and small silicon nanoparticles in the visible range, and it can be useful for a design of nonlinear nanoantennas and silicon-based integrated light sources.

Characterization of second and third order optical nonlinearities of ZnO sputtered films

NASA Astrophysics Data System (ADS)

Larciprete, M. C.; Haertle, D.; Belardini, A.; Bertolotti, M.; Sarto, F.; Günter, P.

2006-03-01

We measured the second and third order optical nonlinearity of zinc oxide, grown on glass substrates by the ion beam sputtering technique. Second and third harmonic generation measurements were performed by means of the rotational Maker fringes technique for different polarization configurations, thus allowing the determination of all non-zero components of the second order susceptibility at three different fundamental beam wavelengths, i.e., 1064 nm, 1542 nm and 1907 nm. The dispersion of the nonlinear optical coefficients has been evaluated, while the nonlinear optical coefficients were found to range between 0.9 pm/V and 0.16 pm/V for d33, 0.53 pm/V and 0.08 pm/V for |d15|, 0.31 and 0.08 pm/V for |d31|, with increasing wavelength. Finally, one third order susceptibility, χijkl (3), has been determined by third harmonic generation measurements at a fundamental wavelength λ=1907 nm and a value for χ3333 (3) of 185×10-20 m2/V2 has been found.

Anomalous transport from holography: part II

NASA Astrophysics Data System (ADS)

Bu, Yanyan; Lublinsky, Michael; Sharon, Amir

2017-03-01

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous U(1)_V× U(1)_A Maxwell theory in Schwarzschild-AdS_5 spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative B^2-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Discontinuous Observers Design for Finite-Time Consensus of Multiagent Systems With External Disturbances.

PubMed

Liu, Xiaoyang; Ho, Daniel W C; Cao, Jinde; Xu, Wenying

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

NASA Astrophysics Data System (ADS)

Vasoya, Manish; Unni, Aparna Beena; Leblond, Jean-Baptiste; Lazarus, Veronique; Ponson, Laurent

2016-04-01

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of material parameters and loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

Optical response of semiconductors in a dc-electric field

NASA Astrophysics Data System (ADS)

Prussel, Lucie; Veniard, Valerie

A deep understanding of the optical properties of solids is crucial for the improvement of nonlinear materials and devices. It offers the opportunity to search for new materials with specific properties. One way to tune some of those properties is to apply an electrostatic field. This gives rise to electro-optic effects. The most known among those is the Pockel or linear electro-optic effect (LEO), which is a second order response property described by the susceptibility χ (2) (- ω ω , 0) . An important nonlinear process is the second harmonic generation (SHG), where two photons are absorbed by the material. While this process is sensitive to the symmetry of the material, adding a static field would enable a nonlinear response from every material, including centrosymmetric ones. This happens through a third order process, named EFISH (Electric Field Induced Second Harmonic) for which the susceptibility of interest is χ (3) (- 2 ω ω , ω , 0) . We have developed a theoretical approach and a numerical tool to study these two nonlinear properties (LEO and EFISH) in the context of Time-dependent Density Functional Theory (TDDFT), and we have applied it to the case of bulk SiC and GaAs as well as layered systems such as Ge/SiGe.

Spacecraft attitude determination using a second-order nonlinear filter

NASA Technical Reports Server (NTRS)

Vathsal, S.

1987-01-01

The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Gauniyal, Rakhi

2016-01-15

The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically tomore » study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.« less

Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV - Multi-discrete time method

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1987-01-01

It is shown that a discrete multi-time method can be constructed to obtain approximations to the periodic solutions of a special class of second-order nonlinear difference equations containing a small parameter. Three examples illustrating the method are presented.

Structural, thermal and optical characterization of a Schiff base as a new organic material for nonlinear optical crystals and films with reversible noncentrosymmetry.

PubMed

Rodríguez, Mario; Ramos-Ortíz, Gabriel; Maldonado, José Luis; Herrera-Ambriz, Víctor M; Domínguez, Oscar; Santillan, Rosa; Farfán, Norberto; Nakatani, Keitaro

2011-09-01

Macroscopic single crystals of (E)-5-(diethylamino)-2-((3,5-dinitrophenylimino)methyl)phenol (DNP) were obtained from slow cooling of chloroform or dichlorometane saturated solutions at controlled temperature. X-ray diffraction analysis showed that this compound crystallizes in a noncentrosymmetric space group (P2(1)2(1)2(1)). Thermal analysis was performed and indicated that the crystals are stable until 260 °C. Second-order nonlinear optical properties of DNP were experimentally investigated in solution through EFISH technique and in solid state through the Kurtz-Perry powder technique. Crystals of compound DNP exhibited a second-harmonic signals 39 times larger than of the technologically useful potassium dihydrogenphosphate (KDP) under excitation at infrared wavelengths. In addition, the second-order nonlinear optical properties of DNP were also studied at visible wavelengths through the photorefractive effect and applied to demonstrate dynamic holographic reconstruction. Copyright © 2011 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Photo-induced second-order nonlinearity in stoichiometric silicon nitride waveguides

NASA Astrophysics Data System (ADS)

Porcel, Marco A. G.; Mak, Jesse; Taballione, Caterina; Schermerhorn, Victoria K.; Epping, Jörn P.; van der Slot, Peter J. M.; Boller, Klaus-J.

2017-12-01

We report the observation of second-harmonic generation in stoichiometric silicon nitride waveguides grown via low-pressure chemical vapour deposition. Quasi-rectangular waveguides with a large cross section were used, with a height of 1 {\\mu}m and various different widths, from 0.6 to 1.2 {\\mu}m, and with various lengths from 22 to 74 mm. Using a mode-locked laser delivering 6-ps pulses at 1064 nm wavelength with a repetition rate of 20 MHz, 15% of the incoming power was coupled through the waveguide, making maximum average powers of up to 15 mW available in the waveguide. Second-harmonic output was observed with a delay of minutes to several hours after the initial turn-on of pump radiation, showing a fast growth rate between 10$^{-4}$ to 10$^{-2}$ s$^{-1}$, with the shortest delay and highest growth rate at the highest input power. After this first, initial build-up, the second-harmonic became generated instantly with each new turn-on of the pump laser power. Phase matching was found to be present independent of the used waveguide width, although the latter changes the fundamental and second-harmonic phase velocities. We address the presence of a second-order nonlinearity and phase matching, involving an initial, power-dependent build-up, to the coherent photogalvanic effect. The effect, via the third-order nonlinearity and multiphoton absorption leads to a spatially patterned charge separation, which generates a spatially periodic, semi-permanent, DC-field-induced second-order susceptibility with a period that is appropriate for quasi-phase matching. The maximum measured second-harmonic conversion efficiency amounts to 0.4% in a waveguide with 0.9 x 1 {\\mu}m$^2$ cross section and 36 mm length, corresponding to 53 {\\mu}W at 532 nm with 13 mW of IR input coupled into the waveguide. The according $\\chi^{(2)}$ amounts to 3.7 pm/V, as retrieved from the measured conversion efficiency.

Investigation of the linear and second-order nonlinear optical properties of molecular crystals within the local field theory.

PubMed

Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît

2013-09-21

In this paper it is shown that modest calculations combining first principles evaluations of the molecular properties with electrostatic interaction schemes to account for the crystal environment effects are reliable for predicting and interpreting the experimentally measured electric linear and second-order nonlinear optical susceptibilities of molecular crystals within the experimental error bars. This is illustrated by considering two molecular crystals, namely: 2-methyl-4-nitroaniline and 4-(N,N-dimethylamino)-3-acetamidonitrobenzene. Three types of surrounding effects should be accounted for (i) the polarization due to the surrounding molecules, described here by static electric fields originating from their electric dipoles or charge distributions, (ii) the intermolecular interactions, which affect the geometry and particularly the molecular conformation, and (iii) the screening of the external electric field by the constitutive molecules. This study further highlights the role of electron correlation on the linear and nonlinear responses of molecular crystals and the challenge of describing frequency dispersion.

Stationary variational estimates for the effective response and field fluctuations in nonlinear composites

NASA Astrophysics Data System (ADS)

Ponte Castañeda, Pedro

2016-11-01

This paper presents a variational method for estimating the effective constitutive response of composite materials with nonlinear constitutive behavior. The method is based on a stationary variational principle for the macroscopic potential in terms of the corresponding potential of a linear comparison composite (LCC) whose properties are the trial fields in the variational principle. When used in combination with estimates for the LCC that are exact to second order in the heterogeneity contrast, the resulting estimates for the nonlinear composite are also guaranteed to be exact to second-order in the contrast. In addition, the new method allows full optimization with respect to the properties of the LCC, leading to estimates that are fully stationary and exhibit no duality gaps. As a result, the effective response and field statistics of the nonlinear composite can be estimated directly from the appropriately optimized linear comparison composite. By way of illustration, the method is applied to a porous, isotropic, power-law material, and the results are found to compare favorably with earlier bounds and estimates. However, the basic ideas of the method are expected to work for broad classes of composites materials, whose effective response can be given appropriate variational representations, including more general elasto-plastic and soft hyperelastic composites and polycrystals.

Prediction of nonlinear optical properties of organic materials. General theoretical considerations

NASA Technical Reports Server (NTRS)

Cardelino, B.; Moore, C.; Zutaut, S.

1993-01-01

The prediction of nonlinear optical properties of organic materials is geared to assist materials scientists in the selection of good candidate molecules. A brief summary of the quantum mechanical methods used for estimating hyperpolarizabilities will be presented. The advantages and limitations of each technique will be discussed. Particular attention will be given to the finite-field method for calculating first and second order hyperpolarizabilities, since this method is better suited for large molecules. Corrections for dynamic fields and bulk effects will be discussed in detail, focusing on solvent effects, conformational isomerization, core effects, dispersion, and hydrogen bonding. Several results will be compared with data obtained from third-harmonic-generation (THG) and dc-induced second harmonic generation (EFISH) measurements. These comparisons will demonstrate the qualitative ability of the method to predict the relative strengths of hyperpolarizabilities of a class of compounds. The future application of molecular mechanics, as well as other techniques, in the study of bulk properties and solid state defects will be addressed. The relationship between large values for nonlinear optical properties and large conjugation lengths is well known, and is particularly important for third-order processes. For this reason, the materials with the largest observed nonresonant third-order properties are conjugated polymers. An example of this type of polymer is polydiacetylene. One of the problems in dealing with polydiacetylene is that substituents which may enhance its nonlinear properties may ultimately prevent it from polymerizing. A model which attempts to predict the likelihood of solid-state polymerization is considered, along with the implications of the assumptions that are used. Calculations of the third-order optical properties and their relationship to first-order properties and energy gaps will be discussed. The relationship between monomeric and polymeric third-order optical properties will also be considered.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Nonlinear breakup of liquid sheets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jazayeri, S.A.; Li, X.

1997-07-01

Sprays formed from the disintegration of liquid sheets have extensive practical applications, ranging from chemical and pharmaceutical processes to power generation and propulsion systems. A knowledge of the liquid sheet breakup process is essential to the understanding of fundamental mechanism of liquid atomization and spray formation processes. The breakup of liquid sheets has been investigated in terms of hydrodynamic stability via linear analysis by Squire, Hagerty and Shea, Li, etc. nonlinear effect has been studied by Clark and Dombrowski up to the second order, and by Rangel and Sirignano through numerical simulation employing vortex discretization method. As shown by Taubmore » for the breakup of circular liquid jets, the closer to the breakup region, the higher the order of nonlinear analysis has to be for adequate description of the breakup behavior. As pointed out by Bogy, a nonlinear analysis up to the third order is generally sufficient to account for the inherent nonlinear nature of the breakup process. Therefore, a third-order nonlinear analysis has been carried out in this study to investigate the process of liquid sheet disruption preceding the spray formation.« less

Multi-scale Eulerian model within the new National Environmental Modeling System

NASA Astrophysics Data System (ADS)

Janjic, Zavisa; Janjic, Tijana; Vasic, Ratko

2010-05-01

The unified Non-hydrostatic Multi-scale Model on the Arakawa B grid (NMMB) is being developed at NCEP within the National Environmental Modeling System (NEMS). The finite-volume horizontal differencing employed in the model preserves important properties of differential operators and conserves a variety of basic and derived dynamical and quadratic quantities. Among these, conservation of energy and enstrophy improves the accuracy of nonlinear dynamics of the model. Within further model development, advection schemes of fourth order of formal accuracy have been developed. It is argued that higher order advection schemes should not be used in the thermodynamic equation in order to preserve consistency with the second order scheme used for computation of the pressure gradient force. Thus, the fourth order scheme is applied only to momentum advection. Three sophisticated second order schemes were considered for upgrade. Two of them, proposed in Janjic(1984), conserve energy and enstrophy, but with enstrophy calculated differently. One of them conserves enstrophy as computed by the most accurate second order Laplacian operating on stream function. The other scheme conserves enstrophy as computed from the B grid velocity. The third scheme (Arakawa 1972) is arithmetic mean of the former two. It does not conserve enstrophy strictly, but it conserves other quadratic quantities that control the nonlinear energy cascade. Linearization of all three schemes leads to the same second order linear advection scheme. The second order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by simply preconditioning the advected quantity. Tests with linear advection of a cone confirm the advantage of the fourth order scheme. However, if a localized, large amplitude and high wave-number pattern is present in initial conditions, the clear advantage of the fourth order scheme disappears. In real data runs, problems with noisy data may appear due to mountains. Thus, accuracy and formal accuracy may not be synonymous. The nonlinear fourth order schemes are quadratic conservative and reduce to the Arakawa Jacobian in case of non-divergent flow. In case of general flow the conservation properties of the new momentum advection schemes impose stricter constraint on the nonlinear cascade than the original second order schemes. However, for non-divergent flow, the conservation properties of the fourth order schemes cannot be proven in the same way as those of the original second order schemes. Therefore, nonlinear tests were carried out in order to check how well the fourth order schemes control the nonlinear energy cascade. In the tests nonlinear shallow water equations are solved in a rotating rectangular domain (Janjic, 1984). The domain is covered with only 17 x 17 grid points. A diagnostic quantity is used to monitor qualitative changes in the spectrum over 116 days of simulated time. All schemes maintained meaningful solutions throughout the test. Among the second order schemes, the best result was obtained with the scheme that conserved enstrophy as computed by the second order Laplacian of the stream function. It was closely followed by the Arakawa (1972) scheme, while the remaining scheme was distant third. The fourth order schemes ranked in the same order, and were competitive throughout the experiments with their second order counterparts in preventing accumulation of energy at small scales. Finally, the impact was examined of the fourth order momentum advection on global medium range forecasts. The 500 mb anomaly correlation coefficient is used as a measure of success of the forecasts. Arakawa, A., 1972: Design of the UCLA general circulation model. Tech. Report No. 7, Department of Meteorology, University of California, Los Angeles, 116 pp. Janjic, Z. I., 1984: Non-linear advection schemes and energy cascade on semi-staggered grids. Monthly Weather Review, 112, 1234-1245.

An approximation technique for predicting the transient response of a second order nonlinear equation

NASA Technical Reports Server (NTRS)

Laurenson, R. M.; Baumgarten, J. R.

1975-01-01

An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.

Non-linear power spectra in the synchronous gauge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hwang, Jai-chan; Noh, Hyerim; Jeong, Donghui

2015-05-01

We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). For the leading correction to the non-linear power spectra, we consider the perturbations up to third order in a zero-pressure fluid in a flat cosmological background. Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order. In particular, the second order hydrodynamic equations in the SG are apparently in the Lagrangian form, whereas those in the CG are in the Eulerian form. The non-linear power spectra naively presented inmore » the original SG show rather pathological behavior quite different from the result of the Newtonian theory even on sub-horizon scales. We show that the pathology in the nonlinear power spectra is due to the absence of the convective terms in, thus the Lagrangian nature of, the SG. We show that there are many different ways of introducing the corrective convective terms in the SG equations. However, the convective terms (Eulerian modification) can be introduced only through gauge transformations to other gauges which should be the same as the CG to the second order. In our previous works we have shown that the density and velocity perturbation equations in the CG exactly coincide with the Newtonian equations to the second order, and the pure general relativistic correction terms starting to appear from the third order are substantially suppressed compared with the relativistic/Newtonian terms in the power spectra. As a result, we conclude that the SG per se is an inappropriate coordinate choice in handling the non-linear matter and velocity power spectra of the large-scale structure where observations meet with theories.« less

Nonlinear histogram binning for quantitative analysis of lung tissue fibrosis in high-resolution CT data

NASA Astrophysics Data System (ADS)

Zavaletta, Vanessa A.; Bartholmai, Brian J.; Robb, Richard A.

2007-03-01

Diffuse lung diseases, such as idiopathic pulmonary fibrosis (IPF), can be characterized and quantified by analysis of volumetric high resolution CT scans of the lungs. These data sets typically have dimensions of 512 x 512 x 400. It is too subjective and labor intensive for a radiologist to analyze each slice and quantify regional abnormalities manually. Thus, computer aided techniques are necessary, particularly texture analysis techniques which classify various lung tissue types. Second and higher order statistics which relate the spatial variation of the intensity values are good discriminatory features for various textures. The intensity values in lung CT scans range between [-1024, 1024]. Calculation of second order statistics on this range is too computationally intensive so the data is typically binned between 16 or 32 gray levels. There are more effective ways of binning the gray level range to improve classification. An optimal and very efficient way to nonlinearly bin the histogram is to use a dynamic programming algorithm. The objective of this paper is to show that nonlinear binning using dynamic programming is computationally efficient and improves the discriminatory power of the second and higher order statistics for more accurate quantification of diffuse lung disease.

Suppression of Even-Order Photodiode Nonlinearities in Multioctave Photonic Links

NASA Astrophysics Data System (ADS)

Hastings, Alexander S.; Urick, Vincent J.; Sunderman, Christopher; Diehl, John F.; McKinney, Jason D.; Tulchinsky, David A.; Devgan, Preetpaul S.; Williams, Keith J.

2008-08-01

A balanced photonic receiver is demonstrated to suppress photodiode-generated even-order nonlinearities in a photonic link. This result is especially important for multioctave analog applications. Experimental results are presented for a high-frequency (2-30 MHz) link exhibiting 33-dB suppression of the second harmonic, resulting in an output intercept point of 99 dBm due to second-order intermodulation distortion at 26-mA average photocurrent.

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

PubMed

Meyn, J P; Fejer, M M

1997-08-15

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

Layer contributions to the nonlinear acoustic radiation from stratified media.

PubMed

Vander Meulen, François; Haumesser, Lionel

2016-12-01

This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.

Non-linear glasses and metaglasses for photonics, a review: Part II. Kerr nonlinearity and metaglasses of positive and negative refraction

NASA Astrophysics Data System (ADS)

Romaniuk, Ryszard S.

2008-01-01

This is the second part of a paper on nonlinear properties of optical glasses and metaglasses. A subject of the paper is a review of the basic properties of several families of high optical quality glasses for photonics. The emphasis is put on nonlinear properties of these glasses, including nonlinearities of higher order. Nonlinear effects were debated and systematized. Interactions between optical wave of high power density with glass were described. All parameters of the glass increasing the optical nonlinearities were categorized. Optical nonlinearities in glasses were grouped into the following categories: time and frequency domain, amplitude and phase, resonant and non-resonant, elastic and inelastic, lossy and lossless, reversible and irreversible, instant and slow, adiabatic and non-adiabatic, with virtual versus real excitation of glass, destroying and non-destroying, etc. Nonlinear effects in glasses are based on the following effects: optical, thermal, mechanical and/or acoustic, electrical, magnetic, density and refraction modulation, chemical, etc.

Ultralong relaxation times in bistable hybrid quantum systems.

PubMed

Angerer, Andreas; Putz, Stefan; Krimer, Dmitry O; Astner, Thomas; Zens, Matthias; Glattauer, Ralph; Streltsov, Kirill; Munro, William J; Nemoto, Kae; Rotter, Stefan; Schmiedmayer, Jörg; Majer, Johannes

2017-12-01

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds-a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Controlled experiments in cosmological gravitational clustering

NASA Technical Reports Server (NTRS)

Melott, Adrian L.; Shandarin, Sergei F.

1993-01-01

A systematic study is conducted of gravitational instability in 3D on the basis of power-law initial spectra with and without spectral cutoff, emphasizing nonlinear effects and measures of nonlinearity; effects due to short and long waves in the initial conditions are separated. The existence of second-general pancakes is confirmed, and it is noted that while these are inhomogeneous, they generate a visually strong signal of filamentarity. An explicit comparison of smoothed initial conditions with smoothed envelope models also reconfirms the need to smooth over a scale larger than any nonlinearity, in order to extrapolate directly by linear theory from Gaussian initial conditions.

A unified model for transfer alignment at random misalignment angles based on second-order EKF

NASA Astrophysics Data System (ADS)

Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo

2017-04-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Unsymmetrical squaraines for nonlinear optical materials

NASA Technical Reports Server (NTRS)

Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)

1996-01-01

Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.

Nonlinear modulation of the HI power spectrum on ultra-large scales. I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umeh, Obinna; Maartens, Roy; Santos, Mario, E-mail: umeobinna@gmail.com, E-mail: roy.maartens@gmail.com, E-mail: mgrsantos@uwc.ac.za

2016-03-01

Intensity mapping of the neutral hydrogen brightness temperature promises to provide a three-dimensional view of the universe on very large scales. Nonlinear effects are typically thought to alter only the small-scale power, but we show how they may bias the extraction of cosmological information contained in the power spectrum on ultra-large scales. For linear perturbations to remain valid on large scales, we need to renormalize perturbations at higher order. In the case of intensity mapping, the second-order contribution to clustering from weak lensing dominates the nonlinear contribution at high redshift. Renormalization modifies the mean brightness temperature and therefore the evolutionmore » bias. It also introduces a term that mimics white noise. These effects may influence forecasting analysis on ultra-large scales.« less

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin

NASA Astrophysics Data System (ADS)

Bennett, Kochise; Chernyak, Vladimir Y.; Mukamel, Shaul

2017-03-01

The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two separate molecules give signals that appear on top of a genuine direct higher-order process with a single molecule. These many-body contributions are known as cascading and complicate the interpretation of multidimensional stimulated Raman and other nonlinear signals. In a quantum electrodynamic treatment, these cascading processes arise from second-order expansion in the molecular coupling to vacuum modes of the radiation field, i.e., single-photon exchange between molecules, which also gives rise to other collective effects. We predict the relative phase of the direct and cascading nonlinear signals and its dependence on the microscopic dynamics as well as the sample geometry. This phase may be used to identify experimental conditions for distinguishing the direct and cascading signals by their phase. Higher-order cascading processes involving the exchange of several photons between more than two molecules are discussed.

Multiple nonlinear Bragg diffraction of femtosecond laser pulses in a {\\chi^{(2)}} photonic lattice with hexagonal domains

NASA Astrophysics Data System (ADS)

Vyunishev, A. M.; Arkhipkin, V. G.; Baturin, I. S.; Akhmatkhanov, A. R.; Shur, V. Ya; Chirkin, A. S.

2018-04-01

The frequency doubling of femtosecond laser pulses in a two-dimensional (2D) rectangular nonlinear photonic lattice with hexagonal domains is studied experimentally and theoretically. The broad fundamental spectrum enables frequency conversion under nonlinear Bragg diffraction for a series of transverse orders at a fixed longitudinal quasi-phase-matching order. The consistent nonstationary theory of the frequency doubling of femtosecond laser pulses is developed using the representation based on the reciprocal lattice of the structure. The calculated spatial distribution of the second-harmonic spectral intensity agrees well with the experimental data. The condition for multiple nonlinear Bragg diffraction in a 2D nonlinear photonic lattice is offered. The hexagonal shape of the domains contributes to multibeam second harmonic excitation. The maximum conversion efficiency for a series of transverse orders in the range 0.01%-0.03% is obtained.

Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

1992-01-01

An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

Nonlinear anomalous photocurrents in Weyl semimetals

NASA Astrophysics Data System (ADS)

Rostami, Habib; Polini, Marco

2018-05-01

We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e., a three-dimensional metal with linear band touchings acting as pointlike sources of Berry curvature in momentum space, termed "Weyl-Berry monopoles." We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Single amino acid mutation in alpha-helical peptide affect second harmonic generation hyperpolarizability

NASA Astrophysics Data System (ADS)

Wei, Jing; Wang, Jin-Yun; Zhang, Min-Yi; Chai, Guo-Liang; Lin, Chen-Sheng; Cheng, Wen-Dan

2013-01-01

We investigate the effect of side chain on the first-order hyperpolarizability in α-helical polyalanine peptide with the 10th alanine mutation (Acetyl(ala)9X(ala)7NH2). Structures of various substituted peptides are optimized by ONIOM (DFT: AM1) scheme, and then linear and nonlinear optical properties are calculated by SOS//CIS/6-31G∗ method. The polarizability and first-order hyperpolarizability increase obviously only when 'X' represents phenylalanine, tyrosine and tryptophan. We also discuss the origin of nonlinear optical response and determine what caused the increase of first-order hyperpolarizability. Our results strongly suggest that side chains containing benzene, phenol and indole have important contributions to first-order hyperpolarizability.

Large enhancement of second harmonic generation from transition-metal dichalcogenide monolayer on grating near bound states in the continuum.

PubMed

Wang, Tiecheng; Zhang, Shihao

2018-01-08

Second harmonic generation from the two-layer structure where a transition-metal dichalcogenide monolayer is put on a one-dimensional grating has been studied. This grating supports bound states in the continuum which have no leakage lying within the continuum of radiation modes, we can enhance the second harmonic generation from the transition-metal dichalcogenide monolayer by more than four orders of magnitude based on the critical field enhancement near the bound states in the continuum. In order to complete this calculation, the scattering matrix theory has been extended to include the nonlinear effect and the scattering matrix of a two-dimensional material including nonlinear terms; furthermore, two methods to observe the bound states in the continuum are considered, where one is tuning the thickness of the grating and the other is changing the incident angle of the electromagnetic wave. We have also discussed various modulation of the second harmonic generation enhancement by adjusting the azimuthal angle of the transition-metal dichalcogenide monolayer.

Synthetic magnetism for photon fluids

NASA Astrophysics Data System (ADS)

Westerberg, N.; Maitland, C.; Faccio, D.; Wilson, K.; Öhberg, P.; Wright, E. M.

2016-08-01

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Localized waves in three-component coupled nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Xu, Tao; Chen, Yong

2016-09-01

We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).

New second order Mumford-Shah model based on Γ-convergence approximation for image processing

NASA Astrophysics Data System (ADS)

Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li

2016-05-01

In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.

Supersonic flow past oscillating airfoils including nonlinear thickness effects

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1954-01-01

A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so enlarge the range of Mach numbers within which torsional instability is possible.

Eye/Sensor Protection against Laser Irradiation Organic Nonlinear Optical Materials

DTIC Science & Technology

1989-06-12

the dipole. When the electric field is small compared to the internal fields due to the electron!, the molecular polarizability (p), which is...polarizability tensors, respectively, the linear polarizability and the second and third-order hyperpolarizability. At lower field intensities ( small E’s) only...nonlinear optical effect: the bonding electrons are well localized so only small changes in charge distribution with changes in local field environments

Complete Galilean-Invariant Lattice BGK Models for the Navier-Stokes Equation

NASA Technical Reports Server (NTRS)

Qian, Yue-Hong; Zhou, Ye

1998-01-01

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

NASA Astrophysics Data System (ADS)

Wang, Bin; Tang, Yougang; Li, Yan; Cai, Runbo

2018-04-01

This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

3D simulation for solitons used in optical fibers

NASA Astrophysics Data System (ADS)

Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.

2016-12-01

In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Further efforts in optimizing nonlinear optical molecules

NASA Astrophysics Data System (ADS)

Dirk, Carl W.; Caballero, Noel; Tan, Alarice; Kuzyk, Mark G.; Cheng, Lap-Tak A.; Katz, Howard E.; Shilling, Marcia; King, Lori A.

1993-02-01

We summarize some of our past work in the field on optimizing molecules for second order and third order nonlinear optical applications. We also present some previously unpublished results suggesting a particular optimization of the popular cyano- and nitrovinyl acceptor groups. In addition we provide some new quadratic electro-optic results which serve to further verify our choice of a restricted three-level model suitable for optimizing third order nonlinearities in molecules. Finally we present a new squarylium dye with a large third order optical nonlinearity (-9.5 X 10-34 cm7/esu2; EFISH (gamma) at 1906 nm).

Nonlinear oscillations and waves in multi-species cold plasmas

NASA Astrophysics Data System (ADS)

Verma, Prabal Singh

2016-12-01

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.

Remarkable Second-Order Optical Nonlinearity of Nano-Sized Au Cluster: A TDDFT Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Kechen; Li, Jun; Lin, Chensheng

2004-04-21

The dipole polarizability, static first hyperpolarizability, and UV-vis spectrum of the recently identified nano-sized tetrahedral cluster of Au have been investigated by using time-dependent density functional response theory. We have discovered that the Au cluster possesses remarkably large molecular second-order optical nonlinearity with the first hyperpolarizabilty (xyz) calculated to be 14.3 x 10 electrostatic unit (esu). The analysis of the low-energy absorption band suggests that the charge transfer from the edged gold atoms to the vertex ones plays the key role in nonlinear optical (NLO) response of Au.

Nonlinear optical properties and excited state dynamics of sandwich-type mixed (phthalocyaninato)(Schiff-base) triple-decker complexes: Effect of rare earth atom

NASA Astrophysics Data System (ADS)

Li, Zhongguo; Gao, Feng; Xiao, Zhengguo; Wu, Xingzhi; Zuo, Jinglin; Song, Yinglin

2018-07-01

The third-order nonlinear optical properties of two di-lanthanide (Ln = Tb and Dy) sandwich complexes with mixed phthalocyanine and Schiff-base ligands were studied using Z-scan technique at 532 nm with 20 ps and 4 ns pulses. Both complexes exhibit reverse saturable absorption and self-focusing effect in ps regime, while the second-order hyperpolarizability decreases from Dy to Tb. Interestingly, the Tb triple-decker complexes show larger nonlinear absorption than Dy complexes on ns timescale. The time-resolved pump-probe measurements demonstrate that the nonlinear optical response was caused by excited-state mechanism related to the five-level model, while the singlet state lifetime of Dy complexes is 3 times shorter than that of Tb complexes. Our results indicate the lanthanide ions play a critical role in the photo-physical properties of triple-decker phthalocyanine complexes for their application as optical limiting materials.

Modeling of second-harmonic generation of circumferential guided wave propagation in a composite circular tube

NASA Astrophysics Data System (ADS)

Li, Mingliang; Deng, Mingxi; Gao, Guangjian; Xiang, Yanxun

2018-05-01

This paper investigated modeling of second-harmonic generation (SHG) of circumferential guided wave (CGW) propagation in a composite circular tube, and then analyzed the influences of interfacial properties on the SHG effect of primary CGW. Here the effect of SHG of primary CGW propagation is treated as a second-order perturbation to its linear wave response. Due to the convective nonlinearity and the inherent elastic nonlinearity of material, there are second-order bulk driving forces and surface/interface driving stresses in the interior and at the surface/interface of a composite circular tube, when a primary CGW mode propagates along its circumference. Based on the approach of modal expansion analysis for waveguide excitation, the said second-order driving forces/stresses are regarded as the excitation sources to generate a series of double-frequency CGW modes that constitute the second-harmonic field of the primary CGW propagation. It is found that the modal expansion coefficient of each double-frequency CGW mode is closely related to the interfacial stiffness constants that are used to describe the interfacial properties between the inner and outer circular parts of the composite tube. Furthermore, changes in the interfacial stiffness constants essentially influence the dispersion relation of CGW propagation. This will remarkably affect the efficiency of cumulative SHG of primary CGW propagation. Some finite element simulations have been implemented of response characteristics of cumulative SHG to the interfacial properties. Both the theoretical analyses and numerical simulations indicate that the effect of cumulative SHG is found to be much more sensitive to changes in the interfacial properties than primary CGW propagation. The potential of using the effect of cumulative SHG by primary CGW propagation to characterize a minor change in the interfacial properties is considered.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Nonlinear Optical Spectroscopy of Two-Dimensional Materials

NASA Astrophysics Data System (ADS)

Cui, Qiannan

Nonlinear optical properties of two-dimensional (2D) materials, such as transition metal dichalcogenides (TMDs), graphene, black phosphorus, and so on, play a key role of understanding nanoscale light-matter interactions, as well as developing nanophotonics applications from solar cells to quantum computation. With ultrafast lasers, we experimentally study nonlinear optical properties of 2D materials. Employing transient absorption microscopy, we study several members of 2D materials, such as WSe2, TiS3 and ReS2. The dynamical saturable absorption process of 2D excitons is spatiotemporally resolved. Intrinsic parameters of these 2D materials, such as exciton lifetime, exciton diffusion coefficient, and exciton mobility, are effectively measured. Especially, in-plane anisotropy of transient absorption and diffusive transport is observed for 2D excitons in monolayer ReS2, demonstrating the in-plane degree of freedom. Furthermore, with quantum interference and control nanoscopy, we all-optically inject, detect and manipulate nanoscale ballistic charge currents in a ReS2 thin film. By tuning the phase difference between one photon absorption and two photon absorption transition paths, sub-picosecond timescale of ballistic currents is coherently controlled for the first time in TMDs. In addition, the spatial resolution is two-order of magnitude smaller than optical diffraction limit. The second-order optical nonlinearity of 2D monolayers is resolved by second harmonic generation (SHG) microscopy. We measure the second-order susceptibility of monolayer MoS 2. The angular dependence of SHG in monolayer MoS2 shows strong symmetry dependence on its crystal lattice structure. Hence, second harmonic generation microscopy can serve as a powerful tool to noninvasively determine the crystalline directions of 2D monolayers. The real and imaginary parts of third-order optical nonlinearity of 2D monolayers are resolved by third harmonic generation (THG) microscopy and two-photon transient absorption microscopy, respectively. With third harmonic generation microscopy, we observe strong and anisotropic THG in monolayer and multilayer ReS2. Comparing with 2D materials with hexagonal lattice, such as MoS2, the third-order susceptibility is higher by one order of magnitude in ReS2 with a distorted 1T structure. The in-plane anisotropy of THG is attributed to the lattice distortion in ReS2 after comparing with a symmetry analysis. With two-photon transient absorption microscopy, we observe a giant two-photon absorption coefficient of monolayer WS2.

Nonlinear Optics and Applications

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

A new line-of-sight approach to the non-linear Cosmic Microwave Background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fidler, Christian; Koyama, Kazuya; Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com

2015-04-01

We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level. This formalism utilises a transformation operator that removes all inhomogeneous propagation effects acting on the photon distribution function, thus achieving a split between perturbative collisional effects at recombination and non-perturbative line-of-sight effects at later times. The former can be computed in the framework of standard cosmological perturbation theory with a second-order Boltzmann code such as SONG, while the latter can be treated within a separate perturbative scheme allowing the use of non-linear Newtonianmore » potentials. We thus provide a consistent framework to compute all physical effects contained in the Boltzmann equation and to combine the standard remapping approach with Boltzmann codes at any order in perturbation theory, without assuming that all sources are localised at recombination.« less

Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

NASA Astrophysics Data System (ADS)

Sarma, Bijita; Sarma, Amarendra K.

2018-04-01

Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

Photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling

NASA Astrophysics Data System (ADS)

Zhang, X. Y.; Zhou, Y. H.; Guo, Y. Q.; Yi, X. X.

2018-03-01

We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling, i.e. H_int˜\\hat{a}\\dagger2\\hat{a}^2(\\hat{b}_1^\\dagger+\\hat{b}_1) . We find that the Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time second-order correlation function of the cavity photons and find that the optimal photon blockade does not happen at the single photon resonance. By working within the few-photon subspace, we get an approximate analytical expression for the correlation function and the condition for the optimal photon blockade. We also find that the photon blockade effect is not always enhanced as the Kerr-type nonlinear coupling strength g 2 increases. At some values of g 2, the photon blockade is even weakened. For the system we considered here, the second-order correlation function can be smaller than 1 even in the unresolved sideband regime. By numerically simulating the master equation of the system, we also find that the thermal noise of the mechanical environment can enhance the photon blockade. We give out an explanation for this counter-intuitive phenomenon qualitatively.

Second-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient.

PubMed

Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2015-02-09

Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.

Supercritical nonlinear parametric dynamics of Timoshenko microbeams

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Ghayesh, Mergen H.

2018-06-01

The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically, by means of different numerical techniques, and employing a high-dimensional analysis. The time-variant axial load is assumed to consist of a mean value along with harmonic fluctuations. In terms of modelling, a continuous expression for the elastic potential energy of the system is developed based on the modified couple stress theory, taking into account small-size effects; the kinetic energy of the system is also modelled as a continuous function of the displacement field. Hamilton's principle is employed to balance the energies and to obtain the continuous model of the system. Employing the Galerkin scheme along with an assumed-mode technique, the energy terms are reduced, yielding a second-order reduced-order model with finite number of degrees of freedom. A transformation is carried out to convert the second-order reduced-order model into a double-dimensional first order one. A bifurcation analysis is performed for the system in the absence of the axial load fluctuations. Moreover, a mean value for the axial load is selected in the supercritical range, and the principal parametric resonant response, due to the time-variant component of the axial load, is obtained - as opposed to transversely excited systems, for parametrically excited system (such as our problem here), the nonlinear resonance occurs in the vicinity of twice any natural frequency of the linear system; this is accomplished via use of the pseudo-arclength continuation technique, a direct time integration, an eigenvalue analysis, and the Floquet theory for stability. The natural frequencies of the system prior to and beyond buckling are also determined. Moreover, the effect of different system parameters on the nonlinear supercritical parametric dynamics of the system is analysed, with special consideration to the effect of the length-scale parameter.

Redox control of ferrocene-based complexes with systematically extended π-conjugated connectors: switchable and tailorable second order nonlinear optics.

PubMed

Wang, Wen-Yong; Ma, Na-Na; Sun, Shi-Ling; Qiu, Yong-Qing

2014-03-14

The studies of geometrical structures, thermal stabilities, redox properties, nonlinear responses and optoelectronic properties have been carried out on a series of novel ferrocenyl (Fc) chromophores with the view of assessing their switchable and tailorable second order nonlinear optics (NLO). The use of a constant Fc donor and a 4,4'-bipyridinium acceptor and varied conjugated bridges makes it possible to systematically determine the contribution of organic connectors to chromophore nonlinear optical activities. The structures reveal that both the reduction reactions and organic connectors have a significant influence on 4,4'-bipyridinium. The potential energy surface maps along with plots of reduced density gradient mirror the thermal stabilities of the Fc-based chromophores. The first and second reductions take place preferentially at the 4,4'-bipyridinium moieties. Significantly, the reduction processes result in the molecular switches with large NLO contrast varying from zero or very small to a large value. Moreover, time-dependent density functional theory results indicate that the absorption peaks are mainly attributed to Fc to 4,4'-bipyridinium charge transfer and the mixture of intramolecular charge transfer within the two respective 4,4'-bipyridinium moieties coupled with interlayer charge transfer between the two 4,4'-bipyridinium moieties. This provides us with comprehensive information on the effect of organic connectors on the NLO properties.

Kuznetsov-Ma waves train generation in a left-handed material

NASA Astrophysics Data System (ADS)

Atangana, Jacques; Giscard Onana Essama, Bedel; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Crépin Kofane, Timoléon

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. I. Experimental determination

NASA Astrophysics Data System (ADS)

Dalstein, L.; Revel, A.; Humbert, C.; Busson, B.

2018-04-01

We experimentally determine the effective nonlinear second-order susceptibility of gold over the visible spectral range. To reach that goal, we probe by vibrational two-color sum-frequency generation spectroscopy the methyl stretching region of a dodecanethiol self-assembled monolayer adsorbed on a gold film. The sum-frequency generation spectra show a remarkable shape reversal when the visible probe wavelength is tuned from 435 to 705 nm. After correcting from Fresnel effects, the methyl stretching vibrations serve as an internal reference, allowing to extract the dispersion of the absolute phase and relative amplitude of the effective nonlinear optical response of gold in the visible range.

Multiple Positive Solutions in the Second Order Autonomous Nonlinear Boundary Value Problems

NASA Astrophysics Data System (ADS)

Atslega, Svetlana; Sadyrbaev, Felix

2009-09-01

We construct the second order autonomous equations with arbitrarily large number of positive solutions satisfying homogeneous Dirichlet boundary conditions. Phase plane approach and bifurcation of solutions are the main tools.

An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

NASA Astrophysics Data System (ADS)

Milic, Vladimir; Kasac, Josip; Novakovic, Branko

2015-10-01

This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Spectroscopic, DFT and Z-scan supported investigation of dicyanoisophorone based push-pull NLOphoric styryl dyes

NASA Astrophysics Data System (ADS)

Erande, Yogesh; Sreenath, Mavila C.; Chitrambalam, Subramaniyan; Joe, Isaac H.; Sekar, Nagaiyan

2017-04-01

The dicyanoisophorone acceptor based NLOphores with Intramolecular Charge Transfer (ICT) character are newly synthesised, characterised and explored for linear and non linear optical (NLO) property investigation. Strong ICT character of these D-π-A styryl NLOphores is established with support of emission solvatochromism, polarity functions and Generalised Mulliken Hush (GMH) analysis. First, second and third order polarizability of these NLOphores is investigated by spectroscopic and TDDFT computational approach using CAM/B3LYP-6-311 + g (d, p) method. BLA and BOA values of these chromophores are evaluated from ground and excited state optimized geometries and found that the respective structures are approaching towards cyanine limit. Third order nonlinear susceptibility (X(3)) along with nonlinear absorption coefficient (β) and nonlinear refraction (n2) are evaluated for these NLOphores using Z-scan experiment. All four chromophores exhibit large polarization anisotropy (Δα), first order hyperpolarizability (β0), second order hyperpolarizability (γ) and third order nonlinear susceptibility (X(3)). TGA analysis proved these NLOphores are stable up to 320 °C and hence can be used in device fabrication.

Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

NASA Astrophysics Data System (ADS)

Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner

2017-07-01

A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (<1 s). Moreover, the nonlinear observer shows good robustness against variations in the initial values of the internal states, but less robustness against variations in system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung

2017-09-01

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

Computing general-relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach

NASA Astrophysics Data System (ADS)

Bruni, Marco; Thomas, Daniel B.; Wands, David

2014-02-01

We present the first calculation of an intrinsically relativistic quantity, the leading-order correction to Newtonian theory, in fully nonlinear cosmological large-scale structure studies. Traditionally, nonlinear structure formation in standard ΛCDM cosmology is studied using N-body simulations, based on Newtonian gravitational dynamics on an expanding background. When one derives the Newtonian regime in a way that is a consistent approximation to the Einstein equations, the first relativistic correction to the usual Newtonian scalar potential is a gravitomagnetic vector potential, giving rise to frame dragging. At leading order, this vector potential does not affect the matter dynamics, thus it can be computed from Newtonian N-body simulations. We explain how we compute the vector potential from simulations in ΛCDM and examine its magnitude relative to the scalar potential, finding that the power spectrum of the vector potential is of the order 10-5 times the scalar power spectrum over the range of nonlinear scales we consider. On these scales the vector potential is up to two orders of magnitudes larger than the value predicted by second-order perturbation theory extrapolated to the same scales. We also discuss some possible observable effects and future developments.

Second and third order nonlinear optical properties of conjugated molecules and polymers

NASA Technical Reports Server (NTRS)

Perry, Joseph W.; Stiegman, Albert E.; Marder, Seth R.; Coulter, Daniel R.; Beratan, David N.; Brinza, David E.

1988-01-01

Second- and third-order nonlinear optical properties of some newly synthesized organic molecules and polymers are reported. Powder second-harmonic-generation efficiencies of up to 200 times urea have been realized for asymmetric donor-acceptor acetylenes. Third harmonic generation chi(3)s have been determined for a series of small conjugated molecules in solution. THG chi(3)s have also been determined for a series of soluble conjugated copolymers prepared using ring-opening metathesis polymerization. The results are discussed in terms of relevant molecular and/or macroscopic structural features of these conjugated organic materials.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Berry curvature dipole in Weyl semimetal materials: An ab initio study

NASA Astrophysics Data System (ADS)

Zhang, Yang; Sun, Yan; Yan, Binghai

2018-01-01

Noncentrosymmetric metals are anticipated to exhibit a dc photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an ab initio scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and the MoTe2-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole in which type-II Weyl points are usually superior to the type-I WSM because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the dc field limit, which is within the experimentally detectable range.

Second-order nonlinear optical properties of composite material of an azo-chromophore with a tricyanodiphenyl acceptor in a poly(styrene-co-methyl methacrylate) matrix

NASA Astrophysics Data System (ADS)

Shelkovnikov, Vladimir; Selivanova, Galina; Lyubas, Gleb; Korotaev, Sergey; Shundrina, Inna; Tretyakov, Evgeny; Zueva, Ekaterina; Plekhanov, Alexander; Mikerin, Sergey; Simanchuk, Andrey

2017-07-01

The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS-PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

Xie, Dexuan

1996-01-01

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Nonlinear identification of the total baroreflex arc.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2015-12-15

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This "Uryson" model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. Copyright © 2015 the American Physiological Society.

Nonlinear identification of the total baroreflex arc

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2015-01-01

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This “Uryson” model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. PMID:26354845

Analysis of helicopter flight dynamics through modeling and simulation of primary flight control actuation system

NASA Astrophysics Data System (ADS)

Nelson, Hunter Barton

A simplified second-order transfer function actuator model used in most flight dynamics applications cannot easily capture the effects of different actuator parameters. The present work integrates a nonlinear actuator model into a nonlinear state space rotorcraft model to determine the effect of actuator parameters on key flight dynamics. The completed actuator model was integrated with a swashplate kinematics where step responses were generated over a range of key hydraulic parameters. The actuator-swashplate system was then introduced into a nonlinear state space rotorcraft simulation where flight dynamics quantities such as bandwidth and phase delay analyzed. Frequency sweeps were simulated for unique actuator configurations using the coupled nonlinear actuator-rotorcraft system. The software package CIFER was used for system identification and compared directly to the linearized models. As the actuator became rate saturated, the effects on bandwidth and phase delay were apparent on the predicted handling qualities specifications.

Nonlinear gravitational self-force: Field outside a small body

NASA Astrophysics Data System (ADS)

Pound, Adam

2012-10-01

A small extended body moving through an external spacetime gαβ creates a metric perturbation hαβ, which forces the body away from geodesic motion in gαβ. The foundations of this effect, called the gravitational self-force, are now well established, but concrete results have mostly been limited to linear order. Accurately modeling the dynamics of compact binaries requires proceeding to nonlinear orders. To that end, I show how to obtain the metric perturbation outside the body at all orders in a class of generalized wave gauges. In a small buffer region surrounding the body, the form of the perturbation can be found analytically as an expansion for small distances r from a representative worldline. Given only a specification of the body’s multipole moments, the field obtained in the buffer region suffices to find the metric everywhere outside the body via a numerical puncture scheme. Following this procedure at first and second order, I calculate the field in the buffer region around an arbitrarily structured compact body at sufficiently high order in r to numerically implement a second-order puncture scheme, including effects of the body’s spin. I also define nth-order (local) generalizations of the Detweiler-Whiting singular and regular fields and show that in a certain sense, the body can be viewed as a skeleton of multipole moments.

Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soh, Daniel Beom Soo

We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2), particularly for those linear and nonlinear transition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matrices that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibilities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Efficiency of unconstrained minimization techniques in nonlinear analysis

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

Nonlinear chiral plasma transport in rotating coordinates

NASA Astrophysics Data System (ADS)

Dayi, Ömer F.; Kilinçarslan, Eda

2017-08-01

The nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms arising from the Coriolis and fictitious centrifugal forces. Then in the short relaxation time regime the angular velocity and electromagnetic fields are treated as perturbations. The current densities are obtained by retaining the terms up to second order in perturbations. The time evolution equations of the inhomogeneous chemical potentials are derived by demanding that collisions conserve the particle number densities.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

Vowel selection and its effects on perturbation and nonlinear dynamic measures.

PubMed

Maccallum, Julia K; Zhang, Yu; Jiang, Jack J

2011-01-01

Acoustic analysis of voice is typically conducted on recordings of sustained vowel phonation. This study applied perturbation and nonlinear dynamic analyses to the vowels /a/, /i/, and /u/ in order to determine vowel selection effects on analysis. Forty subjects (20 males and 20 females) with normal voices participated in recording. Traditional parameters of fundamental frequency, signal-to-noise ratio, percent jitter, and percent shimmer were calculated for the signals using CSpeech. Nonlinear dynamic parameters of correlation dimension and second-order entropy were also calculated. Perturbation analysis results were largely incongruous in this study and in previous research. Fundamental frequency results corroborated previous work, indicating higher fundamental frequency for /i/ and /u/ and lower fundamental frequency for /a/. Signal-to-noise ratio results showed that /i/ and /u/ have greater harmonic levels than /a/. Results of nonlinear dynamic analysis suggested that more complex activity may be evident in /a/ than in /i/ or /u/. Percent jitter and percent shimmer may not be useful for description of acoustic differences between vowels. Fundamental frequency, signal-to-noise ratio, and nonlinear dynamic parameters may be applied to characterize /a/ as having lower frequency, higher noise, and greater nonlinear components than /i/ and /u/. Copyright © 2010 S. Karger AG, Basel.

Nonlinear Aeroelastic Equations of Motion of Twisted, Nonuniform, Flexible Horizontal-Axis Wind Turbine Blades

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.

1980-01-01

The second-degree nonlinear equations of motion for a flexible, twisted, nonuniform, horizontal axis wind turbine blade were developed using Hamilton's principle. A mathematical ordering scheme which was consistent with the assumption of a slender beam was used to discard some higher-order elastic and inertial terms in the second-degree nonlinear equations. The blade aerodynamic loading which was employed accounted for both wind shear and tower shadow and was obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible, unsteady, airfoil theory. The resulting equations had periodic coefficients and were suitable for determining the aeroelastic stability and response of large horizontal-axis wind turbine blades.

Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves.

PubMed

Lu, Jian; Li, Xian; Hwang, Harold Y; Ofori-Okai, Benjamin K; Kurihara, Takayuki; Suemoto, Tohru; Nelson, Keith A

2017-05-19

We report a demonstration of two-dimensional (2D) terahertz (THz) magnetic resonance spectroscopy using the magnetic fields of two time-delayed THz pulses. We apply the methodology to directly reveal the nonlinear responses of collective spin waves (magnons) in a canted antiferromagnetic crystal. The 2D THz spectra show all of the third-order nonlinear magnon signals including magnon spin echoes, and 2-quantum signals that reveal pairwise correlations between magnons at the Brillouin zone center. We also observe second-order nonlinear magnon signals showing resonance-enhanced second-harmonic and difference-frequency generation. Numerical simulations of the spin dynamics reproduce all of the spectral features in excellent agreement with the experimental 2D THz spectra.

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Synthesis, characterization and nonlinear optical properties of symmetrically substituted dibenzylideneacetone derivatives

NASA Astrophysics Data System (ADS)

Sunil Kumar Reddy, N.; Badam, Rajashekar; Sattibabu, Romala; Molli, Muralikrishna; Sai Muthukumar, V.; Siva Sankara Sai, S.; Rao, G. Nageswara

2014-11-01

We report here the nonlinear optical (NLO) properties of eight bis-chalcones of D-π-A-π-D type. These dibenzylideneacetone (DBA) derivatives are synthesized by Claisen-Schmidt reaction. The compounds are characterized by UV-vis, FTIR, 1H NMR, 13C NMR, mass spectroscopy and powder XRD. By substituting different groups (electron withdrawing and electron donating) at 'para' and 'meta' positions of the aromatic ring, we observed an enhancement in second harmonic generation with substitution at 'para' position. These compounds have also showed higher two-photon absorption compared to other chalcones reported in literature. These compounds, exhibiting both second and third order NLO effects, are plausible candidate materials in photonic devices.

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Off-resonant third-order optical nonlinearities of squarylium and croconium dyes

NASA Astrophysics Data System (ADS)

Li, Zhongyu; Xu, Song; Niu, Lihong; Zhang, Zhi; Chen, Zihui; Zhang, Fushi

2008-01-01

The magnitude and dynamic response of the third-order optical nonlinearities of squarylium and croconium dyes in methanol solution were measured by femtosecond degenerate four-wave mixing (DFWM) technique at 800 nm. Ultrafast nonlinear optical responses have been observed, and the magnitude of the second-order hyperpolarizabilities was evaluated to be 5.80 × 10 -31 esu for the squarylium dye and 8.69 × 10 -31 esu for the croconium dye, respectively. The large optical nonlinearities of the dyes can be attributed to their rigid and intramolecular charge transfer structure, and the instantaneous NLO responses of dyes are shorter than the experimental time resolution (50 fs), which is mainly contributed from the electron delocalization. The fast nonlinear response and large third-order optical nonlinearities show that the studied squarylium and croconium dyes might a kind of promising materials for the applications in all-optical switching and modulator.

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

PubMed

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

2014-09-01

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

Second harmonic generation in resonant optical structures

DOEpatents

Eichenfield, Matt; Moore, Jeremy; Friedmann, Thomas A.; Olsson, Roy H.; Wiwi, Michael; Padilla, Camille; Douglas, James Kenneth; Hattar, Khalid Mikhiel

2018-01-09

An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.

Implicit integration methods for dislocation dynamics

DOE PAGES

Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; ...

2015-01-20

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

DOE PAGES

Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

2015-09-15

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

Optical nonlinearity in gelatin layer film containing Au nanoparticles

NASA Astrophysics Data System (ADS)

Hirose, Tomohiro; Arisawa, Michiko; Omatsu, Takashige; Kuge, Ken'ichi; Hasegawa, Akira; Tateda, Mitsuhiro

2002-09-01

We demonstrate a novel technique to fabricate a gelatin film containing Au-nano-particles. The technique is based on silver halide photographic development. We investigated third-order non-linearity of the film by forward-four-wave-mixing technique. Peak absorption appeared at the wavelength of 560nm. Self-diffraction by the use of third order nonlinear grating formed by intense pico-second pulses was observed. Experimental diffraction efficiency was proportional to the square of the pump intensity. Third-order susceptibility c(3) of the film was estimated to be 1.8?~10^-7esu.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

A Comparison Study of Second-Order Screening Designs and Their Extension

DTIC Science & Technology

2013-12-01

H2 97 V. Nonlinear Screening Designs for Defense Testing: An Overview and Case Study 5.1 Introduction “Necessity is the Mother of Invention.” Plato is...involved concepts like design resolution, minimum aber- ration , power, the number of clear (non-confounded) effects, concepts like rotatability

Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters

NASA Technical Reports Server (NTRS)

Smith, M.

1972-01-01

Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

A comparative examination of the adsorption mechanism of an anionic textile dye (RBY 3GL) onto the powdered activated carbon (PAC) using various the isotherm models and kinetics equations with linear and non-linear methods

NASA Astrophysics Data System (ADS)

Açıkyıldız, Metin; Gürses, Ahmet; Güneş, Kübra; Yalvaç, Duygu

2015-11-01

The present study was designed to compare the linear and non-linear methods used to check the compliance of the experimental data corresponding to the isotherm models (Langmuir, Freundlich, and Redlich-Peterson) and kinetics equations (pseudo-first order and pseudo-second order). In this context, adsorption experiments were carried out to remove an anionic dye, Remazol Brillant Yellow 3GL (RBY), from its aqueous solutions using a commercial activated carbon as a sorbent. The effects of contact time, initial RBY concentration, and temperature onto adsorbed amount were investigated. The amount of dye adsorbed increased with increased adsorption time and the adsorption equilibrium was attained after 240 min. The amount of dye adsorbed enhanced with increased temperature, suggesting that the adsorption process is endothermic. The experimental data was analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to predict adsorption isotherm. It was determined that the isotherm data were fitted to the Langmuir and Redlich-Peterson isotherms. The adsorption process was also found to follow a pseudo second-order kinetic model. According to the kinetic and isotherm data, it was found that the determination coefficients obtained from linear method were higher than those obtained from non-linear method.

Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.

PubMed

Ciampa, Francesco; Mankar, Akash; Marini, Andrea

2017-11-07

Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.

Studies on third-order nonlinear optical properties of chalcone derivatives in polymer host

NASA Astrophysics Data System (ADS)

Shettigar, Seetharam; Umesh, G.; Chandrasekharan, K.; Sarojini, B. K.; Narayana, B.

2008-04-01

In this paper we present the experimental study of the third-order nonlinear optical properties of two chalcone derivatives, viz., 1-(4-methoxyphenyl)-3-(4-butyloxyphenyl)-prop-2-en-1-one and 1-(4-methoxyphenyl)-3-(4-propyloxyphenyl)-prop-2-en-1-one in PMMA host, with the prospective of reaching a compromise between good processability and high nonlinear optical properties. The nonlinear optical properties have been investigated by Z-scan technique using 7 ns laser pulses at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, magnitude of third-order susceptibility and the coupling factor have been determined. The values obtained are of the order of 10 -14 cm 2/W, 1 cm/GW, 10 -13 esu and 0.2, respectively. The molecular second hyperpolarizability for the chalcone derivatives in polymer is of the order of 10 -31 esu. Different guest/host concentrations have also been studied. The results suggest that the nonlinear properties of the chalcones have been improved when they are used as dopants in polymer matrix. The nonlinear parameters obtained are comparable with the reported values of II-VI compound semiconductors. Hence, these chalcons are a promising class of nonlinear optical dopant materials for optical device applications.

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

Characterization of the third-order optical nonlinearity spectrum of barium borate glasses

NASA Astrophysics Data System (ADS)

Santos, S. N. C.; Almeida, J. M. P.; Paula, K. T.; Tomazio, N. B.; Mastelaro, V. R.; Mendonça, C. R.

2017-11-01

Borate glasses have proven to be an important material for applications ranging from radiation dosimetry to nonlinear optics. In particular, B2O3-BaO based glasses are attractive to frequency generation since their barium metaborate phase (β-BaB2O4 or β-BBO) may be crystallized under proper heat treatment. Despite the vast literature covering their linear and second-order optical nonlinear properties, their third-order nonlinearities remain overlooked. This paper thus reports a study on the nonlinear refraction (n2) of BBO and BBS-DyEu glasses through femtosecond Z-scan technique. The results were modeled using the BGO approach, which showed that oxygen ions are playing a role in the nonlinear optical properties of the glasses studied here. In addition, the barium borate glasses containing rare-earths ions were found to exhibit larger nonlinearities, which is in agreement with previous studies.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons.

PubMed

Bennett, Kochise; Mukamel, Shaul

2014-01-28

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Second harmonic generation and crystal growth of new chalcone derivatives

NASA Astrophysics Data System (ADS)

Patil, P. S.; Dharmaprakash, S. M.; Ramakrishna, K.; Fun, Hoong-Kun; Sai Santosh Kumar, R.; Narayana Rao, D.

2007-05-01

We report on the synthesis, crystal structure and optical characterization of chalcone derivatives developed for second-order nonlinear optics. The investigation of a series of five chalcone derivatives with the second harmonic generation powder test according to Kurtz and Perry revealed that these chalcones show efficient second-order nonlinear activity. Among them, high-quality single crystals of 3-Br-4'-methoxychalcone (3BMC) were grown by solvent evaporation solution growth technique. Grown crystals were characterized by X-ray powder diffraction (XRD), laser damage threshold, UV-vis-NIR and refractive index measurement studies. Infrared spectroscopy, thermogravimetric analysis and differential thermal analysis measurements were performed to study the molecular vibration and thermal behavior of 3BMC crystal. Thermal analysis does not show any structural phase transition.

Nonlinear optical response of the collagen triple helix and second harmonic microscopy of collagen liquid crystals

NASA Astrophysics Data System (ADS)

Deniset-Besseau, A.; De Sa Peixoto, P.; Duboisset, J.; Loison, C.; Hache, F.; Benichou, E.; Brevet, P.-F.; Mosser, G.; Schanne-Klein, M.-C.

2010-02-01

Collagen is characterized by triple helical domains and plays a central role in the formation of fibrillar and microfibrillar networks, basement membranes, as well as other structures of the connective tissue. Remarkably, fibrillar collagen exhibits efficient Second Harmonic Generation (SHG) and SHG microscopy proved to be a sensitive tool to score fibrotic pathologies. However, the nonlinear optical response of fibrillar collagen is not fully characterized yet and quantitative data are required to further process SHG images. We therefore performed Hyper-Rayleigh Scattering (HRS) experiments and measured a second order hyperpolarisability of 1.25 10-27 esu for rat-tail type I collagen. This value is surprisingly large considering that collagen presents no strong harmonophore in its amino-acid sequence. In order to get insight into the physical origin of this nonlinear process, we performed HRS measurements after denaturation of the collagen triple helix and for a collagen-like short model peptide [(Pro-Pro-Gly)10]3. It showed that the collagen large nonlinear response originates in the tight alignment of a large number of weakly efficient harmonophores, presumably the peptide bonds, resulting in a coherent amplification of the nonlinear signal along the triple helix. To illustrate this mechanism, we successfully recorded SHG images in collagen liquid solutions by achieving liquid crystalline ordering of the collagen triple helices.

Nonlinear saturation amplitudes in classical Rayleigh-Taylor instability at arbitrary Atwood numbers

NASA Astrophysics Data System (ADS)

Liu, W. H.; Wang, L. F.; Ye, W. H.; He, X. T.

2012-04-01

In this research, nonlinear saturation amplitudes (NSAs) of the first two harmonics in Rayleigh-Taylor instability (RTI) for irrotational, incompressible, and inviscid fluids, with a discontinuous profile at arbitrary Atwood numbers, are investigated analytically, by considering nonlinear corrections up to the tenth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth. The NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the higher-order correction (HOC) and the Atwood number (A) play an important role in the NSA of the RTI. It is found that the NSA of the fundamental mode decreases with increasing A. And when the HOC effects are considered, the NSA of the fundamental mode is significantly larger than the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. We find that the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the NSAs of the first two harmonics demonstrate the trend of convergence as the order of corrections increases. Thus, it should be included in applications where the NSAs play a role, such as inertial confinement fusion ignition target design.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Analysis of nonlinear axial vibration of single-walled carbon nanotubes using Homotopy perturbation method

NASA Astrophysics Data System (ADS)

Fatahi-Vajari, A.; Azimzadeh, Z.

2018-05-01

This paper investigates the nonlinear axial vibration of single-walled carbon nanotubes (SWCNTs) based on Homotopy perturbation method (HPM). A second order partial differential equation that governs the nonlinear axial vibration for such nanotubes is derived using doublet mechanics (DM) theory. To obtain the nonlinear natural frequency in axial vibration mode, this nonlinear equation is solved using HPM. The influences of some commonly used boundary conditions, amplitude of vibration, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear axial vibration characteristics of SWCNTs are discussed. It was shown that unlike the linear one, the nonlinear natural frequency is dependent to maximum vibration amplitude. Increasing the maximum vibration amplitude decreases the natural frequency of vibration compared to the predictions of the linear models. However, with increase in tube length, the effect of the amplitude on the natural frequency decreases. It was also shown that the amount and variation of nonlinear natural frequency is more apparent in higher mode vibration and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein were compared with the fourth order Runge-Kuta numerical results and good agreement was observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Self-Phase-Matched Second-Harmonic and White-Light Generation in a Biaxial Zinc Tungstate Single Crystal

PubMed Central

Osewski, Pawel; Belardini, Alessandro; Petronijevic, Emilija; Centini, Marco; Leahu, Grigore; Diduszko, Ryszard; Pawlak, Dorota A.; Sibilia, Concita

2017-01-01

Second-order nonlinear optical materials are used to generate new frequencies by exploiting second-harmonic generation (SHG), a phenomenon where a nonlinear material generates light at double the optical frequency of the input beam. Maximum SHG is achieved when the pump and the generated waves are in phase, for example through birefringence in uniaxial crystals. However, applying these materials usually requires a complicated cutting procedure to yield a crystal with a particular orientation. Here we demonstrate the first example of phase matching under the normal incidence of SHG in a biaxial monoclinic single crystal of zinc tungstate. The crystal was grown by the micro-pulling-down method with the (102) plane perpendicular to the growth direction. Additionally, at the same time white light was generated as a result of stimulated Raman scattering and multiphoton luminescence induced by higher-order effects such as three-photon luminescence enhanced by cascaded third-harmonic generation. The annealed crystal offers SHG intensities approximately four times larger than the as grown one; optimized growth and annealing conditions may lead to much higher SHG intensities. PMID:28338074

Self-Phase-Matched Second-Harmonic and White-Light Generation in a Biaxial Zinc Tungstate Single Crystal

NASA Astrophysics Data System (ADS)

Osewski, Pawel; Belardini, Alessandro; Petronijevic, Emilija; Centini, Marco; Leahu, Grigore; Diduszko, Ryszard; Pawlak, Dorota A.; Sibilia, Concita

2017-03-01

Second-order nonlinear optical materials are used to generate new frequencies by exploiting second-harmonic generation (SHG), a phenomenon where a nonlinear material generates light at double the optical frequency of the input beam. Maximum SHG is achieved when the pump and the generated waves are in phase, for example through birefringence in uniaxial crystals. However, applying these materials usually requires a complicated cutting procedure to yield a crystal with a particular orientation. Here we demonstrate the first example of phase matching under the normal incidence of SHG in a biaxial monoclinic single crystal of zinc tungstate. The crystal was grown by the micro-pulling-down method with the (102) plane perpendicular to the growth direction. Additionally, at the same time white light was generated as a result of stimulated Raman scattering and multiphoton luminescence induced by higher-order effects such as three-photon luminescence enhanced by cascaded third-harmonic generation. The annealed crystal offers SHG intensities approximately four times larger than the as grown one; optimized growth and annealing conditions may lead to much higher SHG intensities.

Suppression and nonlinear excitation of parasitic modes in second harmonic gyrotrons operating in a very high order mode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nusinovich, Gregory S.; Pu, Ruifeng; Granatstein, Victor L.

2015-07-06

In recent years, there was an active development of high-power, sub-terahertz (sub-THz) gyrotrons for numerous applications. For example, a 0.67 THz gyrotron delivering more than 200 kW with about 20% efficiency was developed. This record high efficiency was achieved because the gyrotron operated in a high-order TE{sub 31,8}-mode with the power of ohmic losses less than 10% of the power of outgoing radiation. That gyrotron operated at the fundamental cyclotron resonance, and a high magnetic field of about 27 T was created by a pulse solenoid. For numerous applications, it is beneficial to use gyrotrons at cyclotron harmonics which can operate inmore » available cryomagnets with fields not exceeding 15 T. However, typically, the gyrotron operation at harmonics faces severe competition from parasitic modes at the fundamental resonance. In the present paper, we consider a similar 0.67 THz gyrotron designed for operation in the same TE{sub 31,8}-mode, but at the second harmonic. We focus on two nonlinear effects typical for interaction between the fundamental and second harmonic modes, viz., the mode suppression and the nonlinear excitation of the mode at the fundamental harmonic by the second harmonic oscillations. Our study includes both the analytical theory and numerical simulations performed with the self-consistent code MAGY. The simulations show that stable second harmonic operation in the TE{sub 31,8} mode is possible with only modest sacrifice of efficiency and power.« less

Strongly nonlinear composite dielectrics: A perturbation method for finding the potential field and bulk effective properties

NASA Astrophysics Data System (ADS)

Blumenfeld, Raphael; Bergman, David J.

1991-10-01

A class of strongly nonlinear composite dielectrics is studied. We develop a general method to reduce the scalar-potential-field problem to the solution of a set of linear Poisson-type equations in rescaled coordinates. The method is applicable for a large variety of nonlinear materials. For a power-law relation between the displacement and the electric fields, it is used to solve explicitly for the value of the bulk effective dielectric constant ɛe to second order in the fluctuations of its local value. A simlar procedure for the vector potential, whose curl is the displacement field, yields a quantity analogous to the inverse dielectric constant in linear dielectrics. The bulk effective dielectric constant is given by a set of linear integral expressions in the rescaled coordinates and exact bounds for it are derived.

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials.

PubMed

Sodemann, Inti; Fu, Liang

2015-11-20

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, in this work, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Random attractor of non-autonomous stochastic Boussinesq lattice system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Min, E-mail: zhaomin1223@126.com; Zhou, Shengfan, E-mail: zhoushengfan@yahoo.com

2015-09-15

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Second Order Accurate Finite Difference Methods

DTIC Science & Technology

1984-08-20

34Nonlinear Modulation of Torsional Waves in Elastic Rods," 3. Phys. Soc. Japan, V. 42, No. 6, pp. 2056-2064, 1977. 10. S. S. Antman and T. Liu. "Travelling...waves in a circular rod. The equations have been solved for coupling effects in torsional and longitudinal waves. Antman and Liu (10) have studied

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

Nonlinearity characterization of temperature sensing systems for integrated circuit testing by intermodulation products monitoring.

PubMed

Altet, J; Mateo, D; Perpiñà, X; Grauby, S; Dilhaire, S; Jordà, X

2011-09-01

This work presents an alternative characterization strategy to quantify the nonlinear behavior of temperature sensing systems. The proposed approach relies on measuring the temperature under thermal sinusoidal steady state and observing the intermodulation products that are generated within the sensing system itself due to its nonlinear temperature-output voltage characteristics. From such intermodulation products, second-order interception points can be calculated as a figure of merit of the measuring system nonlinear behavior. In this scenario, the present work first shows a theoretical analysis. Second, it reports the experimental results obtained with three thermal sensing techniques used in integrated circuits. © 2011 American Institute of Physics

Semirational rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

NASA Astrophysics Data System (ADS)

Du, Zhong; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Wu, Xiao-Yu

2017-12-01

Investigated in this paper are the three-coupled fourth-order nonlinear Schrödinger equations, which describe the dynamics of alpha helical protein with the interspine coupling at the higher order. We show that the representation of the Lax pair with Expressions (42) -(45) in Ref. [25] is not correct, because the three-coupled fourth-order nonlinear Schrödinger equations can not be reproduced by the Lax pair with Expressions (42) -(45) in Ref. [25] through the compatibility condition. Therefore, we recalculate the Lax pair. Based on the recalculated Lax pair, we construct the generalized Darboux transformation, and derive the first- and second-order semirational solutions. Through such solutions, dark-bright-bright soliton, breather-breather-bright soliton, breather soliton and rogue waves are analyzed. It is found that the rogue waves in the three components are mutually proportional. Moreover, three types of the semirational rogue waves consisting of the rogue waves and solitons are presented: (1) consisting of the first-order rogue wave and one soliton; (2) consisting of the first-order rogue wave and two solitons; (3) consisting of the second-order rogue wave and two solitons.

Laterally azo-bridged h-shaped ferroelectric dimesogens for second-order nonlinear optics: ferroelectricity and second harmonic generation.

PubMed

Zhang, Yongqiang; Martinez-Perdiguero, Josu; Baumeister, Ute; Walker, Christopher; Etxebarria, Jesus; Prehm, Marko; Ortega, Josu; Tschierske, Carsten; O'Callaghan, Michael J; Harant, Adam; Handschy, Mark

2009-12-30

Two classes of laterally azo-bridged H-shaped ferroelectric liquid crystals (FLCs), incorporating azobenzene and disperse red 1 (DR-1) chromophores along the FLC polar axes, were synthesized and characterized by polarized light microscopy, differential scanning calorimetry, 2D X-ray diffraction analysis, and electro-optical investigations. They represent the first H-shaped FLC materials exhibiting the ground-state, thermodynamically stable enantiotropic SmC* phase, i.e., ground-state ferroelectricity. Second harmonic generation measurements of one compound incorporating a DR-1 chromophore at the incident wavelength of 1064 nm give a nonlinear coefficient of d(22) = 17 pm/V, the largest nonlinear optics coefficient reported to date for calamitic FLCs. This value enables viable applications of FLCs in nonlinear optics.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

Characterization of the Nonlinear Elastic Properties of Graphite/Epoxy Composites Using Ultrasound

NASA Technical Reports Server (NTRS)

Prosser, William H.; Green, Robert E., Jr.

1990-01-01

The normalized change in ultrasonic "natural" velocity as a function of stress and temperature was measured in a unidirectional laminate of T300/5208 graphite/epoxy composite using a pulsed phase locked loop ultrasonic interferometer. These measurements were used together with the linear (second order) elastic moduli to calculate some of the nonlinear (third order) moduli of this material.

High-resolution schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Harten, A.

1982-01-01

A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

Numerical investigation of sixth order Boussinesq equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.; Vucheva, V.

2017-10-01

We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

Time accurate application of the MacCormack 2-4 scheme on massively parallel computers

NASA Technical Reports Server (NTRS)

Hudson, Dale A.; Long, Lyle N.

1995-01-01

Many recent computational efforts in turbulence and acoustics research have used higher order numerical algorithms. One popular method has been the explicit MacCormack 2-4 scheme. The MacCormack 2-4 scheme is second order accurate in time and fourth order accurate in space, and is stable for CFL's below 2/3. Current research has shown that the method can give accurate results but does exhibit significant Gibbs phenomena at sharp discontinuities. The impact of adding Jameson type second, third, and fourth order artificial viscosity was examined here. Category 2 problems, the nonlinear traveling wave and the Riemann problem, were computed using a CFL number of 0.25. This research has found that dispersion errors can be significantly reduced or nearly eliminated by using a combination of second and third order terms in the damping. Use of second and fourth order terms reduced the magnitude of dispersion errors but not as effectively as the second and third order combination. The program was coded using Thinking Machine's CM Fortran, a variant of Fortran 90/High Performance Fortran, and was executed on a 2K CM-200. Simple extrapolation boundary conditions were used for both problems.

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

Nonlinear optical effects in organic microstructures

NASA Astrophysics Data System (ADS)

Novikov, Vladimir B.; Mamonov, Evgeniy A.; Kopylov, Denis A.; Mitetelo, Nikolai V.; Venkatakrishnarao, D.; Narayana, YSLV; Chandrasekar, R.; Murzina, Tatiana V.

2017-05-01

Organic microstructures attract much attention due to their unique properties originating from the design of their shape and optical parameters. In this work we discuss the linear, second- and third-order nonlinear optical effects in arrays and in individual organic microstructures composed by self-assembling technique and formed randomly on top of a solid substrate. The structures under study consist of micro-spheres, -hemispheres or -frustums made of red laser dye and reveal an intense fluorescence (FL) in the visible spectral range. Importantly, that due to a high value of the refractive index and confined geometry, such micro-structures support the excitation of whispering gallery modes (WGM), which brings about strong and spectrally-selected light localization. We show that an amplification of the nonlinear optical effects is observed for these structures as compared to a homogeneous dye film of similar composition. The obtained data are in agreement with the results of the FDTD calculations performed for the structures of different dimensions. Perspectives of application of such type of organic nonlinear microresonators in optical devices are discussed.

Solution of second order quasi-linear boundary value problems by a wavelet method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Lei; Zhou, Youhe; Wang, Jizeng, E-mail: jzwang@lzu.edu.cn

2015-03-10

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can evenmore » reach orders of 5.8.« less

The second– and third– order nonlinear optical properties and electronic transition of a NLO chromophore: A DFT study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altürk, Sümeyye, E-mail: sumeyye-alturk@hotmail.com; Avci, Davut, E-mail: davci@sakarya.edu.tr; Tamer, Ömer, E-mail: omertamer@sakarya.edu.tr

2016-03-25

It is well known that the practical applications of second-order and third-order nonlinear optical (NLO) materials have been reported in modern technology, such as optical data processing, transmission and storage, etc. In this respect, the linear and nonlinear optical parameters (the molecular static polarizability (α), and the first–order static hyperpolarizability (β{sub 0}), the second–order static hyperpolarizability (γ)), UV-vis spectra and HOMO and LUMO energies of 2-(1′-(4’’’-Methoxyphenyl)-5′-(thien-2″-yl)pyrrol-2′-yl)-1,3-benzothiazole were investigated by using the HSEh1PBE/6–311G(d,p) level of density functional theory. The UV–vis spectra were simulated using TD/HSEh1PBE/6– 311G(d,p) level, and the major contributions to the electronic transitions were obtained. The molecular hardness (η)more » and electronegativity (χ) parameters were also obtained by using molecular frontier orbital energies. The NLO parameters of the title compound were calculated, and obtained data were compared with that of para-Nitroaniline (pNA) which is a typical NLO material and the corresponding experimental data. Obtained data of the chromosphere display significant molecular second-and third-nonlinearity.« less

Experimental demonstration of 1535-1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal.

PubMed

Chowdhury, A; Staus, C; Boland, B F; Kuech, T F; McCaughan, L

2001-09-01

We present results of what is to our knowledge the first experimental demonstration of simultaneous optical wavelength interchange by use of a two-dimensional second-order nonlinear photonic crystal. Fabrication and performance parameters of a 1535-1555-nm wavelength interchange nonlinear photonic crystal fabricated in lithium niobate are discussed.

Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

NASA Astrophysics Data System (ADS)

Cianchi, Andrea; Maz'ya, Vladimir G.

2018-05-01

Best possible second-order regularity is established for solutions to p-Laplacian type equations with {p \\in (1, ∞)} and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L 2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

Image storage in coumarin-based copolymer thin films by photoinduced dimerization.

PubMed

Gindre, Denis; Iliopoulos, Konstantinos; Krupka, Oksana; Champigny, Emilie; Morille, Yohann; Sallé, Marc

2013-11-15

We report a technique to encode grayscale digital images in thin films composed of copolymers containing coumarins. A nonlinear microscopy setup was implemented and two nonlinear optical processes were used to store and read information. A third-order process (two-photon absorption) was used to photoinduce a controlled dimer-to-monomer ratio within a defined tiny volume in the material, which corresponds to each recorded bit of data. Moreover, a second-order process (second-harmonic generation) was used to read the stored information, which has been found to be highly dependent upon the monomer-to-dimer ratio.

Probing the interatomic potential of solids with strong-field nonlinear phononics

NASA Astrophysics Data System (ADS)

von Hoegen, A.; Mankowsky, R.; Fechner, M.; Först, M.; Cavalleri, A.

2018-03-01

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A1 (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

Microgravity Processing and Photonic Applications of Organic and Polymeric Materials

NASA Technical Reports Server (NTRS)

Frazier, Donald 0; Penn, Benjamin G.; Smith, David; Witherow, William K.; Paley, M. S.; Abdeldayem, Hossin A.

1998-01-01

In recent years, a great deal of interest has been directed toward the use of organic materials in the development of high-efficiency optoelectronic and photonic devices. There is a myriad of possibilities among organic which allow flexibility in the design of unique structures with a variety of functional groups. The use of nonlinear optical (NLO) organic materials such as thin-film waveguides allows full exploitation of their desirable qualities by permitting long interaction lengths and large susceptibilities allowing modest power input. There are several methods in use to prepare thin films, such as Langmuir-Blodgett (LB) and self-assembly techniques, vapor deposition, growth from sheared solution or melt, and melt growth between glass plates. Organics have many features that make Abstract: them desirable for use in optical devices such as high second- and third-order nonlinearities, flexibility of molecular design, and damage resistance to optical radiation. However, their use in devices has been hindered by processing difficulties for crystals and thin films. In this chapter, we discuss photonic and optoelectronic applications of a few organic materials and the potential role of microgravity on processing these materials. It is of interest to note how materials with second- and third-order nonlinear optical behavior may be improved in a diffusion-limited environment and ways in which convection may be detrimental to these materials. We focus our discussion on third-order materials for all-optical switching, and second-order materials for all-optical switching, and second-order materials for frequency conversion and electrooptics.

The analysis of harmonic generation coefficients in the ablative Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Lu, Yan; Fan, Zhengfeng; Lu, Xinpei; Ye, Wenhua; Zou, Changlin; Zhang, Ziyun; Zhang, Wen

2017-10-01

In this research, we use the numerical simulation method to investigate the generation coefficients of the first three harmonics and the zeroth harmonic in the Ablative Rayleigh-Taylor Instability. It is shown that the interface shifts to the low temperature side during the ablation process. In consideration of the third-order perturbation theory, the first three harmonic amplitudes of the weakly nonlinear regime are calculated and then the harmonic generation coefficients are obtained by curve fitting. The simulation results show that the harmonic generation coefficients changed with time and wavelength. Using the higher-order perturbation theory, we find that more and more harmonics are generated in the later weakly nonlinear stage, which is caused by the negative feedback of the later higher harmonics. Furthermore, extending the third-order theory to the fifth-order theory, we find that the second and the third harmonics coefficients linearly depend on the wavelength, while the feedback coefficients are almost constant. Further analysis also shows that when the fifth-order theory is considered, the normalized effective amplitudes of second and third harmonics can reach about 25%-40%, which are only 15%-25% in the frame of the previous third-order theory. Therefore, the third order perturbation theory is needed to be modified by the higher-order theory when ηL reaches about 20% of the perturbation wavelength.

State estimation with incomplete nonlinear constraint

NASA Astrophysics Data System (ADS)

Huang, Yuan; Wang, Xueying; An, Wei

2017-10-01

A problem of state estimation with a new constraints named incomplete nonlinear constraint is considered. The targets are often move in the curve road, if the width of road is neglected, the road can be considered as the constraint, and the position of sensors, e.g., radar, is known in advance, this info can be used to enhance the performance of the tracking filter. The problem of how to incorporate the priori knowledge is considered. In this paper, a second-order sate constraint is considered. A fitting algorithm of ellipse is adopted to incorporate the priori knowledge by estimating the radius of the trajectory. The fitting problem is transformed to the nonlinear estimation problem. The estimated ellipse function is used to approximate the nonlinear constraint. Then, the typical nonlinear constraint methods proposed in recent works can be used to constrain the target state. Monte-Carlo simulation results are presented to illustrate the effectiveness proposed method in state estimation with incomplete constraint.

The intrinsic matter bispectrum in ΛCDM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tram, Thomas; Crittenden, Robert; Koyama, Kazuya

2016-05-01

We present a fully relativistic calculation of the matter bispectrum at second order in cosmological perturbation theory assuming a Gaussian primordial curvature perturbation. For the first time we perform a full numerical integration of the bispectrum for both baryons and cold dark matter using the second-order Einstein-Boltzmann code, SONG. We review previous analytical results and provide an improved analytic approximation for the second-order kernel in Poisson gauge which incorporates Newtonian nonlinear evolution, relativistic initial conditions, the effect of radiation at early times and the cosmological constant at late times. Our improved kernel provides a percent level fit to the fullmore » numerical result at late times for most configurations, including both equilateral shapes and the squeezed limit. We show that baryon acoustic oscillations leave an imprint in the matter bispectrum, making a significant impact on squeezed shapes.« less

Nonlinearly driven harmonics of Alfvén modes

NASA Astrophysics Data System (ADS)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Effect of the magnetic field on the nonlinear optical rectification and second and third harmonic generation in double δ-doped GaAs quantum wells

NASA Astrophysics Data System (ADS)

Martínez-Orozco, J. C.; Rojas-Briseño, J. G.; Rodríguez-Magdaleno, K. A.; Rodríguez-Vargas, I.; Mora-Ramos, M. E.; Restrepo, R. L.; Ungan, F.; Kasapoglu, E.; Duque, C. A.

2017-11-01

In this paper we are reporting the computation for the Nonlinear Optical Rectification (NOR) and the Second and Third Harmonic Generation (SHG and THG) related with electronic states of asymmetric double Si-δ-doped quantum well in a GaAs matrix when this is subjected to an in-plane (x-oriented) constant magnetic field effect. The work is performed in the effective mass and parabolic band approximations in order to compute the electronic structure for the system by a diagonalization procedure. The expressions for the nonlinear optical susceptibilities, χ0(2), χ2ω(2), and χ3ω(3), are those arising from the compact matrix density formulation and stand for the NOR, SHG, and THG, respectively. This asymmetric double δ-doped quantum well potential profile actually exhibits nonzero NOR, SHG, and THG responses which can be easily controlled by the in-plane (x-direction) externally applied magnetic field. In particular we find that for the chosen configuration the harmonic generation is in the far-infrared/THz region, thus and becoming suitable building blocks for photodetectors in this range of the electromagnetic spectra.

Dispersion dependence of second-order refractive index and complex third-order optical susceptibility in oxide glasses

NASA Astrophysics Data System (ADS)

Abdel Wahab, F. A.; El-Diasty, Fouad; Abdel-Baki, Manal

2009-10-01

A method correlates Fresnel-based spectrophotometric measurements and Lorentz dispersion theory is presented to study the dispersion of nonlinear optical parameters in particularly oxide glasses in a very wide range of angular frequency. The second-order refractive index and third-order optical susceptibility of Cr-doped glasses are determined from linear refractive index. Furthermore, both real and imaginary components of the complex susceptibility are carried out. The study reveals the importance of determining the dispersion of nonlinear absorption (two-photon absorption coefficient) to find the maximum resonant and nonresonant susceptibilities of investigated glasses. The present method is applied on Cr-doped lithium aluminum silicate (LAS) glasses due to their semiconductor-like behavior and also to their application in laser industry.

Competition between SFG and two SHGs in broadband type-I QPM

NASA Astrophysics Data System (ADS)

Dang, Weirui; Chen, Yuping; Gong, Mingjun; Chen, Xianfeng

2013-03-01

In this paper, we have studied the characteristics of second-order nonlinear interactions with band-overlapped type-I quasi-phase-matching (QPM) second harmonic generation (SHG) and sum-frequency generation (SFG), and predicted a blue-shift with a band-narrowing of their bands and a sunken response in the SFG curve, which are due to the phase-matching-dependent competition between band-overlapped SHG and SFG processes. This prediction is then verified by the experiment in an 18-mm-long bulk MgO-doped periodically poled lithium niobate crystal (MgO:PPLN) and may provide the candidate solution to output controlling for flexible broadcast wavelength conversion, channel-selective wavelength conversion and all-optical logic gates by cascaded QPM second-order nonlinear processes.

Ultrafast frequency-selective optical switching based on thin self-assembled organic chromophoric films with a large second-order nonlinear response

NASA Astrophysics Data System (ADS)

Wang, Gang; Zhu, Peiwang; Marks, Tobin J.; Ketterson, J. B.

2002-09-01

Thin films consisting of self-assembled chromophoric superlattices exhibit very large second-order nonlinear responses [chi](2). Using such films, a "static" diffraction grating is created by the interference of two coherent infrared beams from a pulsed yttritium-aluminum-garnet laser. This grating is used to switch the second-harmonic and third-harmonic "signal" beams (generated from the fundamental "pump" beam or mixed within the chromophoric superlattice) into different channels (directions). Ultrafast switching response as a function of the time overlap of the pumping beams is demonstrated. It is suggested that such devices can be used to spatially and temporally separate signal trains consisting of pulses having different frequencies and arrival times.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

PubMed

Liu, Wei; Huang, Jie

2018-03-01

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Sequential double second-order nonlinear optical switch by an acido-triggered photochromic cyclometallated platinum(II) complex.

PubMed

Boixel, Julien; Guerchais, Véronique; Le Bozec, Hubert; Chantzis, Agisilaos; Jacquemin, Denis; Colombo, Alessia; Dragonetti, Claudia; Marinotto, Daniele; Roberto, Dominique

2015-05-07

An unprecedented DTE-based Pt(II) complex, 2(o), which stands as the first example of a sequential double nonlinear optical switch, induced first by protonation and next upon irradiation with UV light is presented.

Polyspectral signal analysis techniques for condition based maintenance of helicopter drive-train system

NASA Astrophysics Data System (ADS)

Hassan Mohammed, Mohammed Ahmed

For an efficient maintenance of a diverse fleet of air- and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components monitored vibration signals. In this dissertation, we present theory and applications of polyspectral signal processing techniques for condition monitoring of critical components in the AH-64D helicopter tail rotor drive train system. Currently available vibration-monitoring tools are mostly built around auto- and cross-power spectral analysis which have limited performance in detecting frequency correlations higher than second order. Studying higher order correlations and their Fourier transforms, higher order spectra, provides more information about the vibration signals which helps in building more accurate diagnostic models of the mechanical system. Based on higher order spectral analysis, different signal processing techniques are developed to assess health conditions of different critical rotating-components in the AH-64D helicopter drive-train. Based on cross-bispectrum, quadratic nonlinear transfer function is presented to model second order nonlinearity in a drive-shaft running between the two hanger bearings. Then, quadratic-nonlinearity coupling coefficient between frequency harmonics of the rotating shaft is used as condition metric to study different seeded shaft faults compared to baseline case, namely: shaft misalignment, shaft imbalance, and combination of shaft misalignment and imbalance. The proposed quadratic-nonlinearity metric shows better capabilities in distinguishing the four studied shaft settings than the conventional linear coupling based on cross-power spectrum. We also develop a new concept of Quadratic-Nonlinearity Power-Index spectrum, QNLPI(f), that can be used in signal detection and classification, based on bicoherence spectrum. The proposed QNLPI(f) is derived as a projection of the three-dimensional bicoherence spectrum into two-dimensional spectrum that quantitatively describes how much of the mean square power at certain frequency f is generated due to nonlinear quadratic interaction between different frequency components. The proposed index, QNLPI(f), can be used to simplify the study of bispectrum and bicoherence signal spectra. It also inherits useful characteristics from the bicoherence such as high immunity to additive Gaussian noise, high capability of nonlinear-systems identifications, and amplification invariance. The quadratic-nonlinear power spectral density PQNL(f) and percentage of quadratic nonlinear power PQNLP are also introduced based on the QNLPI(f). Concept of the proposed indices and their computational considerations are discussed first using computer generated data, and then applied to real-world vibration data to assess health conditions of different rotating components in the drive train including drive-shaft, gearbox, and hanger bearing faults. The QNLPI(f) spectrum enables us to gain more details about nonlinear harmonic generation patterns that can be used to distinguish between different cases of mechanical faults, which in turn helps to gaining more diagnostic/prognostic capabilities.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

The determination of third order linear models from a seventh order nonlinear jet engine model

NASA Technical Reports Server (NTRS)

Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex

1989-01-01

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Second-order nonlinear optical microscopy of spider silk

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

NASA Technical Reports Server (NTRS)

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Interface width effect on the classical Rayleigh-Taylor instability in the weakly nonlinear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, L. F.; State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083; Ye, W. H.

2010-05-15

In this paper, the interface width effects (i.e., the density gradient effects or the density transition layer effects) on the Rayleigh-Taylor instability (RTI) in the weakly nonlinear (WN) regime are investigated by numerical simulation (NS). It is found that the interface width effects dramatically influence the linear growth rate in the linear growth regime and the mode coupling process in the WN growth regime. First, the interface width effects decrease the linear growth rate of the RTI, particularly for the short perturbation wavelengths. Second, the interface width effects suppress (reduce) the third-order feedback to the fundamental mode, which induces themore » nonlinear saturation amplitude (NSA) to exceed the classical prediction, 0.1lambda. The wider the density transition layer is, the larger the NSA is. The NSA in our NS can reach a half of its perturbation wavelength. Finally, the interface width effects suppress the generation and the growth of the second and the third harmonics. The ability to suppress the harmonics' growth increases with the interface width but decreases with the perturbation wavelength. On the whole, in the WN regime, the interface width effects stabilize the RTI, except for an enhancement of the NSA, which is expected to improve the understanding of the formation mechanism for the astrophysical jets, and for the jetlike long spikes in the high energy density physics.« less

Nonlinear optical conductivity and subharmonic instabilities of graphene in a strong electromagnetic field

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dimitri; Fogler, Michael

We study theoretically the second-order nonlinear optical conductivity σ (2) of graphene as a function of frequency and momentum. We distinguish two regimes. At frequencies ω higher than the temperature-dependent electron-electron collision rate γee- 1 , the conductivity σ (2) can be derived from the semiclassical kinetic equation. The calculation requires taking into account the photon drag (Lorentz force) due to the ac magnetic field. In the low-frequency hydrodynamic regime ω <<γee- 1 , the nonlinear conductivity has a different form and the photon drag effect is suppressed. As a consequence of the nonlinearity, a strong enough photoexcitation can cause spontaneous generation of collective modes in a graphene strip: plasmons in the high-frequency regime and energy waves (demons) in the hydrodynamic one. The dominant instability occurs at frequency ω / 2 .

Computational procedures for mixed equations with shock waves

NASA Technical Reports Server (NTRS)

Yu, N. J.; Seebass, R.

1974-01-01

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

Key functions analysis of a novel nonlinear optical D-π-A bridge type (2E)-3-(4-Methylphenyl)-1-(3-nitrophenyl) prop-2-en-1-one chalcone: An experimental and theoretical approach

NASA Astrophysics Data System (ADS)

Patil, Parutagouda Shankaragouda; Shkir, Mohd; Maidur, Shivaraj R.; AlFaify, S.; Arora, M.; Rao, S. Venugopal; Abbas, Haider; Ganesh, V.

2017-10-01

In the current work a new third-order nonlinear optical organic single crystal of (2E)-3-(4-Methylphenyl)-1-(3-nitrophenyl) prop-2-en-1-one (ML3NC) has been grown with well-defined morphology using the slow evaporation solution growth technique. X-ray diffraction technique was used to confirm the crystal system. The presence of functional groups in the molecular structure was identified by robust FT-IR and FT-Raman spectra by experimental and theoretical analysis. The ultraviolet-visible-near infrared and photoluminescence studies shows that the grown crystals possess excellent transparency window and green emission band (∼560 nm) confirms their use in green OLEDs. The third-order nonlinear and optical limiting studies have been performed using femtosecond (fs) Z-scan technique. The third-order nonlinear optical susceptibility (χ(3)), second-order hyperpolarizability (γ), nonlinear refractive index (n2) and limiting threshold values are found to be 4.03 × 10-12 esu, 14.2 × 10-32 esu, -4.33 × 10-14 cm2/W and 2.41 mJ/cm2, respectively. Furthermore, the quantum chemical studies were carried out to achieve the ground state molecular geometry and correlate with experimental results. The experimental value of absorption wavelength (λabs = 328 nm) is found to be in excellent accord with the theoretical value (λabs = 328 nm) at TD-DFT/B3LYP/6-31G* level of theory. To understand the static and dynamic NLO behavior, the polarizability (α) and second hyperpolarizability (γ) values were determined using TD-HF method. The computed second hyperpolarizability γ(-3ω; ω,ω,ω) at 800 nm wavelength was found to be 0.499 × 10-32 esu which is in good agreement with experimental value at the same wavelength. These results confirms the applied nature of title molecule in optoelectronic and nonlinear optical devices.

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

NASA Astrophysics Data System (ADS)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

Influence of optical activity on rogue waves propagating in chiral optical fibers.

PubMed

Temgoua, D D Estelle; Kofane, T C

2016-06-01

We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Nonlinear probabilistic finite element models of laminated composite shells

NASA Technical Reports Server (NTRS)

Engelstad, S. P.; Reddy, J. N.

1993-01-01

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

Effects of the non-extensive parameter on the propagation of ion acoustic waves in five-component cometary plasma system

NASA Astrophysics Data System (ADS)

Mahmoud, Abeer A.

2018-01-01

Some important evolution nonlinear partial differential equations are derived using the reductive perturbation method for unmagnetized collisionless system of five component plasma. This plasma system is a multi-ion contains negatively and positively charged Oxygen ions (heavy ions), positive Hydrogen ions (lighter ions), hot electrons from solar origin and colder electrons from cometary origin. The positive Hydrogen ion and the two types of electrons obey q-non-extensive distributions. The derived equations have three types of ion acoustic waves, which are soliton waves, shock waves and kink waves. The effects of the non-extensive parameters for the hot electrons, the colder electrons and the Hydrogen ions on the propagation of the envelope waves are studied. The compressive and rarefactive shapes of the three envelope waves appear in this system for the first order of the power of the nonlinearity strength with different values of non-extensive parameters. For the second order, the strength of nonlinearity will increase and the compressive type of the envelope wave only appears.

Strong photon antibunching in weakly nonlinear two-dimensional exciton-polaritons

NASA Astrophysics Data System (ADS)

Ryou, Albert; Rosser, David; Saxena, Abhi; Fryett, Taylor; Majumdar, Arka

2018-06-01

A deterministic and scalable array of single photon nonlinearities in the solid state holds great potential for both fundamental physics and technological applications, but its realization has proved extremely challenging. Despite significant advances, leading candidates such as quantum dots and group III-V quantum wells have yet to overcome their respective bottlenecks in random positioning and weak nonlinearity. Here we consider a hybrid light-matter platform, marrying an atomically thin two-dimensional material to a photonic crystal cavity, and analyze its second-order coherence function. We identify several mechanisms for photon antibunching under different system parameters, including one characterized by large dissipation and weak nonlinearity. Finally, we show that by patterning the two-dimensional material into different sizes, we can drive our system dynamics from a coherent state into a regime of strong antibunching with second-order coherence function g(2 )(0 ) ˜10-3 , opening a possible route to scalable, on-chip quantum simulations with correlated photons.

Improved stability of the induced second-order nonlinearity in soft glass by thermal poling

NASA Astrophysics Data System (ADS)

Moura, A. L.; de Araujo, M. T.; Vermelho, M. V. D.; Aitchison, J. S.

2006-08-01

Stable and intense second-order nonlinearity in soda lime glass is investigated tailoring the induced electric current. This procedure allows the determination of the relative contributions of the dipole orientation as well as the ionic contributions to the poling process. The experiments are developed in the light of multiple-carrier models controlling the output power supply applied current to tailor the frozen-in induced electric field — Edc. This method permits the induction of the stable nonlinearity for applied electric fields above ˜5kV/cm and temperatures ˜250°C. It is also possible to reach higher temperatures than the ones used in normal poling procedures avoiding the electric current breakdown. The controlled Edc formation enables it to participate in essential chemical reactions that determine the intensity and stability of the nonlinearity. The induced d33 of ˜0.41pm/V measured 20 days after poling reduced only ˜50% during the next seven months.

Flat nonlinear optics: metasurfaces for efficient frequency mixing

NASA Astrophysics Data System (ADS)

Nookala, Nishant; Lee, Jongwon; Liu, Yingnan; Bishop, Wells; Tymchenko, Mykhailo; Gomez-Diaz, J. Sebastian; Demmerle, Frederic; Boehm, Gerhard; Amann, Markus-Christian; Wolf, Omri; Brener, Igal; Alu, Andrea; Belkin, Mikhail A.

2017-02-01

Gradient metasurfaces, or ultrathin optical components with engineered transverse impedance gradients along the surface, are able to locally control the phase and amplitude of the scattered fields over subwavelength scales, enabling a broad range of linear components in a flat, integrable platform1-4. On the contrary, due to the weakness of their nonlinear optical responses, conventional nonlinear optical components are inherently bulky, with stringent requirements associated with phase matching and poor control over the phase and amplitude of the generated beam. Nonlinear metasurfaces have been recently proposed to enable frequency conversion in thin films without phase-matching constraints and subwavelength control of the local nonlinear phase5-8. However, the associated optical nonlinearities are far too small to produce significant nonlinear conversion efficiency and compete with conventional nonlinear components for pump intensities below the materials damage threshold. Here, we report multi-quantum-well based gradient nonlinear metasurfaces with second-order nonlinear susceptibility over 106 pm/V for second harmonic generation at a fundamental pump wavelength of 10 μm, 5-6 orders of magnitude larger than traditional crystals. Further, we demonstrate the efficacy of this approach to designing metasurfaces optimized for frequency conversion over a large range of wavelengths, by reporting multi-quantum-well and metasurface structures optimized for a pump wavelength of 6.7 μm. Finally, we demonstrate how the phase of this nonlinearly generated light can be locally controlled well below the diffraction limit using the Pancharatnam-Berry phase approach5,7,9, opening a new paradigm for ultrathin, flat nonlinear optical components.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

Probing Graphene χ((2)) Using a Gold Photon Sieve.

PubMed

Lobet, Michaël; Sarrazin, Michaël; Cecchet, Francesca; Reckinger, Nicolas; Vlad, Alexandru; Colomer, Jean-François; Lis, Dan

2016-01-13

Nonlinear second harmonic optical activity of graphene covering a gold photon sieve was determined for different polarizations. The photon sieve consists of a subwavelength gold nanohole array placed on glass. It combines the benefits of efficient light trapping and surface plasmon propagation to unravel different elements of graphene second-order susceptibility χ((2)). Those elements efficiently contribute to second harmonic generation. In fact, the graphene-coated photon sieve produces a second harmonic intensity at least two orders of magnitude higher compared with a bare, flat gold layer and an order of magnitude coming from the plasmonic effect of the photon sieve; the remaining enhancement arises from the graphene layer itself. The measured second harmonic generation yield, supplemented by semianalytical computations, provides an original method to constrain the graphene χ((2)) elements. The values obtained are |d31 + d33| ≤ 8.1 × 10(3) pm(2)/V and |d15| ≤ 1.4 × 10(6) pm(2)/V for a second harmonic signal at 780 nm. This original method can be applied to any kind of 2D materials covering such a plasmonic structure.

Towards a unifying theory for the first-, second-, and third-order molecular (non)linear optical response

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2010-05-01

We present a procedure for the modeling of the dispersion of the nonlinear optical response of complex molecular structures that is based strictly on the results from experimental characterization. We show how under some general conditions, the use of the Thomas-Kuhn sum-rules leads to a successful modeling of the nonlinear response of complex molecular structures.

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

NASA Astrophysics Data System (ADS)

Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt

2018-02-01

A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.

A reduced-order nonlinear sliding mode observer for vehicle slip angle and tyre forces

NASA Astrophysics Data System (ADS)

Chen, Yuhang; Ji, Yunfeng; Guo, Konghui

2014-12-01

In this paper, a reduced-order sliding mode observer (RO-SMO) is developed for vehicle state estimation. Several improvements are achieved in this paper. First, the reference model accuracy is improved by considering vehicle load transfers and using a precise nonlinear tyre model 'UniTire'. Second, without the reference model accuracy degraded, the computing burden of the state observer is decreased by a reduced-order approach. Third, nonlinear system damping is integrated into the SMO to speed convergence and reduce chattering. The proposed RO-SMO is evaluated through simulation and experiments based on an in-wheel motor electric vehicle. The results show that the proposed observer accurately predicts the vehicle states.

Fundamental Limits:. Developing New Tools for a Better Understanding of Second-Order Molecular Nonlinear Optics

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen

The generalized Thomas-Kuhn sum rules are used to characterize the nonlinear optical response of organic chromophores in terms of fundamental parameters that can be measured experimentally. The nonlinear optical performance of organic molecules is evaluated from the combination of hyper-Rayleigh scattering measurements and the analysis in terms of the fundamental limits. Different strategies for the enhancement of nonlinear optical behavior at the molecular and supramolecular level are evaluated and new paradigms for the design of more efficient nonlinear optical molecules are proposed and investigated.

Nonlinear, anisotropic, and giant photoconductivity in intrinsic and doped graphene

NASA Astrophysics Data System (ADS)

Singh, Ashutosh; Ghosh, Saikat; Agarwal, Amit

2018-01-01

We present a framework to calculate the anisotropic and nonlinear photoconductivity for two band systems with application to graphene. In contrast to the usual perturbative (second order in the optical field strength) techniques, we calculate photoconductivity to all orders in the optical field strength. In particular, for graphene, we find the photoresponse to be giant (at large optical field strengths) and anisotropic. The anisotropic photoresponse in graphene is correlated with polarization of the incident field, with the response being similar to that of a half-wave plate. We predict that the anisotropy in the simultaneous measurement of longitudinal (σx x) and transverse (σy x) photoconductivity, with four probes, offers a unique experimental signature of the photovoltaic response, distinguishing it from the thermal-Seebeck and bolometric effects in photoresponse.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

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

NASA Astrophysics Data System (ADS)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

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

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

NASA Astrophysics Data System (ADS)

Bai, Jing; Wen, Guoguang; Rahmani, Ahmed

2018-04-01

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems' convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems' stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1986-01-01

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

PubMed

Leszczynski, Henryk; Wrzosek, Monika

2017-02-01

We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

Improvements to embedded shock wave calculations for transonic flow-applications to wave drag and pressure rise predictions

NASA Technical Reports Server (NTRS)

Seebass, A. R.

1974-01-01

The numerical solution of a single, mixed, nonlinear equation with prescribed boundary data is discussed. A second order numerical procedure for solving the nonlinear equation and a shock fitting scheme was developed to treat the discontinuities that appear in the solution.

Second order sliding mode control for a quadrotor UAV.

PubMed

Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang

2014-07-01

A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Investigation of broadband terahertz generation from metasurface

NASA Astrophysics Data System (ADS)

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E. I.; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M.

2018-05-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Investigation of broadband terahertz generation from metasurface.

PubMed

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E I; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M

2018-05-28

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG.

PubMed

Li, Xiujian; Liao, Jiali; Nie, Yongming; Marko, Matthew; Jia, Hui; Liu, Ju; Wang, Xiaochun; Wong, Chee Wei

2015-04-20

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Application of discrete solvent reaction field model with self-consistent atomic charges and atomic polarizabilities to calculate the χ(1) and χ(2) of organic molecular crystals

NASA Astrophysics Data System (ADS)

Lu, Shih-I.

2018-01-01

We use the discrete solvent reaction field model to evaluate the linear and second-order nonlinear optical susceptibilities of 3-methyl-4-nitropyridine-1-oxyde crystal. In this approach, crystal environment is created by supercell architecture. A self-consistent procedure is used to obtain charges and polarizabilities for environmental atoms. Impact of atomic polarizabilities on the properties of interest is highlighted. This approach is shown to give the second-order nonlinear optical susceptibilities within error bar of experiment as well as the linear optical susceptibilities in the same order as experiment. Similar quality of calculations are also applied to both 4-N,N-dimethylamino-3-acetamidonitrobenzene and 2-methyl-4-nitroaniline crystals.

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

Zhang, Shuzeng; Jeong, Hyunjo; Cho, Sungjong; Li, Xiongbing

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Absolute second order nonlinear susceptibility of Pt nanowire arrays on MgO faceted substrates with various cross-sectional shapes

NASA Astrophysics Data System (ADS)

Ogata, Yoichi; Mizutani, Goro

2013-08-01

We have measured optical second harmonic generation (SHG) intensity from three types of Pt nanowires with 7 nm widths of elliptical and boomerang cross-sectional shapes and with 2 nm width elliptical cross-sectional shapes on the MgO faceted templates. From the SHG intensities, we calculated the absolute value of the nonlinear susceptibility χ(2) integrated in the direction of the wire-layer thickness. The tentatively obtained bulk χ(2)B of the wire layer was very large, approaching the value of the well-known nonlinear optical material BaTiO3.

Second harmonic generation by all-optical poling and its relaxation in the polymer films containing azo sulfonamide chromophores

NASA Astrophysics Data System (ADS)

Ortyl, E.; Chan, S. W.; Nunzi, J.-M.; Kucharski, S.

2006-11-01

Polyurethane polymers containing azo sulfonamide chromophores were obtained by coupling reaction of the precursor polyurethane with corresponding diazonium salts. The chromophores, showing high hyperpolarizability value on molecular scale, were found to undergo orientation by all-optical poling method yielding macroscopic nonlinear optical response. The rate of generation and decay of the second-order nonlinear susceptibility was evaluated as a function of time. It was established that the polymers containing sulfonamide type chromophores showed higher stability of the nonlinear optical signal as compared with those modified with a nitro-acceptor groups of the Disperse Red type.

A Computational Procedure for Identifying Bilinear Representations of Nonlinear Systems Using Volterra Kernels

NASA Technical Reports Server (NTRS)

Kvaternik, Raymond G.; Silva, Walter A.

2008-01-01

A computational procedure for identifying the state-space matrices corresponding to discrete bilinear representations of nonlinear systems is presented. A key feature of the method is the use of first- and second-order Volterra kernels (first- and second-order pulse responses) to characterize the system. The present method is based on an extension of a continuous-time bilinear system identification procedure given in a 1971 paper by Bruni, di Pillo, and Koch. The analytical and computational considerations that underlie the original procedure and its extension to the title problem are presented and described, pertinent numerical considerations associated with the process are discussed, and results obtained from the application of the method to a variety of nonlinear problems from the literature are presented. The results of these exploratory numerical studies are decidedly promising and provide sufficient credibility for further examination of the applicability of the method.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

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

NASA Astrophysics Data System (ADS)

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.

Large enhancement of interface second-harmonic generation near the zero-n(-) gap of a negative-index Bragg grating.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Scalora, Michael

2006-03-01

We predict a large enhancement of interface second-harmonic generation near the zero-n(-) gap of a Bragg grating made of alternating layers of negative- and positive-index materials. Field localization and coherent oscillations of the nonlinear dipoles located at the structure's interfaces conspire to yield conversion efficiencies at least an order of magnitude greater than those achievable in the same length of nonlinear, phase-matched bulk material. These findings thus point to a new class of second-harmonic-generation devices made of standard centrosymmetric materials.

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

Solution of second order supersymmetrical intertwining relations in Minkowski plane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru; Nishnianidze, D. N., E-mail: cutaisi@yahoo.com

2016-08-15

Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1986-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1987-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Incorporation of New Benzofulvene Derivatives Into Polymers to Give New NLO Materials

NASA Technical Reports Server (NTRS)

Bowens, Andrea D.; Bu, Xiu; Mintz, Eric A.; Zhang, Yue

1996-01-01

The need for fast electro-optic switches and modulators for optical communication, and laser frequency conversion has created a demand for new second-order non-linear optical materials. One approach to produce such materials is to align chromophores with large molecular hyperpolarizabilities in polymers. Recently fulvenes and benzofulvenes which contain electron donating groups have been shown to exhibit large second-order non-linear optical properties. The resonance structures shown below suggest that intramolecular charge transfer (ICT) should be favorable in omega - (hydroxyphenyl)benzofulvenes and even more favorable in omega-omega - (phenoxy)benzofulvenes because of the enhanced donor properties of the O group. This ICT should lead to enormously enhanced second-order hyperpolarizability. We have prepared all three new omega - (hydroxyphenyl)benzofulvenes by the condensation of indene with the appropriate hydroxyaryl aldehyde in MeOH or MeOH/H2O under base catalysis. In a similar fashion we have prepared substituted benzofulvenes with multipal donor groups. Preliminary studies show that some of our benzofulvene derivatives exhibit second order harmonic generation (SHG). Measurements were carried out by preparing host-guest polymers. The results of our work on benzofulvene derivatives in host-guest polymers when covalently bonded in the polymer will be described.

Second-harmonic generation from a positive-negative index material heterostructure.

PubMed

Mattiucci, Nadia; D'Aguanno, Giuseppe; Bloemer, Mark J; Scalora, Michael

2005-12-01

Resonant cavities have been widely used in the past to enhance material, nonlinear response. Traditional mirrors include metallic films and distributed Bragg reflectors. In this paper we propose negative index material mirrors as a third alternative. With the help of a rigorous Green function approach, we investigate second harmonic generation from single and coupled cavities, and theoretically prove that negative index material mirrors can raise the nonlinear conversion efficiency of a bulk material by at least four orders of magnitude compared to a bulk medium.

Optimum sensitivity derivatives of objective functions in nonlinear programming

NASA Technical Reports Server (NTRS)

Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.

1983-01-01

The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.

High pressure ferroelastic phase transition in SrTiO3

NASA Astrophysics Data System (ADS)

Salje, E. K. H.; Guennou, M.; Bouvier, P.; Carpenter, M. A.; Kreisel, J.

2011-07-01

High pressure measurements of the ferroelastic phase transition of SrTiO3 (Guennou et al 2010 Phys. Rev. B 81 054115) showed a linear pressure dependence of the transition temperature between the cubic and tetragonal phase. Furthermore, the pressure induced transition becomes second order while the temperature dependent transition is near a tricritical point. The phase transition mechanism is characterized by the elongation and tilt of the TiO6 octahedra in the tetragonal phase, which leads to strongly nonlinear couplings between the structural order parameter, the volume strain and the applied pressure. The phase diagram is derived from the Clausius-Clapeyron relationship and is directly related to a pressure dependent Landau potential. The nonlinearities of the pressure dependent strains lead to an increase of the fourth order Landau coefficient with increasing pressure and, hence, to a tricritical-second order crossover. This behaviour is reminiscent of the doping related crossover in isostructural KMnF3.

Nonlinear phenomena in general relativity

NASA Astrophysics Data System (ADS)

Allahyari, Alireza; Firouzjaee, Javad T.; Mansouri, Reza

2018-04-01

The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, it is necessary to study exact solutions or higher-order perturbations. Specifically, we study black hole (apparent) horizons and the cosmological event horizon formation in the perturbation theory. We emphasize that in the perturbative regime of the gravitational potential these horizons cannot form in the lower order. Studying the infinite plane metric, we show that, to capture the cosmological constant effect, we need at least a second-order expansion.

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Choe, C. Y.

1972-01-01

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Nonlinear optical response in narrow graphene nanoribbons

NASA Astrophysics Data System (ADS)

Karimi, Farhad; Knezevic, Irena

We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films

NASA Astrophysics Data System (ADS)

Bhowmik, Achintya; Thakur, Mrinal

1998-03-01

Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.

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

USGS Publications Warehouse

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

2011-01-01

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

Adaptive control of servo system based on LuGre model

NASA Astrophysics Data System (ADS)

Jin, Wang; Niancong, Liu; Jianlong, Chen; Weitao, Geng

2018-03-01

This paper established a mechanical model of feed system based on LuGre model. In order to solve the influence of nonlinear factors on the system running stability, a nonlinear single observer is designed to estimate the parameter z in the LuGre model and an adaptive friction compensation controller is designed. Simulink simulation results show that the control method can effectively suppress the adverse effects of friction and external disturbances. The simulation show that the adaptive parameter kz is between 0.11-0.13, and the value of gamma1 is between 1.9-2.1. Position tracking error reaches level 10-3 and is stabilized near 0 values within 0.3 seconds, the compensation method has better tracking accuracy and robustness.

Duffing's Equation and Nonlinear Resonance

ERIC Educational Resources Information Center

Fay, Temple H.

2003-01-01

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

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

NASA Astrophysics Data System (ADS)

Saravanan, M.; Abraham Rajasekar, S.

2016-04-01

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

Fast smooth second-order sliding mode control for systems with additive colored noises.

PubMed

Yang, Pengfei; Fang, Yangwang; Wu, Youli; Liu, Yunxia; Zhang, Danxu

2017-01-01

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.

Using surface lattice resonances to engineer nonlinear optical processes in metal nanoparticle arrays

NASA Astrophysics Data System (ADS)

Huttunen, Mikko J.; Rasekh, Payman; Boyd, Robert W.; Dolgaleva, Ksenia

2018-05-01

Collective responses of localized surface plasmon resonances, known as surface lattice resonances (SLRs) in metal nanoparticle arrays, can lead to high quality factors (˜100 ), large local-field enhancements, and strong light-matter interactions. SLRs have found many applications in linear optics, but little work of the influence of SLRs on nonlinear optics has been reported. Here we show how SLRs could be utilized to enhance nonlinear optical interactions. We devote special attention to the sum-frequency, difference-frequency, and third-harmonic generation processes because of their potential for the realization of novel sources of light. We also demonstrate how such arrays could be engineered to enhance higher-order nonlinear optical interactions through cascaded nonlinear processes. In particular, we demonstrate how the efficiency of third-harmonic generation could be engineered via cascaded second-order responses.

Tunable pulsed narrow bandwidth light source

DOEpatents

Powers, Peter E.; Kulp, Thomas J.

2002-01-01

A tunable pulsed narrow bandwidth light source and a method of operating a light source are provided. The light source includes a pump laser, first and second non-linear optical crystals, a tunable filter, and light pulse directing optics. The method includes the steps of operating the pump laser to generate a pulsed pump beam characterized by a nanosecond pulse duration and arranging the light pulse directing optics so as to (i) split the pulsed pump beam into primary and secondary pump beams; (ii) direct the primary pump beam through an input face of the first non-linear optical crystal such that a primary output beam exits from an output face of the first non-linear optical crystal; (iii) direct the primary output beam through the tunable filter to generate a sculpted seed beam; and direct the sculpted seed beam and the secondary pump beam through an input face of the second non-linear optical crystal such that a secondary output beam characterized by at least one spectral bandwidth on the order of about 0.1 cm.sup.-1 and below exits from an output face of the second non-linear optical crystal.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-01-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, Ming; Niu, Kaikun; Huang, ZHixiang

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-05-21

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Influence of Tm+3 concentration on the non-linear optical effects of the BiB3O6 : Tm3+ glass nanoparticle-doped polymer

NASA Astrophysics Data System (ADS)

Majchrowski, A.; Ebothe, J.; Ozga, K.; Kityk, I. V.; Reshak, A. H.; Lukasiewicz, T.; Brik, M. G.

2010-01-01

It is shown that BiB3O6 : Tm3+ glass nanoparticles incorporated into polymethylmethacrylate (PMMA) and polycarbonate (PC) polymer matrices show good second-order susceptibilities under bicolour coherent laser treatment. It is found that only during incorporation into highly polarized PC matrices could one observe an enhancement of the second-order susceptibilities with increasing laser treated power densities. The main increase is observed for all samples at power densities equal to about 0.4 GW cm-2. After passing this value there is a saturation of the output susceptibilities and even an abrupt decrease. The most striking feature is the achievement of second-order susceptibilities equal to about 5 pm V-1 for samples containing 4% nanoparticle (NP) content in the PC matrix. A further increase in the NP concentration to 6% leads to a decrease in susceptibility to 15%. In the case of PMMA matrices these changes do not exceed the background. The same situation is present for the pure BIBO and low-doped Tm materials. The effect is maximal for a low concentration of Tm—about 0.75%. In the case of bulk glasses the intensity dependences of the second-harmonic generation unambiguously show that the achieved maximal values of second-order susceptibilities do not exceed 3 pm V-1 for 0.5% Tm concentration.

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Multi-Hamiltonian structure of Plebanski's second heavenly equation

NASA Astrophysics Data System (ADS)

Neyzi, F.; Nutku, Y.; Sheftel, M. B.

2005-09-01

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.

Mechanisms of the anomalous Pockels effect in bulk water

NASA Astrophysics Data System (ADS)

Yukita, Shunpei; Suzuki, Yuto; Shiokawa, Naoyuki; Kobayashi, Takayoshi; Tokunaga, Eiji

2018-04-01

The "anomalous" Pockels effect is a phenomenon that a light beam passing between two electrodes in an aqueous electrolyte solution is deflected by an AC voltage applied between the electrodes: the deflection angle is proportional to the voltage such that the incident beam alternately changes its direction. This phenomenon, the Pockels effect in bulk water, apparently contradicts what is believed in nonlinear optics, i.e., macroscopic inversion symmetry should be broken for the second-order nonlinear optical effect to occur such as the first-order electro-optic effect, i.e., the Pockels effect. To clarify the underlying mechanism, the dependence of the effect on the electrode material is investigated to find that the Pockels coefficient with Pt electrodes is two orders of magnitude smaller than with indium tin oxide (ITO) electrodes. It is experimentally confirmed that the Pockels effect of interfacial water in the electric double layer (EDL) on these electrodes shows an electrode dependence similar to the effect in bulk water while the effects depend on the frequency of the AC voltage such that the interfacial signal decreases with frequency but the bulk signal increases with frequency up to 221 Hz. These experimental results lead to a conclusion that the beam deflection is caused by the refractive index gradient in the bulk water region, which is formed transiently by the Pockels effect of interfacial water in the EDL when an AC electric field is applied. The refractive index gradient is caused by the diffuse layer spreading into the bulk region to work as a breaking factor of inversion symmetry of bulk water due to its charge-biased ionic distribution. This mechanism does not contradict the principle of nonlinear optics.

Multipolar second harmonic generation in a symmetric nonlinear metamaterial

DOE PAGES

Wolf, Omri; Campione, Salvatore; Yang, Yuanmu; ...

2017-08-14

Optical nonlinearities are intimately related to the spatial symmetry of the nonlinear media. For example, the second order susceptibility vanishes for centrosymmetric materials under the dipole approximation. The latter concept has been naturally extended to the metamaterials’ realm, sometimes leading to the (erroneous) hypothesis that second harmonic (SH) generation is negligible in highly symmetric meta-atoms. In this work we aim to show that such symmetric meta-atoms can radiate SH light efficiently. In particular, we investigate in-plane centrosymmetric meta-atom designs where the approximation for meta-atoms breaks down. In a periodic array this building block allows us to control the directionality ofmore » the SH radiation. We conclude by showing that the use of symmetry considerations alone allows for the manipulation of the nonlinear multipolar response of a meta-atom, resulting in e.g. dipolar, quadrupolar, or multipolar emission on demand. This is because the size of the meta-atom is comparable with the free-space wavelength, thus invalidating the dipolar approximation for meta-atoms.« less

Universal linear and nonlinear electrodynamics of a Dirac fluid

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dmitry N.; Fogler, Michael M.

2018-03-01

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

Modeling Systematicity and Individuality in Nonlinear Second Language Development: The Case of English Grammatical Morphemes

ERIC Educational Resources Information Center

Murakami, Akira

2016-01-01

This article introduces two sophisticated statistical modeling techniques that allow researchers to analyze systematicity, individual variation, and nonlinearity in second language (L2) development. Generalized linear mixed-effects models can be used to quantify individual variation and examine systematic effects simultaneously, and generalized…

Nonlinear structure formation in flat cosmological models

NASA Technical Reports Server (NTRS)

Martel, Hugo

1995-01-01

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Measurement of Shear Elastic Moduli in Quasi-Incompressible Soft Solids

NASA Astrophysics Data System (ADS)

Rénier, Mathieu; Gennisson, Jean-Luc; Barrière, Christophe; Catheline, Stefan; Tanter, Mickaël; Royer, Daniel; Fink, Mathias

2008-06-01

Recently a nonlinear equation describing the plane shear wave propagation in isotropic quasi-incompressible media has been developed using a new expression of the strain energy density, as a function of the second, third and fourth order shear elastic constants (respectively μ, A, D) [1]. In such a case, the shear nonlinearity parameter βs depends only from these last coefficients. To date, no measurement of the parameter D have been carried out in soft solids. Using a set of two experiments, acoustoelasticity and finite amplitude shear waves, the shear elastic moduli up to the fourth order of soft solids are measured. Firstly, this theoretical background is applied to the acoustoelasticity theory, giving the variations of the shear wave speed as a function of the stress applied to the medium. From such variations, both linear (μ) and third order shear modulus (A) are deduced in agar-gelatin phantoms. Experimentally the radiation force induced by a focused ultrasound beam is used to generate quasi-plane linear shear waves within the medium. Then the shear wave propagation is imaged with an ultrafast ultrasound scanner. Secondly, in order to give rise to finite amplitude plane shear waves, the radiation force generation technique is replaced by a vibrating plate applied at the surface of the phantoms. The propagation is also imaged using the same ultrafast scanner. From the assessment of the third harmonic amplitude, the nonlinearity parameter βS is deduced. Finally, combining these results with the acoustoelasticity experiment, the fourth order modulus (D) is deduced. This set of experiments provides the characterization, up to the fourth order, of the nonlinear shear elastic moduli in quasi-incompressible soft media. Measurements of the A moduli reveal that while the behaviors of both soft solids are close from a linear point of view, the corresponding nonlinear moduli A are quite different. In a 5% agar-gelatin phantom, the fourth order elastic constant D is found to be 30±10 kPa.

Linear and non-linear flow mode in Pb-Pb collisions at √{sNN} = 2.76 TeV

NASA Astrophysics Data System (ADS)

Acharya, S.; Adamová, D.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, N.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Alba, J. L. B.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altenkamper, L.; Altsybeev, I.; Alves Garcia Prado, C.; An, M.; Andrei, C.; Andreou, D.; Andrews, H. A.; Andronic, A.; Anguelov, V.; Anson, C.; Antičić, T.; Antinori, F.; Antonioli, P.; Anwar, R.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Baldisseri, A.; Ball, M.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barioglio, L.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Blair, J. T.; Blau, D.; Blume, C.; Boca, G.; Bock, F.; Bogdanov, A.; Boldizsár, L.; Bombara, M.; Bonomi, G.; Bonora, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buhler, P.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Caines, H.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Capon, A. A.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cerello, P.; Chandra, S.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Chowdhury, T.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Concas, M.; Conesa Balbastre, G.; Conesa Del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Costanza, S.; Crkovská, J.; Crochet, P.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; de, S.; de Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; de Falco, A.; de Gruttola, D.; De Marco, N.; de Pasquale, S.; de Souza, R. D.; Degenhardt, H. F.; Deisting, A.; Deloff, A.; Deplano, C.; Dhankher, P.; di Bari, D.; di Mauro, A.; di Nezza, P.; di Ruzza, B.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Doremalen, L. V. V.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Duggal, A. K.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erhardt, F.; Espagnon, B.; Esumi, S.; Eulisse, G.; Eum, J.; Evans, D.; Evdokimov, S.; Fabbietti, L.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Garg, K.; Garg, P.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Gay Ducati, M. B.; Germain, M.; Ghosh, J.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Graczykowski, L. K.; Graham, K. L.; Greiner, L.; Grelli, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grion, N.; Gronefeld, J. M.; Grosa, F.; Grosse-Oetringhaus, J. F.; Grosso, R.; Gruber, L.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Guzman, I. B.; Haake, R.; Hadjidakis, C.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hassan, H.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Herrmann, F.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hills, C.; Hippolyte, B.; Hladky, J.; Hohlweger, B.; Horak, D.; Hornung, S.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Iga Buitron, S. A.; Ilkaev, R.; Inaba, M.; Ippolitov, M.; Irfan, M.; Isakov, V.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jaelani, S.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jercic, M.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Ketzer, B.; Khabanova, Z.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Khatun, A.; Khuntia, A.; Kielbowicz, M. M.; Kileng, B.; Kim, D.; Kim, D. W.; Kim, D. J.; Kim, H.; Kim, J. S.; Kim, J.; Kim, M.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Konyushikhin, M.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kundu, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kushpil, S.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Lagana Fernandes, C.; Lai, Y. S.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lavicka, R.; Lazaridis, L.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.; Lehner, S.; Lehrbach, J.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lim, B.; Lindal, S.; Lindenstruth, V.; Lindsay, S. W.; Lippmann, C.; Lisa, M. A.; Litichevskyi, V.; Ljunggren, H. M.; Llope, W. J.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Loncar, P.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Mao, Y.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martinengo, P.; Martinez, J. A. L.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Masson, E.; Mastroserio, A.; Mathis, A. M.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzilli, M.; Mazzoni, M. A.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mihaylov, D.; Mihaylov, D. L.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Mohisin Khan, M.; Montes, E.; Moreira de Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Münning, K.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Myers, C. J.; Myrcha, J. W.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Narayan, A.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Negrao de Oliveira, R. A.; Nellen, L.; Nesbo, S. V.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Nobuhiro, A.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Ohlson, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Pachmayer, Y.; Pacik, V.; Pagano, D.; Pagano, P.; Paić, G.; Palni, P.; Pan, J.; Pandey, A. K.; Panebianco, S.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, J.; Parmar, S.; Passfeld, A.; Pathak, S. P.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Peng, X.; Pereira, L. G.; Pereira da Costa, H.; Peresunko, D.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Pezzi, R. P.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pliquett, F.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Porter, J.; Pozdniakov, V.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Rana, D. B.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Ratza, V.; Ravasenga, I.; Read, K. F.; Redlich, K.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rodríguez Cahuantzi, M.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Rokita, P. S.; Ronchetti, F.; Rosas, E. D.; Rosnet, P.; Rossi, A.; Rotondi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rueda, O. V.; Rui, R.; Russo, R.; Rustamov, A.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Saha, S. K.; Sahlmuller, B.; Sahoo, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandoval, A.; Sarkar, D.; Sarkar, N.; Sarma, P.; Sas, M. H. P.; Scapparone, E.; Scarlassara, F.; Scharenberg, R. P.; Scheid, H. S.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M. O.; Schmidt, M.; Schuchmann, S.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sett, P.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shahoyan, R.; Shaikh, W.; Shangaraev, A.; Sharma, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Soramel, F.; Sorensen, S.; Sozzi, F.; Spiriti, E.; Sputowska, I.; Srivastava, B. K.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Suzuki, K.; Swain, S.; Szabo, A.; Szarka, I.; Szczepankiewicz, A.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thakur, D.; Thakur, S.; Thomas, D.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Tripathy, S.; Trogolo, S.; Trombetta, G.; Tropp, L.; Trubnikov, V.; Trzaska, W. H.; Trzeciak, B. A.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Umaka, E. N.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; van der Maarel, J.; van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vázquez Doce, O.; Vechernin, V.; Veen, A. M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Vértesi, R.; Vickovic, L.; Vigolo, S.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Voscek, D.; Vranic, D.; Vrláková, J.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wenzel, S. C.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Willsher, E.; Windelband, B.; Witt, W. E.; Yalcin, S.; Yamakawa, K.; Yang, P.; Yano, S.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zhu, X.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zmeskal, J.; Zou, S.; Alice Collaboration

2017-10-01

The second and the third order anisotropic flow, V2 and V3, are mostly determined by the corresponding initial spatial anisotropy coefficients, ε2 and ε3, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow Vn for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range | η | < 0.8 and the transverse momentum range 0.2

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Acharya, S.; Adamová, D.; Adolfsson, J.

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

DOE PAGES

Acharya, S.; Adamová, D.; Adolfsson, J.; ...

2017-08-04

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Matter bispectrum beyond Horndeski theories

NASA Astrophysics Data System (ADS)

Hirano, Shin'ichi; Kobayashi, Tsutomu; Tashiro, Hiroyuki; Yokoyama, Shuichiro

2018-05-01

The Horndeski scalar-tensor theory and its recent extensions allow nonlinear derivative interactions of the scalar degree of freedom. We study the matter bispectrum of large scale structure as a probe of these modified gravity theories, focusing in particular on the effect of the terms that newly appear in the so-called "beyond Horndeski" theories. We derive the second-order solution for the matter density perturbations and find that the interactions beyond Horndeski lead to a new time-dependent coefficient in the second-order kernel which differs in general from the standard value of general relativity and the Horndeski theory. This can deform the matter bispectrum at the folded triangle configurations (k1+k2=k3 ), while it is never possible within the Horndeski theory.

Field-controllable second harmonic generation at a graphene oxide heterointerface

NASA Astrophysics Data System (ADS)

Fernandes, Gustavo E.; Kim, Jin Ho; Osgood, Richard, III; Xu, Jimmy

2018-03-01

We report on the voltage-dependent SHG signal obtained in a reduced-graphene oxide (rGO)/p-type Si heterointerface. A simple qualitative model considering the interaction between the heterointerface depletion region potential and the naturally occurring surface dipole layer on the rGO is introduced to account for the characteristics of the SHG signal, specifically, a minimum point at ≈ -3 V bias on the rGO side of the interface. This feature-rich system has the potential to provide field-controllable surface-dipole moments and second-order nonlinearities, which may find applications in tunable nonlinear photonic devices for realizing second-harmonic generation and optical-rectification.

Ultrafast light-induced symmetry changes in single BaTiO 3 nanowires

DOE PAGES

Kuo, Yi -Hong; Nah, Sanghee; He, Kai; ...

2017-01-23

The coupling of light to nanoscale ferroelectric materials enables novel means of controlling their coupled degrees of freedom and engineering new functionality. Here we present femtosecond time-resolution nonlinear-optical measurements of light-induced dynamics within single ferroelectric barium titanate nanowires. By analyzing the time-dependent and polarization-dependent second harmonic intensity generated by the nanowire, we identify its crystallographic orientation and then make use of this information in order to probe its dynamic structural response and change in symmetry. Here, we show that photo-excitation leads to ultrafast, non-uniform modulations in the second order nonlinear susceptibility tensor, indicative of changes in the local symmetry ofmore » the nanostructure occurring on sub-picosecond time-scales.« less

Resonantly enhanced second-harmonic generation using III–V semiconductor all-dielectric metasurfaces

DOE PAGES

Liu, Sheng; Sinclair, Michael B.; Saravi, Sina; ...

2016-08-08

Nonlinear optical phenomena in nanostructured materials have been challenging our perceptions of nonlinear optical processes that have been explored since the invention of lasers. For example, the ability to control optical field confinement, enhancement, and scattering almost independently allows nonlinear frequency conversion efficiencies to be enhanced by many orders of magnitude compared to bulk materials. Also, the subwavelength length scale renders phase matching issues irrelevant. Compared with plasmonic nanostructures, dielectric resonator metamaterials show great promise for enhanced nonlinear optical processes due to their larger mode volumes. Here, we present, for the first time, resonantly enhanced second-harmonic generation (SHG) using galliummore » arsenide (GaAs) based dielectric metasurfaces. Using arrays of cylindrical resonators we observe SHG enhancement factors as large as 10 4 relative to unpatterned GaAs. At the magnetic dipole resonance, we measure an absolute nonlinear conversion efficiency of ~2 × 10 –5 with ~3.4 GW/cm 2 pump intensity. In conclusion, the polarization properties of the SHG reveal that both bulk and surface nonlinearities play important roles in the observed nonlinear process.« less

Second Order Non-Linear Optical Polyphosphazenes. Proceedings of Symposium on Non-Linear Optics, ACS Meeting, Held in Boston, Massachusetts 1990

DTIC Science & Technology

1990-03-23

Paciorek Dr. William B. Moniz Ultrasystems Defense and Space, Inc. Code 6120 16775 Von Karman Avenue Naval Research Laboratory Irvine, CA 92714 Washington...413h004 Dr. Les H. Sperling Dr. Richard S. Stein Materials Research Center #32 Polymer Research Institute Lehigh University University of Massachusetts

Higher-order Kerr effect and harmonic cascading in gases.

PubMed

Bache, Morten; Eilenberger, Falk; Minardi, Stefano

2012-11-15

The higher-order Kerr effect (HOKE) has recently been advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth-order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths, cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.

Computer program for analysis of imperfection sensitivity of ring stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1971-01-01

A FORTRAN 4 digital computer program is presented for the initial postbuckling and imperfection sensitivity analysis of bifurcation buckling modes for ring-stiffened orthotropic multilayered shells of revolution. The boundary value problem for the second-order contribution to the buckled state was solved by the forward integration technique using the Runge-Kutta method. The effects of nonlinear prebuckling states and live pressure loadings are included.

Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient

NASA Astrophysics Data System (ADS)

Li, Huanhuan; Chen, Diyi; Zhang, Hao; Wang, Feifei; Ba, Duoduo

2016-12-01

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.

The surface-induced spatial-temporal structures in confined binary alloys

NASA Astrophysics Data System (ADS)

Krasnyuk, Igor B.; Taranets, Roman M.; Chugunova, Marina

2014-12-01

This paper examines surface-induced ordering in confined binary alloys. The hyperbolic initial boundary value problem (IBVP) is used to describe a scenario of spatiotemporal ordering in a disordered phase for concentration of one component of binary alloy and order parameter with non-linear dynamic boundary conditions. This hyperbolic model consists of two coupled second order differential equations for order parameter and concentration. It also takes into account effects of the “memory” on the ordering of atoms and their densities in the alloy. The boundary conditions characterize surface velocities of order parameter and concentration changing which is due to surface (super)cooling on walls confining the binary alloy. It is shown that for large times there are three classes of dynamic non-linear boundary conditions which lead to three different types of attractor’s elements for the IBVP. Namely, the elements of attractor are the limit periodic simple shock waves with fronts of “discontinuities” Γ. If Γ is finite, then the attractor contains spatiotemporal functions of relaxation type. If Γ is infinite and countable then we observe the functions of pre-turbulent type. If Γ is infinite and uncountable then we obtain the functions of turbulent type.

Nonparaxial rogue waves in optical Kerr media.

PubMed

Temgoua, D D Estelle; Kofane, T C

2015-06-01

We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.

Multilevel adaptive control of nonlinear interconnected systems.

PubMed

Motallebzadeh, Farzaneh; Ozgoli, Sadjaad; Momeni, Hamid Reza

2015-01-01

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Negative effective mass in acoustic metamaterial with nonlinear mass-in-mass subsystems

NASA Astrophysics Data System (ADS)

Cveticanin, L.; Zukovic, M.

2017-10-01

In this paper the dynamics of the nonlinear mass-in-mass system as the basic subsystem of the acoustic metamaterial is investigated. The excitation of the system is in the form of the Jacobi elliptic function. The corresponding model to this forcing is the mass-in-mass system with cubic nonlinearity of the Duffing type. Mathematical model of the motion is a system of two coupled strong nonlinear and nonhomogeneous second order differential equations. Particular solution to the system is obtained. The analytical solution of the problem is based on the simple and double integral of the cosine Jacobi function. In the paper the integrals are given in the form of series of trigonometric functions. These results are new one. After some modification the simplified solution in the first approximation is obtained. The result is convenient for discussion. Conditions for elimination of the motion of the mass 1 by connection of the nonlinear dynamic absorber (mass - spring system) are defined. In the consideration the effective mass ratio is introduced in the nonlinear mass-in-mass system. Negative effective mass ratio gives the absorption of vibrations with certain frequencies. The advantage of the nonlinear subunit in comparison to the linear one is that the frequency gap is significantly wider. Nevertheless, it has to be mentioned that the amplitude of vibration differs from zero for a small value. In the paper the analytical results are compared with numerical one and are in agreement.

Nonlinear Force on an Unpolarized Relativistic Test Particle to Second Order in the Total Field in a Nonequilibrium Beam-Plasma System.

DTIC Science & Technology

1983-08-01

631Al b NONLINEAR FORCE ON AN UNP LARI ED RELATIVISTIC TEST / i , L11 -1 PARTICLE TO SECOND OR..Ii HARR DIAMOND LABS AIDELPHI I MD H E BRANDT AUG 83...Cmthanm erverse ai I n eeawand Ideanll by block number) For a nonequilibrium relativistic beam-plasma system, an expression is obtained for the time...Nonequilibrium Beam-Plasma System, Harry Diamond Laboratories, HDL-PRL-82-6 (May 1982) to be published as HDL-TR-1994. 5 ’ ’ I

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

NASA Astrophysics Data System (ADS)

Yang, Peng-fei; Fang, Yang-wang; Wu, You-li; Zhang, Dan-xu; Xu, Yang

2018-01-01

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein-Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

Influence of wave modelling on the prediction of fatigue for offshore wind turbines

NASA Astrophysics Data System (ADS)

Veldkamp, H. F.; van der Tempel, J.

2005-01-01

Currently it is standard practice to use Airy linear wave theory combined with Morison's formula for the calculation of fatigue loads for offshore wind turbines. However, offshore wind turbines are typically placed in relatively shallow water depths of 5-25 m where linear wave theory has limited accuracy and where ideally waves generated with the Navier-Stokes approach should be used. This article examines the differences in fatigue for some representative offshore wind turbines that are found if first-order, second-order and fully non-linear waves are used. The offshore wind turbines near Blyth are located in an area where non-linear wave effects are common. Measurements of these waves from the OWTES project are used to compare the different wave models with the real world in spectral form. Some attention is paid to whether the shape of a higher-order wave height spectrum (modified JONSWAP) corresponds to reality for other places in the North Sea, and which values for the drag and inertia coefficients should be used. Copyright

Concerted Mitigation of O···H and C(π)···H Interactions Prospects Sixfold Gain in Optical Nonlinearity of Ionic Stilbazolium Derivatives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cole, Jacqueline M.; Lin, Tze-Chia; Edwards, Alison J.

2015-03-04

DAST (4-dimethylamino-N-methyl-4-stilbazolium tosylate) is the most commercially successful organic nonlinear optical (NLO) material for frequency-doubling, integrated optics, and THz wave applications. Its success is predicated on its high optical nonlinearity with concurrent sufficient thermal stability. Many chemical derivatives of DAST have therefore been developed to optimize their properties; yet, to date, none have surpassed the overall superiority of DAST for NLO photonic applications. This is perhaps because DAST is an ionic salt wherein its NLO-active cation is influenced by multiple types of subtle intermolecular forces that are hard to quantify, thus, making difficult the molecular engineering of better functioning DASTmore » derivatives. Here, we establish a model parameter, ηinter, that isolates the influence of intermolecular interactions on second-order optical nonlinearity in DAST and its derivatives, using second-harmonic generation (SHG) as a qualifier; by systematically mapping intercorrelations of all possible pairs of intermolecular interactions to ηinter, we uncover a relationship between concerted intermolecular interactions and SHG output. This correlation reveals that a sixfold gain in the intrinsic second-order NLO performance of DAST is possible, by eliminating the identified interactions. This prediction offers the first opportunity to systematically design next-generation DAST-based photonic device nanotechnology to realize such a prospect.« less

Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals.

PubMed

Liu, Xing; Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-08-15

We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between λ=2.2-2.4  μm as a resonant dispersive wave. This process relies on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation.

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

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

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

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

PubMed

Einkemmer, Lukas; Ostermann, Alexander

2014-07-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.

An almost symmetric Strang splitting scheme for nonlinear evolution equations☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2014-01-01

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017

Probability function of breaking-limited surface elevation. [wind generated waves of ocean

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.; Yuan, Y.; Long, S. R.

1989-01-01

The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Optical increase of photo-integrated micro- and nano-periodic susceptibility lattices

NASA Astrophysics Data System (ADS)

Smirnov, Vitaly A.; Vostrikova, Liubov I.

2015-03-01

It is demonstrated that the nonlinear photo-integrated micro- and nano-periodic second-order susceptibility lattices with very small amplitudes which were preliminarily recorded using bi-chromatic powerful laser light in amorphous glass materials can be increased up to some orders of magnitude under the action of a simple coherent monochromatic radiation. The optical increase of the small lattices takes place independent of the polarization and direction of propagation of the optical amplifying radiation and is achieved at various wavelengths. The observed phenomenon is not be explained only by nonlinear wave interaction in medium and also may be related to the microscopic asymmetry processes of the optical transitions between local centers in an isotropic medium that leads to the appearance and growth of the all-optically induced small micro- and nano-periodic electrical charges separations inside the sample. Possible mechanisms that may be responsible for the observed effects in the studied phosphate glasses are discussed.

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oboh, I., E-mail: innocentoboh@uniuyo.edu.ng; Aluyor, E.; Audu, T.

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R{sup 2}), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used tomore » predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.« less

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems.

PubMed

Han, Yaozhen; Liu, Xiangjie

2016-05-01

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

NASA Astrophysics Data System (ADS)

Oboh, I.; Aluyor, E.; Audu, T.

2015-03-01

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R2), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used to predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.

Optimal antibunching in passive photonic devices based on coupled nonlinear resonators

NASA Astrophysics Data System (ADS)

Ferretti, S.; Savona, V.; Gerace, D.

2013-02-01

We propose the use of weakly nonlinear passive materials for prospective applications in integrated quantum photonics. It is shown that strong enhancement of native optical nonlinearities by electromagnetic field confinement in photonic crystal resonators can lead to single-photon generation only exploiting the quantum interference of two coupled modes and the effect of photon blockade under resonant coherent driving. For realistic system parameters in state of the art microcavities, the efficiency of such a single-photon source is theoretically characterized by means of the second-order correlation function at zero-time delay as the main figure of merit, where major sources of loss and decoherence are taken into account within a standard master equation treatment. These results could stimulate the realization of integrated quantum photonic devices based on non-resonant material media, fully integrable with current semiconductor technology and matching the relevant telecom band operational wavelengths, as an alternative to single-photon nonlinear devices based on cavity quantum electrodynamics with artificial atoms or single atomic-like emitters.

Femtosecond Kerr index of cyclic olefin co/polymers for THz nonlinear optics

NASA Astrophysics Data System (ADS)

Noskovicova, E.; Lorenc, D.; Slusna, L.; Velic, D.

2016-10-01

The second-order nonlinear refractive index n2 (Kerr index) of cyclic olefin copolymer (TOPAS) and cyclic olefin polymers (ZEONEX, ZEONOR) was determined at the wavelength of 800 nm within this work. Bulk samples of ZEONEX, ZEONOR and TOPAS were measured using the single-beam Z-scan technique and the values of their nonlinear refractive index were determined to be approximately 2 × 10-20 m2W-1 for all cases. The obtained values of n2 play a vital role for ultrafast pulse evolution and corresponding phenomena such as nonlinear spectral transformation.

Design considerations for multi component molecular-polymeric nonlinear optical materials

NASA Astrophysics Data System (ADS)

Singer, K. D.; Kuzyk, M. G.; Fang, T.; Holland, W. R.; Cahill, P. A.

1990-08-01

We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85 deg and possess an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to possess a large third order nonlinearity, and may display two-level behavior.

Ultrasonic Nondestructive Characterization of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Qu, Jianmin

1999-01-01

Adhesives and adhesive joints are widely used in various industrial applications to reduce weight and costs, and to increase reliability. For example, advances in aerospace technology have been made possible, in part, through the use of lightweight materials and weight-saving structural designs. Joints, in particular, have been and continue to be areas in which weight can be trimmed from an airframe through the use of novel attachment techniques. In order to save weight over traditional riveted designs, to avoid the introduction of stress concentrations associated with rivet holes, and to take full advantage of advanced composite materials, engineers and designers have been specifying an ever-increasing number of adhesively bonded joints for use on airframes. Nondestructive characterization for quality control and remaining life prediction has been a key enabling technology for the effective use of adhesive joints. Conventional linear ultrasonic techniques generally can only detect flaws (delamination, cracks, voids, etc) in the joint assembly. However, more important to structural reliability is the bond strength. Although strength, in principle, cannot be measured nondestructively, a slight change in material nonlinearity may indicate the onset of failure. Furthermore, microstructural variations due to aging or under-curing may also cause changes in the third order elastic constants, which are related to the ultrasonic nonlinear parameter of the polymer adhesive. It is therefore reasonable to anticipate a correlation between changes in the ultrasonic nonlinear acoustic parameter and the remaining bond strength. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasonic wave passes through a nonlinear material. It seems that such nonlinearity can be effectively used to characterize bond strength. Several theories have been developed to model this nonlinear effect. Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented. Recently, a comparison between the experimental and simulated results based on a similar theoretical model was presented. A through-transmission setup for water immersion mode-converted shear waves was used to analyze the ultrasonic nonlinear parameter of an adhesive bond. In addition, ultrasonic guided waves have been used to analyze adhesive or diffusion bonded joints. In this paper, the ultrasonic nonlinear parameter is used to characterize the curing state of a polymer/aluminum adhesive joint. Ultrasonic through-transmission tests were conducted on samples cured under various conditions. The magnitude of the second order harmonic was measured and the corresponding ultrasonic nonlinear parameter was evaluated. A fairly good correlation between the curing condition and the nonlinear parameter is observed. The results show that the nonlinear parameter might be used as a good indicator of the cure state for adhesive joints.

Application of TVD schemes for the Euler equations of gas dynamics. [total variation diminishing for nonlinear hyperbolic systems

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1985-01-01

First-order, second-order, and implicit total variation diminishing (TVD) schemes are reviewed using the modified flux approach. Some transient and steady-state calculations are then carried out to illustrate the applicability of these schemes to the Euler equations. It is shown that the second-order explicit TVD schemes generate good shock resolution for both transient and steady-state one-dimensional and two-dimensional problems. Numerical experiments for a quasi-one-dimensional nozzle problem show that the second-order implicit TVD scheme produces a fairly rapid convergence rate and remains stable even when running with a Courant number of 10 to the 6th.

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

Quaternion-valued echo state networks.

PubMed

Xia, Yili; Jahanchahi, Cyrus; Mandic, Danilo P

2015-04-01

Quaternion-valued echo state networks (QESNs) are introduced to cater for 3-D and 4-D processes, such as those observed in the context of renewable energy (3-D wind modeling) and human centered computing (3-D inertial body sensors). The introduction of QESNs is made possible by the recent emergence of quaternion nonlinear activation functions with local analytic properties, required by nonlinear gradient descent training algorithms. To make QENSs second-order optimal for the generality of quaternion signals (both circular and noncircular), we employ augmented quaternion statistics to introduce widely linear QESNs. To that end, the standard widely linear model is modified so as to suit the properties of dynamical reservoir, typically realized by recurrent neural networks. This allows for a full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances, and a rigorous account of second-order noncircularity (improperness), and the corresponding power mismatch and coupling between the data components. Simulations in the prediction setting on both benchmark circular and noncircular signals and on noncircular real-world 3-D body motion data support the analysis.

Evaluation of polymer based third order nonlinear integrated optics devices

NASA Astrophysics Data System (ADS)

Driessen, A.; Hoekstra, H. J. W. M.; Blom, F. C.; Horst, F.; Krijnen, G. J. M.; van Schoot, J. B. P.; Lambeck, P. V.; Popma, Th. J. A.; Diemeer, M. B.

1998-01-01

Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS side-chain polymer that exhibits large second and third order coefficients. This material has been characterized by third harmonic generation, z-scan and pump-probe measurements. In addition, various waveguiding structures have been used to measure the nonlinear absorption (two photon absorption) on a ps time-scale. Finally an integrated optics Mach Zehnder interferometer has been realized and evaluated. It is shown that the DANS side-chain polymer has many of the desired properties: the material is easily processable in high-quality optical waveguiding structures, has low linear absorption and its nonlinearity has a pure electronic origin. More materials research has to be done to arrive at materials with higher nonlinear coefficients to allow switching at moderate light intensity ( < 1 W peak power) and also with lower nonlinear absorption coefficients.

Phased-array sources based on nonlinear metamaterial nanocavities

PubMed Central

Wolf, Omri; Campione, Salvatore; Benz, Alexander; Ravikumar, Arvind P.; Liu, Sheng; Luk, Ting S.; Kadlec, Emil A.; Shaner, Eric A.; Klem, John F.; Sinclair, Michael B.; Brener, Igal

2015-01-01

Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum. PMID:26126879

Polar self-assembled thin films for non-linear optical materials

DOEpatents

Yang, XiaoGuang; Swanson, Basil I.; Li, DeQuan

2000-01-01

The design and synthesis of a family of calix[4]arene-based nonlinear optical (NLO) chromophores are discussed. The calixarene chromophores are macrocyclic compounds consisting of four simple D-.pi.-A units bridged by methylene groups. These molecules were synthesized such that four D-.pi.-A units of the calix[4]arene were aligned along the same direction with the calixarene in a cone conformation. These nonlinear optical super-chromophores were subsequently fabricated into covalently bound self-assembled monolayers on the surfaces of fused silica and silicon. Spectroscopic second harmonic generation (SHG) measurements were carried out to determine the absolute value of the dominant element of the second-order nonlinear susceptibility, d.sub.33, and the average molecular alignment, .PSI.. A value of d.sub.33 =60 pm/V at a fundamental wavelength of 890 nm, and .PSI..about.36.degree. was found with respect to the surface normal.

Fabrication and Characterization of Linear and Nonlinear Photonic Devices in Fused Silica by Femtosecond Laser Writing

NASA Astrophysics Data System (ADS)

Ng, Jason Clement

Femtosecond laser processing is a flexible, three-dimensional (3D) fabrication technique used to make integrated low-loss photonic devices in fused silica. My work expanded the suite of available optical devices through the design and optimization of linear optical components such as low-loss (< 0.5 dB) curved waveguides, directional couplers (DCs), and Mach-Zehnder interferometers (MZIs). The robustness and consistency of this maturing fabrication process was also reinforced through the scalable design and integration of a more complex, multi-component flat-top interleaver over a wide >70-nm spectral window. My work further complemented femtosecond laser processing with the development of nonlinear device capabilities. While thermal poling is a well known process, significant challenges had restricted the development of nonlinear devices in fused silica. The laser writing process would erase the induced nonlinearity (erasing) while a written waveguide core acted as a barrier to the thermal poling process (blocking). Using second harmonic (SH) microscopy, the effectiveness of thermal poling on laser-written waveguides was systematically analyzed leading to the technique of "double poling", which effectively overcomes the two challenges of erasing and blocking. In this new process the substrate is poled before and after waveguide writing to restore the induced nonlinearity within the vicinity of the waveguide to enable effective poling for inducing a second-order nonlinearity (SON) in fused silica. A new flexible, femtosecond laser based erasure process was also developed to enable quasi-phase matching and to form arbitrarily chirped gratings. Following this result, second harmonic generation (SHG) in a quasiphase-matched (QPM) femtosecond laser written waveguide device was demonstrated. SHG in a chirped QPM structure was also demonstrated to illustrate the flexibility of the femtosecond laser writing technique. These are the first demonstration of frequency doubling in an all-femtosecond-laser-written structure. A maximum SHG conversion efficiency of 1.3 +/- 0.1x10 -11/W-cm-2 was achieved for the fundamental wavelength of 1552.8 nm with a phase-matching bandwidth of 4.4 nm for a 10.0-mm-long waveguide. For a shorter sample, an effective SON of chi(2) = 0:020 +/- 0:002 pm/V was measured. The results collectively demonstrate the versatility of femtosecond laser additive and subtractive fabrication and opens up the development of integrated nonlinear applications and photonic devices for future lab-on-a-chip and lab-in-a-fiber devices.

Second- and third-order nonlinear optical properties of unsubstituted and mono-substituted chalcones

NASA Astrophysics Data System (ADS)

Abegão, Luis M. G.; Fonseca, Ruben D.; Santos, Francisco A.; Souza, Gabriela B.; Barreiros, André Luis B. S.; Barreiros, Marizeth L.; Alencar, M. A. R. C.; Mendonça, Cleber R.; Silva, Daniel L.; De Boni, Leonardo; Rodrigues, J. J.

2016-03-01

This work describes the second and third orders of nonlinear optics properties of unsubstituted chalcone (C15H12O) and mono-substituted chalcone (C16H14O2) in solution, using hyper-Rayleigh scattering and Z-Scan techniques to determine the first molecular hyperpolarizability (β) and the two-photon absorption (2PA) cross section respectively. β Values of 25.4 × 10-30 esu and 31.6 × 10-30 esu, for unsubstituted and mono-substituted chalcone, respectively, dissolved in methanol have been obtained. The highest values of 2PA cross-sections obtained were 9 GM and 14 GM for unsubstituted and mono-substituted chalcone, respectively. The experimental 2PA cross sections obtained for each chalcone are in good agreement with theoretical results.

Nonlinear Time Series Analysis in the Absence of Strong Harmonics

NASA Astrophysics Data System (ADS)

Stine, Peter; Jevtic, N.

2010-05-01

Nonlinear time series analysis has successfully been used for noise reduction and for identifying long term periodicities in variable star light curves. It was thought that good noise reduction could be obtained when a strong fundamental and second harmonic are present. We show that, quite unexpectedly, this methodology for noise reduction can be efficient for data with very noisy power spectra without a strong fundamental and second harmonic. Not only can one obtain almost two orders of magnitude noise reduction of the white noise tail, insight can also be gained into the short time scale of organized behavior. Thus, we are able to obtain an estimate of this short time scale, which is on the order of 1.5 hours in the case of a variable white dwarf.

Non-phase-matched enhancement of second-harmonic generation in multilayer nonlinear structures with internal reflections.

PubMed

Centini, Marco; D'Aguanno, Giuseppe; Sciscione, Letizia; Sibilia, Concita; Bertolotti, Mario; Scalora, Michael; Bloemer, Mark J

2004-08-15

Traditional notions of second-harmonic generation rely on phase matching or quasi phase matching to achieve good conversion efficiencies. We present an entirely new concept for efficient second-harmonic generation that is based on the interference of counterpropagating waves in multilayer structures. Conversion efficiencies are an order of magnitude larger than with phase-matched second-harmonic generation in similar multilayer structures.

Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Liu, Wanhai; Yu, Changping; Li, Xinliang

2014-11-01

Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough ( r0≫λ ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲ 2 λ while increase it for A ≲ 0.6 at r0≳ 2 λ . Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.

Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Wanhai; LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190; Yu, Changping

2014-11-15

Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radiusmore » of the interface (r{sub 0}) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r{sub 0}/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r{sub 0}/λ is large enough (r{sub 0}≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r{sub 0} can reduce the NSA of the second harmonic for arbitrary A at r{sub 0}≲2λ while increase it for A ≲ 0.6 at r{sub 0}≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.« less

Tunable room temperature THz sources based on nonlinear mixing in a hybrid optical and THz micro-ring resonator.

PubMed

Sinha, Raju; Karabiyik, Mustafa; Al-Amin, Chowdhury; Vabbina, Phani K; Güney, Durdu Ö; Pala, Nezih

2015-03-24

We propose and systematically investigate a novel tunable, compact room temperature terahertz (THz) source based on difference frequency generation in a hybrid optical and THz micro-ring resonator. We describe detailed design steps of the source capable of generating THz wave in 0.5-10 THz with a tunability resolution of 0.05 THz by using high second order optical susceptibility (χ((2))) in crystals and polymers. In order to enhance THz generation compared to bulk nonlinear material, we employ a nonlinear optical micro-ring resonator with high-Q resonant modes for infrared input waves. Another ring oscillator with the same outer radius underneath the nonlinear ring with an insulation of SiO2 layer supports the generated THz with resonant modes and out-couples them into a THz waveguide. The phase matching condition is satisfied by engineering both the optical and THz resonators with appropriate effective indices. We analytically estimate THz output power of the device by using practical values of susceptibility in available crystals and polymers. The proposed source can enable tunable, compact THz emitters, on-chip integrated spectrometers, inspire a broader use of THz sources and motivate many important potential THz applications in different fields.

Tunable Room Temperature THz Sources Based on Nonlinear Mixing in a Hybrid Optical and THz Micro-Ring Resonator

PubMed Central

Sinha, Raju; Karabiyik, Mustafa; Al-Amin, Chowdhury; Vabbina, Phani K.; Güney, Durdu Ö.; Pala, Nezih

2015-01-01

We propose and systematically investigate a novel tunable, compact room temperature terahertz (THz) source based on difference frequency generation in a hybrid optical and THz micro-ring resonator. We describe detailed design steps of the source capable of generating THz wave in 0.5–10 THz with a tunability resolution of 0.05 THz by using high second order optical susceptibility (χ(2)) in crystals and polymers. In order to enhance THz generation compared to bulk nonlinear material, we employ a nonlinear optical micro-ring resonator with high-Q resonant modes for infrared input waves. Another ring oscillator with the same outer radius underneath the nonlinear ring with an insulation of SiO2 layer supports the generated THz with resonant modes and out-couples them into a THz waveguide. The phase matching condition is satisfied by engineering both the optical and THz resonators with appropriate effective indices. We analytically estimate THz output power of the device by using practical values of susceptibility in available crystals and polymers. The proposed source can enable tunable, compact THz emitters, on-chip integrated spectrometers, inspire a broader use of THz sources and motivate many important potential THz applications in different fields. PMID:25800287

Total Variation Diminishing (TVD) schemes of uniform accuracy

NASA Technical Reports Server (NTRS)

Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

1988-01-01

Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balyan, M. K., E-mail: mbalyan@ysu.am

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Multi-photon absorption limits to heralded single photon sources

PubMed Central

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

2013-01-01

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

Nonlinear responses of chiral fluids from kinetic theory

NASA Astrophysics Data System (ADS)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities.

PubMed

Zouari, Farouk; Ibeas, Asier; Boulkroune, Abdesselem; Cao, Jinde; Mehdi Arefi, Mohammad

2018-06-01

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo's definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller. Copyright © 2018 Elsevier Ltd. All rights reserved.

NLOphoric rigid pyrazino-phenanthroline donor-π-acceptor compounds: Investigation of structural and solvent effects on non-linear optical properties using computational methods

NASA Astrophysics Data System (ADS)

Kothavale, Shantaram; Katariya, Santosh; Sekar, Nagaiyan

2018-01-01

Rigid pyrazino-phenanthroline based donor-π-acceptor-π-auxiliary acceptor type compounds have been studied for their linear and non-linear optical properties. The non-linear optical (NLO) behavior of these dyes was studied by calculating the values of static α , β and γ using solvatochromic as well as computational methods. The results obtained by solvatochromic method are correlated theoretically with Density Functional Theory (DFT) using B3LYP/6-31G (d), CAM B3LYP/6-31 G(d), B3LYP/6-31++ g(d,P) and CAM B3LYP/6-31++ g(d,P) methods. The results reveal that, among all four computational methods CAM-B3LYP/6-31++ g(d,P) performs well for the calculation of linear polarizability (α) and first order hyperpolarizability (β), while CAM-B3LYP/6-31 g(d,P) for the calculation of second order hyperpolarizability (ϒ). Overall TPA depends on the molecular structure variation with increase in complexity and molecular weight, which implies that both the number of branches and the size of π-framework are important factors for the molecular TPA in this chromophoric system. Generalized Mulliken-Hush (GMH) analysis is performed to study the effective charge transfer from donor to acceptor.

A higher-order theory for geometrically nonlinear analysis of composite laminates

NASA Technical Reports Server (NTRS)

Reddy, J. N.; Liu, C. F.

1987-01-01

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Predicting the nonlinear optical response in the resonant region from the linear characterization: a self-consistent theory for the first-, second-, and third-order (non)linear optical response

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2010-08-01

We introduce a self-consistent theory for the description of the optical linear and nonlinear response of molecules that is based strictly on the results of the experimental characterization. We show how the Thomas-Kuhn sum-rules can be used to eliminate the dependence of the nonlinear response on parameters that are not directly measurable. Our approach leads to the successful modeling of the dispersion of the nonlinear response of complex molecular structures with different geometries (dipolar and octupolar), and can be used as a guide towards the modeling in terms of fundamental physical parameters.

Ultrafast Optical Modulation of Second- and Third-Harmonic Generation from Cut-Disk-Based Metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sartorello, Giovanni; Olivier, Nicolas; Zhang, Jingjing

2016-08-17

We design and fabricate a metasurface composed of gold cut-disk resonators that exhibits a strong coherent nonlinear response. We experimentally demonstrate all-optical modulation of both second- and third-harmonic signals on a subpicosecond time scale. Pump probe experiments and numerical models show that the observed effects are due to the ultrafast response of the electronic excitations in the metal under external illumination. These effects pave the way for the development of novel active nonlinear metasurfaces with controllable and switchable coherent nonlinear response.

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Cheong R.

The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-ordermore » equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.« less

Estimation of groundwater recharge parameters by time series analysis

USGS Publications Warehouse

Naff, Richard L.; Gutjahr, Allan L.

1983-01-01

A model is proposed that relates water level fluctuations in a Dupuit aquifer to effective precipitaton at the top of the unsaturated zone. Effective precipitation, defined herein as that portion of precipitation which becomes recharge, is related to precipitation measured in a nearby gage by a two-parameter function. A second-order stationary assumption is used to connect the spectra of effective precipitation and water level fluctuations. Measured precipitation is assumed to be Gaussian, in order to develop a transfer function that relates the spectra of measured and effective precipitation. A nonlinear least squares technique is proposed for estimating parameters of the effective-precipitation function. Although sensitivity analyses indicate difficulties that may be encountered in the estimation procedure, the methods developed did yield convergent estimates for two case studies.

Continuous-Variable Triple-Photon States Quantum Entanglement

NASA Astrophysics Data System (ADS)

González, E. A. Rojas; Borne, A.; Boulanger, B.; Levenson, J. A.; Bencheikh, K.

2018-01-01

We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second-order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show, for example, the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show robust, seeding-dependent, genuine triple-photon entanglement in the fully seeded case.

Continuous-Variable Triple-Photon States Quantum Entanglement.

PubMed

González, E A Rojas; Borne, A; Boulanger, B; Levenson, J A; Bencheikh, K

2018-01-26

We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second-order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show, for example, the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show robust, seeding-dependent, genuine triple-photon entanglement in the fully seeded case.

Axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects

NASA Astrophysics Data System (ADS)

Nasir, Nor Ain Azeany Mohd; Ishak, Anuar; Pop, Ioan

2018-04-01

In this paper, the heat and mass transfer of an axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects are investigated. An appropriate similarity transformation is used to reduce the highly non-linear partial differential equation into second and third order non-linear ordinary differential equations. Numerical solutions of the reduced governing equations are computed numerically by utilizing the MATLAB's built-in boundary value problem solver, bvp4c. The physical significance of various parameters such as Biot number, fluid parameters and Prandtl number on the velocity and temperature evolution profiles are illustrated graphically. The effects of these governing parameters on the skin friction coefficient and the local Nusselt number are also displayed graphically. It is noticed that the Powell-Eyring fluid parameter gives significant influence on the rates of heat and mass transfer of the fluid.

Modulation instability and dissipative rogue waves in ion-beam plasma: Roles of ionization, recombination, and electron attachment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Shimin, E-mail: gsm861@126.com; Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn

The amplitude modulation of ion-acoustic waves is investigated in an unmagnetized plasma containing positive ions, negative ions, and electrons obeying a kappa-type distribution that is penetrated by a positive ion beam. By considering dissipative mechanisms, including ionization, negative-positive ion recombination, and electron attachment, we introduce a comprehensive model for the plasma with the effects of sources and sinks. Via reductive perturbation theory, the modified nonlinear Schrödinger equation with a dissipative term is derived to govern the dynamics of the modulated waves. The effect of the plasma parameters on the modulation instability criterion for the modified nonlinear Schrödinger equation is numericallymore » investigated in detail. Within the unstable region, first- and second-order dissipative ion-acoustic rogue waves are present. The effect of the plasma parameters on the characteristics of the dissipative rogue waves is also discussed.« less

On the dimensionally correct kinetic theory of turbulence for parallel propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Pockels effect in strained silicon photonics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Vivien, Laurent; Berciano, Mathias; Damas, Pedro; Marcaud, Guillaume; Le Roux, Xavier; Crozat, Paul; Alonso-Ramos, Carlos A.; Benedikovic, Daniel; Marris-Morini, Delphine; Cassan, Eric

2017-05-01

Silicon photonics has generated a strong interest in recent years, mainly for optical communications and optical interconnects in CMOS circuits. The main motivations for silicon photonics are the reduction of photonic system costs and the increase of the number of functionalities on the same integrated chip by combining photonics and electronics, along with a strong reduction of power consumption. However, one of the constraints of silicon as an active photonic material is its vanishing second order optical susceptibility, the so called χ(2) , due to the centrosymmety of the silicon crystal. To overcome this limitation, strain has been used as a way to deform the crystal and destroy the centrosymmetry which inhibits χ(2). The paper presents the recent advances in the development of second-order nonlinearities including discussions from fundamental origin of Pockels effect in silicon until its implementation in a real device. Carrier effects induced by an electric field leading to an electro-optics behavior will also be discussed.

Investigations on nucleation, HRXRD, optical, piezoelectric, polarizability and Z-scan analysis of L-arginine maleate dihydrate single crystals

NASA Astrophysics Data System (ADS)

Sakthy Priya, S.; Alexandar, A.; Surendran, P.; Lakshmanan, A.; Rameshkumar, P.; Sagayaraj, P.

2017-04-01

An efficient organic nonlinear optical single crystal of L-arginine maleate dihydrate (LAMD) has been grown by slow evaporation solution technique (SEST) and slow cooling technique (SCT). The crystalline perfection of the crystal was examined using high-resolution X-ray diffractometry (HRXRD) analysis. Photoluminescence study confirmed the optical properties and defects level in the crystal lattice. Electromechanical behaviour was observed using piezoelectric co-efficient (d33) analysis. The photoconductivity analysis confirmed the negative photoconducting nature of the material. The dielectric constant and loss were measured as a function of frequency with varying temperature and vice-versa. The laser damage threshold (LDT) measurement was carried out using Nd:YAG Laser with a wavelength of 1064 nm (Focal length is 35 cm) and the obtained results showed that LDT value of the crystal is high compared to KDP crystal. The high laser damage threshold of the grown crystal makes it a potential candidate for second and higher order nonlinear optical device application. The third order nonlinear optical parameters of LAMD crystal is determined by open-aperture and closed-aperture studies using Z-scan technique. The third order linear and nonlinear optical parameters such as the nonlinear refractive index (n2), two photon absorption coefficient (β), Real part (Reχ3) and imaginary part (Imχ3) of third-order nonlinear optical susceptibility are calculated.

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

PubMed

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

2018-05-17

The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer). We observe that a small high layer can already account for the variations of β as a function of the nature of the FP, provided the low layer is treated at an ab initio level to describe properly the effects of key H-bonds. Then, for semiquantitative reproduction of the experimental values obtained from hyper-Rayleigh scattering experiments, it is necessary to incorporate electron correlation as described at the second-order Møller-Plesset perturbation theory (MP2) level as well as implicit solvent effects accounted for using the polarizable continuum model (PCM). This led us to define the MP2/6-31+G(d):HF/6-31+G(d)/IEFPCM scheme as an efficient ONIOM approach and the MP2/6-31+G(d):HF/6-31G(d)/IEFPCM as a better compromise between accuracy and computational needs. Using these methods, we demonstrate that many parameters play a role on the β response of FPs, including the length of the π-conjugated segment, the variation of the bond length alternation, and the presence of π-stacking interactions. Then, noticing the small diversity of the FP chromophores, these results highlight the key role of the β-barrel and surrounding residues on β, not only because they can locally break the noncentrosymmetry vital to a β response but also because it can impose geometrical constraints on the chromophore.

A statistical methodology for estimating transport parameters: Theory and applications to one-dimensional advectivec-dispersive systems

USGS Publications Warehouse

Wagner, Brian J.; Gorelick, Steven M.

1986-01-01

A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

NASA Astrophysics Data System (ADS)

Nigro, A.; De Bartolo, C.; Crivellini, A.; Bassi, F.

2017-12-01

In this paper we investigate the possibility of using the high-order accurate A (α) -stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.

Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan

2016-01-01

The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anharmonic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear nonclassical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode.

Structural characterization, spectroscopic signatures, nonlinear optical response, and antioxidant property of 4-benzyloxybenzaldehyde and its binding activity with microtubule-associated tau protein

NASA Astrophysics Data System (ADS)

Anbu, V.; Vijayalakshmi, K. A.; Karthick, T.; Tandon, Poonam; Narayana, B.

2017-09-01

In the proposed work, the non-linear optical response, spectroscopic signature and binding activity of 4-Benzyloxybenzaldehyde (4BB) has been investigated. In order to find the vibrational contribution of functional groups in mixed or coupled modes in the experimental FT-IR and FT-Raman spectra, the potential energy distribution (PED) based on the internal coordinates have been computed. Since the molecule exists in the form of dimer in solid state, the electronic structure of dimer has been proposed in order to explain the intermolecular hydrogen bonding interactions via aldehyde group. The experimental and simulated powder X-ray diffraction data was compared and the miller indices which define the crystallographic planes in the crystal lattices were identified. Optical transmittance and absorbance measurement were taken at ambient temperature in order to investigate the transparency and optical band gap. For screening the material for nonlinear applications, theoretical second order hyperpolarizability studies were performed and compared with the standard reference urea. To validate the theoretical results, powder second harmonic generation (SHG) studies were carried out using Kurtz and Perry technique. The results show that the molecule studied in this work exhibit considerable non-linear optical (NLO) response. In addition to the characterization and NLO studies, we also claimed based on the experimental and theoretical data that the molecule shows antioxidant property and inhibition capability. Since the title molecule shows significant binding with Tau protein that helps to stabilize microtubules in the nervous system, the molecular docking investigation was performed to find the inhibition constant, binding affinity and active binding residues.

Fully decoupled monolithic projection method for natural convection problems

NASA Astrophysics Data System (ADS)

Pan, Xiaomin; Kim, Kyoungyoun; Lee, Changhoon; Choi, Jung-Il

2017-04-01

To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. The proposed method applies the Crank-Nicolson scheme in time and the second-order central finite difference in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of the proposed method for velocity, pressure, and temperature in terms of a discrete l2-norm. Moreover, according to the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. In addition, we provide numerical simulations of two-dimensional Rayleigh-Bénard convection and periodic forced flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional Rayleigh-Bénard convection for different Rayleigh numbers.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bičiūnas, A.; Arlauskas, A.; Adamonis, J.

We report on terahertz (THz) emission from tellurium crystal surfaces excited by femtosecond optical pulses. Measurements were performed on three differently cut Te samples and with different wavelength optical excitation pulses. THz pulse amplitude dependences on the azimuthal angle measured at various excitation wavelengths have evidenced that three different mechanisms are responsible for THz generation in tellurium: second order nonlinear optical rectification effect, dominating at lower excitation photon energies, as well as transverse and ordinary photo-Dember effects, which emerge at energies larger than 0.9 eV. The shapes of the azimuthal angle dependences were also explained by theoretical model.

Second-order non-linear optical studies on CdS microcrystallite-doped alkali borosilicate glasses

NASA Astrophysics Data System (ADS)

Liu, Hao; Liu, Qiming; Wang, Mingliang; Zhao, Xiujian

2007-05-01

CdS microcrystal-doped alkali borosilicate glasses were prepared by conventional fusion and heat-treatment method. Utilizing Maker fringe method, second-harmonic generation (SHG) was both observed from CdS-doped glasses before and after certain thermal/electrical poling. While because the direction of polarization axes of CdS crystals formed in the samples is random or insufficient interferences of generated SH waves occur, the fringe patterns obtained in samples without poling treatments showed no fine structures. For the poled samples, larger SH intensity has been obtained than that of the samples without any poling treatments. It was considered that the increase of an amount of hexagonal CdS in the anode surface layer caused by the applied dc field increased the SH intensity. The second-order non-linearity χ(2) was estimated to be 1.23 pm/V for the sample poled with 2.5 kV at 360 °C for 30 min.

Giant Kerr response of ultrathin gold films from quantum size effect.

PubMed

Qian, Haoliang; Xiao, Yuzhe; Liu, Zhaowei

2016-10-10

With the size of plasmonic devices entering into the nanoscale region, the impact of quantum physics needs to be considered. In the past, the quantum size effect on linear material properties has been studied extensively. However, the nonlinear aspects have not been explored much so far. On the other hand, much effort has been put into the field of integrated nonlinear optics and a medium with large nonlinearity is desirable. Here we study the optical nonlinear properties of a nanometre scale gold quantum well by using the z-scan method and nonlinear spectrum broadening technique. The quantum size effect results in a giant optical Kerr susceptibility, which is four orders of magnitude higher than the intrinsic value of bulk gold and several orders larger than traditional nonlinear media. Such high nonlinearity enables efficient nonlinear interaction within a microscopic footprint, making quantum metallic films a promising candidate for integrated nonlinear optical applications.

On the Coriolis effect in acoustic waveguides.

PubMed

Wegert, Henry; Reindl, Leonard M; Ruile, Werner; Mayer, Andreas P

2012-05-01

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.

Biomolecular Imaging with Coherent Nonlinear Vibrational Microscopy

PubMed Central

Chung, Chao-Yu; Boik, John; Potma, Eric O.

2014-01-01

Optical imaging with spectroscopic vibrational contrast is a label-free solution for visualizing, identifying, and quantifying a wide range of biomolecular compounds in biological materials. Both linear and nonlinear vibrational microscopy techniques derive their imaging contrast from infrared active or Raman allowed molecular transitions, which provide a rich palette for interrogating chemical and structural details of the sample. Yet nonlinear optical methods, which include both second-order sum-frequency generation (SFG) and third-order coherent Raman scattering (CRS) techniques, offer several improved imaging capabilities over their linear precursors. Nonlinear vibrational microscopy features unprecedented vibrational imaging speeds, provides strategies for higher spatial resolution, and gives access to additional molecular parameters. These advances have turned vibrational microscopy into a premier tool for chemically dissecting live cells and tissues. This review discusses the molecular contrast of SFG and CRS microscopy and highlights several of the advanced imaging capabilities that have impacted biological and biomedical research. PMID:23245525

Theoretical study on the spectroscopic and third-order nonlinear optical properties of two-dimensional charge-transfer pyrazine derivatives

NASA Astrophysics Data System (ADS)

Li, Haipeng; Zhang, Yi; Bi, Zetong; Xu, Runfeng; Li, Mingxue; Shen, Xiaopeng; Tang, Gang; Han, Kui

2017-12-01

In this paper, density functional theory method was employed to study the electronic absorption spectrum and electronic static second hyperpolarisability of X-shaped pyrazine derivatives with two-dimensional charge-transfer structures. Computational results show that the push-pull electron abilities of the substituent groups and the length of the conjugated chains affect the electronic spectrum and static second hyperpolarisability of the pyrazine derivatives. As the push-pull electron abilities of the substituent groups or the length of the conjugated chains increases, the frontier molecular orbital energy gap decreases, resulting in increased second hyperpolarisability and redshift of the electronic absorption bands. The electronic absorption spectra of the pyrazine derivatives maintain good transparency in the blue light band. The electronic static second hyperpolarisability exhibits a linear relationship to the frontier molecular orbital energy gap. Particularly, increasing/decreasing the push-pull electron abilities of the substituent groups considerably affect the static second hyperpolarisability in long conjugated systems, which is important to the modulation of molecular organic nonlinear optical (NLO) properties. The studied pyrazine derivatives show large third-order NLO response and good transparency in the blue light band and are thus promising candidates as NLO materials for photonics applications.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

On the reduced dynamics of a subset of interacting bosonic particles

NASA Astrophysics Data System (ADS)

Gessner, Manuel; Buchleitner, Andreas

2018-03-01

The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M ≤ N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.

Kinetic theory of turbulence for parallel propagation revisited: Formal results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Peter H., E-mail: yoonp@umd.edu

2015-08-15

In a recent paper, Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. The original work was according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)], but Gaelzer et al. noted that the terms pertaining to discrete-particle effects in Yoon and Fang's theory did not enjoy proper dimensionality. The purpose of Gaelzer et al. was to restore the dimensional consistency associated with such terms. However, Gaelzer et al. was concerned only with linear wave-particle interaction terms. The present paper completes the analysis bymore » considering the dimensional correction to nonlinear wave-particle interaction terms in the wave kinetic equation.« less

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

NASA Astrophysics Data System (ADS)

Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

2013-06-01

This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'silva, E.D., E-mail: deepak.dsilva@gmail.com; Podagatlapalli, G. Krishna; Venugopal Rao, S., E-mail: soma_venu@yahoo.com

Graphical abstract: Photograph and schematic representation of Z-scan experimental setup used to investigate third order nonlinear properties of the chalcone materials. Highlights: ► Br and NO{sub 2} substituted chalcone derivatives were exposed to picosecond laser pulses. ► Third-order nonlinear optical (NLO) properties were investigated. ► Compounds show promising third-order and optical limiting properties. ► These materials found suitable for electrical and optical applications. -- Abstract: In this paper we present results from the experimental study of third-order nonlinear optical (NLO) properties of three molecules of Br and NO{sub 2} substituted chalcone derivatives namely (2E)-1-(4-bromophenyl)-3-[4(methylsulfanyl)phenyl]prop-2-en-1-one (4Br4MSP), (2E)-1-(3-bromophenyl)-3-[4-(methylsulfanyl) phenyl]prop-2-en-1-one (3Br4MSP) and (2E)-3[4(methylsulfanyl)more » phenyl]-1-(4-nitrophenyl)prop-2-en-1-one (4N4MSP). The NLO properties have been investigated by Z-scan technique using 2 ps laser pulses at 800 nm. The nonlinear refractive indices, nonlinear absorption coefficient, and the magnitude of third-order susceptibility have been determined. The values obtained are of the order of 10{sup −7} cm{sup 2}/GW, 10{sup −3} cm/GW and 10{sup −14} esu respectively. The molecular second hyperpolarizability for the chalcone derivatives is of the order of 10{sup −32} esu. The coupling factor, excited state cross section, ground state cross section etc. were determined. The optical limiting (OL) property was studied. The results suggest that the nonlinear properties investigated for present chalcones are comparable with some of the reported chalcone derivatives and can be desirable for NLO applications.« less

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Behroozian, B.; Askari, H. R.

2018-07-01

The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

Triphenylamine Derived 3-Acetyl and 3-Benzothiazolyl Bis and Tris Coumarins: Synthesis, Photophysical and DFT Assisted Hyperpolarizability Study

NASA Astrophysics Data System (ADS)

Erande, Yogesh; Kothavale, Shantaram; Sreenath, Mavila C.; Chitrambalam, Subramaniyan; Joe, Isaac H.; Sekar, Nagaiyan

2018-02-01

Triphenylamine derived bis- and tris-branched donor-pi-acceptor coumarins with acetyl and benzothiazolyl acceptors are studied for their linear and nonlinear optical properties that originate from their photophysical and molecular structure. Plots of solvent polarities versus the Stokes shift, frontier molecular orbital analysis and Generalised Mulliken Hush analysis have established their strong charge transfer character supported by the strong emission solvatochromism of these chromophores. On the basis of excited state intramolecular charge transfer, the first-, second- and third-order polarizability of these dyes are determined by a solvatochromic method and supported by density functional theory calculations using CAM-B3LYP/6-31g(d). Compared to the acetyl group, the benzothiazolyl group is a strong acceptor, and its corresponding derivatives show enhanced absorption, emission maxima and non-linear optical response. Bond length alternation and bond order alternation analysis reveals that these chromophores approach the cyanine-like framework which is responsible for maximum perturbation to produce high nonlinear optical response. Third order nonlinear susceptibility for dyes 1 and 2 is determined by Z-scan measurement. All of these methods are used to determine the nonlinear optical properties, and thermogravimetric analysis suggests that these chromophores are thermally robust and efficient nonlinear optical materials.

Canonical equations of Hamilton for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liang, Guo; Guo, Qi; Ren, Zhanmei

2015-09-01

We define two different systems of mathematical physics: the second order differential system (SODS) and the first order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which exhibit some kind of symmetry in form and are formally different from the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison- Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but not introduced by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way.

Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges

PubMed Central

Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang

2013-01-01

Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388

Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.

PubMed

Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang

2013-01-01

Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed.

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2016-08-01

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

Second-order sliding mode controller with model reference adaptation for automatic train operation

NASA Astrophysics Data System (ADS)

Ganesan, M.; Ezhilarasi, D.; Benni, Jijo

2017-11-01

In this paper, a new approach to model reference based adaptive second-order sliding mode control together with adaptive state feedback is presented to control the longitudinal dynamic motion of a high speed train for automatic train operation with the objective of minimal jerk travel by the passengers. The nonlinear dynamic model for the longitudinal motion of the train comprises of a locomotive and coach subsystems is constructed using multiple point-mass model by considering the forces acting on the vehicle. An adaptation scheme using Lyapunov criterion is derived to tune the controller gains by considering a linear, stable reference model that ensures the stability of the system in closed loop. The effectiveness of the controller tracking performance is tested under uncertain passenger load, coupler-draft gear parameters, propulsion resistance coefficients variations and environmental disturbances due to side wind and wet rail conditions. The results demonstrate improved tracking performance of the proposed control scheme with a least jerk under maximum parameter uncertainties when compared to constant gain second-order sliding mode control.

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

1993-01-01

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Novel procedure for characterizing nonlinear systems with memory: 2017 update

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

Growth of thin films of dicyanovinylanisole on quartz and teflon-coated quartz by physical vapor transport

NASA Technical Reports Server (NTRS)

Pearson, Earl F.

1994-01-01

Organic compounds offer the possibility of molecular engineering in order to optimize the nonlinearity and minimize damage due to the high-power lasers used in nonlinear optical devices. Recently dicyanovinylanisole (DIVA), ((2-methoxyphenyl) methylenepropanedinitrile) has been shown to have a second order nonlinearity 40 times that of alpha-quartz. Debe et. al. have shown that a high degree of orientational order exists for thin films of phthalocyanine grown by physical vapor transport in microgravity. The microgravity environment eliminates convective flow and was critical to the formation of highly ordered dense continuous films in these samples. This work seeks to discover the parameters necessary for the production of thin continuous films of high optical quality in Earth gravity. These parameters must be known before the experiment can be planned for growing DIVA in a microgravity environment. The microgravity grown films are expected to be denser and of better optical quality than the unit gravity films as was observed in the phthalocyanine films.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Apparatus and methods for using achromatic phase matching at high orders of dispersion

DOEpatents

Richman, Bruce; Trebino, Rick; Bisson, Scott; Sidick, Erkin

2001-01-01

Achromatic phase-matching (APM) is used for efficiently multiplying the frequency of broad bandwidth light by using a nonlinear optical medium comprising a second-harmonic generation (SHG) crystal. Stationary optical elements whose configuration, properties, and arrangement have been optimized to match the dispersion characteristics of the SHG crystal to at least the second order. These elements include a plurality of prismatic elements for directing an input light beam onto the SHG crystal such that each ray wavelength is aligned to match the phase-matching angle for the crystal at each wavelength of light to at least the second order and such that every ray wavelength overlap within the crystal.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Label-free super-resolution with coherent nonlinear structured-illumination microscopy

NASA Astrophysics Data System (ADS)

Huttunen, Mikko J.; Abbas, Aazad; Upham, Jeremy; Boyd, Robert W.

2017-08-01

Structured-illumination microscopy enables up to a two-fold lateral resolution improvement by spatially modulating the intensity profile of the illumination beam. We propose a novel way to generalize the concept of structured illumination to nonlinear widefield modalities by spatially modulating, instead of field intensities, the phase of the incident field while interferometrically measuring the complex-valued scattered field. We numerically demonstrate that for second-order and third-order processes an almost four- and six-fold increase in lateral resolution is achievable, respectively. This procedure overcomes the conventional Abbe diffraction limit and provides new possibilities for label-free super-resolution microscopy.

Thermal expansion behavior study of Co nanowire array with in situ x-ray diffraction and x-ray absorption fine structure techniques

NASA Astrophysics Data System (ADS)

Mo, Guang; Cai, Quan; Jiang, Longsheng; Wang, Wei; Zhang, Kunhao; Cheng, Weidong; Xing, Xueqing; Chen, Zhongjun; Wu, Zhonghua

2008-10-01

In situ x-ray diffraction and x-ray absorption fine structure techniques were used to study the structural change of ordered Co nanowire array with temperature. The results show that the Co nanowires are polycrystalline with hexagonal close packed structure without phase change up until 700 °C. A nonlinear thermal expansion behavior has been found and can be well described by a quadratic equation with the first-order thermal expansion coefficient of 4.3×10-6/°C and the second-order thermal expansion coefficient of 5.9×10-9/°C. The mechanism of this nonlinear thermal expansion behavior is discussed.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Nonlinear Optical Properties of High-Temperature Organic Structures

NASA Astrophysics Data System (ADS)

Shi, Rui-Fang

In this thesis, we report the discovery of a new class of electro-optic organic structures, 1,8-naphthoylene -benzimidazoles, developed with computer aided molecular design combined with actual syntheses. These structures are similar to polyimide repeat units and possess high thermal, chemical and photo stabilities. Thermal analysis shows that the new class retains its linear and nonlinear optical properties well above 300^circ C in both pure forms and guest/host polyimide systems. Importantly, side group substitutions not only increase the second-order optical responses but also enhance the thermal stability. The origin of the relatively large second order optical responses of the new class is revealed by quantum many-electron calculations that explicitly take electron -electron correlations into consideration. Contour diagrams indicate that electrons are decreased on the benzimidazole -donor-substituted side and increased on the naphthoylene side upon virtual excitations, illustrating the fact that the naphthoylene group acts both as an electron acceptor and a pi-bridge that provides the necessary electron delocalization. Results for most structures show that the most dominant virtual excitation process to beta_{ijk}(-omega _3;omega_1,omega_2) involves the ground (S_0) and first excited (S_1) pi -electronic states. Importantly, increasing the electron donor strength increase the electric dipole moments and transition moments, therefore second order optical responses are enhanced. Interestingly, it is found that the position of a donor group in the new class has a significant effect on second order optical responses. DC-induced second harmonic generation (DCSHG) dispersion measurements characterize the nonlinear optical properties of the new class, using both nanosecond and picosecond tunable laser sources ranging from 1400 to 2148 nm in wavelength. Comparison between theory and experiment demonstrates that there is good agreement between them over a wide nonresonant photon energy region, illustrating the great success of our understanding of the nonlinear optical responses even in these relatively complicated organic structures. In addition, it is found that these chromophores have large beta_{ijk }: for SY177 in solution with 1,4-dioxane, mu_{x}beta_ {x}(-2omega;omega,omega) + < gamma(-2omega;omega,omega,0) > 5kT = 418 times 10 ^{-48} esu and beta _{x}(-2omega;omega,omega ) 92 times 10^ {-30} esu at hbaromega = 0.65 eV. For SY215 in solution with CH _2Cl_2, mu_ {x}beta_{x}(-2omega; omega,omega) + < gamma( -2omega;omega,omega,0) > 5kT = 1468 times 10^{-48} esu and beta_{x}(-2omega; omega,omega) = 268 times 10^{-30} esu at hbaromega = 0.65 eV. The discovery and characterization of the new high temperature class represents a critical step in the development of new materials that are suitable for practical device applications. Work is underway to optimize these structures and incorporate them into waveguide devices.

Tackling non-linearities with the effective field theory of dark energy and modified gravity

NASA Astrophysics Data System (ADS)

Frusciante, Noemi; Papadomanolakis, Georgios

2017-12-01

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Nonlinear Optical Properties of Carotenoid and Chlorophyll Harmonophores

NASA Astrophysics Data System (ADS)

Tokarz, Danielle Barbara

Information regarding the structure and function of living tissues and cells is instrumental to the advancement of cell biology and biophysics. Nonlinear optical microscopy can provide such information, but only certain biological structures generate nonlinear optical signals. Therefore, structural specificity can be achieved by introducing labels for nonlinear optical microscopy. Few studies exist in the literature about labels that facilitate harmonic generation, coined "harmonophores". This thesis consists of the first major investigation of harmonophores for third harmonic generation (THG) microscopy. Carotenoids and chlorophylls were investigated as potential harmonophores. Their nonlinear optical properties were studied by the THG ratio technique. In addition, a tunable refractometer was built in order to determine their second hyperpolarizability (gamma). At 830 nm excitation wavelength, carotenoids and chlorophylls were found to have large negative gamma values however, at 1028 nm, the sign of gamma reversed for carotenoids and remained negative for chlorophylls. Consequently, at 1028 nm wavelength, THG signal is canceled with mixtures of carotenoids and chlorophylls. Furthermore, when such molecules are covalently bonded as dyads or interact within photosynthetic pigment-protein complexes, it is found that additive effects with the gamma values still play a role, however, the overall gamma value is also influenced by the intra-pigment and inter-pigment interaction. The nonlinear optical properties of aggregates containing chlorophylls and carotenoids were the target of subsequent investigations. Carotenoid aggregates were imaged with polarization-dependent second harmonic generation and THG microscopy. Both techniques revealed crystallographic information pertaining to H and J aggregates and beta-carotene crystalline aggregates found in orange carrot. In order to demonstrate THG enhancement due to labeling, cultured cells were labeled with carotenoid incorporated liposomes. In addition, Drosophila melanogaster larvae muscle as well as keratin structures in the hair cortex were labeled with beta-carotene. Polarization-dependent THG studies may be particularly useful in understanding the structural organization that occurs within biological structures containing carotenoids and chlorophylls such as photosynthetic pigment-protein complexes and carotenoid aggregates in plants and alga. Further, artificial labeling with carotenoids and chlorophylls may be useful in clinical applications since they are nontoxic, nutritionally valuable, and they can aid in visualizing structural changes in cellular components.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

On the determination of χ(2) in thin films: a comparison of one-beam second-harmonic generation measurement methodologies

PubMed Central

Hermans, Artur; Kieninger, Clemens; Koskinen, Kalle; Wickberg, Andreas; Solano, Eduardo; Dendooven, Jolien; Kauranen, Martti; Clemmen, Stéphane; Wegener, Martin; Koos, Christian; Baets, Roel

2017-01-01

The determination of the second-order susceptibility (χ(2)) of thin film samples can be a delicate matter since well-established χ(2) measurement methodologies such as the Maker fringe technique are best suited for nonlinear materials with large thicknesses typically ranging from tens of microns to several millimeters. Here we compare two different second-harmonic generation setups and the corresponding measurement methodologies that are especially advantageous for thin film χ(2) characterization. This exercise allows for cross-checking the χ(2) obtained for identical samples and identifying the main sources of error for the respective techniques. The development of photonic integrated circuits makes nonlinear thin films of particular interest, since they can be processed into long waveguides to create efficient nonlinear devices. The investigated samples are ABC-type nanolaminates, which were reported recently by two different research groups. However, the subsequent analysis can be useful for all researchers active in the field of thin film χ(2) characterization. PMID:28317938

Second harmonic generation polarization properties of myofilaments

NASA Astrophysics Data System (ADS)

Samim, Masood; Prent, Nicole; Dicenzo, Daniel; Stewart, Bryan; Barzda, Virginijus

2014-05-01

Second harmonic generation (SHG) polarization microscopy was used to investigate the organization of myosin nanomotors in myofilaments of muscle cells. The distribution of the second-order nonlinear susceptibility component ratio χzzz(2)/χzxx(2) along anisotropic bands of sarcomeres revealed differences between the headless and head-containing regions of myofilaments. The polarization-in polarization-out SHG measurements of headless myosin mutants of indirect flight muscle in Drosophila melanogaster confirmed a lower susceptibility component ratio compared to the head-containing myocytes with wild-type myosins. The increase in the ratio is assigned to the change in the deflection angle of the myosin S2 domain and possible contribution of myosin heads. The nonlinear susceptibility component ratio is a sensitive indicator of the myosin structure, and therefore, it can be used for conformational studies of myosin nanomotors. The measured ratio values can also be used as the reference for ab initio calculations of nonlinear optical properties of different parts of myosins.

Benzothiazolium Single Crystals: A New Class of Nonlinear Optical Crystals with Efficient THz Wave Generation.

PubMed

Lee, Seung-Heon; Lu, Jian; Lee, Seung-Jun; Han, Jae-Hyun; Jeong, Chan-Uk; Lee, Seung-Chul; Li, Xian; Jazbinšek, Mojca; Yoon, Woojin; Yun, Hoseop; Kang, Bong Joo; Rotermund, Fabian; Nelson, Keith A; Kwon, O-Pil

2017-08-01

Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Layer-Dependent Third-Harmonic Generation in Graphene

NASA Astrophysics Data System (ADS)

Yang, Hao; Guan, Honghua; Dadap, Jerry; Osgood, Richard; Richard Osgood Team

Graphene has become a subject of intense interest and study because of its remarkable 2D electronic properties. Multilayer graphene also offers an array of properties that are also of interest for optical physics and devices. Despite its second-order-nonlinear optical response is intrinsically weak, third-order nonlinear optical effects in graphene are symmetry-allowed thus leading to studies of several third-order process in few-layer graphene. In this work, we report third-harmonic generation in multilayer graphene mounted on fused silica and with thicknesses which approach the bulk continuum. THG signals show cubic power dependence with respect to the intensity of fundamental beam. Third-harmonic generation spectroscopy enables a good fit using linear optical detection, which shows strong contrast for different layer number graphene. The maximum THG efficiency appears at layer number around 30. Two models are used for describing this layer dependent phenomenon and shows absorption plays a key role in THG of multilayer graphene. This work also provides a new imaging technology for graphene detection and identification with better contrast and resolution. U.S. Department of Energy under Contract No. DE-FG 02-04-ER-46157.

Stability of nonuniform rotor blades in hover using a mixed formulation

NASA Technical Reports Server (NTRS)

Stephens, W. B.; Hodges, D. H.; Avila, J. H.; Kung, R. M.

1980-01-01

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Nonlinear optical and light emission studies of special organic molecules and crystals

NASA Astrophysics Data System (ADS)

Bhowmik, Achintya K.

The nonlinear optical properties and light emission characteristics of some special organic molecules and crystals have been studied in detail. The second-order nonlinear optical effects were measured in the single- crystal films of the materials. The crystallographic orientations of the films were determined using x-ray diffraction measurements. The second-order susceptibility tensor elements of 4-aminobenzophenone (ABP) and 8- (4'-acetylphenyl)-1,4-dioxa-8- azaspiro[4.5]decane (APDA) films were measured using polarization selective second-harmonic generation experiments. The d-coefficients of ABP are: d 23 = 7.3 +/- 0.4 pm/V and d22 = 0.73 +/- 0.04 pm/V, while those of APDA are: d33 = 54 +/- 6 pm/V and d15 = 18 +/- 3 pm/V at 1064 nm. Phase-matched propagation directions were identified on the films. The application of these films in measuring ultra-short laser pulse-width was demonstrated. Polarized optical absorption and photo- luminescence were measured in 4'- dimethylamino-N-methyl-4-stilbazolium tosylate (DAST). The electro-optic properties of single- crystal films of DAST and styryl pyridinium cyanine dye (SPCD) were studied over a broad range of wavelengths. The measured r-coefficients are the largest reported in any material. Thin-film electro-optic modulators were demonstrated using these films which have insignificant insertion and propagation losses compared to the traditional waveguide based devices. The response was observed to be flat over the measured frequency range (2 kHz-100 MHz), which indicates the origin of the electro-optic effect to be predominantly electronic. Thus these materials have significant potential for applications in high-speed optical signal processing. Spectral broadening of femtosecond laser pulses in poly- [2,4 hexadiyne-1,6 diol-bis-(p-toluene sulfonate)] (PTS) single-crystals due to self-phase modulation was studied. The magnitudes of the nonlinear refractive index were determined over the wavelength range of 720-1064 nm. The two-photon absorption spectrum, determined from nonlinear transmission measurements, was observed to have no discernible influence on the dispersion of the nonlinear index at these wavelengths. Highly efficient spectrally narrowed emission has been observed for the first time in strongly dipolar organic salts based on the stilbazolium chromophore. An unusually high conversion efficiency (40%) with a low excitation threshold (<1 μJ) has been observed despite a very low photoluminescence efficiency (~0.3%). The results are explained in terms of cooperative emission upon short-pulse optical excitation. These materials have a wide range of potential applications in photonics, including frequency conversion, high-speed electro-optic modulation, sensors, and novel laser-like light sources.

Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects

PubMed Central

Zhang, Jian-Hui; Liu, Chong

2017-01-01

We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing the propagation of ultrashort optical pulse in optical fibres. By using Darboux transformation, we derive the superregular breather solution that develops from a small localized perturbation. This type of solution can be used to characterize the nonlinear stage of the modulation instability (MI) of the condensate. In particular, we show some novel characteristics of the nonlinear stage of MI arising from higher-order effects: (i) coexistence of a quasi-Akhmediev breather and a multipeak soliton; (ii) two multipeak solitons propagation in opposite directions; (iii) a beating pattern followed by two multipeak solitons in the same direction. It is found that these patterns generated from a small localized perturbation do not have the analogues in the standard NLS equation. Our results enrich Zakharov’s theory of superregular breathers and could provide helpful insight on the nonlinear stage of MI in presence of the higher-order effects. PMID:28413335

An exponential time-integrator scheme for steady and unsteady inviscid flows

NASA Astrophysics Data System (ADS)

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

2018-07-01

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows.

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2016-01-01

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

PubMed

Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

2008-03-01

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

Strain-induced three-photon effects

NASA Astrophysics Data System (ADS)

Jeong, Jae-Woo; Shin, Sung-Chul; Lyubchanskii, I. L.; Varyukhin, V. N.

2000-11-01

Strain-induced three-photon effects such as optical second-harmonic generation and hyper-Rayleigh light scattering, characterized by electromagnetic radiation at the double frequency of an incident light, are phenomenologically investigated by adopting a nonlinear photoelastic interaction. The relations between the strain and the nonlinear optical susceptibility for crystal surfaces with point symmetries of 4mm and 3m are described by a symmetry analysis of the nonlinear photoelastic tensor. We theoretically demonstrate a possibility of determining the strain components by measuring the rotational anisotropy of radiation at the second-harmonic frequency. Hyper-Rayleigh light scattering by dislocation strain is also described using a nonlinear photoelastic tensor. The angular dependencies of light scattered at the double frequency of an incident light for different scattering geometries are analyzed.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Cascaded second-order processes for the efficient generation of narrowband terahertz radiation

NASA Astrophysics Data System (ADS)

Cirmi, Giovanni; Hemmer, Michael; Ravi, Koustuban; Reichert, Fabian; Zapata, Luis E.; Calendron, Anne-Laure; Çankaya, Hüseyin; Ahr, Frederike; Mücke, Oliver D.; Matlis, Nicholas H.; Kärtner, Franz X.

2017-02-01

The generation of high-energy narrowband terahertz radiation has gained heightened importance in recent years due to its potentially transformative impact on spectroscopy, high-resolution radar and more recently electron acceleration. Among various applications, such terahertz radiation is particularly important for table-top free electron lasers, which are at the moment a subject of extensive research. Second-order nonlinear optical methods are among the most promising techniques to achieve the required coherent radiation with energy > 10 mJ, peak field > 100 MV m-1, and frequency between 0.1 and 1 THz. However, they are conventionally thought to suffer from low efficiencies < ˜10-3, due to the high ratio between optical and terahertz photon energies, in what is known as the Manley-Rowe limitation. In this paper, we review the current second-order nonlinear optical methods for the generation of narrowband terahertz radiation. We explain how to employ spectral cascading to increase the efficiency beyond the Manley-Rowe limit and describe the first experimental results in the direction of a terahertz-cascaded optical parametric amplifier, a novel technique which promises to fully exploit spectral cascading to generate narrowband terahertz radiation with few percent optical-to-terahertz conversion efficiency.

Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

NASA Technical Reports Server (NTRS)

Barker, R. E., Jr.; Campbell, K. W.

1984-01-01

A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.

Third order nonlinear optical response exhibited by mono- and few-layers of WS 2

DOE PAGES

Torres-Torres, Carlos; Perea-López, Néstor; Elías, Ana Laura; ...

2016-04-13

In this work, strong third order nonlinear optical properties exhibited by WS 2 layers are presented. Optical Kerr effect was identified as the dominant physical mechanism responsible for these third order optical nonlinearities. An extraordinary nonlinear refractive index together with an important contribution of a saturated absorptive response was observed to depend on the atomic layer stacking. Comparative experiments performed in mono- and few-layer samples of WS 2 revealed that this material is potentially capable of modulating nonlinear optical processes by selective near resonant induced birefringence. In conclusion, we envision applications for developing all-optical bidimensional nonlinear optical devices.

Strong second harmonic generation in two-dimensional ferroelectric IV-monochalcogenides

NASA Astrophysics Data System (ADS)

Panday, Suman Raj; Fregoso, Benjamin M.

2017-11-01

The two-dimensional ferroelectrics GeS, GeSe, SnS and SnSe are expected to have large spontaneous in-plane electric polarization and enhanced shift-current response. Using density functional methods, we show that these materials also exhibit the largest effective second harmonic generation reported so far. It can reach magnitudes up to 10~nm~V-1 which is about an order of magnitude larger than that of prototypical GaAs. To rationalize this result we model the optical response with a simple one-dimensional two-band model along the spontaneous polarization direction. Within this model the second-harmonic generation tensor is proportional to the shift-current response tensor. The large shift current and second harmonic responses of GeS, GeSe, SnS and SnSe make them promising non-linear materials for optoelectronic applications.

Homotopy perturbation method: a versatile tool to evaluate linear and nonlinear fuzzy Volterra integral equations of the second kind.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

In this article, we focus on linear and nonlinear fuzzy Volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method (HPM) to obtain fuzzy approximate solutions to them. To facilitate the benefits of this proposal, an algorithmic form of the HPM is also designed to handle the same. In order to illustrate the potentiality of the approach, two test problems are offered and the obtained numerical results are compared with the existing exact solutions and are depicted in terms of plots to reveal its precision and reliability.

Nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis ismore » on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.« less

Effects of electromagnetic fields on the nonlinear optical properties of asymmetric double quantum well under intense laser field

NASA Astrophysics Data System (ADS)

Yesilgul, U.; Sari, H.; Ungan, F.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Sökmen, I.

2017-03-01

In this study, the effects of electric and magnetic fields on the optical rectification and second and third harmonic generation in asymmetric double quantum well under the intense non-resonant laser field is theoretically investigated. We calculate the optical rectification and second and third harmonic generation within the compact density-matrix approach. The theoretical findings show that the influence of electric, magnetic, and intense laser fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation.

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

PubMed Central

Lipson, E D

1975-01-01

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model. PMID:1203444

Phased-array sources based on nonlinear metamaterial nanocavities

DOE PAGES

Wolf, Omri; Campione, Salvatore; Benz, Alexander; ...

2015-07-01

Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization.more » As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (~5 μm): a beam splitter and a polarizing beam splitter. As a result, proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.« less

Sub-wavelength modulation of χ (2) optical nonlinearity in organic thin films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Yixin; Yuan, Yakun; Wang, Baomin

Modulating the second-order nonlinear optical susceptibility (χ (2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor–acceptor (DA) interface, as a means to control the magnitude and sign of χ (2) at the nanoscale. Focusing initially on a single pentacene-C 60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed viamore » second harmonic generation that is sufficient to achieve d 33 > 10pm V –1, when incorporated in a non-centrosymmetric DA multilayer stack. Lastly, using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ (2) grating with 280 nm periodicity, which is the shortest reported to date.« less

Sub-wavelength modulation of χ(2) optical nonlinearity in organic thin films

NASA Astrophysics Data System (ADS)

Yan, Yixin; Yuan, Yakun; Wang, Baomin; Gopalan, Venkatraman; Giebink, Noel C.

2017-01-01

Modulating the second-order nonlinear optical susceptibility (χ(2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor-acceptor (DA) interface, as a means to control the magnitude and sign of χ(2) at the nanoscale. Focusing initially on a single pentacene-C60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed via second harmonic generation that is sufficient to achieve d33>10 pm V-1, when incorporated in a non-centrosymmetric DA multilayer stack. Using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ(2) grating with 280 nm periodicity, which is the shortest reported to date.

Sub-wavelength modulation of χ (2) optical nonlinearity in organic thin films

DOE PAGES

Yan, Yixin; Yuan, Yakun; Wang, Baomin; ...

2017-01-27

Modulating the second-order nonlinear optical susceptibility (χ (2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor–acceptor (DA) interface, as a means to control the magnitude and sign of χ (2) at the nanoscale. Focusing initially on a single pentacene-C 60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed viamore » second harmonic generation that is sufficient to achieve d 33 > 10pm V –1, when incorporated in a non-centrosymmetric DA multilayer stack. Lastly, using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ (2) grating with 280 nm periodicity, which is the shortest reported to date.« less

Effect of second harmonic in pulse-width-modulation-based DAC for feedback of digital fluxgate magnetometer

NASA Astrophysics Data System (ADS)

Belyayev, Serhiy; Ivchenko, Nickolay

2018-04-01

Digital fluxgate magnetometers employ processing of the measured pickup signal to produce the value of the compensation current. Using pulse-width modulation with filtering for digital to analog conversion is a convenient approach, but it can introduce an intrinsic source of nonlinearity, which we discuss in this design note. A code shift of one least significant bit changes the second harmonic content of the pulse train, which feeds into the pick-up signal chain despite the heavy filtering. This effect produces a code-dependent nonlinearity. This nonlinearity can be overcome by the specific design of the timing of the pulse train signal. The second harmonic is suppressed if the first and third quarters of the excitation period pulse train are repeated in the second and fourth quarters. We demonstrate this principle on a digital magnetometer, achieving a magnetometer noise level corresponding to that of the sensor itself.

Kolakoski sequence as an element to radiate giant forward and backward second harmonic signals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parvini, T. S.; Tehranchi, M. M., E-mail: m-hamidi@sbu.ac.ir, E-mail: teranchi@sbu.ac.ir; Laser and Plasma Research Institute, Shahid Beheshti University, Tehran

2015-11-14

We propose a novel type of aperiodic one-dimensional photonic crystal structures which can be used for generating giant forward and backward second harmonic signals. The studied structure is formed by stacking together the air and nonlinear layers according to the Kolakoski self-generation scheme in which each nonlinear layer contains a pair of antiparallel 180° poled LiNbO{sub 3} crystal layers. For different generation stages of the structure, conversion efficiencies of forward and backward second harmonic waves have been calculated by nonlinear transfer matrix method. Numerical simulations show that conversion efficiencies in the Kolakoski-based multilayer are larger than the perfect ones formore » at least one order of magnitude. Especially for 33rd and 39th generation stages, forward second harmonic wave are 42 and 19 times larger, respectively. In this paper, we validate the strong fundamental field enhancement and localization within Kolakoski-based multilayer due to periodicity breaking which consequently leads to very strong radiation of backward and forward second harmonic signals. Following the applications of analogous aperiodic structures, we expect that Kolakosi-based multilayer can play a role in optical parametric devices such as multicolor second harmonic generators with high efficiency.« less

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

NASA Technical Reports Server (NTRS)

Wang, K. S.; Vaidya, P. G.

1975-01-01

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow.

Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection

NASA Astrophysics Data System (ADS)

Meyer, Bettina; Schneider, Tapio

2017-04-01

There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the environment (e.g., entrainment and detrainment). In a second part, we employ the possibility to include non-local statistical correlations in a second-order closure scheme. Such non-local correlations allow to directly incorporate the spatially coherent structures that occur in the form of convective updrafts penetrating the boundary layer. This allows us to extend the work that has been done using assumed-PDF schemes for parameterising boundary layer turbulence and shallow convection in a non-local sense.

Nonlinear viscous higher harmonics generation due to incident and reflecting internal wave beam collision

NASA Astrophysics Data System (ADS)

Aksu, Anil A.

2017-09-01

In this paper, we have considered the non-linear effects arising due to the collision of incident and reflected internal wave beams. It has already been shown analytically [Tabaei et al., "Nonlinear effects in reflecting and colliding internal wave beams," J. Fluid Mech. 526, 217-243 (2005)] and numerically [Rodenborn et al., "Harmonic generation by reflecting internal waves," Phys. Fluids 23, 026601 (2011)] that the internal wave beam collision generates the higher harmonics and mean flow in a linear stratification. In this paper, similar to previous analytical work, small amplitude wave theory is employed; however, it is formulated from energetics perspective which allows considering internal wave beams as the product of slowly varying amplitude and fast complex exponential. As a result, the mean energy propagation equation for the second harmonic wave is obtained. Finally, a similar dependence on the angle of incidence is obtained for the non-linear energy transfer to the second harmonic with previous analyses. A possible physical mechanism for this angle dependence on the second harmonic generation is also discussed here. In addition to previous studies, the viscous effects are also included in the mean energy propagation equation for the incident, the reflecting, and the second harmonic waves. Moreover, even though the mean flow obtained here is only confined to the interaction region, it is also affected by viscosity via the decay in the incident and the reflecting internal wave beams. Furthermore, a framework for the non-linear harmonic generation in non-linear stratification is also proposed here.

Generalized predictive control for a coupled four tank MIMO system using a continuous-discrete time observer.

PubMed

Gouta, Houssemeddine; Hadj Saïd, Salim; Barhoumi, Nabil; M'Sahli, Faouzi

2017-03-01

This paper deals with the problem of the observer based control design for a coupled four-tank liquid level system. For this MIMO system's dynamics, motivated by a desire to provide precise and sensorless liquid level control, a nonlinear predictive controller based on a continuous-discrete observer is presented. First, an analytical solution from the model predictive control (MPC) technique is developed for a particular class of nonlinear MIMO systems and its corresponding exponential stability is proven. Then, a high gain observer that runs in continuous-time with an output error correction time that is updated in a mixed continuous-discrete fashion is designed in order to estimate the liquid levels in the two upper tanks. The effectiveness of the designed control schemes are validated by two tests; The first one is maintaining a constant level in the first bottom tank while making the level in the second bottom tank to follow a sinusoidal reference signal. The second test is more difficult and it is made using two trapezoidal reference signals in order to see the decoupling performance of the system's outputs. Simulation and experimental results validate the objective of the paper. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Second-Order Nonlinear Optical Dendrimers and Dendronized Hyperbranched Polymers.

PubMed

Tang, Runli; Li, Zhen

2017-01-01

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

A photon thermal diode

PubMed Central

Chen, Zhen; Wong, Carlaton; Lubner, Sean; Yee, Shannon; Miller, John; Jang, Wanyoung; Hardin, Corey; Fong, Anthony; Garay, Javier E.; Dames, Chris

2014-01-01

A thermal diode is a two-terminal nonlinear device that rectifies energy carriers (for example, photons, phonons and electrons) in the thermal domain, the heat transfer analogue to the familiar electrical diode. Effective thermal rectifiers could have an impact on diverse applications ranging from heat engines to refrigeration, thermal regulation of buildings and thermal logic. However, experimental demonstrations have lagged far behind theoretical proposals. Here we present the first experimental results for a photon thermal diode. The device is based on asymmetric scattering of ballistic energy carriers by pyramidal reflectors. Recent theoretical work has predicted that this ballistic mechanism also requires a nonlinearity in order to yield asymmetric thermal transport, a requirement of all thermal diodes arising from the second Law of Thermodynamics, and realized here using an ‘inelastic thermal collimator’ element. Experiments confirm both effects: with pyramids and collimator the thermal rectification is 10.9±0.8%, while without the collimator no rectification is detectable (<0.3%). PMID:25399761

Breathers and rogue waves in a Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Lan, Zhong-Zhou

2017-07-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation for a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or an alpha helical protein has been investigated. Breathers and rogue waves are constructed via the Darboux transformation and generalized Darboux transformation, respectively. Results of the breathers and rogue waves are presented: (1) The first- and second-order Akhmediev breathers and Kuznetsov-Ma solitons are presented with different values of variable coefficients which are related to the energy transfer or higher-order excitations and interactions in the helical protein, or related to the spin excitations resulting from the lowest order continuum approximation and octupole-dipole interaction in a Heisenberg ferromagnetic spin chain, and the nonlinear periodic breathers resulting from the Akhmediev breathers are studied as well; (2) For the first- and second-order rogue waves, we find that they can be split into many similar components when the variable coefficients are polynomial functions of time; (3) Rogue waves can also be split when the variable coefficients are hyperbolic secant functions of time, but the profile of each component in such a case is different.

New generation of one-dimensional photonic crystal cavities as robust high-efficient frequency converter

NASA Astrophysics Data System (ADS)

Parvini, T. S.; Tehranchi, M. M.; Hamidi, S. M.

2017-07-01

An effective method is proposed to design finite one-dimensional photonic crystal cavities (PhCCs) as robust high-efficient frequency converter. For this purpose, we consider two groups of PhCCs which are constructed by stacking m nonlinear (LiNbO3) and n linear (air) layers with variable thicknesses. In the first group, the number of linear layers is less than the nonlinear layers by one and in the second group by two. The conversion efficiency is calculated as a function of the arrangement and thicknesses of the linear and nonlinear layers by benefiting from nonlinear transfer matrix method. Our numerical simulations show that for each group of PhCCs, there is a structural formula by which the configurations with the highest efficiency can be constructed for any values of m and n (i.e. any number of layers). The efficient configurations are equivalent to Fabry-Pérot cavities that depend on the relationship between m and n and the mirrors in two sides of these cavities can be periodic or nonperiodic. The conversion efficiencies of these designed PhCCs are more than 5 orders of magnitude higher than the perfect ones which satisfy photonic bandgap edge and quasi-phase matching. Moreover, the results reveal that conversion efficiencies of Fabry-Pérot cavities with non-periodic mirrors are one order of magnitude higher than those with periodic mirrors. The major physical mechanisms of the enhancement are quasi-phase matching effect, cavity effect induced by dispersive mirrors, and double resonance for the pump and the harmonic fields in defect state. We believe that this method is very beneficial to the design of high-efficient compact optical frequency converters.

Mode stabilization in quantum cascade lasers via an intra-cavity cascaded nonlinearity.

PubMed

St-Jean, M Renaudat; Amanti, M I; Bismuto, A; Beck, M; Faist, J; Sirtori, C

2017-02-06

We present self-stabilization of the inter-mode separation of a quantum cascade laser (QCL) emitting at 9 μm via cascaded second order nonlinearity. This effect has been observed in lasers that have the optical cavity embedded into a microwave strip-line. The intermodal beat note spectra narrow with increasing laser output power, up to less than 100 kHz. A flat frequency response to direct modulation up to 14 GHz is reported for these microstrip QCLs. The laser inter-mode spacing can be locked to an external RF signal and tuned by more than 1 MHz from the free-running spacing. A parallel study on the same laser material in a non-microstrip line waveguide shows superior performances of the microstrip QCL in terms of the intermodal spectral locking and stability. Finally by analyzing our results with the theory of the injection locking of coupled oscillators, we deduce that the microwave power injected in the microstrip QCL is 2 orders of magnitude higher than in the reference laser.

Solid-state reversible quadratic nonlinear optical molecular switch with an exceptionally large contrast.

PubMed

Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun

2013-08-14

Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Finite element analysis of hysteresis effects in piezoelectric transducers

NASA Astrophysics Data System (ADS)

Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard

2000-06-01

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

Decrease and enhancement of third-order optical nonlinearity in metal-dielectric composite films

NASA Astrophysics Data System (ADS)

Ning, Tingyin; Lu, Heng; Zhou, Yueliang; Man, Baoyuan

2018-04-01

We investigate third-order optical nonlinearity in gold nanoparticles embedded in CaCu3Ti4O12 (CCTO) films using the Z-scan method. We observe that the effective third-order nonlinear optical susceptibilities in such composite films can not only be enhanced, in line with the conventional behavior, but also be decreased, depending on the volume concentration of gold. In particular, the nonlinear absorption behavior can be changed from saturable absorption in pure CCTO films to reversed saturable absorption in composite films, and theoretically, even zero nonlinear absorption could be obtained. These results indicate that it should be possible to tune the third-order optical nonlinearity in Au:CCTO composite films by altering the gold concentration, thus making them suitable for applications in photonic devices.

Simulation of non-linear acoustic field and thermal pattern of phased-array high-intensity focused ultrasound (HIFU).

PubMed

Wang, Mingjun; Zhou, Yufeng

2016-08-01

HIFU becomes an effective and non-invasive modality of solid tumour/cancer ablation. Simulation of the non-linear acoustic wave propagation using a phased-array transducer in multiple layered media using different focusing strategies and the consequent lesion formation are essential in HIFU planning in order to enhance the efficacy and efficiency of treatment. An angular spectrum approach with marching fractional steps was applied in the wave propagation from phased-array HIFU transducer, and diffraction, attenuation, and non-linearity effects were accounted for by a second-order operator splitting scheme. The simulated distributions of the first three harmonics along and transverse to the transducer axis were compared to the hydrophone measurements. The bioheat equation was used to simulate the subsequent temperature elevation using the deposited acoustic energy, and lesion formation was determined by the thermal dose. Better agreement was found between the measured harmonics distribution and simulation using the proposed algorithm than the Khokhlov-Zabozotskaya-Kuznetsov equation. Variable focusing of the phased-array transducer (geometric focusing, transverse shifting and the generation of multiple foci) can be simulated successfully. The shifting and splitting of focus was found to result in significantly less temperature elevation at the focus and the subsequently, the smaller lesion size, but the larger grating lobe grating lobe in the pre-focal region. The proposed algorithm could simulate the non-linear wave propagation from the source with arbitrary shape and distribution of excitation through multiple tissue layers in high computation accuracy. The performance of phased-array HIFU can be optimised in the treatment planning.

Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir

2015-10-15

The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show thatmore » the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.« less

A method searching for optimum fractional order and its application in self-phase modulation induced nonlinear phase noise estimation in coherent optical fiber transmission systems

NASA Astrophysics Data System (ADS)

Huang, Chuan; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-07-01

In single channel systems, the nonlinear phase noise only comes from the channel itself through self-phase modulation (SPM). In this paper, a fast-nonlinear effect estimation method is proposed based on fractional Fourier transformation (FrFT). The nonlinear phase noise caused by Self-phase modulation effect is accurately estimated for single model 10Gbaud OOK and RZ-QPSK signals with the fiber length range of 0-200 km and the launch power range of 1-10 mW. The pulse windowing is adopted to search the optimum fractional order for the OOK and RZ-QPSK signals. Since the nonlinear phase shift caused by the SPM effect is very small, the accurate optimum fractional order of the signal cannot be found based on the traditional method. In this paper, a new method magnifying the phase shift is proposed to get the accurate optimum order and thus the nonlinear phase shift is calculated. The simulation results agree with the theoretical analysis and the method is applicable to signals whose pulse type has the similar characteristics with Gaussian pulse.

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

NASA Astrophysics Data System (ADS)

Wang, Liwei; Liu, Xinggao; Zhang, Zeyin

2017-02-01

An efficient primal-dual interior-point algorithm using a new non-monotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

2016-06-01

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

Nonlinear transient chirp signal modeling of the aortic and pulmonary components of the second heart sound.

PubMed

Xu, J; Durand, L G; Pibarot, P

2000-10-01

This paper describes a new approach based on the time-frequency representation of transient nonlinear chirp signals for modeling the aortic (A2) and the pulmonary (P2) components of the second heart sound (S2). It is demonstrated that each component is a narrow-band signal with decreasing instantaneous frequency defined by its instantaneous amplitude and its instantaneous phase. Each component is also a polynomial phase signal, the instantaneous phase of which can be accurately represented by a polynomial having an order of thirty. A dechirping approach is used to obtain the instantaneous amplitude of each component while reducing the effect of the background noise. The analysis-synthesis procedure is applied to 32 isolated A2 and 32 isolated P2 components recorded in four pigs with pulmonary hypertension. The mean +/- standard deviation of the normalized root-mean-squared error (NRMSE) and the correlation coefficient (rho) between the original and the synthesized signal components were: NRMSE = 2.1 +/- 0.3% and rho = 0.97 +/- 0.02 for A2 and NRMSE = 2.52 +/- 0.5% and rho = 0.96 +/- 0.02 for P2. These results confirm that each component can be modeled as mono-component nonlinear chirp signals of short duration with energy distributions concentrated along its decreasing instantaneous frequency.

Extending High-Order Flux Operators on Spherical Icosahedral Grids and Their Applications in the Framework of a Shallow Water Model

NASA Astrophysics Data System (ADS)

Zhang, Yi

2018-01-01

This study extends a set of unstructured third/fourth-order flux operators on spherical icosahedral grids from two perspectives. First, the fifth-order and sixth-order flux operators of this kind are further extended, and the nominally second-order to sixth-order operators are then compared based on the solid body rotation and deformational flow tests. Results show that increasing the nominal order generally leads to smaller absolute errors. Overall, the standard fifth-order scheme generates the smallest errors in limited and unlimited tests, although it does not enhance the convergence rate. Even-order operators show higher limiter sensitivity than the odd-order operators. Second, a triangular version of these high-order operators is repurposed for transporting the potential vorticity in a space-time-split shallow water framework. Results show that a class of nominally third-order upwind-biased operators generates better results than second-order and fourth-order counterparts. The increase of the potential enstrophy over time is suppressed owing to the damping effect. The grid-scale noise in the vorticity is largely alleviated, and the total energy remains conserved. Moreover, models using high-order operators show smaller numerical errors in the vorticity field because of a more accurate representation of the nonlinear Coriolis term. This improvement is especially evident in the Rossby-Haurwitz wave test, in which the fluid is highly rotating. Overall, high-order flux operators with higher damping coefficients, which essentially behave like the Anticipated Potential Vorticity Method, present better results.

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

PubMed

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

Nonlinear elastic effects on the energy flux deviation of ultrasonic waves in gr/ep composites

NASA Technical Reports Server (NTRS)

Prosser, William H.; Kriz, R. D.; Fitting, Dale W.

1992-01-01

The effects of nonlinear elasticity on energy flux deviation in undirectional gr/ep composites are examined. The shift in the flux deviation is modeled using acoustoelasticity theory and the second- and third-order elastic stiffness coefficients for T300/5208 gr/ep. Two conditions of applied uniaxial stress are considered. In the first case, the direction of applied uniaxial stress was along the fiber axis (x3), while in the second case it was perpendicular to the fiber axis along the laminate stacking direction (x1). For both conditions, the change in the energy flux deviation angle from the condition of zero applied stress is computed over the range of propagation directions of 0 to 60 deg from the fiber axis at two-degree intervals. A positive flux deviation angle implies the energy deviates away from the fiber direction toward the x1 axis, while a negative deviation means that the energy deviates toward the fibers. Over this range of fiber orientation angles, the energy of the quasi-longitudinal and pure mode transverse waves deviates toward the fibers, while that of the quasi-transverse mode deviates away from the fibers.

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Study of self-focusing of Non Gaussian laser beam in a plasma with density variation using moment theory approach

NASA Astrophysics Data System (ADS)

Pathak, Nidhi; Kaur, Sukhdeep; Singh, Sukhmander

2018-05-01

In this paper, self-focusing/defocusing effects have been studied by taking into account the combined effect of ponder-motive and relativistic non linearity during the laser plasma interaction with density variation. The formulation is based on the numerical analysis of second order nonlinear differential equation for appropriate set of laser and plasma parameters by employing moment theory approach. We found that self-focusing increases with increasing the laser intensity and density variation. The results obtained are valuable in high harmonic generation, inertial confinement fusion and charge particle acceleration.

Complete spatial and temporal locking in phase-mismatched second-harmonic generation.

PubMed

Fazio, Eugenio; Pettazzi, Federico; Centini, Marco; Chauvet, Mathieu; Belardini, Alessandro; Alonzo, Massimo; Sibilia, Concita; Bertolotti, Mario; Scalora, Micheal

2009-03-02

We experimentally demonstrate simultaneous phase and group velocity locking of fundamental and generated second harmonic pulses in Lithium Niobate, under conditions of material phase mismatch. In phase-mismatched, pulsed second harmonic generation in addition to a reflected signal two forward-propagating pulses are also generated at the interface between a linear and a second order nonlinear material: the first pulse results from the solution of the homogeneous wave equation, and propagates at the group velocity expected from material dispersion; the second pulse is the solution of the inhomogeneous wave equation, is phase-locked and trapped by the pump pulse, and follows the pump trajectory. At normal incidence, the normal and phase locked pulses simply trail each other. At oblique incidence, the consequences can be quite dramatic. The homogeneous pulse refracts as predicted by material dispersion and Snell's law, yielding at least two spatially separate second harmonic spots at the medium's exit. We thus report the first experimental results showing that, at oblique incidence, fundamental and phase-locked second harmonic pulses travel with the same group velocity and follow the same trajectory. This is direct evidence that, at least up to first order, the effective dispersion of the phase-locked pulse is similar to the dispersion of the pump pulse.

Device and method for generating a beam of acoustic energy from a borehole, and applications thereof

DOEpatents

Vu, Cung Khac; Sinha, Dipen N; Pantea, Cristian; Nihei, Kurt T; Schmitt, Denis P; Skelt, Christopher

2013-10-01

In some aspects of the invention, a method of generating a beam of acoustic energy in a borehole is disclosed. The method includes generating a first acoustic wave at a first frequency; generating a second acoustic wave at a second frequency different than the first frequency, wherein the first acoustic wave and second acoustic wave are generated by at least one transducer carried by a tool located within the borehole; transmitting the first and the second acoustic waves into an acoustically non-linear medium, wherein the composition of the non-linear medium produces a collimated beam by a non-linear mixing of the first and second acoustic waves, wherein the collimated beam has a frequency based upon a difference between the first frequency and the second frequency; and transmitting the collimated beam through a diverging acoustic lens to compensate for a refractive effect caused by the curvature of the borehole.

Measurement of the Acoustic Nonlinearity Parameter for Biological Media.

NASA Astrophysics Data System (ADS)

Cobb, Wesley Nelson

In vitro measurements of the acoustic nonlinearity parameter are presented for several biological media. With these measurements it is possible to predict the distortion of a finite amplitude wave in biological tissues of current diagnostic and research interest. The measurement method is based on the finite amplitude distortion of a sine wave that is emmitted by a piston source. The growth of the second harmonic component of this wave is measured by a piston receiver which is coaxial with and has the same size as the source. The experimental measurements and theory are compared in order to determine the nonlinearity parameter. The density, sound speed, and attenuation for the medium are determined in order to make this comparison. The theory developed for this study accounts for the influence of both diffraction and attenuation on the experimental measurements. The effects of dispersion, tissue inhomogeneity and gas bubbles within the excised tissues are studied. To test the measurement method, experimental results are compared with established values for the nonlinearity parameter of distilled water, ethylene glycol and glycerol. The agreement between these values suggests that the measurement uncertainty is (+OR-) 5% for liquids and (+OR-) 10% for solid tissues. Measurements are presented for dog blood and bovine serum albumen as a function of concentration. The nonlinearity parameters for liver, kidney and spleen are reported for both human and canine tissues. The values for the fresh tissues displayed little variation (6.8 to 7.8). Measurements for fixed, normal and cirrhotic tissues indicated that the nonlinearity parameter does not depend strongly on pathology. However, the values for fixed tissues were somewhat higher than those of the fresh tissues.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

Experimental and numerical analysis of pre-compressed masonry walls in two-way-bending with second order effects

NASA Astrophysics Data System (ADS)

Milani, Gabriele; Olivito, Renato S.; Tralli, Antonio

2014-10-01

The buckling behavior of slender unreinforced masonry (URM) walls subjected to axial compression and out-of-plane lateral loads is investigated through a combined experimental and numerical homogenizedapproach. After a preliminary analysis performed on a unit cell meshed by means of elastic FEs and non-linear interfaces, macroscopic moment-curvature diagrams so obtained are implemented at a structural level, discretizing masonry by means of rigid triangular elements and non-linear interfaces. The non-linear incremental response of the structure is accounted for a specific quadratic programming routine. In parallel, a wide experimental campaign is conducted on walls in two way bending, with the double aim of both validating the numerical model and investigating the behavior of walls that may not be reduced to simple cantilevers or simply supported beams. Panels investigated are dry-joint in scale square walls simply supported at the base and on a vertical edge, exhibiting the classical Rondelet's mechanism. The results obtained are compared with those provided by the numerical model.

Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback

NASA Astrophysics Data System (ADS)

You, Xiang; Li, Zongyang; Li, Yongmin

2017-12-01

A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.

Rogue waves for a discrete (2+1)-dimensional Ablowitz-Ladik equation in the nonlinear optics and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Du, Zhong

2018-03-01

Under investigation in this paper is a discrete (2+1)-dimensional Ablowitz-Ladik equation, which is used to model the nonlinear waves in the nonlinear optics and Bose-Einstein condensation. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue wave solutions in terms of the Gramian. We graphically study the first-, second- and third-order rogue waves with the influence of the focusing coefficient and coupling strength. When the value of the focusing coefficient increases, both the peak of the rogue wave and background decrease. When the value of the coupling strength increases, the rogue wave raises and decays in a shorter time. High-order rogue waves are exhibited as one single highest peak and some lower humps, and such lower humps are shown as the triangular and circular patterns.

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Stabilization Approaches for Linear and Nonlinear Reduced Order Models

NASA Astrophysics Data System (ADS)

Rezaian, Elnaz; Wei, Mingjun

2017-11-01

It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.

Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

NASA Technical Reports Server (NTRS)

Hodges, D. H.; Dowell, E. H.

1974-01-01

The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.

Studies of third-order optical nonlinearities and optical limiting properties of azo dyes.

PubMed

Gayathri, C; Ramalingam, A

2008-03-01

In order to protect optical sensors and human eyes from debilitating laser effects, the intensity of the incoming laser light has to be opportunely reduced. Here, we report our results on the third-order optical nonlinearity and optical limiting properties of three azo dyes exposed to a 532nm continuous wave laser. We have observed low power optical limiting based on nonlinear refraction in our samples.

Secondary Instability of Second Modes in Hypersonic Boundary Layers

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2012-01-01

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

Modulation instability induced by cross-phase modulation with higher-order dispersions and cubic-quintic nonlinearities in metamaterials

NASA Astrophysics Data System (ADS)

Yu, Chuanxi; Xue, Yan Ling; Liu, Ying

2014-07-01

Based on the dispersive Drude model in metamaterials (MMs), coupled nonlinear Schodinger equations are derived for two co-propagating optical waves with higher-order dispersions and cubic-quintic nonlinearities. And modulation instabilities induced by the cross -phase modulation (XMI) are studied. The impact of 3rd-, 4th-order of dispersion and quintic nonlinearity on the gain spectra of XMI is analyzed. It is shown that the 3rd-order dispersion has no effect on XMI and its gain spectra. With the increment of 4th-order dispersion, the gain spectra appear in higher frequency region (2nd spectrum region) and gain peaks become smaller.

Wave Propagation in Second-order Nonlinear Piezoelectric Media

DTIC Science & Technology

2011-09-01

the theory of invariants, from invariant polynomial constitutive relations, Yang and Batra (23) investigated the second-order theory for piezoelectric...29, 30). Several commonly used transformation are shown in table 1. Yang and Batra (31) used a set of transformations that are very different from... Yang /Batra (31) DA = JF−1Aa D̂a EA = JF −1 Aa Êa ΠA = JF −1 Aa P̂a Dorfmann/Ogden (29) DA = JF−1Aa D̂a EA = FaAÊa ΠA = JF −1 Aa P̂a Clayton (30) DA

Chaos without nonlinear dynamics.

PubMed

Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

2006-07-14

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

Nonlinear Optical Properties of Traditional and Novel Materials

NASA Astrophysics Data System (ADS)

Krupa, Sean J.

Nonlinear optical processes are an excellent candidate to provide the heralded, indistinguishable, or entangled photons necessary for development of quantum mechanics based technology which currently lack bright sources of these photons. In order to support these technologies, and others, two classes of materials: traditional and novel, were investigated via optical characterization methods with goal of gaining insight into which materials and experimental conditions yield the greatest nonlinear optical effects. Optical characterization of periodically poled lithium niobate (PPLN) helped support the development of a simple, efficient photon pair source that could be easily integrated into optical networks. Additionally, an in-situ measurement of the 2nd order nonlinear optical coefficient was developed to aid in the characterization of PPLN pair sources. Lastly, an undergraduate demonstration of quantum key distribution was constructed such that students could see the primary application for PPLN photon pair sources in an affordable, approachable demonstration. A class of novel optical materials known as 2D materials has been identified as potential replacements to the traditional nonlinear optical materials discussed in Part I. Through optical characterization of second harmonic generation (SHG) the ideal conditions for spontaneous parametric downconversion were established as well as signal thresholds for successful detection. Attempts to observe SPDC produces hints that weak generate SPDC may be present in WS2 samples however this is incredibly difficult to confirm. As growth techniques of 2D materials improve, a photonic device constructed from these materials may be possible, however it will need some mechanism e.g. stacking, a cavity, etc. to help enhance the SPDC signal.