Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1975-01-01

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

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.

New Materials Directions for the Realization of Ultra-High Performance 3rd Order Non-Linear Optical Organics

DTIC Science & Technology

2015-03-13

Nowacki, H.S. Oh, C. Zanlorenzi, H.S. Jee, A. Baev, P.N. Prasad, and L. Akcelrud, "Design and synthesis of polymers for chiral photonics ...rationally design and create organic materials with high nonlinear refractive index and low single· and two- photon absorption at wavelengths relevant to...can also enhance 3rd-order NLO response through microscopic cascading of 2nd-order nonlinearity. Chiral control of nonlinearity bas also been

Enhanced nonlinear optical response of an endohedral metallofullerene through metal-to-cage charge transfer

NASA Astrophysics Data System (ADS)

Heflin, J. R.; Marciu, D.; Figura, C.; Wang, S.; Burbank, P.; Stevenson, S.; Dorn, H. C.

1998-06-01

A new mechanism for increasing the third-order nonlinear optical susceptibility, χ(3), is described for endohedral metallofullerenes. A two to three orders of magnitude increase in the nonlinear response is reported for degenerate four-wave mixing experiments conducted with solutions of Er2@C82 (isomer III) relative to empty-cage fullerenes. A value of -8.7×10-32esu is found for the molecular susceptibility, γxyyx, of Er2@C82 compared to previously reported values of γxxxx=3×10-34 esu and γxyyx=4×10-35 esu for C60. The results confirm the importance of the metal-to-cage charge-transfer mechanism for enhancing the nonlinear optical response in endohedral metallofullerenes.

Resonant third-order optical nonlinearities of thin films containing J-aggregates of a cyanine dye or a squarylium dye

NASA Astrophysics Data System (ADS)

Li, Zhongyu; Jin, Zhaohui; Kasatani, Kazuo

2005-01-01

The third-order optical nonlinearities and responses of thin films containing the J-aggregates of a cyanine dye or a squarylium dye were measured using the degenerate four-wave mixing (DFWM) technique under resonant conditions. The sol-gel silica coating films containing the J-aggregates of the cyanine dye, NK-3261, are stable at room temperature and durable against laser beam irradiation. The temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of at least three components, i.e., the coherent instantaneous nonlinear response and the two slow responses with delay time constants of ca. 1.0 ps and ca. 5.6 ps. The contribution of the later was small. The electronic component of the effective third-order optical nonlinear susceptibility of the film had value of as high as ca. 3.0 x 10-7 esu. We also studied the neat film of a squarylium dye J-aggregates. The temporal profile of the DFWM signal of the neat film of squarylium dye was also found to consist of at least three components, the coherent instantaneous nonlinear response and the delayed response with decay time constants of ca. 0.6 ps and ca. 6.5 ps. The contribution of the slow tail was also very small. The electronic component of effective third-order optical nonlinear susceptibility of the neat film of squarylium dye had value of as high as ca. 3.6 x 10-8 esu.

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.

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.

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.

Coherent source interaction, third-order nonlinear response of synthesized PEG coated magnetite nanoparticles in polyethylene glycol and its application

NASA Astrophysics Data System (ADS)

Gopal, S. Veena; Chitrambalam, S.; Joe, I. Hubert

2018-01-01

Third-order nonlinear response of synthesized polyethylene glycol coated Fe3O4 nanoparticles dispersed in a suitable solvent, polyethylene glycol has been studied. The structural characterization of the synthesized magnetite nanoparticles were carried out. The linear optical property of the synthesized magnetite nanoparticles was investigated using UV-visible technique. Both closed and open aperture Z-scan techniques have been performed at 532 nm with pulse width 5 ns and repetition rate 10 Hz. It was found that polyethylene glycol coated magnetite exhibits reverse saturable absorption, with significant nonlinear absorption coefficient. Two-photon absorption intensity dependent positive nonlinear refraction coefficients indicate self focusing phenomena. Results show that higher concentration gives better nonlinear and optical limiting properties.

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2006-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2005-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

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.

Jump Resonance in Fractional Order Circuits

NASA Astrophysics Data System (ADS)

Buscarino, Arturo; Caponetto, Riccardo; Famoso, Carlo; Fortuna, Luigi

The occurrence of an hysteretic loop in the frequency response of a driven nonlinear system is a phenomenon deeply investigated in nonlinear control theory. Such a phenomenon, which is linked to the multistable behavior of the system, is called jump resonance, since the magnitude of the frequency response is subjected to an abrupt jump up/down with respect to the increasing/decreasing of the frequency of the driving signal. In this paper, we aim at investigating fractional order nonlinear systems showing jump resonance, that is systems in which the order of the derivative is noninteger and their frequency response has a magnitude that is a multivalued function in a given range of frequencies. Furthermore, a strategy for designing fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows one to assess that the phenomenon is robust to the difference in the derivative order, enlightening the first example of a system with order lower than two which is able to demonstrate a jump resonance behavior.

Periodic response of nonlinear systems

NASA Technical Reports Server (NTRS)

Nataraj, C.; Nelson, H. D.

1988-01-01

A procedure is developed to determine approximate periodic solutions of autonomous and non-autonomous systems. The trignometric collocation method (TCM) is formalized to allow for the analysis of relatively small order systems directly in physical coordinates. The TCM is extended to large order systems by utilizing modal analysis in a component mode synthesis strategy. The procedure was coded and verified by several check cases. Numerical results for two small order mechanical systems and one large order rotor dynamic system are presented. The method allows for the possibility of approximating periodic responses for large order forced and self-excited nonlinear systems.

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

Recent Applications of Higher-Order Spectral Analysis to Nonlinear Aeroelastic Phenomena

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Hajj, Muhammad R.; Dunn, Shane; Strganac, Thomas W.; Powers, Edward J.; Stearman, Ronald

2005-01-01

Recent applications of higher-order spectral (HOS) methods to nonlinear aeroelastic phenomena are presented. Applications include the analysis of data from a simulated nonlinear pitch and plunge apparatus and from F-18 flight flutter tests. A MATLAB model of the Texas A&MUniversity s Nonlinear Aeroelastic Testbed Apparatus (NATA) is used to generate aeroelastic transients at various conditions including limit cycle oscillations (LCO). The Gaussian or non-Gaussian nature of the transients is investigated, related to HOS methods, and used to identify levels of increasing nonlinear aeroelastic response. Royal Australian Air Force (RAAF) F/A-18 flight flutter test data is presented and analyzed. The data includes high-quality measurements of forced responses and LCO phenomena. Standard power spectral density (PSD) techniques and HOS methods are applied to the data and presented. The goal of this research is to develop methods that can identify the onset of nonlinear aeroelastic phenomena, such as LCO, during flutter testing.

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.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients.

PubMed

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A Ryan; Belyanin, Alexey; Raschke, Markus B

2018-05-18

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2ω_{1}-ω_{2} four-wave mixing response as a function of detuning ω_{1}-ω_{2}, we find up to 10^{-5} conversion efficiency with a gradient-field contribution to χ_{Au}^{(3)} of up to 10^{-19}  m^{2}/V^{2}. The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients

NASA Astrophysics Data System (ADS)

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A. Ryan; Belyanin, Alexey; Raschke, Markus B.

2018-05-01

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2 ω1-ω2 four-wave mixing response as a function of detuning ω1-ω2, we find up to 10-5 conversion efficiency with a gradient-field contribution to χAu(3 ) of up to 10-19 m2/V2 . The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

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

NASA Astrophysics Data System (ADS)

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

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

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

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.

Alternative Modal Basis Selection Procedures for Nonlinear Random Response Simulation

NASA Technical Reports Server (NTRS)

Przekop, Adam; Guo, Xinyun; Rizzi, Stephen A.

2010-01-01

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of the three reduced-order analyses are compared with the results of the computationally taxing simulation in the physical degrees of freedom. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Fast novel nonlinear optical NLC system with local response

NASA Astrophysics Data System (ADS)

Iljin, Andrey; Residori, Stefania; Bortolozzo, Umberto

2017-06-01

Nonlinear optical performance of a novel liquid crystalline (LC) cell has been studied in two-wave mixing experiments revealing high diffraction efficiency within extremely wide intensity range, fast recording times and spatial resolution. Photo-induced modulation of the LC order parameter resulting from trans-cis isomerisation of dye molecules causes consequent changes of refractive indices of the medium (Light-Induced Order Modification, LIOM-mechanism) and is proved to be the main mechanism of optical nonlinearity. The proposed arrangement of the electric-field-stabilised homeotropic alignment hinders the LC director reorientation, prevents appearance of surface effects and ensures the optical cell quality. The LIOM-type nonlinearity, characterised with the substantially local nonlinear optical response, could also be extended for the recording of arbitrary phase profiles as requested in several applications for light-beam manipulation, recording of dynamic volume holograms and photonic lattices.

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.

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

NASA Astrophysics Data System (ADS)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

Bandlimited computerized improvements in characterization of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2016-05-01

The present article discusses some inroads 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 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system 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 in order to combat and reasonably alleviate the curse of dimensionality.

Mixed higher-order flow harmonics and nonlinear response coefficients in PbPb collisions at 2.76 and 5.02 TeV with CMS

NASA Astrophysics Data System (ADS)

Tuo, Shengquan; CMS Collaboration

2017-11-01

The mixed higher-order flow harmonics and nonlinear response coefficients of charged particles are presented as a function of pT and centrality in PbPb collisions at √{sNN} = 2.76 TeV and 5.02 TeV with the CMS detector. The results are obtained using the scalar product method, and cover a pT range from 0.3 GeV/c to 8.0 GeV/c, pseudorapidity | η | < 2.4, and a centrality range of 0-60%. The mixed harmonic results at 5.02 TeV are compared to the matching higher-order flow harmonics from two-particle correlations, which measure vn values with respect to the n-th order event plane. It is observed that the nonlinear response coefficients of the odd harmonics are larger than the even harmonics ones. The results are compared with hydrodynamic predictions using different shear viscosity to entropy density ratios and different initial conditions.

Analysis of tristable energy harvesting system having fractional order viscoelastic material

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

Oumbé Tékam, G. T.; Woafo, P.; Kitio Kwuimy, C. A.

2015-01-15

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the systemmore » response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.« less

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

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.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

Enhancing light-atom interactions via atomic bunching

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2014-07-01

There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives measured by resonant femtosecond degenerate four-wave mixing technique

NASA Astrophysics Data System (ADS)

Kasatani, Kazuo; Okamoto, Hiroaki; Takenaka, Shunsuke

2003-11-01

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several to several hundred ps. The latter can be attributed to population grating of an excited state, and contribution of slow component was very little for a zinc porphyrin derivative. The values of electronic component of the optical nonlinear susceptibility, χ(3) xxxx, for these films were ca. 2 x 10-10 esu.

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.

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.

β-Octakis(methylthio)porphycenes: synthesis, characterisation and third order nonlinear optical studies.

PubMed

Rana, Anup; Lee, Sangsu; Kim, Dongho; Panda, Pradeepta K

2015-05-04

A novel electron deficient β-octakis(methylthio)porphycene, along with its Zn(ii) and Ni(ii) derivatives, was synthesized for the first time. The macrocyclic structure exhibits core ruffling with a largely red shifted absorption band (∼750 nm) and also a large enhancement in the third order nonlinear optical response.

Blind identification of nonlinear models with non-Gaussian inputs

NASA Astrophysics Data System (ADS)

Prakriya, Shankar; Pasupathy, Subbarayan; Hatzinakos, Dimitrios

1995-12-01

Some methods are proposed for the blind identification of finite-order discrete-time nonlinear models with non-Gaussian circular inputs. The nonlinear models consist of two finite memory linear time invariant (LTI) filters separated by a zero-memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI models). The linear subsystems are allowed to be of non-minimum phase (NMP). The methods base their estimates of the impulse responses on slices of the N plus 1th order polyspectra of the output sequence. It is shown that the identification of LTI-ZMNL systems requires only a 1-D moment or polyspectral slice. The coefficients of the ZMNL are not estimated, and need not be known. The order of the nonlinearity can, in theory, be estimated from the received signal. These methods possess several noise and interference suppression characteristics, and have applications in modeling nonlinearly amplified QAM/QPSK signals in digital satellite and microwave communications.

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.

Nonequilibrium response of an electron-mediated charge density wave ordered material to a large dc electric field

NASA Astrophysics Data System (ADS)

Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

2016-01-01

Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

NASA Technical Reports Server (NTRS)

Harstad, K. G.; Strand, L. D.

1987-01-01

An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

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 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.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Extrinsic Contribution and Instability Properties in Lead-Based and Lead-Free Piezoceramics

PubMed Central

García, José Eduardo

2015-01-01

Piezoceramic materials generally exhibit a notable instability of their functional properties when they work under real external conditions. This undesirable effect, known as nonlinear behavior, is mostly associated with the extrinsic contribution to material response. In this article, the role of the ferroelectric domain walls’ motion in the nonlinear response in the most workable lead-based and lead-free piezoceramics is reviewed. Initially, the extrinsic origin of the nonlinear response is discussed in terms of the temperature dependence of material response. The influence of the crystallographic phase and of the phase boundaries on the material response are then reviewed. Subsequently, the impact of the defects created by doping in order to control the extrinsic contribution is discussed as a way of tuning material properties. Finally, some aspects related to the grain-size effect on the nonlinear response of piezoceramics are surveyed. PMID:28793681

Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

NASA Astrophysics Data System (ADS)

Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

2018-06-01

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

Method for conducting nonlinear electrochemical impedance spectroscopy

DOEpatents

Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.

2015-06-02

A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

Large electronic third-order optical nonlinearities of cyanine dyes measured by resonant femtosecond degenerate four-wave mixing

NASA Astrophysics Data System (ADS)

Kasatani, Kazuo

2003-01-01

Third-order optical nonlinearities of several cyanine dyes were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of at least two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several hundred picoseconds. The latter can be attributed to molecular rotational relaxation of these dyes. The values of electronic component of the optical nonlinear susceptibility, χ e xxxx (3), for these dyes were ≈2×10 -12 esu at the very low concentration of 1×10 -5 mol dm -3. The electronic component of molecular hyperpolarizability, γe, was calculated to be ≈1×10 -28 esu for each dye.

Thermo-optical properties and nonlinear optical response of smectic liquid crystals containing gold nanoparticles.

PubMed

de Melo, P B; Nunes, A M; Omena, L; do Nascimento, S M S; da Silva, M G A; Meneghetti, M R; de Oliveira, I N

2015-10-01

The present work is devoted to the study of the thermo-optical and nonlinear optical properties of smectic samples containing gold nanoparticles with different shapes. By using the time-resolved Z-scan technique, we determine the effects of nanoparticle addition on the critical behavior of the thermal diffusivity and thermo-optical coefficient at the vicinity of the smectic-A-nematic phase transition. Our results reveal that introduction of gold nanoparticles affects the temperature dependence of thermo-optical parameters, due to the local distortions in the orientational order and heat generation provided by guest particles during the laser exposure. Further, we show that a nonlinear optical response may take place at temperatures where the smectic order is well established. We provide a detailed discussion of the effects associated with the introduction gold nanoparticles on the mechanisms behind the thermal transport and optical nonlinearity in liquid-crystal samples.

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.

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 multilayers as optical limiters

NASA Astrophysics Data System (ADS)

Turner-Valle, Jennifer Anne

1998-10-01

In this work we present a non-iterative technique for computing the steady-state optical properties of nonlinear multilayers and we examine nonlinear multilayer designs for optical limiters. Optical limiters are filters with intensity-dependent transmission designed to curtail the transmission of incident light above a threshold irradiance value in order to protect optical sensors from damage due to intense light. Thin film multilayers composed of nonlinear materials exhibiting an intensity-dependent refractive index are used as the basis for optical limiter designs in order to enhance the nonlinear filter response by magnifying the electric field in the nonlinear materials through interference effects. The nonlinear multilayer designs considered in this work are based on linear optical interference filter designs which are selected for their spectral properties and electric field distributions. Quarter wave stacks and cavity filters are examined for their suitability as sensor protectors and their manufacturability. The underlying non-iterative technique used to calculate the optical response of these filters derives from recognizing that the multi-valued calculation of output irradiance as a function of incident irradiance may be turned into a single-valued calculation of incident irradiance as a function of output irradiance. Finally, the benefits and drawbacks of using nonlinear multilayer for optical limiting are examined and future research directions are proposed.

Transmission Measurement of the Third-Order Susceptibility of Gold

NASA Technical Reports Server (NTRS)

Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Crooks, Richard M.; George, Michael

1999-01-01

Gold nanoparticle composites are known to display large optical nonlinearities. In order to assess the validity of generalized effective medium theories (EMT's) for describing the linear and nonlinear optical properties of metal nanoparticle composites, knowledge of the linear and nonlinear susceptibilities of the constituent materials is a prerequisite. In this study the inherent nonlinearity of the metal is measured directly (rather than deduced from a suitable EMT) using a very thin gold film. Specifically, we have used the z-scan technique at a wavelength near the transmission window of bulk gold to measure the third-order susceptibility of a continuous thin gold film deposited on a quartz substrate surface-modified with a self-assembled monolayer to promote adhesion and uniformity without affecting the optical properties. We compare our results with predictions which ascribe the nonlinear response to a Fermi-smearing mechanism. Further, we note that the sign of the nonlinear susceptibility is reversed from that of gold nanoparticle composites.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

NASA Astrophysics Data System (ADS)

Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

Robust fast controller design via nonlinear fractional differential equations.

PubMed

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

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

Application of Nonlinear Elastic Resonance Spectroscopy For Damage Detection In Concrete: An Interesting Story

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

Byers, Loren W.; Ten Cate, James A.; Johnson, Paul A.

2012-06-28

Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately,more » nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.« less

POD/MAC-Based Modal Basis Selection for a Reduced Order Nonlinear Response Analysis

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2007-01-01

A feasibility study was conducted to explore the applicability of a POD/MAC basis selection technique to a nonlinear structural response analysis. For the case studied the application of the POD/MAC technique resulted in a substantial improvement of the reduced order simulation when compared to a classic approach utilizing only low frequency modes present in the excitation bandwidth. Further studies are aimed to expand application of the presented technique to more complex structures including non-planar and two-dimensional configurations. For non-planar structures the separation of different displacement components may not be necessary or desirable.

Study of nonlinear refraction of organic dye by Z-scan technique using He-Ne laser

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

Medhekar, S.; Kumar, R.; Mukherjee, S.

2013-02-05

Laser induced third-order nonlinear optical responses of Brilliant Green solution has been investigated by utilizing single beam Z-scan technique with a continuous-wave He-Ne laser radiation at 632.8 nm. It was observed that the material exhibits self-defocusing type optical nonlinearity. The measurements of nonlinear refraction were carried out at different dye concentrations and found that the increase in solution concentration leads to the linear increase of the nonlinear refractive index. The experimental results confirm great potential of the Brilliant Green for the application in nonlinear optical devices.

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.

Separating higher-order nonlinearities in transient absorption microscopy

NASA Astrophysics Data System (ADS)

Wilson, Jesse W.; Anderson, Miguel; Park, Jong Kang; Fischer, Martin C.; Warren, Warren S.

2015-08-01

The transient absorption response of melanin is a promising optically-accessible biomarker for distinguishing malignant melanoma from benign pigmented lesions, as demonstrated by earlier experiments on thin sections from biopsied tissue. The technique has also been demonstrated in vivo, but the higher optical intensity required for detecting these signals from backscattered light introduces higher-order nonlinearities in the transient response of melanin. These components that are higher than linear with respect to the pump or the probe introduce intensity-dependent changes to the overall response that complicate data analysis. However, our data also suggest these nonlinearities might be advantageous to in vivo imaging, in that different types of melanins have different nonlinear responses. Therefore, methods to separate linear from nonlinear components in transient absorption measurements might provide additional information to aid in the diagnosis of melanoma. We will discuss numerical methods for analyzing the various nonlinear contributions to pump-probe signals, with the ultimate objective of real time analysis using digital signal processing techniques. To that end, we have replaced the lock-in amplifier in our pump-probe microscope with a high-speed data acquisition board, and reprogrammed the coprocessor field-programmable gate array (FPGA) to perform lock-in detection. The FPGA lock-in offers better performance than the commercial instrument, in terms of both signal to noise ratio and speed. In addition, the flexibility of the digital signal processing approach enables demodulation of more complicated waveforms, such as spread-spectrum sequences, which has the potential to accelerate microscopy methods that rely on slow relaxation phenomena, such as photo-thermal and phosphorescence lifetime imaging.

Nonlinear response of a harmonic diatomic molecule: Algebraic nonperturbative calculation

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

Recamier, Jose; Mochan, W. Luis; Maytorena, Jesus A.

2005-08-15

Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We calculate the response of single harmonic molecules to a monochromatic time and space dependent electric field E(r,t) of frequency {omega} employing exact algebraic methods. We evaluate the responses at the fundamental frequency {omega} and at successive harmonics 2{omega}, 3{omega}, etc., as a function of the intensity and of the frequency of the field and compare the results with those of first and second order perturbation theory.

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.

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.

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.

Nonlinear optical behavior of DNA-functionalized gold nanoparticles

NASA Astrophysics Data System (ADS)

Kulyk, B.; Krupka, O.; Smokal, V.; Figà, V.; Czaplicki, R.; Sahraoui, B.

2018-03-01

The third-order nonlinear optical properties of gold nanoparticles embedded in the DNA-based composites were investigated by means of the third harmonic generation. With this purpose, the thin films comprising DNA-based complexes and Au nanoparticles were spin-deposited on glass substrate and their optical and nonlinear optical features were studied using the Maker-fringe technique at a laser fundamental wavelength of 1064 nm. The values of the third-order susceptibility χ (3)(- 3ω; ω, ω, ω) of the composite films based on DNA complex doped with 5 wt% of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo)aniline were found to be significantly higher than those for pure composite films. Meanwhile, the presence of Au nanoparticles noticeable decreases the third-order nonlinear response of DNA-based composite mainly due to the enhanced absorption and scattering of laser and generated beam, respectively.

Anisotropy in Third-Order Nonlinear Optical Susceptibility of a Squarylium Dye in a Nematic Liquid Crystal

NASA Astrophysics Data System (ADS)

Jin, Zhao-Hui; Li, Zhong-Yu; Kasatani, Kazuo; Okamoto, Hiroaki

2006-03-01

A squarylium dye is dissolved in 4-cyano-4'-pentylbiphenyl (5CB) and oriented by sandwiching mixtures between two pieces of rubbed glass plates. The optical absorption spectra of the oriented squarylium dye-5CB layers exhibit high anisotropy. The third-order nonlinear optical responses and susceptibilities χ(3)e of squarylium dye in 5CB are measured with light polarizations parallel and perpendicular to the orientational direction by the resonant femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal of the oriented squarylium dye-5CB layers with light polarizations parallel and perpendicular to the orientational direction are measured with a time resolution of 0.3 ps (FWHM), and are found to consist of two components, i.e., the coherent instantaneous nonlinear response and slow response due to the formation of excited molecules. A high anisotropic ratio of χ(3)e, 10.8±1.2, is observed for the oriented layers.

Transient response of nonlinear magneto-optic rotation in a paraffin-coated Rb vapor cell

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

Momeen, M. Ummal; Rangarajan, G.; Natarajan, Vasant

2010-01-15

We study resonant nonlinear magneto-optic rotation (NMOR) in a paraffin-coated Rb vapor cell as the magnetic field is swept. At low sweep rates, the nonlinear rotation appears as a narrow resonance signal with a linewidth of about '300 muG' (2pix420 Hz). At high sweep rates, the signal shows transient response with an oscillatory decay. The decay time constant is of order 100 ms. The behavior is different for transitions starting from the lower or the upper hyperfine level of the ground state because of optical pumping effects.

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.

Nonlinear Terahertz Absorption of Graphene Plasmons.

PubMed

Jadidi, Mohammad M; König-Otto, Jacob C; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin

2016-04-13

Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump-terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing.

Recent Applications of the Volterra Theory to Aeroelastic Phenomena

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Haji, Muhammad R; Prazenica, Richard J.

2005-01-01

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in experimental aeroelasticity are reviewed. These results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the Active Aeroelastic Wing (AAW) aircraft.

Implementation of Improved Transverse Shear Calculations and Higher Order Laminate Theory Into Strain Rate Dependent Analyses of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Zhu, Lin-Fa; Kim, Soo; Chattopadhyay, Aditi; Goldberg, Robert K.

2004-01-01

A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

NASA Astrophysics Data System (ADS)

Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

2018-04-01

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

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.

Irrationality and Quasiperiodicity in Driven Nonlinear Systems

NASA Astrophysics Data System (ADS)

Cubero, David; Casado-Pascual, Jesús; Renzoni, Ferruccio

2014-05-01

We analyze the relationship between irrationality and quasiperiodicity in nonlinear driven systems. To that purpose, we consider a nonlinear system whose steady-state response is very sensitive to the periodic or quasiperiodic character of the input signal. In the infinite time limit, an input signal consisting of two incommensurate frequencies will be recognized by the system as quasiperiodic. We show that this is, in general, not true in the case of finite interaction times. An irrational ratio of the driving frequencies of the input signal is not sufficient for it to be recognized by the nonlinear system as quasiperiodic, resulting in observations which may differ by several orders of magnitude from the expected quasiperiodic behavior. Thus, the system response depends on the nature of the irrational ratio, as well as the observation time. We derive a condition for the input signal to be identified by the system as quasiperiodic. Such a condition also takes into account the sub-Fourier response of the nonlinear system.

Optical Kerr effect in graphene: Theoretical analysis of the optical heterodyne detection technique

NASA Astrophysics Data System (ADS)

Savostianova, N. A.; Mikhailov, S. A.

2018-04-01

Graphene is an atomically thin two-dimensional material demonstrating strong optical nonlinearities, including harmonics generation, four-wave mixing, Kerr, and other nonlinear effects. In this paper we theoretically analyze the optical heterodyne detection (OHD) technique of measuring the optical Kerr effect (OKE) in two-dimensional crystals and show how to relate the quantities measured in such experiments with components of the third-order conductivity tensor σαβ γ δ (3 )(ω1,ω2,ω3) of the two-dimensional crystal. Using results of a recently developed quantum theory of the third-order nonlinear electrodynamic response of graphene, we analyze the frequency, charge carrier density, temperature, and other dependencies of the OHD-OKE response of this material. We compare our results with a recent OHD-OKE experiment in graphene and find good agreement between the theory and experiment.

Non-destructive testing techniques based on nonlinear methods for assessment of debonding in single lap joints

NASA Astrophysics Data System (ADS)

Scarselli, G.; Ciampa, F.; Ginzburg, D.; Meo, M.

2015-04-01

Nonlinear ultrasonic non-destructive evaluation (NDE) methods can be used for the identification of defects within adhesive bonds as they rely on the detection of nonlinear elastic features for the evaluation of the bond strength. In this paper the nonlinear content of the structural response of a single lap joint subjected to ultrasonic harmonic excitation is both numerically and experimentally evaluated to identify and characterize the defects within the bonded region. Different metallic samples with the same geometry were experimentally tested in order to characterize the debonding between two plates by using two surface bonded piezoelectric transducers in pitch-catch mode. The dynamic response of the damaged samples acquired by the single receiver sensor showed the presence of higher harmonics (2nd and 3rd) and subharmonics of the fundamental frequencies. These nonlinear elastic phenomena are clearly due to nonlinear effects induced by the poor adhesion between the two plates. A new constitutive model aimed at representing the nonlinear material response generated by the interaction of the ultrasonic waves with the adhesive joint is also presented. Such a model is implemented in an explicit FE software and uses a nonlinear user defined traction-displacement relationship implemented by means of a cohesive material user model interface. The developed model is verified for the different geometrical and material configurations. Good agreement between the experimental and numerical nonlinear response showed that this model can be used as a simple and useful tool for understanding the quality of the adhesive joint.

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Complex motor task associated with non-linear BOLD responses in cerebro-cortical areas and cerebellum.

PubMed

Alahmadi, Adnan A S; Samson, Rebecca S; Gasston, David; Pardini, Matteo; Friston, Karl J; D'Angelo, Egidio; Toosy, Ahmed T; Wheeler-Kingshott, Claudia A M

2016-06-01

Previous studies have used fMRI to address the relationship between grip force (GF) applied to an object and BOLD response. However, whilst the majority of these studies showed a linear relationship between GF and neural activity in the contralateral M1 and ipsilateral cerebellum, animal studies have suggested the presence of non-linear components in the GF-neural activity relationship. Here, we present a methodology for assessing non-linearities in the BOLD response to different GF levels, within primary motor as well as sensory and cognitive areas and the cerebellum. To be sensitive to complex forms, we designed a feasible grip task with five GF targets using an event-related visually guided paradigm and studied a cohort of 13 healthy volunteers. Polynomial functions of increasing order were fitted to the data. (1) activated motor areas irrespective of GF; (2) positive higher-order responses in and outside M1, involving premotor, sensory and visual areas and cerebellum; (3) negative correlations with GF, predominantly involving the visual domain. Overall, our results suggest that there are physiologically consistent behaviour patterns in cerebral and cerebellar cortices; for example, we observed the presence of a second-order effect in sensorimotor areas, consistent with an optimum metabolic response at intermediate GF levels, while higher-order behaviour was found in associative and cognitive areas. At higher GF levels, sensory-related cortical areas showed reduced activation, interpretable as a redistribution of the neural activity for more demanding tasks. These results have the potential of opening new avenues for investigating pathological mechanisms of neurological diseases.

Enhancing the nonlinear thermoelectric response of a correlated quantum dot in the Kondo regime by asymmetrical coupling to the leads

NASA Astrophysics Data System (ADS)

Pérez Daroca, Diego; Roura-Bas, Pablo; Aligia, Armando A.

2018-04-01

We study the low-temperature properties of the differential response of the current to a temperature gradient at finite voltage in a single-level quantum dot including electron-electron interaction, nonsymmetric couplings to the leads, and nonlinear effects. The calculated response is significantly enhanced in setups with large asymmetries between the tunnel couplings. In the investigated range of voltages and temperatures with corresponding energies up to several times the Kondo energy scale, the maximum response is enhanced nearly an order of magnitude with respect to symmetric coupling to the leads.

Ratcheting in a nonlinear viscoelastic adhesive

NASA Astrophysics Data System (ADS)

Lemme, David; Smith, Lloyd

2017-11-01

Uniaxial time-dependent creep and cycled stress behavior of a standard and toughened film adhesive were studied experimentally. Both adhesives exhibited progressive accumulation of strain from an applied cycled stress. Creep tests were fit to a viscoelastic power law model at three different applied stresses which showed nonlinear response in both adhesives. A third order nonlinear power law model with a permanent strain component was used to describe the creep behavior of both adhesives and to predict creep recovery and the accumulation of strain due to cycled stress. Permanent strain was observed at high stress but only up to 3% of the maximum strain. Creep recovery was under predicted by the nonlinear model, while cycled stress showed less than 3% difference for the first cycle but then over predicted the response above 1000 cycles by 4-14% at high stress. The results demonstrate the complex response observed with structural adhesives, and the need for further analytical advancements to describe their behavior.

Probing optically silent superfluid stripes in cuprates

NASA Astrophysics Data System (ADS)

Rajasekaran, S.; Okamoto, J.; Mathey, L.; Fechner, M.; Thampy, V.; Gu, G. D.; Cavalleri, A.

2018-02-01

Unconventional superconductivity in the cuprates coexists with other types of electronic order. However, some of these orders are invisible to most experimental probes because of their symmetry. For example, the possible existence of superfluid stripes is not easily validated with linear optics, because the stripe alignment causes interlayer superconducting tunneling to vanish on average. Here we show that this frustration is removed in the nonlinear optical response. A giant terahertz third harmonic, characteristic of nonlinear Josephson tunneling, is observed in La1.885Ba0.115CuO4 above the transition temperature Tc = 13 kelvin and up to the charge-ordering temperature Tco = 55 kelvin. We model these results by hypothesizing the presence of a pair density wave condensate, in which nonlinear mixing of optically silent tunneling modes drives large dipole-carrying supercurrents.

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.

Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal

NASA Astrophysics Data System (ADS)

Folpini, Giulia; Reimann, Klaus; Woerner, Michael; Elsaesser, Thomas; Hoja, Johannes; Tkatchenko, Alexandre

2017-09-01

The nonlinear response of soft-mode excitations in polycrystalline acetylsalicylic acid (aspirin) is studied with two-dimensional terahertz spectroscopy. We demonstrate that the correlation of CH3 rotational modes with collective oscillations of π electrons drives the system into the nonperturbative regime of light-matter interaction, even for a moderate strength of the THz driving field on the order of 50 kV /cm . Nonlinear absorption around 1.1 THz leads to a blueshifted coherent emission at 1.7 THz, revealing the dynamic breakup of the strong electron-phonon correlations. The observed behavior is reproduced by theoretical calculations including dynamic local-field correlations.

Parametric system identification of resonant micro/nanosystems operating in a nonlinear response regime

NASA Astrophysics Data System (ADS)

Sabater, A. B.; Rhoads, J. F.

2017-02-01

The parametric system identification of macroscale resonators operating in a nonlinear response regime can be a challenging research problem, but at the micro- and nanoscales, experimental constraints add additional complexities. For example, due to the small and noisy signals micro/nanoresonators produce, a lock-in amplifier is commonly used to characterize the amplitude and phase responses of the systems. While the lock-in enables detection, it also prohibits the use of established time-domain, multi-harmonic, and frequency-domain methods, which rely upon time-domain measurements. As such, the only methods that can be used for parametric system identification are those based on fitting experimental data to an approximate solution, typically derived via perturbation methods and/or Galerkin methods, of a reduced-order model. Thus, one could view the parametric system identification of micro/nanosystems operating in a nonlinear response regime as the amalgamation of four coupled sub-problems: nonparametric system identification, or proper experimental design and data acquisition; the generation of physically consistent reduced-order models; the calculation of accurate approximate responses; and the application of nonlinear least-squares parameter estimation. This work is focused on the theoretical foundations that underpin each of these sub-problems, as the methods used to address one sub-problem can strongly influence the results of another. To provide context, an electromagnetically transduced microresonator is used as an example. This example provides a concrete reference for the presented findings and conclusions.

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 solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

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.

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

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.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

Measurements of the third-order nonlinear optical properties exhibited by a ZnO thin solid film deposited on a SnO2 substrate are presented. The samples were prepared by a spray pyrolysis processing route. Scanning electron microscopy analysis and UV-Vis spectroscopy studies were carried out. The picosecond response at 1064 nm was explored by the z-scan technique. A large optical Kerr effect with two-photon absorption was obtained. The inhibition of the nonlinear optical absorption together with a noticeable enhancement in the optical Kerr effect in the sample was achieved by the incorporation of Au nanoparticles into the ZnO film. Additionally, a two-wave mixing configuration at 532 nm was performed and an optical Kerr effect was identified as the main cause of the nanosecond third-order optical nonlinearity. The relaxation time of the photothermal response of the sample was estimated to be about 1 s when the sample was excited by nanosecond single-shots. The rotation of the sample during the nanosecond two-wave mixing experiments was analyzed. It was stated that a non-monotonic relation between rotating frequency and pulse repetition rate governs the thermal contribution to the nonlinear refractive index exhibited by a rotating film. Potential applications for switching photothermal interactions in rotating samples can be contemplated. A rotary logic system dependent on Kerr transmittance in a two-wave mixing experiment was proposed.

Do film soundtracks contain nonlinear analogues to influence emotion?

PubMed Central

Blumstein, Daniel T.; Davitian, Richard; Kaye, Peter D.

2010-01-01

A variety of vertebrates produce nonlinear vocalizations when they are under duress. By their very nature, vocalizations containing nonlinearities may sound harsh and are somewhat unpredictable; observations that are consistent with them being particularly evocative to those hearing them. We tested the hypothesis that humans capitalize on this seemingly widespread vertebrate response by creating nonlinear analogues in film soundtracks to evoke particular emotions. We used lists of highly regarded films to generate a set of highly ranked action/adventure, dramatic, horror and war films. We then scored the presence of a variety of nonlinear analogues in these film soundtracks. Dramatic films suppressed noise of all types, contained more abrupt frequency transitions and musical sidebands, and fewer noisy screams than expected. Horror films suppressed abrupt frequency transitions and musical sidebands, but had more non-musical sidebands, and noisy screams than expected. Adventure films had more male screams than expected. Together, our results suggest that film-makers manipulate sounds to create nonlinear analogues in order to manipulate our emotional responses. PMID:20504815

Do film soundtracks contain nonlinear analogues to influence emotion?

PubMed

Blumstein, Daniel T; Davitian, Richard; Kaye, Peter D

2010-12-23

A variety of vertebrates produce nonlinear vocalizations when they are under duress. By their very nature, vocalizations containing nonlinearities may sound harsh and are somewhat unpredictable; observations that are consistent with them being particularly evocative to those hearing them. We tested the hypothesis that humans capitalize on this seemingly widespread vertebrate response by creating nonlinear analogues in film soundtracks to evoke particular emotions. We used lists of highly regarded films to generate a set of highly ranked action/adventure, dramatic, horror and war films. We then scored the presence of a variety of nonlinear analogues in these film soundtracks. Dramatic films suppressed noise of all types, contained more abrupt frequency transitions and musical sidebands, and fewer noisy screams than expected. Horror films suppressed abrupt frequency transitions and musical sidebands, but had more non-musical sidebands, and noisy screams than expected. Adventure films had more male screams than expected. Together, our results suggest that film-makers manipulate sounds to create nonlinear analogues in order to manipulate our emotional responses.

Detailed analysis and test correlation of a stiffened composite wing panel

NASA Technical Reports Server (NTRS)

Davis, D. Dale, Jr.

1991-01-01

Nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings supplied by the Bell Helicopter Textron Corporation, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain (ANS) elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain displacements relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis. Strain predictions from both the linear and nonlinear stress analyses are shown to compare well with experimental data up through the Design Ultimate Load (DUL) of the panel. However, due to the extreme nonlinear response of the panel, the linear analysis was not accurate at loads above the DUL. The nonlinear analysis more accurately predicted the strain at high values of applied load, and even predicted complicated nonlinear response characteristics, such as load reversals, at the observed failure load of the test panel. In order to understand the failure mechanism of the panel, buckling and first ply failure analyses were performed. The buckling load was 17 percent above the observed failure load while first ply failure analyses indicated significant material damage at and below the observed failure load.

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.

Uncertainty Analysis of Ozone Formation and Response to Emission Controls Using Higher-Order Sensitivities

EPA Science Inventory

Understanding ozone response to its precursor emissions is crucial for effective air quality management practices. This nonlinear response is usually simulated using chemical transport models, and the modeling results are affected by uncertainties in emissions inputs. In this stu...

Topological nature of nonlinear optical effects in solids.

PubMed

Morimoto, Takahiro; Nagaosa, Naoto

2016-05-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Topological nature of nonlinear optical effects in solids

PubMed Central

Morimoto, Takahiro; Nagaosa, Naoto

2016-01-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials. PMID:27386523

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry.

PubMed

Legland, Jean-Baptiste; Zhang, Yuxiang; Abraham, Odile; Durand, Olivier; Tournat, Vincent

2017-10-01

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

On the dimension of complex responses in nonlinear structural vibrations

NASA Astrophysics Data System (ADS)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

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

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

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…

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

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.

Nonlinear absorption enhancement of AuNPs based polymer nanocomposites

NASA Astrophysics Data System (ADS)

Zulina, Natalia A.; Baranov, Mikhail A.; Kniazev, Kirill I.; Kaliabin, Viacheslav O.; Denisyuk, Igor Yu.; Achor, Susan U.; Sitnikova, Vera E.

2018-07-01

Au nanoparticles (AuNPs) based polymer nanocomposites with high nonlinear absorption coefficient were synthesized by UV-photocuring. AuNPs were synthesized by laser ablation method in liquid monomer isodecyl acrylate (IDA). In this research, two colloids with 70 nm and 20 nm nanoparticles average sizes were studied. Size control was performed with SEM and STEM. Prepared nanomaterials exhibit strong third-order nonlinear optical responses under CW laser irradiation at 532 nm, which was estimated by using z-scan technique performed with open aperture. It was found experimentally that nonlinear absorption β is almost twice higher for nanocomposites with smaller AuNPs.

Modeling off-resonant nonlinear-optical cascading in mesoscopic thin films and guest-host molecular systems

NASA Astrophysics Data System (ADS)

Dawson, Nathan J.; Andrews, James H.; Crescimanno, Michael

2013-12-01

A model for off-resonant microscopic cascading of (hyper)polarizabilities is developed using a self-consistent field approach to study mesoscopic systems of nonlinear polarizable atoms and molecules. We find enhancements in the higher-order susceptibilities resulting from geometrical and boundary orientation effects. We include an example of the dependence on excitation beam cross sectional structure and a simplified derivation of the microscopic cascading of the nonlinear-optical response in guest-host systems.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response

NASA Technical Reports Server (NTRS)

Wicker, J. M.; Greene, W. D.; Kim, S. I.; Yang, V.

1995-01-01

Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.

General response formula and application to topological insulator in quantum open system.

PubMed

Shen, H Z; Qin, M; Shao, X Q; Yi, X X

2015-11-01

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Measuring nonlinear signal combination using EEG.

PubMed

Cunningham, Darren G M; Baker, Daniel H; Peirce, Jonathan W

2017-05-01

Relatively little is known about the processes, both linear and nonlinear, by which signals are combined beyond V1. By presenting two stimulus components simultaneously, flickering at different temporal frequencies (frequency tagging) while measuring steady-state visual evoked potentials, we can assess responses to the individual components, including direct measurements of suppression on each other, and various nonlinear responses to their combination found at intermodulation frequencies. The result is a rather rich dataset of frequencies at which responses can be found. We presented pairs of sinusoidal gratings at different temporal frequencies, forming plaid patterns that were "coherent" (looking like a checkerboard) and "noncoherent" (looking like a pair of transparently overlaid gratings), and found clear intermodulation responses to compound stimuli, indicating nonlinear summation. This might have been attributed to cross-orientation suppression except that the pattern of intermodulation responses differed for coherent and noncoherent patterns, whereas the effects of suppression (measured at the component frequencies) did not. A two-stage model of nonlinear summation involving conjunction detection with a logical AND gate described the data well, capturing the difference between coherent and noncoherent plaids over a wide array of possible response frequencies. Multistimulus frequency-tagged EEG in combination with computational modeling may be a very valuable tool in studying the conjunction of these signals. In the current study the results suggest a second-order mechanism responding selectively to coherent plaid patterns.

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

NASA Technical Reports Server (NTRS)

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

Correction of complex nonlinear signal response from a pixel array detector

PubMed Central

van Driel, Tim Brandt; Herrmann, Sven; Carini, Gabriella; Nielsen, Martin Meedom; Lemke, Henrik Till

2015-01-01

The pulsed free-electron laser light sources represent a new challenge to photon area detectors due to the intrinsic spontaneous X-ray photon generation process that makes single-pulse detection necessary. Intensity fluctuations up to 100% between individual pulses lead to high linearity requirements in order to distinguish small signal changes. In real detectors, signal distortions as a function of the intensity distribution on the entire detector can occur. Here a robust method to correct this nonlinear response in an area detector is presented for the case of exposures to similar signals. The method is tested for the case of diffuse scattering from liquids where relevant sub-1% signal changes appear on the same order as artifacts induced by the detector electronics. PMID:25931072

Correction of complex nonlinear signal response from a pixel array detector.

PubMed

van Driel, Tim Brandt; Herrmann, Sven; Carini, Gabriella; Nielsen, Martin Meedom; Lemke, Henrik Till

2015-05-01

The pulsed free-electron laser light sources represent a new challenge to photon area detectors due to the intrinsic spontaneous X-ray photon generation process that makes single-pulse detection necessary. Intensity fluctuations up to 100% between individual pulses lead to high linearity requirements in order to distinguish small signal changes. In real detectors, signal distortions as a function of the intensity distribution on the entire detector can occur. Here a robust method to correct this nonlinear response in an area detector is presented for the case of exposures to similar signals. The method is tested for the case of diffuse scattering from liquids where relevant sub-1% signal changes appear on the same order as artifacts induced by the detector electronics.

Micro-/nanoscale multi-field coupling in nonlinear photonic devices

NASA Astrophysics Data System (ADS)

Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

2017-08-01

The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

Self-Organization of Light in Optical Media with Competing Nonlinearities.

PubMed

Maucher, F; Pohl, T; Skupin, S; Krolikowski, W

2016-04-22

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

Nonlinear self-reflection of intense ultra-wideband femtosecond pulses in optical fiber

NASA Astrophysics Data System (ADS)

Konev, Leonid S.; Shpolyanskiy, Yuri A.

2013-05-01

We simulated propagation of few-cycle femtosecond pulses in fused silica fiber based on the set of first-order equations for forward and backward waves that generalizes widely used equation of unidirectional approximation. Appearance of a weak reflected field in conditions default to the unidirectional approach is observed numerically. It arises from nonmatched initial field distribution with the nonlinear medium response. Besides additional field propagating forward along with the input pulse is revealed. The analytical solution of a simplified set of equations valid over distances of a few wavelengths confirms generation of reflected and forward-propagating parts of the backward wave. It allowed us to find matched conditions when the reflected field is eliminated and estimate the amplitude of backward wave via medium properties. The amplitude has the order of the nonlinear contribution to the refractive index divided by the linear refractive index. It is small for the fused silica so the conclusions obtained in the unidirectional approach are valid. The backward wave should be proportionally higher in media with stronger nonlinear response. We did not observe in simulations additional self-reflection not related to non-matched boundary conditions.

The preparation of a new type of ferrocene-based compounds with large conjugated system containing symmetrical aromatic vinyl with Schiff base moieties and the study of their third-order nonlinear optical properties

NASA Astrophysics Data System (ADS)

Yu, Weiguo; Jia, Jianhong; Gao, Jianrong; Han, Liang; Li, Yujin

2016-09-01

Herein we reported the preparation of a new type of ferrocene-based compounds with large conjugated system containing symmetrical aromatic vinyl and Schiff base moieties and the study of their third-order nonlinear optical (NLO) properties. Their third-order NLO properties were measured using femtosecond laser and degenerate four-wave mixing (DFWM) technique. The obtained χ(3), n2 and γ values of these molecules were found in the range of 0.998-1.429 × 10-12 esu,1.847-2.646 × 10-11 esu and 1.026-1.449 × 10-30 esu, respectively. The response time ranged from 43.65 fs to 61.71 fs. The results indicate that these compounds have potential nonlinear optical applications.

Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

NASA Astrophysics Data System (ADS)

Solodov, Igor; Busse, Gerd

The concept of defect-selective ultrasonic nonlinear imaging is based on visualization of strongly nonlinear inclusions in the form of localized cracked defects. For intense excitation, the ultrasonic response of defects is affected by mechanical constraint between their fragments that makes their vibrations extremely nonlinear. The cracked flaws, therefore, efficiently generate multiple new frequencies, which can be used as a nonlinear "tag" to detect and image them. In this paper, the methodologies of nonlinear scanning laser vibrometry (NSLV) and nonlinear air-coupled emission (NACE) are applied for nonlinear imaging of various defects in hi-tech and constructional materials. A broad database obtained demonstrates evident advantages of the nonlinear approach over its linear counterpart. The higher-order nonlinear frequencies provide increase in signal-to-noise ratio and enhance the contrast of imaging. Unlike conventional ultrasonic instruments, the nonlinear approach yields abundant multi-frequency information on defect location. The application of image recognition and processing algorithms is described and shown to improve reliability and quality of ultrasonic imaging.

Validation of a High-Order Prefactored Compact Scheme on Nonlinear Flows with Complex Geometries

NASA Technical Reports Server (NTRS)

Hixon, Ray; Mankbadi, Reda R.; Povinelli, L. A. (Technical Monitor)

2000-01-01

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.

Ultralow-power and ultrafast all-optical tunable plasmon-induced transparency in metamaterials at optical communication range.

PubMed

Zhu, Yu; Hu, Xiaoyong; Fu, Yulan; Yang, Hong; Gong, Qihuang

2013-01-01

Actively all-optical tunable plasmon-induced transparency in metamaterials paves the way for achieving ultrahigh-speed quantum information processing chips. Unfortunately, up to now, very small experimental progress has been made for all-optical tunable plasmon-induced transparency in metamaterials in the visible and near-infrared range because of small third-order optical nonlinearity of conventional materials. The achieved operating pump intensity was as high as several GW/cm(2) order. Here, we report an ultralow-power and ultrafast all-optical tunable plasmon-induced transparency in metamaterials coated on polycrystalline indium-tin oxide layer at the optical communication range. Compared with previous reports, the threshold pump intensity is reduced by four orders of magnitude, while an ultrafast response time of picoseconds order is maintained. This work not only offers a way to constructing photonic materials with large nonlinearity and ultrafast response, but also opens up the possibility for realizing quantum solid chips and ultrafast integrated photonic devices based on metamaterials.

Ultralow-power and ultrafast all-optical tunable plasmon-induced transparency in metamaterials at optical communication range

PubMed Central

Zhu, Yu; Hu, Xiaoyong; Fu, Yulan; Yang, Hong; Gong, Qihuang

2013-01-01

Actively all-optical tunable plasmon-induced transparency in metamaterials paves the way for achieving ultrahigh-speed quantum information processing chips. Unfortunately, up to now, very small experimental progress has been made for all-optical tunable plasmon-induced transparency in metamaterials in the visible and near-infrared range because of small third-order optical nonlinearity of conventional materials. The achieved operating pump intensity was as high as several GW/cm2 order. Here, we report an ultralow-power and ultrafast all-optical tunable plasmon-induced transparency in metamaterials coated on polycrystalline indium-tin oxide layer at the optical communication range. Compared with previous reports, the threshold pump intensity is reduced by four orders of magnitude, while an ultrafast response time of picoseconds order is maintained. This work not only offers a way to constructing photonic materials with large nonlinearity and ultrafast response, but also opens up the possibility for realizing quantum solid chips and ultrafast integrated photonic devices based on metamaterials. PMID:23903825

Third-order nonlinear optical properties of thin sputtered gold films

NASA Astrophysics Data System (ADS)

Xenogiannopoulou, E.; Aloukos, P.; Couris, S.; Kaminska, E.; Piotrowska, A.; Dynowska, E.

2007-07-01

Au films of thickness ranging between 5 and 52 nm were prepared by sputtering on quartz substrates and their third-order nonlinear optical response was investigated by Optical Kerr effect (OKE) and Z-scan techniques using 532 nm, 35 ps laser pulses. All prepared films were characterized by XRD, AFM and UV-VIS-NIR spectrophotometry while their third-order susceptibility χ(3) was measured and found to be of the order of 10 -9 esu. The real and imaginary parts of the third-order susceptibility were found in very good agreement with experimental results and theoretical predictions reported by Smith et al. [D.D. Smith, Y. Yoon, R.W. Boyd, Y.K. Cambell, L.A. Baker, R.M. Crooks, M. George, J. Appl. Phys. 86 (1999) 6200].

Probing the non-linear transient response of a carbon nanotube mechanical oscillator

NASA Astrophysics Data System (ADS)

Willick, Kyle; Tang, Xiaowu Shirley; Baugh, Jonathan

2017-11-01

Carbon nanotube (CNT) electromechanical resonators have demonstrated unprecedented sensitivities for detecting small masses and forces. The detection speed in a cryogenic setup is usually limited by the CNT contact resistance and parasitic capacitance of cabling. We report the use of a cold heterojunction bipolar transistor amplifying circuit near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the strongly non-linear regime. The behaviour of transients in both the linear and non-linear regimes is observed and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. We show that the non-linear regime can result in faster mechanical response times, on the order of 10 μs for the device and circuit presented, potentially enabling the magnetic moments of single molecules to be measured within their spin relaxation and dephasing timescales.

Modified two-photon absorption and dispersion of ultrafast third-order polarization beats via twin noisy driving fields

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

Zhang Yanpeng; Department of Electronic Science and Technology, Xi'an Jiaotong University, Xi'an 710049; Gan Chenli

2006-05-15

We investigate the color-locked twin-noisy-field correlation effects in third-order nonlinear absorption and dispersion of ultrafast polarization beats. We demonstrate a phase-sensitive method for studying the two-photon nondegenerate four-wave mixing (NDFWM) due to atomic coherence in a multilevel system. The reference signal is another one-photon degenerate four-wave-mixing signal, which propagates along the same optical path as the NDFWM signal. This method is used for studying the phase dispersion of the third-order susceptibility and for the optical heterodyne detection of the NDFWM signal. The third-order nonlinear response can be controlled and modified through the color-locked correlation of twin noisy fields.

Phase-resolved two-dimensional terahertz spectroscopy - a probe of highly nonlinear light-matter interactions

NASA Astrophysics Data System (ADS)

Elsaesser, Thomas

Terahertz (THz) spectroscopy gives insight into low-frequency excitations and charge dynamics in condensed matter. So far, most experiments in a frequency range from 0.5 to 30 THz have focused on the linear THz response to determine linear absorption and disperion spectra, and/or electric conductivities. The generation of ultrashort THz transients with peak electric fields up to megavolts/cm has allowed for addressing nonlinear light-matter interactions and inducing excitations far from equilibrium. The novel method of two-dimensional THz (2D-THz) spectroscopy allows for mapping ultrafast dynamics and couplings of elementary excitations up to arbitrary nonlinear order in the electric field, both under resonant and nonresonant excitation conditions. In particular, different contributions to the overall nonlinear response are separated by dissecting it as a function of excitation and detection frequencies and for different waiting times after excitation. This talk gives an introduction in 2D-THz spectroscopy, including its recent extension to 3-pulse sequences and interaction schemes. To illustrate the potential of the method, recent results on two-phonon coherences and high-order interband excitations in the semiconductor InSb will be presented. Nonlinear THz excitation of two-phonon coherences exploits a resonance enhancement by the large electronic interband dipole of InSb and is, thus, far more efficient than linear excitation via resonant two-phonon absorption. As a second application, the nonlinear softmode response in a crystal consisting of aspirin molecules will be discussed. At moderate THz driving fields, the pronounced correlation of rotational modes of CH3 groups with collective oscillations of π-electrons drives the system into the regime of nonperturbative light-matter interaction. Nonlinear absorption around 1.1 THz leads to a blue-shifted coherent emission at 1.5 THz, revealing a dynamic breakup of the strong electron-phonon correlations.

Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

PubMed Central

Liang, Wenxi; Vanacore, Giovanni M.; Zewail, Ahmed H.

2014-01-01

In materials, the nature of the strain–stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction. PMID:24706785

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

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 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.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

Polariton biexciton transitions in a ZnSe-based microcavity

NASA Astrophysics Data System (ADS)

Neukirch, U.; Bolton, S. R.; Fromer, N. A.; Sham, L. J.; Chemla, D. S.

2000-06-01

The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton-biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.

Non-Linear Vibroisolation Pads Design, Numerical FEM Analysis and Introductory Experimental Investigations

NASA Astrophysics Data System (ADS)

Zielnica, J.; Ziółkowski, A.; Cempel, C.

2003-03-01

Design and theoretical and experimental investigation of vibroisolation pads with non-linear static and dynamic responses is the objective of the paper. The analytical investigations are based on non-linear finite element analysis where the load-deflection response is traced against the shape and material properties of the analysed model of the vibroisolation pad. A new model of vibroisolation pad of antisymmetrical type was designed and analysed by the finite element method based on the second-order theory (large displacements and strains) with the assumption of material's non-linearities (Mooney-Rivlin model). Stability loss phenomenon was used in the design of the vibroisolators, and it was proved that it would be possible to design a model of vibroisolator in the form of a continuous pad with non-linear static and dynamic response, typical to vibroisolation purposes. The materials used for the vibroisolator are those of rubber, elastomers, and similar ones. The results of theoretical investigations were examined experimentally. A series of models made of soft rubber were designed for the test purposes. The experimental investigations of the vibroisolation models, under static and dynamic loads, confirmed the results of the FEM analysis.

Correction of complex nonlinear signal response from a pixel array detector

DOE PAGES

van Driel, Tim Brandt; Herrmann, Sven; Carini, Gabriella; ...

2015-04-22

The pulsed free-electron laser light sources represent a new challenge to photon area detectors due to the intrinsic spontaneous X-ray photon generation process that makes single-pulse detection necessary. Intensity fluctuations up to 100% between individual pulses lead to high linearity requirements in order to distinguish small signal changes. In real detectors, signal distortions as a function of the intensity distribution on the entire detector can occur. Here a robust method to correct this nonlinear response in an area detector is presented for the case of exposures to similar signals. The method is tested for the case of diffuse scattering frommore » liquids where relevant sub-1% signal changes appear on the same order as artifacts induced by the detector electronics.« less

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.

Third-order optical conductivity of an electron fluid

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, D. N.; Fogler, M. M.

2018-02-01

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor σ(3 ) whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for σ(3 ) for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

Higgs Mode in the d -Wave Superconductor Bi2Sr2CaCu2O8 +x Driven by an Intense Terahertz Pulse

NASA Astrophysics Data System (ADS)

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.; Matsunaga, Ryusuke; Schneeloch, John; Zhong, Ruidan D.; Gu, Genda D.; Aoki, Hideo; Gallais, Yann; Shimano, Ryo

2018-03-01

We investigate the terahertz (THz)-pulse-driven nonlinear response in the d -wave cuprate superconductor Bi2Sr2CaCu2O8 +x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We observe an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is markedly enhanced below Tc . The corresponding third-order nonlinear effect exhibits both A1 g and B1 g symmetry components, which are decomposed from polarization-resolved measurements. A comparison with a BCS calculation of the nonlinear susceptibility indicates that the A1 g component is associated with the Higgs mode of the d -wave order parameter.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

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

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

DOE PAGES

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.; ...

2018-03-14

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems. Version 2.0

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Kenny, Sean P.; Giesy, Daniel P.

1997-01-01

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

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.

Nonlinear viscoelastic characterization of bovine trabecular bone.

PubMed

Manda, Krishnagoud; Wallace, Robert J; Xie, Shuqiao; Levrero-Florencio, Francesc; Pankaj, Pankaj

2017-02-01

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness-density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep-recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples ([Formula: see text]). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery's nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep-recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening-softening behaviour with increasing stress.

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.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Integrated model for pricing, delivery time setting, and scheduling in make-to-order environments

NASA Astrophysics Data System (ADS)

Garmdare, Hamid Sattari; Lotfi, M. M.; Honarvar, Mahboobeh

2018-03-01

Usually, in make-to-order environments which work only in response to the customer's orders, manufacturers for maximizing the profits should offer the best price and delivery time for an order considering the existing capacity and the customer's sensitivity to both the factors. In this paper, an integrated approach for pricing, delivery time setting and scheduling of new arrival orders are proposed based on the existing capacity and accepted orders in system. In the problem, the acquired market demands dependent on the price and delivery time of both the manufacturer and its competitors. A mixed-integer non-linear programming model is presented for the problem. After converting to a pure non-linear model, it is validated through a case study. The efficiency of proposed model is confirmed by comparing it to both the literature and the current practice. Finally, sensitivity analysis for the key parameters is carried out.

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.

Interaction of ultrashort laser pulses with epsilon-near-zero materials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Boyd, Robert W.

2017-05-01

Abstract: The nonlinear optical response of a material is conventionally assumed to be very much smaller than its linear response. Here we report that the nonlinear contribution to the refractive index of a sample of indium-tin oxide can be much larger than the linear contribution when the optical wavelength is close to the material's bulk plasma wavelength, where the material exhibits epsilon-near-zero behavior. In particular, we demonstrate that a change in refractive index as large as 0.7 can be obtained in an ultra-thin indium-tin oxide film using an optical intensity of 140 GW/cm2. Nonlinear optical phenomena result from the light-induced modification of the optical properties of a material lead to a broad range of applications, including microscopy, all-optical data processing, and quantum information. However, nonlinear (NL) effects are typically extremely weak. The size of nonlinear effects is typically limited by the largest intensity that can be used without permanently damaging of the material. Consequently, the resulting change in refractive index is typically of the order of 0.001 or smaller. A long-standing goal of nonlinear optics (NLO) has been the development of materials that can display a light-induced change in the refractive index of the order of unity. Such materials would lead to exciting new applications of NLO. Indeed, much effort in the fields of plasmonics and metamaterials is devoted to the development of such materials. Furthermore, it has been suggested that materials with vanishing permittivity, commonly known as epsilon-nearzero (ENZ) materials, can be used to induce highly nonlinear phenomena and unusual phase-matching behavior. In this work, we describe our studies of indium-tin oxide (ITO) at its ENZ wavelength, and we demonstrate a refractive index change of 0.7. Materials possessing free charges, such as metals and doped semiconductors, exhibit a vanishing permittivity at the bulk plasmon wavelength. The zero-permittivity wavelength in doped semiconductors typically lies at infrared wavelengths and can be fine tuned by controlling the level of doping. Here we study the case of an ultra-thin layer of ITO exhibiting ENZ behavior at wavelengths around 1.24 µm. We show that in this spectral region the nonlinear response (intensity-dependent change in refractive index, Δn) is enhanced approximately 2000-fold with respect to that observed at shorter wavelengths and that a Δn of the order of unity can be observed.

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.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

NASA Astrophysics Data System (ADS)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

Analysis of laterally loaded long or intermediate drilled shafts of small or large diameter in layered soil.

DOT National Transportation Integrated Search

2008-12-01

This study has extended the capability of the SW model in order to predict the response of laterally loaded large diameter shafts considering 1) the influence of shaft type on the lateral shaft response; 2) the nonlinear behavior of shaft material an...

Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels

NASA Astrophysics Data System (ADS)

Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth

2016-11-01

Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.

Third-order nonlinear electro-optic measurements in the smectic-? phase

NASA Astrophysics Data System (ADS)

Nowicka, Kamila; Bielejewska, Natalia

2018-02-01

The chiral smectic subphase with three-layer structure, ?, is now of great interest from the point of view of device technologies such as multistate or symmetric switching. We report that the unique nonlinear electro-optic response can serve as precise mark of the phase transition into three-layer structure. The problem is illustrated with the first and third harmonic electro-optic spectra. Furthermore, the characteristic response of the helical liquid crystal phases correlated with particular collective modes using the Debye-type relaxation method for the well-known prototype liquid crystal material (MHPOBC) are presented.

Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive.

PubMed

Richardson, Magnus J E

2007-08-01

Integrate-and-fire models are mainstays of the study of single-neuron response properties and emergent states of recurrent networks of spiking neurons. They also provide an analytical base for perturbative approaches that treat important biological details, such as synaptic filtering, synaptic conductance increase, and voltage-activated currents. Steady-state firing rates of both linear and nonlinear integrate-and-fire models, receiving fluctuating synaptic drive, can be calculated from the time-independent Fokker-Planck equation. The dynamic firing-rate response is less easy to extract, even at the first-order level of a weak modulation of the model parameters, but is an important determinant of neuronal response and network stability. For the linear integrate-and-fire model the response to modulations of current-based synaptic drive can be written in terms of hypergeometric functions. For the nonlinear exponential and quadratic models no such analytical forms for the response are available. Here it is demonstrated that a rather simple numerical method can be used to obtain the steady-state and dynamic response for both linear and nonlinear models to parameter modulation in the presence of current-based or conductance-based synaptic fluctuations. To complement the full numerical solution, generalized analytical forms for the high-frequency response are provided. A special case is also identified--time-constant modulation--for which the response to an arbitrarily strong modulation can be calculated exactly.

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.

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.

Dynamics of elastic nonlinear rotating composite beams with embedded actuators

NASA Astrophysics Data System (ADS)

Ghorashi, Mehrdaad

2009-08-01

A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2004-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

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.

Sweep excitation with order tracking: A new tactic for beam crack analysis

NASA Astrophysics Data System (ADS)

Wei, Dongdong; Wang, KeSheng; Zhang, Mian; Zuo, Ming J.

2018-04-01

Crack detection in beams and beam-like structures is an important issue in industry and has attracted numerous investigations. A local crack leads to global system dynamics changes and produce non-linear vibration responses. Many researchers have studied these non-linearities for beam crack diagnosis. However, most reported methods are based on impact excitation and constant frequency excitation. Few studies have focused on crack detection through external sweep excitation which unleashes abundant dynamic characteristics of the system. Together with a signal resampling technique inspired by Computed Order Tracking, this paper utilize vibration responses under sweep excitations to diagnose crack status of beams. A data driven method for crack depth evaluation is proposed and window based harmonics extracting approaches are studied. The effectiveness of sweep excitation and the proposed method is experimentally validated.

Ultrasonic Nondestructive Characterization of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Qu, Jianmin

1997-01-01

Qualitative measurements of adhesion or binding forces can be accomplished, for example, by using the reflection coefficient of an ultrasound or by using thermal waves (Light and Kwun, 1989, Achenbach and Parikh, 1991, and Bostrom and wickham, 1991). However, a quantitative determination of binding forces is rather difficult. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasound passes through a nonlinear material. It seems that such non-linearity can be effectively used to characterize the bond strength. Several theories have been developed to model this nonlinear effect (Adler and Nagy, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; and Hirose and Kitahara, 1992; Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) made a comparison between the experimental and simulated results based on this theoretical model. A water immersion mode-converted shear wave through-transmission setup was used by Berndt and Green (1997) to analyze the nonlinear acoustic behavior of the adhesive bond. In this project, the nonlinear responses of an adhesive joint was investigated through transmission tests of ultrasonic wave and analyzed by the finite element simulations. The higher order harmonics were obtained in the tests. It is found that the amplitude of higher harmonics increases as the aging increases, especially the 3dorder harmonics. Results from the numerical simulation show that the material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic behavior generates significant 3rd and 5th order harmonics.

All-optical tunable dual Fano resonance in nonlinear metamaterials in optical communication range

NASA Astrophysics Data System (ADS)

Zhou, Yi; Hu, Xiaoyong; Li, Chong; Yang, Hong; Gong, Qihuang

2018-01-01

Low-power, ultra-fast all-optical tunable dual Fano resonance was realized in a metamaterial coated with a non-linear nanocomposite layer composed of gold nanoparticle-doped polycrystalline barium strontium titanate and multilayer tungsten disulphide microsheets. A high non-linear refractive index of -2.148 × 10-11 m2/W was achieved in the nanocomposite material that originated in the non-linearity enhancement associated with the quantum confinement effect, the local-field enhancement effect, and reinforced interactions between photons and the multilayer tungsten disulphide microsheets. An ultra-low threshold pump intensity of 600 kW/cm2 was obtained. An ultra-fast response time of 25.4 ps was maintained because of the fast relaxation dynamics of the bound electrons in the nanoscale polycrystalline barium strontium titanate grains. The large third-order non-linear responses of the metamaterial were confirmed with a high third harmonic generation conversion efficiency of 5.4 × 10-5. This work may help to pave the way towards realization of ultra-high-speed information processing chips and multifunctional integrated photonic devices based on metamaterials.

Nonlinear optical response in graphene nanoribbons: The critical role of electron scattering

NASA Astrophysics Data System (ADS)

Karimi, F.; Davoody, A. H.; Knezevic, I.

2018-06-01

Nonlinear nanophotonics has many potential applications, such as in mode locking, frequency-comb generation, and all-optical switching. The development of materials with large nonlinear susceptibility is key to realizing nonlinear nanophotonics. Nanostructured graphene systems, such as graphene nanoribbons and nanoislands, have been predicted to have a strong plasmon-enhanced nonlinear optical behavior in the nonretarded regime. Plasmons concentrate the light field down to subwavelength scales and can enhance the nonlinear optical effects; however, plasmon resonances are narrowband and sensitive to the nanostructure geometry. Here we show that graphene nanoribbons, particularly armchair graphene nanoribbons, have a remarkably strong nonlinear optical response in the long-wavelength regime and over a broad frequency range, from terahertz to the near infrared. We use a quantum-mechanical master equation with a detailed treatment of scattering and show that, in the retarded regime, electron scattering has a critical effect on the optical nonlinearity of graphene nanoribbons, which cannot be captured via the commonly used relaxation-time approximation. At terahertz frequencies, where intraband optical transitions dominate, the strong nonlinearity (in particular, third-order Kerr nonlinearity) stems from the jagged shape of the electron energy distribution, caused by the interband electron scattering mechanisms along with the intraband inelastic scattering mechanisms. We show that the relaxation-time approximation fails to capture this quantum-mechanical phenomenon and results in a significant underestimation of the intraband nonlinearity. At the midinfrared to near infrared frequencies, where interband optical transitions dominate, the Kerr nonlinearity is significantly overestimated within the relaxation-time approximation. These findings unveil the critical effect of electron scattering on the optical nonlinearity of nanostructured graphene, and also underscore the capability of this class of materials for nonlinear nanophotonic applications.

Enhanced nonlinear optical properties of L-arginine stabilized gold nanoparticles embedded in PVP polymer

NASA Astrophysics Data System (ADS)

Sunatkari, A. L.; Talwatkar, S. S.; Tamgadge, Y. S.; Muley, G. G.

2018-05-01

Highly stable colloidal gold nanoparticles (GNPs) stabilised in l-arginine were synthesized and embedded in polyvinyl pyrrolidone (PVP) polymer matrix to fabricate thin films by spin coating method. Nonlinear optical response of GNP-PVP nanocomposite were investigated using single beam Z-scan technique using He-Ne laser beam in CW regime operated at 632.8 nm as an excitation source. The sign of nonlinear refractive index was found negative, which is of self-defocusing nature. The nonlinear optical parameters estimated for GNP-PVP nanocomposite and found values as large as n2≈(1.7 -3.1 ) ×10-4c m2W-1, β ≈(2.40 -4.69 ) ×10-5c m W-1 and χef f (3 )≈(2.30 -4.34 ) ×10-4e s u . The nonlinear refractive index, absorption coefficient and third order nonlinear susceptibility have found decreasing with the increase in the concentration of l-arginine. Localized surface plasmon resonance (LSPR) peaks show the blue shift. The average size of the GNPs is found reducing from 11 nm to 7.5 nm with the increase in the stabilizer concentration, as analysed by transmission electron microscopy. The XRD study reveals face-centred cubic (fcc) structure of GNPs. The huge nonlinearity is attributed to the thermo-optic phenomenon. The huge enhancement in third order nonlinear susceptibility and nonlinear refractive index indicates that this optical material possess a high potential for various optoelectronic devices applications.

Probing optically silent superfluid stripes in cuprates

DOE PAGES

Rajasekaran, S.; Okamoto, J.; Mathey, L.; ...

2018-02-02

Unconventional superconductivity in the cuprates coexists with other types of electronic order. However, some of these orders are invisible to most experimental probes because of their symmetry. For example, the possible existence of superfluid stripes is not easily validated with linear optics, because the stripe alignment causes interlayer superconducting tunneling to vanish on average. In this paper, we show that this frustration is removed in the nonlinear optical response. A giant terahertz third harmonic, characteristic of nonlinear Josephson tunneling, is observed in La 1.885Ba 0.115CuO 4 above the transition temperature T c = 13 kelvin and up to the charge-orderingmore » temperature T co = 55 kelvin. We model these results by hypothesizing the presence of a pair density wave condensate, in which nonlinear mixing of optically silent tunneling modes drives large dipole-carrying supercurrents.« less

Probing optically silent superfluid stripes in cuprates

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

Rajasekaran, S.; Okamoto, J.; Mathey, L.

Unconventional superconductivity in the cuprates coexists with other types of electronic order. However, some of these orders are invisible to most experimental probes because of their symmetry. For example, the possible existence of superfluid stripes is not easily validated with linear optics, because the stripe alignment causes interlayer superconducting tunneling to vanish on average. In this paper, we show that this frustration is removed in the nonlinear optical response. A giant terahertz third harmonic, characteristic of nonlinear Josephson tunneling, is observed in La 1.885Ba 0.115CuO 4 above the transition temperature T c = 13 kelvin and up to the charge-orderingmore » temperature T co = 55 kelvin. We model these results by hypothesizing the presence of a pair density wave condensate, in which nonlinear mixing of optically silent tunneling modes drives large dipole-carrying supercurrents.« less

Fast analytical model of MZI micro-opto-mechanical pressure sensor

NASA Astrophysics Data System (ADS)

Rochus, V.; Jansen, R.; Goyvaerts, J.; Neutens, P.; O’Callaghan, J.; Rottenberg, X.

2018-06-01

This paper presents a fast analytical procedure in order to design a micro-opto-mechanical pressure sensor (MOMPS) taking into account the mechanical nonlinearity and the optical losses. A realistic model of the photonic MZI is proposed, strongly coupled to a nonlinear mechanical model of the membrane. Based on the membrane dimensions, the residual stress, the position of the waveguide, the optical wavelength and the phase variation due to the opto-mechanical coupling, we derive an analytical model which allows us to predict the response of the total system. The effect of the nonlinearity and the losses on the total performance are carefully studied and measurements on fabricated devices are used to validate the model. Finally, a design procedure is proposed in order to realize fast design of this new type of pressure sensor.

Optical, structural and nonlinear optical properties of laser ablation synthesized Ag nanoparticles and photopolymer nanocomposites based on them

NASA Astrophysics Data System (ADS)

Zulina, Natalia A.; Pavlovetc, Ilia M.; Baranov, Mikhail A.; Denisyuk, Igor Yu.

2017-03-01

In this work Ag nanoparticles (NPs) stable colloid solution were prepared by laser ablation of chemically pure silver rod in liquid monomer isodecyl acrylate (IDA). Sizes of obtained nanoparticles were determined by scanning electron microscope and vary from 27 to 120 nm. Nanocomposites films were prepared from obtained stable colloid solution of AgNPs by photocuring. For aliphatic polymer IDA long molecules cross-linking Diurethane dimethacrylate, 1,6-Hexandiol diacrylate and Tetra (ethylene glycol) diacrylate were used. Prepared nanomaterials exhibit strong third-order nonlinear optical responses, which was estimated by using z-scan technique. The third-order nonlinear optical coefficients of the studied nanocomposites were found to be up to Reχ(3)=1.31×10-5 (esu) and Imχ(3)=7.64×10-5 (esu).

Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers.

PubMed

Khairuzzaman, Md; Zhang, Chao; Igarashi, Koji; Katoh, Kazuhiro; Kikuchi, Kazuro

2010-03-01

We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.

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.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Z-scan theory for nonlocal nonlinear media with simultaneous nonlinear refraction and nonlinear absorption.

PubMed

Rashidian Vaziri, Mohammad Reza

2013-07-10

In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.

Dynamic Snap-Through of Thin-Walled Structures by a Reduced Order Method

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2006-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced order analysis, four categories of modal basis functions are identified including those having symmetric transverse (ST), anti-symmetric transverse (AT), symmetric in-plane (SI), and anti-symmetric in-plane (AI) displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the AT and SI modes must be included in the basis as they participate in the snap-through behavior.

Dynamic Snap-Through of Thermally Buckled Structures by a Reduced Order Method

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2007-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced-order analysis, four categories of modal basis functions are identified including those having symmetric transverse, anti-symmetric transverse, symmetric in-plane, and anti-symmetric in-plane displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the anti-symmetric transverse and symmetric in-plane modes must be included in the basis as they participate in the snap-through behavior.

Synthesis of nanocomposites based on carbon nanotube/smart copolymer with nonlinear optical properties

NASA Astrophysics Data System (ADS)

Sousani, Abbas; Motiei, Hamideh; Najafimoghadam, Peyman; Hasanzade, Reza

2017-05-01

In this study new nanocompoites based on polyglycidylmethacrylate grafted 4-[(4-methoxyphenyl) diazenyl] phenol (Azo-PGMA) and Carboxylicacid functionalized multi-walled carbon nanotubes (MWCNT-COOH) were prepared. The nanocomposites structure was characterized by FT-IR, TGA and SEM. The Z-scan technique was applied for measuring the nonlinear parameters of nanocomposites. The samples after solving in AWM solution (equal ratio of acetone, deionized water and methanol) were investigated by using closed aperture Z-scan technique and a diode-pumped laser at the line 532 nm. All the nonlinear refractive index of the samples at three concentrations of carbon nanotubes in three different intensities of the laser beam were investigated and the nonlinear optical response of them are compared under the same condition. Because of high order of nonlinear refractive coefficient and good nonlinearity, these compounds are suitable candidate for optical switching, optical limiting and electro-optical devices.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

PubMed

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

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

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa

2005-12-15

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, bothmore » theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.« less

Frequency, pressure and strain dependence of nonlinear elasticity in Berea Sandstone

DOE PAGES

Riviere, Jacques; Johnson, Paul Allan; Marone, Chris; ...

2016-04-14

Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static ( f → 0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2–3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1fmore » appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. Furthermore, these findings can be used to improve theories relating the macroscopic elastic response to microstructural features.« less

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

NASA Technical Reports Server (NTRS)

Barut, A.; Madenci, Erdogan; Tessler, A.

1997-01-01

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Z-Scan Measurement of the Nonlinear Absorption of a Thin Gold Film

NASA Technical Reports Server (NTRS)

Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Campbell, Joseph K.; Baker, Lane A.; Crooks, Richard M.; George, Michael

1999-01-01

We have used the z-scan technique at a wavelength (532 nm) near the transmission window of bulk gold to measure the nonlinear absorption coefficient of continuous approximately 50-Angstrom-thick gold films, deposited onto surface-modified quartz substrates. For highly absorbing media such as metals, we demonstrate that determination of either the real or imaginary part of the third-order susceptibility requires a measurement of both nonlinear absorption and nonlinear refraction, i.e. both open- and closed-aperture z-scans must be performed. Closed-aperture z-scans did not yield a sufficient signal for the determination of the nonlinear refraction. However, open-aperture z-scans yielded values ranging from Beta = 1.9 x 10(exp -3) to 5.3 x 10(exp -3) cm/W in good agreement with predictions which ascribe the nonlinear response to a Fermi smearing mechanism. We note that the sign of the nonlinearity is reversed from that of gold nanoparticle composites, in accordance with the predictions of mean field theories.

Polarization- and wavelength-resolved near-field imaging of complex plasmonic modes in Archimedean nanospirals

DOE PAGES

Hachtel, Jordan A.; Davidson, II, Roderick B.; Kovalik, Elena R.; ...

2018-02-15

Asymmetric nanophotonic structures enable a wide range of opportunities in optical nanotechnology because they support efficient optical nonlinearities mediated by multiple plasmon resonances over a broad spectral range. The Archimedean nanospiral is a canonical example of a chiral plasmonic structure because it supports even-order nonlinearities that are not generally accessible in locally symmetric geometries. However, the complex spiral response makes nanoscale experimental characterization of the plasmonic near-field structure highly desirable. As a result, we employ high-efficiency, high-spatial-resolution cathodoluminescence imaging in a scanning transmission electron microscope to describe the spatial, spectral, and polarization response of plasmon modes in the nanospiral geometry.

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.; Carlson, Robert L.; Riff, Richard

1991-01-01

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Polarization- and wavelength-resolved near-field imaging of complex plasmonic modes in Archimedean nanospirals

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

Hachtel, Jordan A.; Davidson, II, Roderick B.; Kovalik, Elena R.

Asymmetric nanophotonic structures enable a wide range of opportunities in optical nanotechnology because they support efficient optical nonlinearities mediated by multiple plasmon resonances over a broad spectral range. The Archimedean nanospiral is a canonical example of a chiral plasmonic structure because it supports even-order nonlinearities that are not generally accessible in locally symmetric geometries. However, the complex spiral response makes nanoscale experimental characterization of the plasmonic near-field structure highly desirable. As a result, we employ high-efficiency, high-spatial-resolution cathodoluminescence imaging in a scanning transmission electron microscope to describe the spatial, spectral, and polarization response of plasmon modes in the nanospiral geometry.

Nonlinear decoding of a complex movie from the mammalian retina

PubMed Central

Deny, Stéphane; Martius, Georg

2018-01-01

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains. PMID:29746463

Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon

NASA Astrophysics Data System (ADS)

Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.

The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.

Reduced-order modeling of soft robots

PubMed Central

Chenevier, Jean; González, David; Aguado, J. Vicente; Chinesta, Francisco

2018-01-01

We present a general strategy for the modeling and simulation-based control of soft robots. Although the presented methodology is completely general, we restrict ourselves to the analysis of a model robot made of hyperelastic materials and actuated by cables or tendons. To comply with the stringent real-time constraints imposed by control algorithms, a reduced-order modeling strategy is proposed that allows to minimize the amount of online CPU cost. Instead, an offline training procedure is proposed that allows to determine a sort of response surface that characterizes the response of the robot. Contrarily to existing strategies, the proposed methodology allows for a fully non-linear modeling of the soft material in a hyperelastic setting as well as a fully non-linear kinematic description of the movement without any restriction nor simplifying assumption. Examples of different configurations of the robot were analyzed that show the appeal of the method. PMID:29470496

Nonlinear Reduced-Order Simulation Using Stress-Free and Pre-Stressed Modal Bases

NASA Technical Reports Server (NTRS)

Przekop, Adam; Stover, Michael A.; Rizzi, Stephen A.

2009-01-01

A study is undertaken to determine the advantages and disadvantages associated with application of stress-free and pre-stressed modal bases in a reduced-order finite-element-based nonlinear simulation. A planar beam is chosen as an application example and its response due to combined thermal and random pressure loadings is examined. Combinations of two random pressure levels and two thermal conditions are investigated. The latter consists of an ambient temperature condition and an elevated temperature condition in the post-buckled regime. It is found that stress-free normal modes establish a broadly applicable modal basis yielding accurate results for all the loading regimes considered. In contrast, the range of applicability for a thermally pre-stressed modal basis is found to be limited. The behavior is explained by scrutinizing the coupling found in the linear stiffness and the effect this coupling has on the structural response characteristics under the range of loading conditions considered.

Designing Hybrids of Graphene Oxide and Gold Nanoparticles for Nonlinear Optical Response

NASA Astrophysics Data System (ADS)

Yadav, Rajesh Kumar; Aneesh, J.; Sharma, Rituraj; Abhiramnath, P.; Maji, Tuhin Kumar; Omar, Ganesh Ji; Mishra, A. K.; Karmakar, Debjani; Adarsh, K. V.

2018-04-01

Nonlinear optical absorption of light by materials is weak due to its perturbative nature, although a strong nonlinear response is of crucial importance to applications in optical limiting and switching. Here we demonstrate experimentally and theoretically an extremely efficient scheme of excited-state absorption by charge transfer between donor and acceptor materials as a method to enhance the nonlinear absorption by orders of magnitude. With this idea, we demonstrate a strong excited-state absorption (ESA) in reduced graphene oxide that otherwise shows an increased transparency at high fluence and enhancement of ESA by one order of magnitude in graphene oxide by attaching gold nanoparticles (Au NP) in the tandem configuration that acts as an efficient charge-transfer pair when excited at the plasmonic wavelength. To explain the unprecedented enhancement, we develop a five-level rate-equation model based on the charge transfer between the two materials and numerically simulate the results. To understand the correlation of interfacial charge transfer with the concentration and type of the functional ligands attached to the graphene oxide sheet, we investigate the Au-NP—graphene oxide interface with various possible ligand configurations from first-principles calculations. By using the strong ESA of our hybrid materials, we fabricate liquid cell-based high-performance optical limiters with important device parameters better than that of the benchmark optical limiters.

Measurement of the optical nonlinearities of water, ethanol and tetrahydrofuran (THF) at 355 nm

NASA Astrophysics Data System (ADS)

Wang, Hongzhen; Ciret, Charles; Godet, Jean-Luc; Cassagne, Christophe; Boudebs, Georges

2018-06-01

The nonlinear (NL) responses of liquid water, ethanol and tetrahydrofuran (THF) are investigated at 355 nm using a Nd:YAG laser delivering pulses of 10 ps. The experiments are performed using the D4σ method combined with the Z-scan technique. Third-order NL refractive indices are determined, as well as the two-photon absorption coefficient and the critical self-focus power. The NL refractive indices are found to be constant for intensity up to 150 GW/cm2 for the three considered solvents, revealing no higher order nonlinearities. Water appears to be a better solvent than ethanol and THF in the UV domain because of its lower NL index and absence of NL absorption. We expect the present study to be useful for NL index measurements in solutions and for numerous future fundamental interest or potential applications.

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.

Laser pulse self-compression in an active fibre with a finite gain bandwidth under conditions of a nonstationary nonlinear response

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.

2018-04-01

We study the influence of a nonstationary nonlinear response of a medium on self-compression of soliton-like laser pulses in active fibres with a finite gain bandwidth. Based on the variational approach, we qualitatively analyse the self-action of the wave packet in the system under consideration in order to classify the main evolution regimes and to determine the minimum achievable laser pulse duration during self-compression. The existence of stable soliton-type structures is shown in the framework of the parabolic approximation of the gain profile (in the approximation of the Gnizburg – Landau equation). An analysis of the self-action of laser pulses in the framework of the nonlinear Schrödinger equation with a sign-constant gain profile demonstrate a qualitative change in the dynamics of the wave field in the case of a nonsta­tionary nonlinear response that shifts the laser pulse spectrum from the amplification region and stops the pulse compression. Expressions for a minimum duration of a soliton-like laser pulse are obtained as a function of the problem parameters, which are in good agreement with the results of numerical simulation.

Optical nonlinearity of D-A-π-D and D-A-π-A type of new chalcones for potential applications in optical limiting and density functional theory studies

NASA Astrophysics Data System (ADS)

Chandra Shekhara Shetty, T.; Chidan Kumar, C. S.; Gagan Patel, K. N.; Chia, Tze Shyang; Dharmaprakash, S. M.; Ramasami, Ponnadurai; Umar, Yunusa; Chandraju, Siddegowda; Quah, Ching Kheng

2017-09-01

Two new chalcones namely, (2E)-1-(3-fluoro-4-methoxyphenyl)-3-(4-methoxyphenyl) prop-2-en-1-one and (2E)-3-(4-chlorophenyl)-1-(3-fluoro-4-methoxyphenyl)prop-2-en-1-one were synthesized and grown as single crystals by slow evaporation technique in methanol. The FTIR spectrum recorded confirms the presence of functional groups in these materials. The molecular conformation of the compounds was achieved by single crystal X-ray diffraction studies. The thermal stability of the crystals was determined from TGA/DSC curve. The third order optical nonlinearity of the chalcone compounds in DMF solution has been carried out using an Nd:YAG laser at 532 nm as the source of excitation. The nonlinear optical response was characterized by measuring the intensity dependent refractive index n2 of the medium using Z-scan technique. It is seen that the molecules exhibit a negative (defocusing) nonlinearity and large nonlinear refractive index of the order of -1.8 × 10-11 esu. The third-order nonlinearity of the studied chalcones is dominated by nonlinear refraction, which leads to strong optical limiting of laser. The result reveals that these two new chalcone molecules would be a promising material for optical limiting applications. In addition, the optimized molecular geometry, vibrational frequencies in gas, and the Molecular Electrostatic Potential (MEP) surface parameters of the two molecules were calculated using DFT/B3LYP method with 6-311++G(d,p) basis set in ground state. All the theoretical calculations were found in good agreement with experimental data.

Photodeposition of Thin Polydiacetylene Films from Solution that Exhibit Large Third-Order Optical Nonlinearities

NASA Technical Reports Server (NTRS)

Paley, M. S.; Frazier, D. O.; Abdeldayem, H.; McManus, S. P.

1994-01-01

One promising class of organic compounds for applications in the field of nonlinear optics (NLO) are polydiacetylenes, which are of interest because they are highly conjugated polymers capable of exhibiting very large optical nonlinearities with fast response times. During the course of crystal growth studies in anticipation of a space experiment, we discovered a novel, simple method for the formation of polydiacetylene thin films by photodeposition from monomer solutions onto quartz or glass substrates. Characterization of these PDAMNA films is not trivial; they are not soluble in common organic solvents, which makes the standard solution-based methods of polymer analysis useless.

Polydiacetylene thin films for nonlinear optical applications

NASA Technical Reports Server (NTRS)

Paley, Mark S.

1993-01-01

One very promising class of organic compounds for nonlinear optical (NLO) applications are polydiacetylenes, which are novel in that they are highly conjugated polymers which can also be crystalline. Polydiacetylenes offer several advantages over other organic materials: because of their highly conjugated electronic structures, they are capable of possessing large optical nonlinearities with fast response times; because they are crystalline, they can be highly ordered, which is essential for optimizing their NLO properties; and, last, because they are polymeric, they can be formed as thin films, which are useful for device fabrication. We have actively been carrying out ground-based research on several compounds of interest.

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.

Z-scan: A simple technique for determination of third-order optical nonlinearity

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

Singh, Vijender, E-mail: chahal-gju@rediffmail.com; Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in

Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to bemore » 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.« less

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.

Dopamine Reward Prediction Error Responses Reflect Marginal Utility

PubMed Central

Stauffer, William R.; Lak, Armin; Schultz, Wolfram

2014-01-01

Summary Background Optimal choices require an accurate neuronal representation of economic value. In economics, utility functions are mathematical representations of subjective value that can be constructed from choices under risk. Utility usually exhibits a nonlinear relationship to physical reward value that corresponds to risk attitudes and reflects the increasing or decreasing marginal utility obtained with each additional unit of reward. Accordingly, neuronal reward responses coding utility should robustly reflect this nonlinearity. Results In two monkeys, we measured utility as a function of physical reward value from meaningful choices under risk (that adhered to first- and second-order stochastic dominance). The resulting nonlinear utility functions predicted the certainty equivalents for new gambles, indicating that the functions’ shapes were meaningful. The monkeys were risk seeking (convex utility function) for low reward and risk avoiding (concave utility function) with higher amounts. Critically, the dopamine prediction error responses at the time of reward itself reflected the nonlinear utility functions measured at the time of choices. In particular, the reward response magnitude depended on the first derivative of the utility function and thus reflected the marginal utility. Furthermore, dopamine responses recorded outside of the task reflected the marginal utility of unpredicted reward. Accordingly, these responses were sufficient to train reinforcement learning models to predict the behaviorally defined expected utility of gambles. Conclusions These data suggest a neuronal manifestation of marginal utility in dopamine neurons and indicate a common neuronal basis for fundamental explanatory constructs in animal learning theory (prediction error) and economic decision theory (marginal utility). PMID:25283778

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Sridharan, Srinivasan

2005-01-01

Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.

Effect of resonant magnetic perturbations on microturbulence in DIII-D pedestal

DOE PAGES

Holod, I.; Lin, Z.; Taimourzadeh, S.; ...

2016-10-03

Vacuum resonant magnetic perturbations (RMP) applied to otherwise axisymmetric tokamak plasmas produce in general a combination of non-resonant effects that preserve closed flux surfaces (kink response) and resonant effects that introduce magnetic islands and/or stochasticity (tearing response). The effect of the plasma kink response on the linear stability and nonlinear transport of edge turbulence is studied using the gyrokinetic toroidal code GTC for a DIII-D plasma with applied n = 2 vacuum RMP. GTC simulations use the 3D equilibrium of DIII-D discharge 158103 (Nazikian et al 2015 Phys. Rev. Lett. 114 105002), which is provided by nonlinear ideal MHD VMECmore » equilibrium solver in order to include the effect of the plasma kink response to the external field but to exclude island formation at rational surfaces. Analysis using the GTC simulation results reveal no increase of growth rates for the electrostatic drift wave instability and for the electromagnetic kinetic-ballooning mode in the presence of the plasma kink response to the RMP. Moreover, nonlinear electrostatic simulations show that the effect of the 3D equilibrium on zonal flow damping is very weak and found to be insufficient to modify turbulent transport in the electrostatic turbulence.« less

Bench-marking effects in the blaming of professionals for incidents of aggression and assault.

PubMed

Carifio, J; Lanza, M

1994-01-01

This study compared all possible orders of responding to three vignettes describing incidents between a male patient and a female nurse in which the nurse is mildly assaulted, severely assaulted, or verbally abused by the patient (the control condition). Subjects were 32 female senior-year nursing students and 28 practicing nurses. It was found that response levels to a given vignette could predict a respondent's response to the other vignettes. Also, a significant "bench-marking" effect was found: if a subject responded to the mild assault vignette first, the subject's overall response pattern best fit the general nonlinear assignment-of-blame pattern observed, but if the subject responded to the severe assault or control vignette first, this vignette set a bench mark for responding from which the subject's subsequent responses did not deviate greatly, which slightly distorted the subject's V-shaped nonlinear response pattern.

Comparisons of linear and nonlinear pyramid schemes for signal and image processing

NASA Astrophysics Data System (ADS)

Morales, Aldo W.; Ko, Sung-Jea

1997-04-01

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.

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.

Quadratic electroabsorption studies of molecular motion in dye-doped polymers

NASA Astrophysics Data System (ADS)

Poga, Constantina; Kuzyk, Mark G.; Dirk, Carl W.

1993-02-01

This paper reports on quadratic electroabsorption studies of thin-film solid solutions of squarylium dye molecules in poly(methylmethacrylate) polymer with the aim of understanding the role of electronic and reorientational mechanisms in the third-order nonlinear-optical susceptibility. We present a generalized theory of the quadratic electrooptic response that includes both electronic mechanisms and molecular reorientation and show that the ratio of two independent third-order susceptibility tensor components, namely (chi) (3)3333/(chi) (3)1133, determines the relative contribution of each mechanism. Based on these theoretical results, we have designed and built an experiment that determines this ratio as a function of temperature and wavelength. Results show that at room temperature and near the first electronic transition wavelength, the response is dominated by the electronic mechanism, and that the reorientational contribution dominates when the sample is heated above its glass transition temperature. Furthermore, results show that, off-resonance, the sign of the imaginary part of the third-order susceptibility is positive. Quadratic electroabsorption is thus shown to be a versatile tool for measuring the imaginary part of the third-order nonlinear-optical susceptibility which yields information about the interaction of polymer and dopant molecule.

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.

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.

High-order nonlinear susceptibilities of He

NASA Astrophysics Data System (ADS)

Liu, W.-C.; Clark, Charles W.

1996-05-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. We have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s^2, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Pont and Shakeshaft (M. Pont and R. Shakeshaft, Phy. Rev. A 51), 257 (1995), and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used(J. D. Baker, Master thesis, U. Delaware (1988); J. D. Baker, R. N. Hill, and J. D. Morgan, AIP Conference Proceedings 189) 123(1989); the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals.

Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

NASA Technical Reports Server (NTRS)

Prezekop, Adam

2008-01-01

Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification leading to formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure gradients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency and span of the oscillating pressure gradient.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Study of the use of a nonlinear, rate limited, filter on pilot control signals

NASA Technical Reports Server (NTRS)

Adams, J. J.

1977-01-01

The use of a filter on the pilot's control output could improve the performance of the pilot-aircraft system. What is needed is a filter with a sharp high frequency cut-off, no resonance peak, and a minimum of lag at low frequencies. The present investigation studies the usefulness of a nonlinear, rate limited, filter in performing the needed function. The nonlinear filter is compared with a linear, first order filter, and no filter. An analytical study using pilot models and a simulation study using experienced test pilots was performed. The results showed that the nonlinear filter does promote quick, steady maneuvering. It is shown that the nonlinear filter attenuates the high frequency remnant and adds less phase lag to the low frequency signal than does the linear filter. It is also shown that the rate limit in the nonlinear filter can be set to be too restrictive, causing an unstable pilot-aircraft system response.

Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures

NASA Astrophysics Data System (ADS)

Fierro, Gian Piero Malfense; Calla', Danielle; Ginzburg, Dmitri; Ciampa, Francesco; Meo, Michele

2017-09-01

Traditional non-destructive evaluation (NDE) and structural health monitoring (SHM) systems are used to analyse that a structure is free of any harmful damage. However, these techniques still lack sensitivity to detect the presence of material micro-flaws in the form of fatigue damage and often require time-consuming procedures and expensive equipment. This research work presents a novel "nonlinear ultrasonic stimulated thermography" (NUST) method able to overcome some of the limitations of traditional linear ultrasonic/thermography NDE-SHM systems and to provide a reliable, rapid and cost effective estimation of fatigue damage in isotropic materials. Such a hybrid imaging approach combines the high sensitivity of nonlinear acoustic/ultrasonic techniques to detect micro-damage, with local defect frequency selection and infrared imaging. When exciting structures with an optimised frequency, nonlinear elastic waves are observed and higher frictional work at the fatigue damaged area is generated due to clapping and rubbing of the crack faces. This results in heat at cracked location that can be measured using an infrared camera. A Laser Vibrometer (LV) was used to evaluate the extent that individual frequency components contribute to the heating of the damage region by quantifying the out-of-plane velocity associated with the fundamental and second order harmonic responses. It was experimentally demonstrated the relationship between a nonlinear ultrasound parameter (βratio) of the material nonlinear response to the actual temperature rises near the crack. These results demonstrated that heat generation at damaged regions could be amplified by exciting at frequencies that provide nonlinear responses, thus improving the imaging of material damage and the reliability of NUST in a quick and reproducible manner.

Mechanisms of the Third-Order Nonlinear Optical Response in Dye-Doped Polymers.

NASA Astrophysics Data System (ADS)

Poga, Constantina

Quadratic Electroabsorption is applied to thin -film solid solutions of squarylium dye molecules in poly(methyl methacrylate) polymer to study the mechanisms in the third order nonlinear optical susceptibility. The data are interpreted with the help of a generalized quadratic electrooptic response theory that includes both electronic and hindered molecular motion mechanisms. This theory predicts the tensor ratio of two independent third order susceptibility tensor components, chi_sp{3333}{(3)}/ chi_sp{1133}{(3)}, whose value distinctly characterizes the relative contribution of each mechanism. Although thickness change mechanisms have not been included in this theory, their effect on the tensor ratio chi_sp{3333 }{(3)}/chi_sp{1133} {(3)} has been taken into account for both electrostriction and electrode attraction mechanisms. We measure the tensor ratio with quadratic electroabsorption spectroscopy as a function of temperature and wavelength and find that the response is predominantly electronic at temperatures below the glass transition temperature, but at temperatures higher than the glass transition temperature both reorientational and thickness changes effects play a dominant role. In particular, the contribution of each mechanism has been found for all wavelengths in the visible and the dominant thickness change mechanism has been identified to be electrode attraction. Additionally, the real part of the third-order nonlinear susceptibility can be found through a Kramers-Kronig transformation of the experimentally measured imaginary part. The knowledge of both the real and imaginary part in the visible allows the calculation of the two-photon figure of merit (defined as the real over the imaginary part of chi^{(3) }) which is necessary for determining a material's suitability for all-optical devices. Furthermore, quadratic electroabsorption can be used to characterize the nature of the excited states which in turn can be used to understand the source of the electronic response. For the ISQ chromophore, a one-photon state (at 657nm) and a two-photon state (at 596nm) have been found, and a three-level fit based on these states has been successful in predicting the low temperature chi^{(3)}^ectrum. Quadratic electroabsorption has been proven to be a versatile tool to study the mechanisms of the third -order nonlinear optical response, to measure the electronic gamma, to study the symmetry of the excited states of a molecule and to characterize the suitability of a material for all-optical devices. In this chapter, we start by calculating the change in the imaginary part of the refractive index under the application of an electric field and proceed with connecting this change with the quantities that are experimentally measured by the quadratic electroabsorption experiment. The sample preparation and the data collection are also described.

Computational Studies on Optoelectronic and Nonlinear Properties of Octaphyrin Derivatives

PubMed Central

Islam, Nasarul; Lone, Irfan H.

2017-01-01

The electronic and nonlinear optical (NLO) properties of octaphyrin derivatives were studied by employing the DFT/TDFT at CAM-B3LYP/6-311++G (2d, 2p) level of the theory. Thiophene, phenyl, methyl and cyano moieties were substituted on the molecular framework of octaphyrin core, in order to observe the change in optoelectronic and nonlinear response of these systems. The frontier molecular orbital studies and values of electron affinity reveals that the studied compounds are stable against the oxygen and moisture present in air. The calculated ionization energies, adiabatic electron affinity and reorganization energy values indicate that octaphyrin derivatives can be employed as effective n-type material for Organic Light Emitting Diodes (OLEDs). This character shows an enhancement with the introduction of an electron withdrawing group in the octaphyrin framework. The polarizability and hyperpolarizability values of octaphyrin derivatives demonstrate that they are good candidates for NLO devices. The nonlinear response of these systems shows enhancement on the introduction of electron donating groups on octaphyrin moiety. However, these claims needs further experimental verification. PMID:28321394

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics

PubMed Central

Tse, Peter W.; Wang, Dong

2017-01-01

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions. PMID:28216586

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics.

PubMed

Tse, Peter W; Wang, Dong

2017-02-14

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Frequency response of nonlinear oscillations of air column in a tube with an array of Helmholtz resonators.

PubMed

Sugimoto, N; Masuda, M; Hashiguchi, T

2003-10-01

Nonlinear cubic theory is developed to obtain a frequency response of shock-free, forced oscillations of an air column in a closed tube with an array of Helmholtz resonators connected axially. The column is assumed to be driven by a plane piston sinusoidally at a frequency close or equal to the lowest resonance frequency with its maximum displacement fixed. By applying the method of multiple scales, the equation for temporal modulation of a complex pressure amplitude of the lowest mode is derived in a case that a typical acoustic Mach number is comparable with the one-third power of the piston Mach number, while the relative detuning of a frequency is comparable with the quadratic order of the acoustic Mach number. The steady-state solution gives the asymmetric frequency response curve with bending (skew) due to nonlinear frequency upshift in addition to the linear downshift. Validity of the theory is checked against the frequency response obtained experimentally. For high amplitude of oscillations, an effect of jet loss at the throat of the resonator is taken into account, which introduces the quadratic loss to suppress the peak amplitude. It is revealed that as far as the present check is concerned, the weakly nonlinear theory can give quantitatively adequate description up to the pressure amplitude of about 3% to the equilibrium pressure.

Nonlinear Whirl Response of a High-Speed Seal Test Rotor With Marginal and Extended Squeeze-Film Dampers

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Gunter, Edgar J.

2005-01-01

Synchronous and nonsynchronous whirl response analysis of a double overhung, high-speed seal test rotor with ball bearings supported in 5.84- and 12.7-mm-long, un-centered squeeze-film oil dampers is presented. Test performance with the original damper of length 5.84 mm was marginal, with nonsynchronous whirling at the overhung seal test disk and high amplitude synchronous response above 32,000 rpm near the drive spline section occurring. A system critical speed analysis of the drive system and the high-speed seal test rotor indicated that the first two critical speeds are associated with the seal test rotor. Nonlinear synchronous unbalance and time transient whirl studies were conducted on the seal test rotor with the original and extended damper lengths. With the original damper design, the nonlinear synchronous response showed that unbalance could cause damper lockup at 33,000 rpm. Alford cross-coupling forces were also included at the overhung seal test disk for the whirl analysis. Sub-synchronous whirling at the seal test disk was observed in the nonlinear time transient analysis. With the extended damper length of 12.7 mm, the sub-synchronous motion was eliminated and the rotor unbalance response was acceptable to 45,000 rpm with moderate rotor unbalance. However, with high rotor unbalance, damper lockup could still occur at 33,000 rpm, even with the extended squeeze-film dampers. Therefore, the test rotor must be reasonably balanced in order for the un-centered dampers to be effective.

Higher-Order Spectral Analysis of F-18 Flight Flutter Data

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Dunn, Shane

2005-01-01

Royal Australian Air Force (RAAF) F/A-18 flight flutter test data is presented and analyzed using various techniques. The data includes high-quality measurements of forced responses and limit cycle oscillation (LCO) phenomena. Standard correlation and power spectral density (PSD) techniques are applied to the data and presented. Novel applications of experimentally-identified impulse responses and higher-order spectral techniques are also applied to the data and presented. The goal of this research is to develop methods that can identify the onset of nonlinear aeroelastic phenomena, such as LCO, during flutter testing.

Synthesis of poly glycidylmethacrylate grafted azobenzene copolymer: Photosensitivity and nonlinear optical properties

NASA Astrophysics Data System (ADS)

Sousani, Abbas; Moghadam, Peyman Najafi; Hasanzadeh, Reza; Motiei, Hamideh; Bagheri, Massoumeh

2016-01-01

In this work poly glycidylmethacrylate grafted 4-hydroxy-4‧-methoxy-azobenzene (Azo-PGMA) was synthesized. For this propose firstly 4-hydroxy-4‧-methoxy-azobenzene (AZO) was prepared, then poly glycidylmethacrylate was prepared by free radical polymerization of glycidylmethacrylate in the presence of benzoyl peroxide as initiator under inert atmosphere in dry THF. Finally the homopolymer was functionalized by AZO moieties. The characterization of the synthesized copolymer was carried out by 1H NMR, FT-IR, thermal gravimetric analyze (TGA), differential scanning calorimetry (DSC) and optical polarizing microscope (POM) analysis. The UV-vis studies were carried out on Azo-PGMA copolymer and the results showed that the synthesized Azo-PGMA copolymer has ultra-fast response to UV light and has slow relaxation time. Also the third-order nonlinear optical properties of the Azo-PGMA copolymer and AZO were studied by using Z-scan technique. Nonlinear refraction and absorption coefficients of the above mentioned materials were measured by the closed and open aperture Z-scan method using a continuous wave Nd-YAG laser at 532 nm. The positive nonlinear absorption in Azo-PGMA and AZO was investigated at the wavelength of λ = 532 nm, respectively and the measured values of nonlinear refraction in both of the samples were from the order of 10-8 cm2/W.

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.

Modelling, validation and analysis of a three-dimensional railway vehicle-track system model with linear and nonlinear track properties in the presence of wheel flats

NASA Astrophysics Data System (ADS)

Uzzal, R. U. A.; Ahmed, A. K. W.; Bhat, R. B.

2013-11-01

This paper presents dynamic contact loads at wheel-rail contact point in a three-dimensional railway vehicle-track model as well as dynamic response at vehicle-track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel-rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle-track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel-rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel-rail impact forces that arise in the wheel-rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.

A third-order class-D amplifier with and without ripple compensation

NASA Astrophysics Data System (ADS)

Cox, Stephen M.; du Toit Mouton, H.

2018-06-01

We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts an input audio signal to a high-frequency train of rectangular pulses, whose widths are modulated according to the input signal (pulse-width modulation) and employs negative feedback. After determining the steady-state operating point for constant input and calculating its stability, we derive a small-signal model (SSM), which yields in closed form the transfer function relating (infinitesimal) input and output disturbances. This SSM shows how the RC technique is able to linearise the small-signal response of the device. We extend this SSM through a fully nonlinear perturbation calculation of the dynamics of the amplifier, based on the disparity in time scales between the pulse train and the audio signal. We obtain the nonlinear response of the amplifier to a general audio signal, avoiding the linearisation inherent in the SSM; we thereby more precisely quantify the reduction in distortion achieved through RC. Finally, simulations corroborate our theoretical predictions and illustrate the dramatic deterioration in performance that occurs when the amplifier is operated in an unstable regime. The perturbation calculation is rather general, and may be adapted to quantify the way in which other nonlinear negative-feedback pulse-modulated devices track a time-varying input signal that slowly modulates the system parameters.

A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver

NASA Technical Reports Server (NTRS)

Telban, Robert J.; Cardullo, Frank M.; Houck, Jacob A.

2002-01-01

This paper discusses the continuation of research into the development of new motion cueing algorithms first reported in 1999. In this earlier work, two viable approaches to motion cueing were identified: the coordinated adaptive washout algorithm or 'adaptive algorithm', and the 'optimal algorithm'. In this study, a novel approach to motion cueing is discussed that would combine features of both algorithms. The new algorithm is formulated as a linear optimal control problem, incorporating improved vestibular models and an integrated visual-vestibular motion perception model previously reported. A control law is generated from the motion platform states, resulting in a set of nonlinear cueing filters. The time-varying control law requires the matrix Riccati equation to be solved in real time. Therefore, in order to meet the real time requirement, a neurocomputing approach is used to solve this computationally challenging problem. Single degree-of-freedom responses for the nonlinear algorithm were generated and compared to the adaptive and optimal algorithms. Results for the heave mode show the nonlinear algorithm producing a motion cue with a time-varying washout, sustaining small cues for a longer duration and washing out larger cues more quickly. The addition of the optokinetic influence from the integrated perception model was shown to improve the response to a surge input, producing a specific force response with no steady-state washout. Improved cues are also observed for responses to a sway input. Yaw mode responses reveal that the nonlinear algorithm improves the motion cues by reducing the magnitude of negative cues. The effectiveness of the nonlinear algorithm as compared to the adaptive and linear optimal algorithms will be evaluated on a motion platform, the NASA Langley Research Center Visual Motion Simulator (VMS), and ultimately the Cockpit Motion Facility (CMF) with a series of pilot controlled maneuvers. A proposed experimental procedure is discussed. The results of this evaluation will be used to assess motion cueing performance.

Second-order nonlinearity induced transparency.

PubMed

Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X

2017-04-01

In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

PubMed

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.

PubMed

Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng

2017-09-15

Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Dopamine reward prediction error responses reflect marginal utility.

PubMed

Stauffer, William R; Lak, Armin; Schultz, Wolfram

2014-11-03

Optimal choices require an accurate neuronal representation of economic value. In economics, utility functions are mathematical representations of subjective value that can be constructed from choices under risk. Utility usually exhibits a nonlinear relationship to physical reward value that corresponds to risk attitudes and reflects the increasing or decreasing marginal utility obtained with each additional unit of reward. Accordingly, neuronal reward responses coding utility should robustly reflect this nonlinearity. In two monkeys, we measured utility as a function of physical reward value from meaningful choices under risk (that adhered to first- and second-order stochastic dominance). The resulting nonlinear utility functions predicted the certainty equivalents for new gambles, indicating that the functions' shapes were meaningful. The monkeys were risk seeking (convex utility function) for low reward and risk avoiding (concave utility function) with higher amounts. Critically, the dopamine prediction error responses at the time of reward itself reflected the nonlinear utility functions measured at the time of choices. In particular, the reward response magnitude depended on the first derivative of the utility function and thus reflected the marginal utility. Furthermore, dopamine responses recorded outside of the task reflected the marginal utility of unpredicted reward. Accordingly, these responses were sufficient to train reinforcement learning models to predict the behaviorally defined expected utility of gambles. These data suggest a neuronal manifestation of marginal utility in dopamine neurons and indicate a common neuronal basis for fundamental explanatory constructs in animal learning theory (prediction error) and economic decision theory (marginal utility). Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1999-01-01

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

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.

Adaptation to Variance of Stimuli in Drosophila Larva Navigation

NASA Astrophysics Data System (ADS)

Wolk, Jason; Gepner, Ruben; Gershow, Marc

In order to respond to stimuli that vary over orders of magnitude while also being capable of sensing very small changes, neural systems must be capable of rapidly adapting to the variance of stimuli. We study this adaptation in Drosophila larvae responding to varying visual signals and optogenetically induced fictitious odors using an infrared illuminated arena and custom computer vision software. Larval navigational decisions (when to turn) are modeled as the output a linear-nonlinear Poisson process. The development of the nonlinear turn rate in response to changes in variance is tracked using an adaptive point process filter determining the rate of adaptation to different stimulus profiles. Supported by NIH Grant 1DP2EB022359 and NSF Grant PHY-1455015.

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

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.

Syntheses of Octasubstituted Metal Phthalocyanines for Nonlinear Optics

NASA Technical Reports Server (NTRS)

Guo, Huaisong; Townsend, Cheryl; Sanghadasa, Mohan; Amai, Robert L. S.; Clark, Ronald D.; Penn, Benjamin

1998-01-01

Many organic materials can be used as nonlinear optical media. Phthalocyanines are of special interest because they show an unusually large third order nonlinear response, they are thermally and photochemically stable and they can be formed into oriented thin films (Langmuir-Blodgett films). They also can be easily complexed by a large variety of metals, which place them at the interface between organics and organometallics, and allows for fine tuning of the macro cycle electronic properties by the coordinated metal and substituent groups. A series of 1,4,8,11,15,18,22,25-octaalkoxy metal-free and metal phthalocyanines and 2,3,9,10,16,17,23,24-octaalkoxy metal phthalocyanines has been synthesized. Their nonlinear optical properties have been measured. The physical properties of all the phthalocyanines synthesized in this work are subject to both acid and solvent effects.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. 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 models were the same. Non-linear regression analysis showed that both Blanchard 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.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Validity Using Pump-Probe Pulses to Determine the Optical Response of Niobate Crystals

NASA Technical Reports Server (NTRS)

Liu, Huimin; Jia, Weiyi

1997-01-01

A variety of niobate crystals have found their places in nonlinear optical applications as well as in laser devices. In recent years much attention has been paid to study the ultrafast optical response in a variety of photorefractive crystals such as KTa(1-x)Nb(x)O3 and KNbO3 crystals, glasses, semiconductors and polymers for applications in optical switching, information processing, optical computing, and all-optical device systems. Third-order optical nonlinearity is the most important property for realization of all-optical switching. Therefore experiments have been performed on the third order susceptibility using a variety of techniques such as the third-order harmonic generation, EFISH and degenerate four-wave mixing(DFWM). The latter has been conducted with a variety of pump wavelengths and with nanosecond, picosecond and femtosecond pulses. Niobate crystals, such as potassium niobate KNbO3, potassium tantalate niobate KTN family (KTa(1-x)Nb(x)O3), strontium barium niobate SBN (Sr(x)Ba(1-x)Nb2O6) and potassium-sodium niobate SBN (KNSBN) are attractive due to their photorefractive properties for application in optical storage and processing. The pulsed probe experiments performed on theses materials have suggested two types of time responses. These responses have been associated with an coherent response due to Chi(sup 3), and a long lived component due to excited state population. Recent study of DFWM on KNbO3 and KTN family reveals that the long lived component of those crystals depends on the crystal orientation. A slowly decaying signal is observable when the grating vector K(sub g) is not perpendicular to the C-axis of those photorefractive crystals', otherwise the optical response signal would be only a narrow coherent peak with FWHM equal to the cross-correlation width of the write beam pulses. Based on this understanding, we study the photodynamical process of a variety of niobate crystals using DFWM in a Kg perpindicular to C geometry with a ps-YAG: Nd laser operating at 532nm. However, the discrepancies in numerical estimations of Chi(sup 3) in these materials and other nonlinear optical media have resulted in a number of discussions. In order to better understand the photodynamical process of niobate crystals after an short pulse excitation we analyze the factors governing the coherent signal and present the DFWM spectra of niobate crystals.

ac response of thin superconductors in the flux-creep regime

NASA Astrophysics Data System (ADS)

Gurevich, A.; Brandt, E. H.

1997-05-01

We calculate both analytically and numerically the ac susceptibility χ(ω) and the nonlinear electromagnetic response of thin superconductor strips and disks of constant thickness in a perpendicular time-dependent magnetic field Ba(t)=B0cos ωt, taking account of the strong nonlinearity of the voltage-current characteristics below the irreversibility line. We consider integral equations of nonlinear nonlocal flux diffusion for a wide class of thermally activated creep models. It is shown that thin superconductors, despite being fully in the critical state, exhibit a universal Meissner-like electromagnetic response in the dissipative flux-creep regime. The expression for the linear ac susceptibility during flux creep appears to be similar to the susceptibility of Ohmic conductors, but with the relaxation time constant replaced by the time t elapsed after flux creep has started. This result is independent of any material parameter or temperature or dc field. For ωt>>:1, we obtain χ(ω)~-1+pln (qiωt)/(iωt), where p and q are constants. Above a critical ac amplitude B0=Bl, the local response of the electric field becomes nonlinear, and there are two distinctive nonlinear regimes at B0>Bl, where Bl~s(d/a)1/2Bp, Bp is a characteristic field of full flux penetration, s(T,B)=\\|dln j/dln t\\| is the dimensionless flux-creep rate and d and a are the sample thickness and width, respectively. For BlBh(ω) the ac field causes hysteresis dissipation due to a periodic remagnetization of the critical state that gives rise to the hysteretic magnetic response of the Bean model at B0>>:Bh. Here Bh(ω) weakly depends on ω and is of order (d/a)1/2Bp for a very wide frequency range, well below the irreversibility field, where s(T,B)<<1. Magnetization and ac losses at B0>>:Bh are calculated accounting for the nonlinearity of E(J) at J

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.

Increased Order Modeling Approach to Unsteady Aerodynamics and Aeroelasticity

DTIC Science & Technology

2010-03-01

dynamic simulation of a maneuvering air vehicle with actuator free play , limit-cycle oscillations (LCO) of platetype fins with nonlinear plate-stiffness...6 2.3 Response to maneuver command with actuator free play ............................................................ 8...15 3.2 LCO Simulations with actuator free play .....................................................................................18

Simulated electron affinity tuning in metal-insulator-metal (MIM) diodes

NASA Astrophysics Data System (ADS)

Mistry, Kissan; Yavuz, Mustafa; Musselman, Kevin P.

2017-05-01

Metal-insulator-metal diodes for rectification applications must exhibit high asymmetry, nonlinearity, and responsivity. Traditional methods of improving these figures of merit have consisted of increasing insulator thickness, adding multiple insulator layers, and utilizing a variety of metal contact combinations. However, these methods have come with the price of increasing the diode resistance and ultimately limiting the operating frequency to well below the terahertz regime. In this work, an Airy Function Transfer Matrix simulation method was used to observe the effect of tuning the electron affinity of the insulator as a technique to decrease the diode resistance. It was shown that a small increase in electron affinity can result in a resistance decrease in upwards of five orders of magnitude, corresponding to an increase in operating frequency on the same order. Electron affinity tuning has a minimal effect on the diode figures of merit, where asymmetry improves or remains unaffected and slight decreases in nonlinearity and responsivity are likely to be greatly outweighed by the improved operating frequency of the diode.

Tunneling induced absorption with competing Nonlinearities.

PubMed

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-12-13

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility.

Dynamics of neurons controlling movements of a locust hind leg. III. Extensor tibiae motor neurons.

PubMed

Newland, P L; Kondoh, Y

1997-06-01

Imposed movements of the apodeme of the femoral chordotonal organ (FeCO) of the locust hind leg elicit resistance reflexes in extensor and flexor tibiae motor neurons. The synaptic responses of the fast and slow extensor tibiae motor neurons (FETi and SETi, respectively) and the spike responses of SETi were analyzed with the use of the Wiener kernel white noise method to determine their response properties. The first-order Wiener kernels computed from soma recordings were essentially monophasic, or low passed, indicating that the motor neurons were primarily sensitive to the position of the tibia about the femorotibial joint. The responses of both extensor motor neurons had large nonlinear components. The second-order kernels of the synaptic responses of FETi and SETi had large on-diagonal peaks with two small off-diagonal valleys. That of SETi had an additional elongated valley on the diagonal, which was accompanied by two off-diagonal depolarizing peaks at a cutoff frequency of 58 Hz. These second-order components represent a half-wave rectification of the position-sensitive depolarizing response in FETi and SETi, and a delayed inhibitory input to SETi, indicating that both motor neurons were directionally sensitive. Model predictions of the responses of the motor neurons showed that the first-order (linear) characterization poorly predicted the actual responses of FETi and SETi to FeCO stimulation, whereas the addition of the second-order (nonlinear) term markedly improved the performance of the model. Simultaneous recordings from the soma and a neuropilar process of FETi showed that its synaptic responses to FeCO stimulation were phase delayed by about -30 degrees at 20 Hz, and reduced in amplitude by 30-40% when recorded in the soma. Similar configurations of the first and second-order kernels indicated that the primary process of FETi acted as a low-pass filter. Cross-correlation between a white noise stimulus and a unitized spike discharge of SETi again produced well-defined first- and second-order kernels that showed that the SETi spike response was also dependent on positional inputs. An elongated negative valley on the diagonal, characteristic of the second-order kernel of the synaptic response in SETi, was absent in the kernel from the spike component, suggesting that information is lost in the spike production process. The functional significance of these results is discussed in relation to the behavior of the locust.

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

NASA Technical Reports Server (NTRS)

Engelstad, S. P.; Knight, N. F., Jr.; Reddy, J. N.

1990-01-01

The influence of shear flexibility on overall postbuckling response was assessed, and transverse shear stress distributions in relation to panel failure were examined. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented analytically substantiate the experimentally observed failure mode.

Large optical second-order nonlinearity of poled WO3-TeO2 glass.

PubMed

Tanaka, K; Narazaki, A; Hirao, K

2000-02-15

Second-harmonic generation, one of the second-order nonlinear optical properties of thermally and electrically poled WO>(3)-TeO>(2) glasses, has been examined. We poled glass samples with two thicknesses (0.60 and 0.86 mm) at various temperatures to explore the effects of external electric field strength and poling temperature on second-order nonlinearity. The dependence of second-harmonic intensity on the poling temperature is maximum at a specific poling temperature. A second-order nonlinear susceptibility of 2.1 pm/V was attained for the 0.60-mm-thick glass poled at 250 degrees C. This value is fairly large compared with those for poled silica and tellurite glasses reported thus far. We speculate that the large third-order nonlinear susceptibility of WO>(3)- TeO>(2) glasses gives rise to the large second-order nonlinearity by means of a X((2)) = 3X((3)) E(dc) process.

Sustainability of transport structures - some aspects of the nonlinear reliability assessment

NASA Astrophysics Data System (ADS)

Pukl, Radomír; Sajdlová, Tereza; Strauss, Alfred; Lehký, David; Novák, Drahomír

2017-09-01

Efficient techniques for both nonlinear numerical analysis of concrete structures and advanced stochastic simulation methods have been combined in order to offer an advanced tool for assessment of realistic behaviour, failure and safety assessment of transport structures. The utilized approach is based on randomization of the non-linear finite element analysis of the structural models. Degradation aspects such as carbonation of concrete can be accounted in order predict durability of the investigated structure and its sustainability. Results can serve as a rational basis for the performance and sustainability assessment based on advanced nonlinear computer analysis of the structures of transport infrastructure such as bridges or tunnels. In the stochastic simulation the input material parameters obtained from material tests including their randomness and uncertainty are represented as random variables or fields. Appropriate identification of material parameters is crucial for the virtual failure modelling of structures and structural elements. Inverse analysis using artificial neural networks and virtual stochastic simulations approach is applied to determine the fracture mechanical parameters of the structural material and its numerical model. Structural response, reliability and sustainability have been investigated on different types of transport structures made from various materials using the above mentioned methodology and tools.

Crystal growth, spectroscopic, DFT computational and third harmonic generation studies of nicotinic acid

NASA Astrophysics Data System (ADS)

Thaya Kumari, C. Rathika; Nageshwari, M.; Raman, R. Ganapathi; Caroline, M. Lydia

2018-07-01

An organic centrosymmetric nicotinic acid (NA) single crystal has been grown employing slow evaporation method in water. NA crystallizes in monoclinic system with centric space group P21/C. The experimental and theoretical investigation includes vibrational spectra based on Hartree - Fock (HF) and density functional theory (DFT) has been applied using different function at B3LYP level of theory using 6-311G++(d,p) basis set. The optical transparency of the title molecule was examined by TD- DFT analysis and for comparison basis experimental UV-Vis spectrum was recorded. The interaction of charge within the molecule was analyzed and the HOMO - LUMO energy gap was evaluated. The value of dipole moment, Mulliken charge and molecular electrostatic potential were estimated at the same level of theory. Also the first order hyper polarizability for NA was calculated. The dielectric behavior of the grown crystal was determined for few selected temperatures. The third order nonlinear response of NA has been examined using Z-scan technique and nonlinear susceptibility (χ3), nonlinear refraction (n2) and nonlinear absorption coefficient (β) has been calculated. The current results clearly indicate that the title compound is an excellent applicant in the domain of opto - electronic applications.

Comparing Pearson, Spearman and Hoeffding's D measure for gene expression association analysis.

PubMed

Fujita, André; Sato, João Ricardo; Demasi, Marcos Angelo Almeida; Sogayar, Mari Cleide; Ferreira, Carlos Eduardo; Miyano, Satoru

2009-08-01

DNA microarrays have become a powerful tool to describe gene expression profiles associated with different cellular states, various phenotypes and responses to drugs and other extra- or intra-cellular perturbations. In order to cluster co-expressed genes and/or to construct regulatory networks, definition of distance or similarity between measured gene expression data is usually required, the most common choices being Pearson's and Spearman's correlations. Here, we evaluate these two methods and also compare them with a third one, namely Hoeffding's D measure, which is used to infer nonlinear and non-monotonic associations, i.e. independence in a general sense. By comparing three different variable association approaches, namely Pearson's correlation, Spearman's correlation and Hoeffding's D measure, we aimed at assessing the most appropriate one for each purpose. Using simulations, we demonstrate that the Hoeffding's D measure outperforms Pearson's and Spearman's approaches in identifying nonlinear associations. Our results demonstrate that Hoeffding's D measure is less sensitive to outliers and is a more powerful tool to identify nonlinear and non-monotonic associations. We have also applied Hoeffding's D measure in order to identify new putative genes associated with tp53. Therefore, we propose the Hoeffding's D measure to identify nonlinear associations between gene expression profiles.

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.

Synthesis, Hirshfeld surface analysis, laser damage threshold, third-order nonlinear optical property and DFT computation studies of Dichlorobis(DL-valine)zinc(II): A spectroscopic approach

NASA Astrophysics Data System (ADS)

Chitrambalam, S.; Manimaran, D.; Hubert Joe, I.; Rastogi, V. K.; Ul Hassan, Israr

2018-01-01

The organometallic crystal of Dichlorobis(DL-valine)zinc(II) was grown by solution growth method. The computed structural geometry, vibrational wavenumbers and UV-visible spectra were compared with experimental results. Hirshfeld surface map was used to locate electron density and the fingerprint plots percentages are responsible for the stabilization of intermolecular interactions in molecular crystal. The second-order hyperpolarizability value of the molecule was also calculated at density functional theory method. The surface resistance and third-order nonlinear optical property of the crystal were studied by laser induced surface damage threshold and Z-scan techniques, respectively using Nd:YAG laser with wavelength 532 nm. The open aperture result exhibits the reverse saturation absorption, which indicate that this material has potential candidate for optical limiting and optoelectronic applications.

The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses

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

Guo, Haitao, E-mail: guoht_001@opt.ac.cn; Chen, Hongyan; Hou, Chaoqi

2011-05-15

Research highlights: {yields} It is firstly demonstrated that the nonlinear refractive index n{sub 2} is dependent on the covalency of bonds in chalcogenide glass. {yields} Homopolar metallic bonds in chalcogenide glass have positive contribution to large nonlinear refractive index n{sub 2} also. {yields} The 80GeS{sub 2}.20Sb{sub 2}S{sub 3} glass would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths. -- Abstract: The third-order optical nonlinearities of 80GeS{sub 2}.(20 - x)Ga{sub 2}S{sub 3}.xY{sub 2}S{sub 3} (x = 0, 5, 10, 15, 20 and Y = Sb or In) chalcogenide glasses were investigatedmore » utilizing the Z-scan method at the wavelength of 800 nm and their linear optical properties and structure were also studied. By analyzing the compositional dependences and possible influencing factors including the linear refractive index, the concentration of lone electron pairs, the optical bandgap and the amount of weak covalent/homopolar bonds, it indicates that the electronic contribution in weak heteropolar covalent and homopolar metallic bonds is responsible for large nonlinear refractive index n{sub 2} in the chalcogenide glasses. These chalcogenide glasses have characteristics of environmentally friendship, wide transparency in the visible region, high nonlinear refractive index n{sub 2} and low nonlinear absorption coefficient {beta}, and would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths.« less

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact

NASA Technical Reports Server (NTRS)

Zheng, Xia-Hua; Goldberg, Robert K.; Binienda, Wieslaw K.; Roberts, Gary D.

2003-01-01

A recently developed constitutive model is implemented into LS-DYNA as a user defined material model (UMAT) to characterize the nonlinear strain rate dependent behavior of polymers. By utilizing this model within a micromechanics technique based on a laminate analogy, an algorithm to analyze the strain rate dependent, nonlinear deformation of a fiber reinforced polymer matrix composite is then developed as a UMAT to simulate the response of these composites under high strain rate impact. The models are designed for shell elements in order to ensure computational efficiency. Experimental and numerical stress-strain curves are compared for two representative polymers and a representative polymer matrix composite, with the analytical model predicting the experimental response reasonably well.

Core reactivity estimation in space reactors using recurrent dynamic networks

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Tsai, Wei K.

1991-01-01

A recurrent multilayer perceptron network topology is used in the identification of nonlinear dynamic systems from only the input/output measurements. The identification is performed in the discrete time domain, with the learning algorithm being a modified form of the back propagation (BP) rule. The recurrent dynamic network (RDN) developed is applied for the total core reactivity prediction of a spacecraft reactor from only neutronic power level measurements. Results indicate that the RDN can reproduce the nonlinear response of the reactor while keeping the number of nodes roughly equal to the relative order of the system. As accuracy requirements are increased, the number of required nodes also increases, however, the order of the RDN necessary to obtain such results is still in the same order of magnitude as the order of the mathematical model of the system. It is believed that use of the recurrent MLP structure with a variety of different learning algorithms may prove useful in utilizing artificial neural networks for recognition, classification, and prediction of dynamic systems.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Nonlinear elastic response of strong solids: First-principles calculations of the third-order elastic constants of diamond

DOE PAGES

Hmiel, A.; Winey, J. M.; Gupta, Y. M.; ...

2016-05-23

Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elasticmore » constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Lastly, our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.« less

Control of optical bistability and third-order nonlinearity via tunneling induced quantum interference in triangular quantum dot molecules

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

Tian, Si-Cong, E-mail: tiansicong@ciomp.ac.cn; Tong, Cun-Zhu, E-mail: tongcz@ciomp.ac.cn; Zhang, Jin-Long

The optical bistability of a triangular quantum dot molecules embedded inside a unidirectional ring cavity is studied. The type, the threshold and the hysteresis loop of the optical bistability curves can be modified by the tunneling parameters, as well as the probe laser field. The linear and nonlinear susceptibilities of the medium are also studied to interpret the corresponding results. The physical interpretation is that the tunneling can induce the quantum interference, which modifies the linear and the nonlinear response of the medium. As a consequence, the characteristics of the optical bistability are changed. The scheme proposed here can bemore » utilized for optimizing and controlling the optical switching process.« less

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.

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.

Tunneling induced absorption with competing Nonlinearities

PubMed Central

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-01-01

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility. PMID:27958303

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Computer simulation of multiple pilots flying a modern high performance helicopter

NASA Technical Reports Server (NTRS)

Zipf, Mark E.; Vogt, William G.; Mickle, Marlin H.; Hoelzeman, Ronald G.; Kai, Fei; Mihaloew, James R.

1988-01-01

A computer simulation of a human response pilot mechanism within the flight control loop of a high-performance modern helicopter is presented. A human response mechanism, implemented by a low order, linear transfer function, is used in a decoupled single variable configuration that exploits the dominant vehicle characteristics by associating cockpit controls and instrumentation with specific vehicle dynamics. Low order helicopter models obtained from evaluations of the time and frequency domain responses of a nonlinear simulation model, provided by NASA Lewis Research Center, are presented and considered in the discussion of the pilot development. Pilot responses and reactions to test maneuvers are presented and discussed. Higher level implementation, using the pilot mechanisms, are discussed and considered for their use in a comprehensive control structure.

An experimental nonlinear low dynamic stiffness device for shock isolation

NASA Astrophysics Data System (ADS)

Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin

2015-07-01

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

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.

Non-isothermal buckling behavior of viscoplastic shell structures

NASA Technical Reports Server (NTRS)

Riff, Richard; Simitses, G. J.

1988-01-01

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Nonparametric Model of Smooth Muscle Force Production During Electrical Stimulation.

PubMed

Cole, Marc; Eikenberry, Steffen; Kato, Takahide; Sandler, Roman A; Yamashiro, Stanley M; Marmarelis, Vasilis Z

2017-03-01

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

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.)

Gyroscopic behavior exhibited by the optical Kerr effect in bimetallic Au-Pt nanoparticles suspended in ethanol

NASA Astrophysics Data System (ADS)

Fernández-Valdés, D.; Torres-Torres, C.; Martínez-González, C. L.; Trejo-Valdez, M.; Hernández-Gómez, L. H.; Torres-Martínez, R.

2016-07-01

The modification in the third-order nonlinear optical response exhibited by rotating bimetallic Au-Pt nanoparticles in an ethanol solution was analyzed. The samples were prepared by a sol-gel processing route. The anisotropy associated to the elemental composition of the nanoparticles was confirmed by high-resolution transmission electron microscopy and energy-dispersive X-ray spectroscopy measurements. The size of the nanoparticles varies in the range from 9 to 13 nm, with an average size of 11 nm. Changes in the spatial orientation of the nanomaterials automatically generated a variation in their plasmonic response evaluated by UV-Vis spectroscopy. A two-wave mixing experiment was conducted to explore an induced birefringence at 532 nm wavelength with nanosecond pulses interacting with the samples. A strong optical Kerr effect was identified to be the main responsible effect for the third-order nonlinear optical phenomenon exhibited by the nanoparticles. It was estimated that the rotation of inhomogeneous nanostructures can provide a remarkable change in the participation of different surface plasmon resonances, if they correspond to multimetallic nanoparticles. Potential applications for developing low-dimensional gyroscopic systems can be contemplated.

Response spectrum method for extreme wave loading with higher order components of drag force

NASA Astrophysics Data System (ADS)

Reza, Tabeshpour Mohammad; Mani, Fatemi Dezfouli; Ali, Dastan Diznab Mohammad; Saied, Mohajernasab; Saied, Seif Mohammad

2017-03-01

Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.

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.

Dynamic analysis of spiral bevel and hypoid gears with high-order transmission errors

NASA Astrophysics Data System (ADS)

Yang, J. J.; Shi, Z. H.; Zhang, H.; Li, T. X.; Nie, S. W.; Wei, B. Y.

2018-03-01

A new gear surface modification methodology based on curvature synthesis is proposed in this study to improve the transmission performance. The generated high-order transmission error (TE) for spiral bevel and hypoid gears is proved to reduce the vibration of geared-rotor system. The method is comprised of the following steps: Firstly, the fully conjugate gear surfaces with pinion flank modified according to the predesigned relative transmission movement are established based on curvature correction. Secondly, a 14-DOF geared-rotor system model considering backlash nonlinearity is used to evaluate the effect of different orders of TE on the dynamic performance a hypoid gear transmission system. For case study, numerical simulation is performed to illustrate the dynamic response of hypoid gear pair with parabolic, fourth-order and sixth-order transmission error derived. The results show that the parabolic TE curve has higher peak to peak amplitude compared to the other two types of TE. Thus, the excited dynamic response also shows larger amplitude at response peaks. Dynamic responses excited by fourth and sixth order TE also demonstrate distinct response components due to their different TE period which is expected to generate different sound quality or other acoustic characteristics.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

Constitutive Models Based on Compressible Plastic Flows

NASA Technical Reports Server (NTRS)

Rajendran, A. M.

1983-01-01

The need for describing materials under time or cycle dependent loading conditions has been emphasized in recent years by several investigators. In response to the need, various constitutive models describing the nonlinear behavior of materials under creep, fatigue, or other complex loading conditions were developed. The developed models for describing the fully dense (non-porous) materials were mostly based on uncoupled plasticity theory. The improved characterization of materials provides a better understanding of the structual response under complex loading conditions. The pesent studies demonstrate that the rate or time dependency of the response of a porous aggregate can be incorporated into the nonlinear constitutive behavior of a porous solid by appropriately modeling the incompressible matrix behavior. It is also sown that the yield function which wads determined by a continuum mechanics approach must be verified by appropriate experiments on void containing sintered materials in order to obtain meaningful numbers for the constants that appear in the yield function.

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.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

NASA Astrophysics Data System (ADS)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to medium peaks and motions with higher than 3 Hz frequencies.

Reduced order modeling and active flow control of an inlet duct

NASA Astrophysics Data System (ADS)

Ge, Xiaoqing

Many aerodynamic applications require the modeling of compressible flows in or around a body, e.g., the design of aircraft, inlet or exhaust duct, wind turbines, or tall buildings. Traditional methods use wind tunnel experiments and computational fluid dynamics (CFD) to investigate the spatial and temporal distribution of the flows. Although they provide a great deal of insight into the essential characteristics of the flow field, they are not suitable for control analysis and design due to the high physical/computational cost. Many model reduction methods have been studied to reduce the complexity of the flow model. There are two main approaches: linearization based input/output modeling and proper orthogonal decomposition (POD) based model reduction. The former captures mostly the local behavior near a steady state, which is suitable to model laminar flow dynamics. The latter obtains a reduced order model by projecting the governing equation onto an "optimal" subspace and is able to model complex nonlinear flow phenomena. In this research we investigate various model reduction approaches and compare them in flow modeling and control design. We propose an integrated model-based control methodology and apply it to the reduced order modeling and active flow control of compressible flows within a very aggressive (length to exit diameter ratio, L/D, of 1.5) inlet duct and its upstream contraction section. The approach systematically applies reduced order modeling, estimator design, sensor placement and control design to improve the aerodynamic performance. The main contribution of this work is the development of a hybrid model reduction approach that attempts to combine the best features of input/output model identification and POD method. We first identify a linear input/output model by using a subspace algorithm. We next project the difference between CFD response and the identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the linear input/output model. Thus, the full system is decomposed into a dominant linear subsystem and a low order nonlinear subsystem. The hybrid model is then used for control design and compared with other modeling methods in CFD simulations. Numerical results indicate that the hybrid model accurately predicts the nonlinear behavior of the flow for a 2D diffuser contraction section model. It also performs best in terms of feedback control design and learning control. Since some outputs of interest (e.g., the AIP pressure recovery) are not observable during normal operations, static and dynamic estimators are designed to recreate the information from available sensor measurements. The latter also provides a state estimation for feedback controller. Based on the reduced order models and estimators, different controllers are designed to improve the aerodynamic performance of the contraction section and inlet duct. The integrated control methodology is evaluated with CFD simulations. Numerical results demonstrate the feasibility and efficacy of the active flow control based on reduced order models. Our reduced order models not only generate a good approximation of the nonlinear flow dynamics over a wide input range, but also help to design controllers that significantly improve the flow response. The tools developed for model reduction, estimator and control design can also be applied to wind tunnel experiment.

Coherent Femtosecond Spectroscopy and Nonlinear Optical Imaging on the Nanoscale

NASA Astrophysics Data System (ADS)

Kravtsov, Vasily

Optical properties of many materials and macroscopic systems are defined by ultrafast dynamics of electronic, vibrational, and spin excitations localized on the nanoscale. Harnessing these excitations for material engineering, optical computing, and control of chemical reactions has been a long-standing goal in science and technology. However, it is challenging due to the lack of spectroscopic techniques that can resolve processes simultaneously on the nanometer spatial and femtosecond temporal scales. This thesis describes the fundamental principles, implementation, and experimental demonstration of a novel type of ultrafast microscopy based on the concept of adiabatic plasmonic nanofocusing. Simultaneous spatio-temporal resolution on a nanometer-femtosecond scale is achieved by using a near-field nonlinear optical response induced by ultrafast surface plasmon polaritons nanofocused on a metal tip. First, we study the surface plasmon response in metallic structures and evaluate its prospects and limitations for ultrafast near-field microscopy. Through plasmon emission-based spectroscopy, we investigate dephasing times and interplay between radiative and non-radiative decay rates of localized plasmons and their modification due to coupling. We identify a new regime of quantum plasmonic coupling, which limits the achievable spatial resolution to several angstroms but at the same time provides a potential channel for generating ultrafast electron currents at optical frequencies. Next, we study propagation of femtosecond wavepackets of surface plasmon polaritons on a metal tip. In time-domain interferometric measurements we detect group delays that correspond to slowing of the plasmon polaritons down to 20% of the speed of light at the tip apex. This provides direct experimental verification of the plasmonic nanofocusing mechanism and suggests enhanced nonlinear optical interactions at the tip apex. We then measure a plasmon-generated third-order nonlinear optical four-wave mixing response from the tip apex and investigate its microscopic mechanism. Our results reveal a significant contribution to the third order nonlinearity of plasmonic structures due to large near-field gradients associated with nanofocused plasmons. In combination with scanning probe imaging and femtosecond pulse shaping, the nanofocused four-wave mixing response provides a basis for a novel type of ultrafast optical microscopy on the nanoscale. We demonstrate its capabilities by nano-imaging the coherent dynamics of localized plasmonic modes in a rough gold film edge with simultaneous sub-50 nm spatial and sub-5 fs temporal resolution. We capture the coherent decay and extract the dephasing times of individual plasmonic modes. Lastly, we apply our technique to study nanoscale spatial heterogeneity of the nonlinear optical response in novel two-dimensional materials: monolayer and few-layer graphene. An enhanced four-wave mixing signal is revealed on the edges of graphene flakes. We investigate the mechanism of this enhancement by performing nano-imaging on a graphene field-effect transistor with the variable carrier density controlled by electrostatic gating.

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

NASA Astrophysics Data System (ADS)

Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

2016-05-01

We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

High-order nonlinear optical processes in ablated carbon-containing materials: Recent approaches in development of the nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range

NASA Astrophysics Data System (ADS)

Ganeev, R. A.

2017-08-01

The nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range became a versatile tool for the analysis of the optical, structural and morphological properties of matter. The carbon-contained materials have shown the advanced properties among other studied species, which allowed both the definition of the role of structural properties on the nonlinear optical response and the analysis of the fundamental features of carbon as the attractive material for generation of coherent short-wavelength radiation. We review the studies of the high-order harmonic generation by focusing ultrashort pulses into the plasmas produced during laser ablation of various organic compounds. We discuss the role of ionic transitions of ablated carbon-containing molecules on the harmonic yield. We also show the similarities and distinctions of the harmonic and plasma spectra of organic compounds and graphite. We discuss the studies of the generation of harmonics up to the 27th order (λ = 29.9 nm) of 806 nm radiation in the boron carbide plasma and analyze the advantages and disadvantages of this target compared with the ingredients comprising B4C (solid boron and graphite) by comparing plasma emission and harmonic spectra from three species. We also show that the coincidence of harmonic and plasma emission wavelengths in most cases does not cause the enhancement or decrease of the conversion efficiency of this harmonic.

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

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

Yoon, Peter H., E-mail: yoonp@umd.edu; School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701

2015-09-15

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. Inmore » the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.« less

An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice

2018-05-01

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

Strain-Engineered Multiferroicity in Pnma NaMnF_{3} Fluoroperovskite.

PubMed

Garcia-Castro, A C; Romero, A H; Bousquet, E

2016-03-18

In this study we show from first principles calculations the possibility to induce multiferroic and magnetoelectric functional properties in the Pnma NaMnF_{3} fluoroperovskite by means of epitaxial strain engineering. Surprisingly, we found a very strong nonlinear polarization-strain coupling that drives an atypical amplification of the ferroelectric polarization for either compression or expansion of the cell. This property is associated with a noncollinear antiferromagnetic ordering, which induces a weak ferromagnetism phase and makes the strained NaMnF_{3} fluoroperovskite multiferroic. The magnetoelectric response was calculated and it was found to be composed of linear and nonlinear components with amplitudes similar to the ones of Cr_{2}O_{3}. These findings show that it is possible to move the fluoride family toward functional applications with unique responses.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

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.

A theoretical investigation of soliton induced supercontinuum generation in liquid core photonic crystal fiber and dual core optical fiber

NASA Astrophysics Data System (ADS)

Porsezian, K.; Nithyanandan, K.; Vasantha Jayakantha Raja, R.; Ganapathy, R.

2013-07-01

The supercontinuum generation (SCG) in liquid core photonic crystal fiber (LCPCF) with versatile nonlinear response and the spectral broadening in dual core optical fiber is presented. The analysis is presented in two phase, phase I deals with the SCG in LCPCF with the effect of saturable nonlinearity and re-orientational nonlinearity. We identify and discuss the generic nature of the saturable nonlinearity and reorientational nonlinearity in the SCG, using suitable model. For the physical explanation, modulational instability and soliton fission techniques is implemented to investigate the impact of saturable nonlinear response and slow nonlinear response, respectively. It is observed that the saturable nonlinearity inevitably suppresses the MI and the subsequent SCG. On the other hand, the re-orientational nonlinearity contributes to the slow nonlinear response in addition to the conventional fast response due to the electronic contribution. The phase II features the exclusive investigation of the spectral broadening in the dual core optical fiber.

Quantification and parametrization of non-linearity effects by higher-order sensitivity terms in scattered light differential optical absorption spectroscopy

NASA Astrophysics Data System (ADS)

Puķīte, Jānis; Wagner, Thomas

2016-05-01

We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on temperature and scattering processes.

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

Third-order elastic constants of diamond determined from experimental data

DOE PAGES

Winey, J. M.; Hmiel, A.; Gupta, Y. M.

2016-06-01

The pressure derivatives of the second-order elastic constants (SOECs) of diamond were determined by analyzing previous sound velocity measurements under hydrostatic stress [McSkimin and Andreatch, J. Appl. Phys. 43, 294 (1972)]. Furthermore, our analysis corrects an error in the previously reported results.We present a complete and corrected set of third-order elastic constants (TOECs) using the corrected pressure derivatives, together with published data for the nonlinear elastic response of shock compressed diamond [Lang and Gupta, Phys. Rev. Lett. 106, 125502 (2011)] and it differs significantly from TOECs published previously.

A Time Domain Analysis of Gust-Cascade Interaction Noise

NASA Technical Reports Server (NTRS)

Nallasamy, M.; Hixon, R.; Sawyer, S. D.; Dyson, R. W.

2003-01-01

The gust response of a 2 D cascade is studied by solving the full nonlinear Euler equations employing higher order accurate spatial differencing and time stepping techniques. The solutions exhibit the exponential decay of the two circumferential mode orders of the cutoff blade passing frequency (BPF) tone and propagation of one circumferential mode order at 2BPF, as would be expected for the flow configuration considered. Two frequency excitations indicate that the interaction between the frequencies and the self interaction contribute to the amplitude of the propagating mode.

High-harmonic generation in graphene enhanced by elliptically polarized light excitation

NASA Astrophysics Data System (ADS)

Yoshikawa, Naotaka; Tamaya, Tomohiro; Tanaka, Koichiro

2017-05-01

The electronic properties of graphene can give rise to a range of nonlinear optical responses. One of the most desirable nonlinear optical processes is high-harmonic generation (HHG) originating from coherent electron motion induced by an intense light field. Here, we report on the observation of up to ninth-order harmonics in graphene excited by mid-infrared laser pulses at room temperature. The HHG in graphene is enhanced by an elliptically polarized laser excitation, and the resultant harmonic radiation has a particular polarization. The observed ellipticity dependence is reproduced by a fully quantum mechanical treatment of HHG in solids. The zero-gap nature causes the unique properties of HHG in graphene, and our findings open up the possibility of investigating strong-field and ultrafast dynamics and nonlinear behavior of massless Dirac fermions.

Nonlinear vibration of viscoelastic beams described using fractional order derivatives

NASA Astrophysics Data System (ADS)

Lewandowski, Roman; Wielentejczyk, Przemysław

2017-07-01

The problem of non-linear, steady state vibration of beams, harmonically excited by harmonic forces is investigated in the paper. The viscoelastic material of the beams is described using the Zener rheological model with fractional derivatives. The constitutive equation, which contains derivatives of both stress and strain, significantly complicates the solution to the problem. The von Karman theory is applied to take into account geometric nonlinearities. Amplitude equations are obtained using the finite element method together with the harmonic balance method, and solved using the continuation method. The tangent matrix of the amplitude equations is determined in an explicit form. The stability of the steady-state solution is also examined. A parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam's responses.

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Analysis of shell type structures subjected to time dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1985-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is considered. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratchetting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model.

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

NASA Technical Reports Server (NTRS)

Engelstad, S. P.; Reddy, J. N.; Knight, N. F., Jr.

1990-01-01

The objectives of the study are to assess the influence of shear flexibility on overall postbuckling response, and to examine transverse shear stress distributions in relation to panel failure. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented in this paper analytically substantiate the experimentally observed failure mode.

Moderately nonlinear diffuse-charge dynamics under an ac voltage.

PubMed

Stout, Robert F; Khair, Aditya S

2015-09-01

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Model based design of electronic throttle control

NASA Astrophysics Data System (ADS)

Cherian, Fenin; Ranjan, Ashish; Bhowmick, Pathikrit; Rammohan, A.

2017-11-01

With the advent of torque based Engine Management Systems, the precise control and robust performance of the throttle body becomes a key factor in the overall performance of the vehicle. Electronic Throttle Control provides benefits such as improved air-fuel ratio for improving the vehicle performance and lower exhausts emissions to meet the stringent emission norms. Modern vehicles facilitate various features such as Cruise Control, Traction Control, Electronic Stability Program and Pre-crash systems. These systems require control over engine power without driver intervention, which is not possible with conventional mechanical throttle system. Thus these systems are integrated to function with the electronic throttle control. However, due to inherent non-linearities in the throttle body, the control becomes a difficult task. In order to eliminate the influence of this hysteresis at the initial operation of the butterfly valve, a control to compensate the shortage must be added to the duty required for starting throttle operation when the initial operation is detected. Therefore, a lot of work is being done in this field to incorporate the various nonlinearities to achieve robust control. In our present work, the ETB was tested to verify the working of the system. Calibration of the TPS sensors was carried out in order to acquire accurate throttle opening angle. The response of the calibrated system was then plotted against a step input signal. A linear model of the ETB was prepared using Simulink and its response was compared with the experimental data to find out the initial deviation of the model from the actual system. To reduce this deviation, non-linearities from existing literature were introduced to the system and a response analysis was performed to check the deviation from the actual system. Based on this investigation, an introduction of a new nonlinearity parameter can be used in future to reduce the deviation further making the control of the ETB more precise and accurate.

Fabrication and notable optical nonlinearities of ultrathin composite films derived from water-soluble Keggin-type polyoxometalates and water-insoluble phthalocyanine.

PubMed

Shehzad, Farooq Khurum; Qu, Ningning; Zhou, Yunshan; Zhang, Lijuan; Ji, Huanyao; Shi, Zonghai; Li, Jiaqi; Hassan, Sadaf Ul

2016-11-28

Composite films with the general formula (POM/CuTAPc) n derived from water-soluble Keggin-type polyoxometalates (POMs = H 5 PMo 10 V 2 O 40 , H 4 SiW 12 O 40 , H 3 PMo 12 O 40 and H 3 PW 12 O 40 ) and water-insoluble 4,9,16,23-copper tetraaminophthalocyanine (denoted CuTAPc) are successfully fabricated by a layer-by-layer self-assembly technique and systematically characterized. The structure of the polyoxometalate anions in the multilayers is kept intact; the deposition amounts of POM and CuTAPc remain constant in every adsorption cycle of the composite film assembly process. The nonlinear optical properties of the composite films were studied by a Z-scan technique at a wavelength of 532 nm and a pulse width of 7 ns. The results not only show that the composite films exhibit notable optical nonlinear self-defocusing behavior and a saturated absorption effect with the nonlinear optical absorption co-efficient β, refractive index n 2 , and third-order NLO susceptibility χ (3) of the films increasing with the increase in number of layers of the films, but also reveal importantly that the discrepancy of LUMO levels between CuTAPc and POMs is proportional to their third-order NLO response.

A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Damage detection in composites using nonlinear ultrasonically modulated thermography

NASA Astrophysics Data System (ADS)

Malfense Fierro, G.-P.; Dionysopoulos, D.; Meo, M.; Ciampa, F.

2018-03-01

This paper proposes a novel nonlinear ultrasonically stimulated thermography technique for a quick and reliable assessment of material damage in carbon fibre reinforced plastic (CFRP) composite materials. The proposed nondestructive evaluation (NDE) method requires narrow sweep ultrasonic excitation using contact piezoelectric transducers in order to identify dual excitation frequencies associated with the damage resonance. High-amplitude signals and higher harmonic generation are necessary conditions for an accurate identification of these two input frequencies. Dual periodic excitation using high- and low-frequency input signals was then performed in order to generate frictional heating at the crack location that was measured by an infrared (IR) camera. To validate this concept, an impact damaged CFRP composite panel was tested and the experimental results were compared with traditional flash thermography. A laser vibrometer was used to investigate the response of the material with dual frequency excitation. The proposed nonlinear ultrasonically modulated thermography successfully detected barely visible impact damage in CFRP composites. Hence, it can be considered as an alternative to traditional flash thermography and thermosonics by allowing repeatable detection of damage in composites.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Third-order nonlinear optical properties of methylammonium lead halide perovskite films

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

Johnson, Justin C.; Li, Zhen; Ndione, Paul F.

2016-01-01

We report third-order nonlinear coefficient values and decay time kinetics vs. halide composition (CH3NH3PbBr3 and CH3NH3PbBr2I), temperature, and excitation wavelength. The maximum values of the third-order nonlinear susceptibility X(3) (-1.6 x 10-6 esu) are similar to or larger than many common third-order materials. The source of the nonlinearity is shown to be primarily excitonic in the tribromide film by virtue of its strong enhancement near the exciton resonance. Nonresonant excitation reduces the nonlinearity significantly, as does increasing the temperature. Substitution of one I for one Br also reduces the nonlinearity by at least one order of magnitude, presumably due tomore » the lack of strong exciton resonance in the substituted form. The thin films are stable, highly homogenous (lacking significant light scattering), and simple and inexpensive to fabricate, making them potentially useful in a variety of optoelectronic applications in which wavelength selectivity is important.« less

Identification and modeling of the electrohydraulic systems of the main gun of a main battle tank

NASA Astrophysics Data System (ADS)

Campos, Luiz C. A.; Menegaldo, Luciano L.

2012-11-01

The black-box mathematical models of the electrohydraulic systems responsible for driving the two degrees of freedom (elevation and azimuth) of the main gun of a main battle tank (MBT) were identified. Such systems respond to gunner's inputs while acquiring and tracking targets. Identification experiments were designed to collect simultaneous data from two inertial measurement units (IMU) installed at the gunner's handle (input) and at the center of rotation of the turret (output), for the identification of the azimuth system. For the elevation system, IMUs were installed at the gunner's handle (input) and at the breech of the gun (output). Linear accelerations and angular rates were collected for both input and output. Several black-box model architectures were investigated. As a result, nonlinear autoregressive with exogenous variables (NARX) second order model and nonlinear finite impulse response (NFIR) fourth order model, demonstrate to best fit the experimental data, with low computational costs. The derived models are being employed in a broader research, aiming to reproduce such systems in a laboratory virtual main gun simulator.

The interaction between a propagating coastal vortex and topographic waves

NASA Astrophysics Data System (ADS)

Parry, Simon Wyn

This thesis investigates the motion of a point vortex near coastal topography in a rotating frame of reference at constant latitude (f-plane) in the linear and weakly nonlinear limits. Topography is considered in the form of an infinitely long escarpment running parallel to a wall. The vortex motion and topographic waves are governed by the conservation of quasi-geostrophic potential vorticity in shallow water, from which a nonlinear system of equations is derived. First the linear limit is studied for three cases; a weak vortex on- and off-shelf and a weak vortex close to the wall. For the first two cases it is shown that to leading order the vortex motion is stationary and a solution for the topographic waves at the escarpment can be found in terms of Fourier integrals. For a weak vortex close to a wall, the leading order solution is a steadily propagating vortex with a topographic wavetrain at the step. Numerical results for the higher order interactions are also presented and explained in terms of conservation of momentum in the along-shore direction. For the second case a resonant interaction between the vortex and the waves occurs when the vortex speed is equal to the maximum group velocity of the waves and the linear response becomes unbounded at large times. Thus it becomes necessary to examine the weakly nonlinear near-resonant case. Using a long wave approximation a nonlinear evolution equation for the interface separating the two regions of differing relative potential vorticity is derived and has similar form to the BDA (Benjamin, Davies, Acrivos 1967) equation. Results for the leading order steadily propagating vortex and for the vortex-wave feedback problem are calculated numerically using spectral multi-step Adams methods.

Three-dimensional characterization of the effective second-order nonlinearity in periodically poled crystals

NASA Astrophysics Data System (ADS)

Holmgren, Stefan J.; Pasiskevicius, Valdas; Wang, Shunhua; Laurell, Fredrik

2003-09-01

A novel technique for characterization of the second-order nonlinearity in nonlinear crystals is presented. It utilizes group-velocity walk-off between femtosecond pulses in type II SHG to achieve three-dimensional resolution of the nonlinearity. The longitudinal and transversal spatial resolution can be set independently. The technique is especially useful for characterizing quasi-phase-matched nonlinear crystals, and it is demonstrated in potassium titanyl phosphate.

Substituent Dependence of Third-Order Optical Nonlinearity in Chalcone Derivatives

NASA Astrophysics Data System (ADS)

Kiran, Anthony John; Satheesh Rai, Nooji; Chandrasekharan, Keloth; Kalluraya, Balakrishna; Rotermund, Fabian

2008-08-01

The third-order nonlinear optical properties of derivatives of dibenzylideneacetone were investigated using the single beam z-scan technique at 532 nm. A strong dependence of third-order optical nonlinearity on electron donor and acceptor type of substituents was observed. An enhancement in χ(3)-value of one order of magnitude was achieved upon the substitution of strong electron donors compared to that of the molecule substituted with an electron acceptor. The magnitude of nonlinear refractive index of these chalcones is as high as of 10-11 esu. Their nonlinear optical coefficients are larger than those of widely used thiophene oligomers and trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide (DABA-PEI) organic compounds.

Third-order nonlinear optical properties of phthalocyanines in solution and in polystyrene films

NASA Astrophysics Data System (ADS)

Reeves, Roger J.; Powell, Richard C.; Chang, Young H.; Ford, Warren T.; Zhu, Weiming

1996-01-01

Degenerate four-wave mixing (DFWM) measurements of third-order nonlinear optical (NLO) coefficients of metal-free, Cu, Pt, Pb and Bi octa(2-ethylhexyloxy) phthalocyanines (MPc's) were done with 20 ps duration laser pulses under resonant conditions at 532 nm in polystyrene films and under nonresonant conditions at 1064 nm in chloroform solutions. The NLO coefficients ξxxxx(3) show saturation with increasing incident intensity and no strong dependence on the central metal atom of the MPc below the saturation intensity. Optical delays of the probe-pulse up to 3 ns show an acoustic phonon response in both the polystyrene films and the chloroform solutions. An intensity-dependent absorption coefficient was measured by a pump/probe experiment and used in a simple model to qualitatively account for the saturation of ξ(3) measured by DFWM.

Nonlinear electrodynamics of high-temperature superconductors

NASA Astrophysics Data System (ADS)

Zutic, Igor

We investigate the effects of nonlinear electrodynamics in unconventional superconductors. These effects can serve as fingerprints to identify the symmetry of the superconducting pairing state and to provide information about the unknown pairing mechanism in High Temperature Superconductors (HTSC). In the Meissner regime, at low temperatures, a nonlinear magnetic response arises from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero. This can be used to perform "node spectroscopy", that is, as a sensitive bulk probe to locate the angular position of those lines. We first compute the nonlinear magnetic moment as a function of applied field and geometry, assuming d-wave pairing and anisotropic penetration depth, for realistic finite sample. Our novel, numerically implemented, perturbative procedure exploits the small ratio of the penetration depths to the sample size and substantially reduces the computational work required. We next generalize these considerations to other candidates for the energy gap and to perform node spectroscopy. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and a-b plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, d+s and s+id). We finally extend our findings to the case of low frequency harmonic magnetic field. The nonlinear magnetic response for various physical quantities generates higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependences of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and torque. They both have separable temporal and angular dependences. In contrast, with gap functions which only have quasinodes, these quantities do not display power laws in the applied field, and their temporal and angular dependences are not separable. We discuss how to perform measurements so as to maximize the nonlinear signal, and how to determine the gap function symmetry.

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).

Incorporation of Keplerate-type Mo-O based macroanions into Zn2Al-LDH results in the formation of all-inorganic composite films with remarkable third-order optical nonlinearity.

PubMed

Ren, Haizhou; Shehzad, Farooq Khurum; Zhou, Yunshan; Zhang, Lijuan; Iqbal, Arshad; Long, Yi

2018-05-01

Herein, new all-inorganic transparent composite films with the formula (Zn2Al-LDH/{Mo132-Ac})n have been fabricated by a layer-by-layer method using the exfoliated Zn2Al-LDH monolayer nanosheets and Keplerate-type macroanion {Mo132-Ac}. They were characterized by UV-vis absorption spectroscopy, SEM, AFM, and XPS techniques. The Z-scan measurements, which were conducted under laser irradiation at a wavelength of 532 nm, a pulse width of 6 ns, a repetition rate of 10 Hz, and the light intensity at a focus E0 of 10 μJ, revealed that all the films had notable saturated absorption and self-defocusing effect with a large third-order optical nonlinear susceptibility χ(3). With an increase in the number of layers (i.e., n) corresponding to the increase in the thickness of the films, the third-order nonlinear absorption β and refractive effects of the films were improved (i.e., the χ(3) value was up to 1.99 × 10-11 esu when n = 24); this implied that the NLO responses could be modified by fine-tuning the thickness of the composite films to meet the demands of different devices.

Crystal growth and DFT insight on sodium para-nitrophenolate para-nitrophenol dihydrate single crystal for NLO applications

NASA Astrophysics Data System (ADS)

Selvakumar, S.; Boobalan, Maria Susai; Anthuvan Babu, S.; Ramalingam, S.; Leo Rajesh, A.

2016-12-01

Single crystals of sodium para-nitrophenolate para-nitrophenol dihydrate (SPPD) were grown by slow evaporation technique and its structure has been studied by FT-IR, FT-Raman and single crystal X-ray diffraction techniques. The optical and electrical properties were characterized by UV-Vis spectrum, and dielectric studies respectively. SPPD was thermally stable up to 128 °C as determined by TG-DTA curves. Using the Kurtz-Perry powder method, the second-harmonic generation efficiency was found to be five times to that of KDP. Third-order nonlinear response was studied using Z-scan technique with a He-Ne laser (632.8 nm) and NLO parameters such as intensity dependent refractive index, nonlinear absorption coefficient and third-order susceptibility were also estimated. The molecular geometry from X-ray experiment in the ground state has been compared using density functional theory (DFT) with appropriate basis set. The first-order hyperpolarizability also calculated using DFT approaches. Stability of the molecule arising from hyperconjugative interactions leading to its nonlinear optical activity and charge delocalization were analyzed using natural bond orbital technique. HOMO-LUMO energy gap value suggests the possibility of charge transfer within the molecule. Based on optimized ground state geometries, Natural bond orbital (NBO) analysis was performed to study donor-acceptor interactions.

Development of a multi-body nonlinear model for a seat-occupant system

NASA Astrophysics Data System (ADS)

Azizi, Yousof

A car seat is an important component of today's cars, which directly affects ride comfort experienced by occupants. Currently, the process of ride comfort evaluation is subjective. Alternatively, the ride comfort can be evaluated by a series of objective metrics in the dynamic response of the occupant. From previous studies it is well known that the dynamic behavior of a seat-occupant system is greatly affected by soft nonlinear viscoelastic materials used in the seat cushion. Therefore, in this research, especial attention was given to efficiently modeling the behavior of seat cushion. In the first part of this research, a phenomenological nonlinear viscoelastic foam model was proposed and its ability to capture uniaxial behavior of foam was investigated. The model is based on the assumption that the total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher order polynomial of strain, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at different rates on two types of low density polyurethane foams and three types of high density CONFOR foams. The performance of the proposed model was compared to that of other traditional continuum models. For each foam type, it was observed that lower order models are sufficient to describe the uniaxial behavior of the foam compressed at different rates. Although, the estimated model parameters were functions of the input strain rate. Alternatively, higher order comprehensive models, with strain independent parameters, were estimated as well. The estimated comprehensive model predicts foam responses under different compression rates. Also, a methodology was proposed to predict the stress-response of a layered foam system using the estimated models of each foam in the layers. Next, the estimated foam model was incorporated into a single-degree of freedom foam-mass model which is also the simplest model of seat-occupant systems. The steady-state response of the system when it is subjected to harmonic base excitation was studied using the incremental harmonic balance method. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. The incremental harmonic balance method was used to reduce the time required to generate the steady-state response of the system. Experiments are conducted on a single-degree of freedom foam-mass system subjected to harmonic base excitation. Initially, the simulated response predictions were found to deviate from the experimental results. The foam-mass model was then modified to incorporate rate dependency of foam parameters resulting in response predictions that were in good agreement with experimental results. In the second part of this research, the dynamic response of a seat-occupant system was examined through a more realistic planar multi-body seat-occupant model. A constraint Lagrangian formulation was used to derive the governing equations for the seat-occupant model. First, the governing equations were solved numerically to obtain the occupant transient response, the occupant's H-Point location and the interfacial pressure distribution. Variations in the H-Point location and the seat-occupant pressure distribution with changes in the seat-occupant parameters, including the seat geometry and the occupant's characteristics, were studied. The estimated pressure was also investigated experimentally and was found to match with the results obtained using the seat-occupant model. Next, the incremental harmonic balance method was modified and used to obtain the occupant's steady-state response when the seat-occupant system was subjected to harmonic base excitation at different frequencies. The system frequency response and mode shapes at different frequencies were also obtained and compared to the previously measured experimental frequency responses. Finally, variations in the estimated frequency response with changes in the seat-occupant parameters, including the seat geometry and the occupant characteristics, were studied.

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness

PubMed Central

Frangi, Attilio; Guerrieri, Andrea; Boni, Nicoló

2017-01-01

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach. PMID:28383483

Accurate Simulation of Parametrically Excited Micromirrors via Direct Computation of the Electrostatic Stiffness.

PubMed

Frangi, Attilio; Guerrieri, Andrea; Boni, Nicoló

2017-04-06

Electrostatically actuated torsional micromirrors are key elements in Micro-Opto-Electro- Mechanical-Systems. When forced by means of in-plane comb-fingers, the dynamics of the main torsional response is known to be strongly non-linear and governed by parametric resonance. Here, in order to also trace unstable branches of the mirror response, we implement a simplified continuation method with arc-length control and propose an innovative technique based on Finite Elements and the concepts of material derivative in order to compute the electrostatic stiffness; i.e., the derivative of the torque with respect to the torsional angle, as required by the continuation approach.

Triggered instabilities in rocket motors and active combustion control for an incinerator afterburner

NASA Astrophysics Data System (ADS)

Wicker, Josef M.

1999-11-01

Two branches of research are conducted in this thesis. The first deals with nonlinear combustion response as a mechanism for triggering combustion instabilities in solid rocket motors. A nonlinear wave equation is developed to study a wide class of combustion response functions to second-order in fluctuation amplitude. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be how the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse. Also, dependence of nonlinear stability upon system parameters is considered. The second part of this thesis presents research for a controller to improve the emissions of an incinerator afterburner. The developed controller was experimentally tested at the Naval Air Warfare Center (NAWC), on a 50kW-scale model of an afterburner for Naval shipboard incinerator applications. Acoustic forcing of the combustor's reacting shear layer is used to control the formation of coherent vortical structures, within which favorable fuel-air mixing and efficient combustion can occur. Laser-based measurements of CO emissions are used as the performance indicator for the combustor. The controller algorithm is based on the downhill simplex method and adjusts the shear layer forcing parameters in order to minimize the CO emissions. The downhill simplex method was analyzed with respect to its behavior in the face of time-variation of the plant and noise in the sensor signal, and was modified to account for these difficulties. The control system has experimentally demonstrated the ability (1) to find optimal control action for single- and multi-variable control, (2) to maintain optimal control for time-varying operating states, and (3) to automatically adjust auxiliary fuel in response to changing stoichiometry of the incoming waste pyrolysis gas. Also presented but not tested in the experiments are an expert-type model-guidance feature to aid convergence of the controller to optimum control, and methodology for maintaining flammability.

Magnetic field induced changes in linear and nonlinear optical properties of Ti incorporated Cr2O3 nanostructured thin film

NASA Astrophysics Data System (ADS)

Baraskar, Priyanka; Chouhan, Romita; Agrawal, Arpana; Choudhary, R. J.; Sen, Pranay K.; Sen, Pratima

2018-03-01

We report the magnetic field effect on the linear and nonlinear optical properties of pulse laser ablated Ti-incorporated Cr2O3 nanostructured thin film. Optical properties have been experimentally analyzed under Voigt geometry by performing ultraviolet-visible spectroscopy and closed aperture Z-scan technique using a continuous wave He-Ne laser source. Nonlinear optical response reveals a single peak-valley feature in the far field diffraction pattern in absence of magnetic field (B = 0) confirming self-defocussing effect. This feature switches to a valley-peak configuration for B = 5000G, suggesting self-focusing effect. For B ≤ 750G, oscillations were observed revealing the occurrence of higher order nonlinearity. Origin of nonlinearity is attributed to the near resonant d-d transitions observed from the broad peak occurring around 2 eV. These transitions are of magnetic origin and get modified under the application of external magnetic field. Our results suggest that magnetic field can be used as an effective tool to monitor the sign of optical nonlinearity and hence the thermal expansion in Ti-incorporated Cr2O3 nanostructured thin film.

Nonlinear resonance of the rotating circular plate under static loads in magnetic field

NASA Astrophysics Data System (ADS)

Hu, Yuda; Wang, Tong

2015-11-01

The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Numerical simulation of incoherent optical wave propagation in nonlinear fibers

NASA Astrophysics Data System (ADS)

Fernandez, Arnaud; Balac, Stéphane; Mugnier, Alain; Mahé, Fabrice; Texier-Picard, Rozenn; Chartier, Thierry; Pureur, David

2013-11-01

The present work concerns the study of pulsed laser systems containing a fiber amplifier for boosting optical output power. In this paper, this fiber amplification device is included into a MOPFA laser, a master oscillator coupled with fiber amplifier, usually a cladding-pumped high-power amplifier often based on an ytterbium-doped fiber. An experimental study has established that the observed nonlinear effects (such as Kerr effect, four waves mixing, Raman effect) could behave very differently depending on the characteristics of the optical source emitted by the master laser. However, it has not yet been possible to determine from the experimental data if the statistics of the photons is alone responsible for the various nonlinear scenarios observed. Therefore, we have developed a numerical simulation software for solving the generalized nonlinear Schrödinger equation with a stochastic source term in order to validate the hypothesis that the coherence properties of the master laser are mainly liable for the behavior of the observed nonlinear effects. Contribution to the Topical Issue "Numelec 2012", Edited by Adel Razek.

Non-Destructive Evaluation of Kissing Bonds using Local Defect Resonance (LDR) Spectroscopy: A Simulation Study

NASA Astrophysics Data System (ADS)

Delrue, S.; Tabatabaeipour, M.; Hettler, J.; Van Den Abeele, K.

With the growing demand from industry to optimize and further develop existing Non-Destructive Testing & Evaluation (NDT&E) techniques or new methods to detect and characterize incipient damage with high sensitivity and increased quality, ample efforts have been devoted to better understand the typical behavior of kissing bonds, such as delaminations and cracks. Recently, it has been shown experimentally that the nonlinear ultrasonic response of kissing bonds could be enhanced by using Local Defect Resonance (LDR) spectroscopy. LDR spectroscopy is an efficient NDT technique that takes advantage of the characteristic fre- quencies of the defect (defect resonances) in order to provide maximum acoustic wave-defect interaction. In fact, for nonlinear methodologies, the ultrasonic excitation of the sample should occur at either multiples or integer ratios of the characteristic defect resonance frequencies, in order to obtain the highest signal-to-noise response in the nonlinear LDR spectroscopy. In this paper, the potential of using LDR spectroscopy for the detection, localization and characterization of kissing bonds is illustrated using a 3D simulation code for elastic wave propagation in materials containing closed but dynamically active cracks or delaminations. Using the model, we are able to define an appropriate method, based on the Scaling Subtraction Method (SSM), to determine the local defect resonance frequencies of a delamination in a composite plate and to illustrate an increase in defect nonlinearity due to LDR. The simulation results will help us to obtain a better understanding of the concept of LDR and to assist in the further design and testing of LDR spectroscopy for the detection, localization and characterization of kissing bonds.

Contact acoustic nonlinearity (CAN)-based continuous monitoring of bolt loosening: Hybrid use of high-order harmonics and spectral sidebands

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Liu, Menglong; Liao, Yaozhong; Su, Zhongqing; Xiao, Yi

2018-03-01

The significance of evaluating bolt tightness in engineering structures, preferably in a continuous manner, cannot be overemphasized. With hybrid use of high-order harmonics (HOH) and spectral sidebands, a contact acoustic nonlinearity (CAN)-based monitoring framework is developed for detecting bolt loosening and subsequently evaluating the residual torque on a loose bolt. Low-frequency pumping vibration is introduced into the bolted joint to produce a "breathing" effect at the joining interface that modulates the propagation characteristics of a high-frequency probing wave when it traverses the bolt, leading to the generation of HOH and vibro-acoustic nonlinear distortions (manifested as sidebands in the signal spectrum). To gain insight into the mechanism of CAN generation and to correlate the acquired nonlinear responses of a loose joint with the residual torque remaining on the bolt, an analytical model based on micro-contact theory is established. Two types of nonlinear index, respectively exploiting the induced HOH and spectral sidebands, are defined without dependence on excitation intensity and are experimentally demonstrated to be effective in continuously monitoring bolt loosening in both aluminum-aluminum and composite-composite bolted joints. Taking a step further, variation of the index pair is quantitatively associated with the residual torque on a loose bolt. The approach developed provides a reliable method of continuous evaluation of bolt tightness in both composite and metallic joints, regardless of their working conditions, from early awareness of bolt loosening at an embryonic stage to quantitative estimation of residual torque.

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.

Quantum Transport Theory of Optical and Plasmonic Response of Nanomaterials

NASA Astrophysics Data System (ADS)

Karimi, Farhad

The light-matter interaction is the cornerstone of photonics and optoelectronics. Advances in the fabrication techniques that has enabled the miniaturization of the semiconductor devices, along with emergence of nanomaterials such as graphene, have brought the fields of photonics and optoelectronics down to the nanoscale. Controlling the light-matter interaction at the nanoscale will impact on the development and improvement of many technologies, ranging from solar-energy harvesting to biosensing. However, the quantum confinement at the nanoscale makes nanostructured devices behave significantly differently than their larger counterparts, which turns the nanoscale control into a grand challenge. In order to pave the path toward it, we need to have a clear and accurate picture of how electrons interact with light at the nanoscale. This dissertation presents a rigorous quantum-transport method for studying the optical and plasmonic properties of nanomaterials. This method is based on a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with the full-wave electromagnetic equations. The SCF-MMEF captures the interband electron-hole generation, as well as the interband and intraband transitions due to multiple competing scattering mechanisms, where the transition rates can have pronounced and widely differing dependencies on both carrier energy and momentum. The SCF-MMEF is applicable to any type of material with an arbitrary band dispersion and Bloch wave functions. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain the plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. We find that plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. In pursuit of finding less dissipative plasmonic materials, we calculate the dielectric function and plasmonic response of armchair (aGNRs)and zigzag (zGNRs) graphene nanoribbons via the SCF-MMEF. Supported GNRs provide almost the same interesting plasmonic features as graphene, with the added benefit of a less dissipative environment for electrons, owing to the low electronic density of states and thus lower electron scattering rates. Midinfrared plasmons in supported (3N+2)-aGNRs can propagate as far as several microns at room temperature, with 4-5-nm-wide ribbons having the longest propagation length. In other types of aGNRs and in zGNRs, the plasmon propagation length seldom exceeds 100 nm. Plasmon propagation lengths are much greater on nonpolar (e.g., diamondlike carbon) than on polar substrates (e.g., SiO2 or hBN), where electrons scatter strongly with surface optical phonons. Another advantage of the SCF-MMEF is that it can be used perturbatively to calculate the nonlinear optical response. We perturbatively employ the SCF-MMEF to calculate the GNRs optical nonlinearity. We show that graphene nanoribbons have a remarkably strong nonlinear optical response in the long-wavelength regime and over a broad frequency range, from terahertz to the nearinfrared. In the retarded regime, electron scattering has a critical effect on the optical nonlinearity of graphene nanoribbons, which cannot be captured via the commonly used relaxation-time approximation. At terahertz frequencies, where intrasubband optical transitions dominate, the strong nonlinearity (in particular, third-order Kerr nonlinearity) stems from the jagged shape of the electron energy distribution, caused by the interband electron scattering mechanisms along with the intraband inelastic scattering mechanisms. At the midinfrared to nearinfrared frequencies, where interband optical transitions dominate, the Kerr nonlinearity is significantly overestimated within the relaxation-time approximation. These findings unveil the critical effect of electron scattering on the optical nonlinearity of nanostructured graphene, and also underscore the capability of this class of materials for nonlinear nanophotonic applications.

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

NASA Astrophysics Data System (ADS)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

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.

Prediction and causal reasoning in planning

NASA Technical Reports Server (NTRS)

Dean, T.; Boddy, M.

1987-01-01

Nonlinear planners are often touted as having an efficiency advantage over linear planners. The reason usually given is that nonlinear planners, unlike their linear counterparts, are not forced to make arbitrary commitments to the order in which actions are to be performed. This ability to delay commitment enables nonlinear planners to solve certain problems with far less effort than would be required of linear planners. Here, it is argued that this advantage is bought with a significant reduction in the ability of a nonlinear planner to accurately predict the consequences of actions. Unfortunately, the general problem of predicting the consequences of a partially ordered set of actions is intractable. In gaining the predictive power of linear planners, nonlinear planners sacrifice their efficiency advantage. There are, however, other advantages to nonlinear planning (e.g., the ability to reason about partial orders and incomplete information) that make it well worth the effort needed to extend nonlinear methods. A framework is supplied for causal inference that supports reasoning about partially ordered events and actions whose effects depend upon the context in which they are executed. As an alternative to a complete but potentially exponential-time algorithm, researchers provide a provably sound polynomial-time algorithm for predicting the consequences of partially ordered events.

Combining in silico evolution and nonlinear dimensionality reduction to redesign responses of signaling networks

NASA Astrophysics Data System (ADS)

Prescott, Aaron M.; Abel, Steven M.

2016-12-01

The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

PubMed Central

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-01-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs. PMID:27934904

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

NASA Astrophysics Data System (ADS)

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-12-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry.

PubMed

Allagui, Anis; Freeborn, Todd J; Elwakil, Ahmed S; Maundy, Brent J

2016-12-09

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal R s C behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics [corrected]. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance R s in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (R s , Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical R s C model. We validate our formulae with the experimental measurements of different EDLCs.

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.

Can we detect a nonlinear response to temperature in European plant phenology?

NASA Astrophysics Data System (ADS)

Jochner, Susanne; Sparks, Tim H.; Laube, Julia; Menzel, Annette

2016-10-01

Over a large temperature range, the statistical association between spring phenology and temperature is often regarded and treated as a linear function. There are suggestions that a sigmoidal relationship with definite upper and lower limits to leaf unfolding and flowering onset dates might be more realistic. We utilised European plant phenological records provided by the European phenology database PEP725 and gridded monthly mean temperature data for 1951-2012 calculated from the ENSEMBLES data set E-OBS (version 7.0). We analysed 568,456 observations of ten spring flowering or leafing phenophases derived from 3657 stations in 22 European countries in order to detect possible nonlinear responses to temperature. Linear response rates averaged for all stations ranged between -7.7 (flowering of hazel) and -2.7 days °C-1 (leaf unfolding of beech and oak). A lower sensitivity at the cooler end of the temperature range was detected for most phenophases. However, a similar lower sensitivity at the warmer end was not that evident. For only ˜14 % of the station time series (where a comparison between linear and nonlinear model was possible), nonlinear models described the relationship significantly better than linear models. Although in most cases simple linear models might be still sufficient to predict future changes, this linear relationship between phenology and temperature might not be appropriate when incorporating phenological data of very cold (and possibly very warm) environments. For these cases, extrapolations on the basis of linear models would introduce uncertainty in expected ecosystem changes.

Linear and nonlinear auditory response properties of interneurons in a high-order avian vocal motor nucleus during wakefulness.

PubMed

Raksin, Jonathan N; Glaze, Christopher M; Smith, Sarah; Schmidt, Marc F

2012-04-01

Motor-related forebrain areas in higher vertebrates also show responses to passively presented sensory stimuli. However, sensory tuning properties in these areas, especially during wakefulness, and their relation to perception, are poorly understood. In the avian song system, HVC (proper name) is a vocal-motor structure with auditory responses well defined under anesthesia but poorly characterized during wakefulness. We used a large set of stimuli including the bird's own song (BOS) and many conspecific songs (CON) to characterize auditory tuning properties in putative interneurons (HVC(IN)) during wakefulness. Our findings suggest that HVC contains a diversity of responses that vary in overall excitability to auditory stimuli, as well as bias in spike rate increases to BOS over CON. We used statistical tests to classify cells in order to further probe auditory responses, yielding one-third of neurons that were either unresponsive or suppressed and two-thirds with excitatory responses to one or more stimuli. A subset of excitatory neurons were tuned exclusively to BOS and showed very low linearity as measured by spectrotemporal receptive field analysis (STRF). The remaining excitatory neurons responded well to CON stimuli, although many cells still expressed a bias toward BOS. These findings suggest the concurrent presence of a nonlinear and a linear component to responses in HVC, even within the same neuron. These characteristics are consistent with perceptual deficits in distinguishing BOS from CON stimuli following lesions of HVC and other song nuclei and suggest mirror neuronlike qualities in which "self" (here BOS) is used as a referent to judge "other" (here CON).

Nonlinear effective theory of dark energy

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article [1], we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.

A solar cycle dependence of nonlinearity in magnetospheric activity

NASA Astrophysics Data System (ADS)

Johnson, Jay R.; Wing, Simon

2005-04-01

The nonlinear dependencies inherent to the historical Kp data stream (1932-2003) are examined using mutual information and cumulant-based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original Kp data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maxima. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solar minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to 1 week. Because the solar wind driver variables, VBs, and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics, suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.

Veering and nonlinear interactions of a clamped beam in bending and torsion

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Hill, Thomas L.; Neild, Simon A.; Cooper, Jonathan E.

2018-03-01

Understanding the linear and nonlinear dynamic behaviour of beams is critical for the design of many engineering structures such as spacecraft antennae, aircraft wings, and turbine blades. When the eigenvalues of such structures are closely-spaced, nonlinearity may lead to interactions between the underlying linear normal modes (LNMs). This work considers a clamped-clamped beam which exhibits nonlinear behaviour due to axial tension from large amplitudes of deformation. An additional cross-beam, mounted transversely and with a movable mass at each tip, allows tuning of the primary torsion LNM such that it is close to the primary bending LNM. Perturbing the location of one mass relative to that of the other leads to veering between the eigenvalues of the bending and torsion LNMs. For a number of selected geometries in the region of veering, a nonlinear reduced order model (NLROM) is created and the nonlinear normal modes (NNMs) are used to describe the underlying nonlinear behaviour of the structure. The relationship between the 'closeness' of the eigenvalues and the nonlinear dynamic behaviour is demonstrated in the NNM backbone curves, and veering-like behaviour is observed. Finally, the forced and damped dynamics of the structure are predicted using several analytical and numerical tools and are compared to experimental measurements. As well as showing a good agreement between the predicted and measured responses, phenomena such as a 1:1 internal resonance and quasi-periodic behaviour are identified.

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.

Strain-Engineered Multiferroicity in P n m a NaMnF3 Fluoroperovskite

NASA Astrophysics Data System (ADS)

Garcia-Castro, A. C.; Romero, A. H.; Bousquet, E.

2016-03-01

In this study we show from first principles calculations the possibility to induce multiferroic and magnetoelectric functional properties in the P n m a NaMnF3 fluoroperovskite by means of epitaxial strain engineering. Surprisingly, we found a very strong nonlinear polarization-strain coupling that drives an atypical amplification of the ferroelectric polarization for either compression or expansion of the cell. This property is associated with a noncollinear antiferromagnetic ordering, which induces a weak ferromagnetism phase and makes the strained NaMnF3 fluoroperovskite multiferroic. The magnetoelectric response was calculated and it was found to be composed of linear and nonlinear components with amplitudes similar to the ones of Cr2O3. These findings show that it is possible to move the fluoride family toward functional applications with unique responses.

NLOphoric multichromophoric auxiliary methoxy aided triphenylamine D-π-A chromophores - Spectroscopic and computational studies

NASA Astrophysics Data System (ADS)

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

2017-11-01

Molecules containing methoxy supported triphenylamine as strong electron-donor and dicyanovinyl as electron-acceptor groups interacting via isophorone as a configurationally locked polyene π-conjugated bridge are studied for their nonlinear optical properties. The photophysical study of examined chromophores in non-polar and polar solvents suggest that they exhibit strong emission solvatochromism and significant charge transfer characteristics supported by Lippert-Mataga plots and Generalised Mulliken Hush analysis. Linear and nonlinear optical properties as well as electronic properties measured by spectroscopic methods and cyclic voltametry and supported by DFT calculation were used to elucidate the structure property relationships. All three chromophores exhibit very high thermal stabilities with the decomposition temperatures higher than 340°C. The vibrational motions play very important role in determining the overall NLO response styryl chromophores which was established by DFT study. Dye 3 with maximum nonlinear optical susceptibility among three D-π-A systems proves that the multibranched push-pull chromophores exhibit a higher third order nonlinear susceptibility and justifies the design strategy.

Nonlinear simulation of the fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, Malik; Faganello, Matteo; Berk, Herbert; Garbet, Xavier; Benkadda, Sadruddin; PIIM Team; IFS Team; IRFM Team

2014-10-01

We propose to extend the Odblom-Breizman precessional fishbone model to account for both the MagnetoHydroDynamic (MHD) nonlinearity at the q = 1 surface and the nonlinear response of the energetic particles contained within the q = 1 surface. This electromagnetic mode, whose excitation, damping and frequency chirping are determined by the self-consistent interaction between an energetic trapped particle population and the bulk plasma evolution, can induce effective transport and losses for the energetic particles, being them alpha-particles in next-future fusion devices or heated particles in present Tokamaks. The model is reduced to its simplest form, assuming a reduced MHD description for the bulk plasma and a two-dimensional phase-space evolution (gyro and bounce averaged) for deeply trapped energetic particles. Numerical simulations have been performed in order to characterize the mode chirping and saturation, in particular looking at the interplay between the development of phase-space structures and the system dissipation associated to the MHD non-linearities at the resonance locations.

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

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

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

Second-Order Nonlinear Optical Properties of a Dithienylethene-Indolinooxazolidine Hybrid: A Joint Experimental and Theoretical Investigation.

PubMed

Bondu, Flavie; Quertinmont, Jean; Rodriguez, Vincent; Pozzo, Jean-Luc; Plaquet, Aurélie; Champagne, Benoît; Castet, Frédéric

2015-12-14

The nonlinear optical (NLO) properties of a double photochrome molecular switch are reported for the first time by considering the four trans forms of a dithienylethene-indolinooxazolidine hybrid. The four forms are characterized by means of hyper-Rayleigh scattering (HRS) experiments and quantum chemical calculations. Experimental measurements provide evidence that the pH- and light-triggered transformations between the different forms of the hybrid are accompanied by large variations of the first hyperpolarizability, which makes this compound an effective multistate NLO switch. Quantum chemical calculations conducted at the time-dependent Hartree-Fock and time-dependent DFT levels agree with the experimental data and allow a complete rationalization of the NLO responses of the different forms. The HRS signal of the forms with an open indolinooxazolidine moiety are more than one order of magnitude larger than that measured for the other forms, whereas the open/closed status of the dithienylethene subunit barely influences the dynamic NLO properties. However, extrapolation of the NLO responses to the static limit leads to univocally distinguishable intrinsic responses for three of the various forms. This hybrid system thus acts as a highly efficient multistate NLO switch for eventual exploitation in optical memory systems with multiple storage and nondestructive readout capacity. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Experimental determination of third-order elastic constants of diamond.

PubMed

Lang, J M; Gupta, Y M

2011-03-25

To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

Influence of laminate sequence and fabric type on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

PubMed

Chakrapani, Sunil Kishore; Barnard, Daniel J; Dayal, Vinay

2016-05-01

This paper presents the study of influence of laminate sequence and fabric type on the baseline acoustic nonlinearity of fiber-reinforced composites. Nonlinear elastic wave techniques are increasingly becoming popular in detecting damage in composite materials. It was earlier observed by the authors that the non-classical nonlinear response of fiber-reinforced composite is influenced by the fiber orientation [Chakrapani, Barnard, and Dayal, J. Acoust. Soc. Am. 137(2), 617-624 (2015)]. The current study expands this effort to investigate the effect of laminate sequence and fabric type on the non-classical nonlinear response. Two hypotheses were developed using the previous results, and the theory of interlaminar stresses to investigate the influence of laminate sequence and fabric type. Each hypothesis was tested by capturing the nonlinear response by performing nonlinear resonance spectroscopy and measuring frequency shifts, loss factors, and higher harmonics. It was observed that the laminate sequence can either increase or decrease the nonlinear response based on the stacking sequence. Similarly, tests were performed to compare unidirectional fabric and woven fabric and it was observed that woven fabric exhibited a lower nonlinear response compared to the unidirectional fabric. Conjectures based on the matrix properties and interlaminar stresses were used in an attempt to explain the observed nonlinear responses for different configurations.

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

Patil, Vidya, E-mail: vidya.patil@ruparel.edu; Patki, Mugdha, E-mail: mugdha.patki@ruparel.edu

Many nonlinear optical (NLO) crystals have been identified as potential candidates in optical and electro-optical devices. Use of NLO organic crystals is expected in photonic applications. Hence organic nonlinear optical materials have been intensely investigated due to their potentially high nonlinearities, and rapid response in electro-optic effect compared to inorganic NLO materials. There are many methods to grow organic crystals such as vapor growth method, melt growth method and solution growth method. Out of these methods, solution growth method is useful in providing constraint free crystal. Single crystals of Dopamine have been grown by evaporating the solvents from aqueous solution.more » Crystals obtained were of the size of orders of mm. The crystal structure of dopamine was determined using XRD technique. Images of crystals were obtained using FEG SEM Quanta Series under high vacuum and low KV.« less

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.

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

NASA Astrophysics Data System (ADS)

Roux Oliveira, Tiago; Jacoud Peixoto, Alessandro; Hsu, Liu

2015-09-01

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

PubMed

Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

2016-02-01

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

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.

Lateral resolution improvement in scanning nonlinear dielectric microscopy by measuring super-higher-order nonlinear dielectric constants

NASA Astrophysics Data System (ADS)

Chinone, N.; Yamasue, K.; Hiranaga, Y.; Honda, K.; Cho, Y.

2012-11-01

Scanning nonlinear dielectric microscopy (SNDM) can be used to visualize polarization distributions in ferroelectric materials and dopant profiles in semiconductor devices. Without using a special sharp tip, we achieved an improved lateral resolution in SNDM through the measurement of super-higher-order nonlinearity up to the fourth order. We observed a multidomain single crystal congruent LiTaO3 (CLT) sample, and a cross section of a metal-oxide-semiconductor (MOS) field-effect-transistor (FET). The imaged domain boundaries of the CLT were narrower in the super-higher-order images than in the conventional image. Compared to the conventional method, the super-higher-order method resolved the more detailed structure of the MOSFET.

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.

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Enhancing power generation of floating wave power generators by utilization of nonlinear roll-pitch coupling

NASA Astrophysics Data System (ADS)

Yerrapragada, Karthik; Ansari, M. H.; Karami, M. Amin

2017-09-01

We propose utilization of the nonlinear coupling between the roll and pitch motions of wave energy harvesting vessels to increase their power generation by orders of magnitude. Unlike linear vessels that exhibit unidirectional motion, our vessel undergoes both pitch and roll motions in response to frontal waves. This significantly magnifies the motion of the vessel and thus improves the power production by several orders of magnitude. The ocean waves result in roll and pitch motions of the vessel, which in turn causes rotation of an onboard pendulum. The pendulum is connected to an electric generator to produce power. The coupled electro-mechanical system is modeled using energy methods. This paper investigates the power generation of the vessel when the ratio between pitch and roll natural frequencies is about 2 to 1. In that case, a nonlinear energy transfer occurs between the roll and pitch motions, causing the vessel to perform coupled pitch and roll motion even though it is only excited in the pitch direction. It is shown that co-existence of pitch and roll motions significantly enhances the pendulum rotation and power generation. A method for tuning the natural frequencies of the vessel is proposed to make the energy generator robust to variations of the frequency of the incident waves. It is shown that the proposed method enhances the power output of the floating wave power generators by multiple orders of magnitude. A small-scale prototype is developed for the proof of concept. The nonlinear energy transfer and the full rotation of the pendulum in the prototype are observed in the experimental tests.

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.

Nonlinear coherent optical image processing using logarithmic transmittance of bacteriorhodopsin films

NASA Astrophysics Data System (ADS)

Downie, John D.

1995-08-01

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

Nonlinear Coherent Optical Image Processing Using Logarithmic Transmittance of Bacteriorhodopsin Films

NASA Technical Reports Server (NTRS)

Downie, John D.

1995-01-01

The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

Influence of electrode width of interdigital transducer on third-order nonlinearity of surface acoustic wave devices on 42°YX-LiTaO3 substrate

NASA Astrophysics Data System (ADS)

Nakagawa, Ryo; Hashimoto, Ken-ya

2018-07-01

In this paper, we discuss the influence of the electrode width of an interdigital transducer on the third-order nonlinearity of surface acoustic wave (SAW) devices. First, an estimation technique of third-order nonlinear signals based on the linear finite element method is proposed, and the variation of nonlinear signal level with electrode width is estimated. Then, several one-port SAW resonators with different electrode widths are fabricated, and measured nonlinear signal levels are compared with simulation. As predicted by the numerical simulation, nonlinear signal levels became large with electrode width. However, harmonics takes a minimum at a certain electrode width. This tendency disagrees with the simulation. The variation of nonlinear coefficients is evaluated by numerical fitting for the measured data using the nonlinear signal simulator proposed by the authors. As the result, it is concluded that the generation mechanism is not limited to the acoustic strain in electrodes.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning.

PubMed

Kumar, Anupam; Kumar, Vijay

2017-05-01

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear optical properties of semiconductor nanocrystals

NASA Astrophysics Data System (ADS)

Ricard, Gianpiero Banfi Vittorio Degiorgio Daniel

1998-05-01

This review is devoted to the description of recent experimental results concerning the nonlinear optical properties of semiconductor-doped glasses SDGs with particular emphasis on the regime in which the energy of the incident photon is smaller than the energy gap. A considerable theoretical and experimental effort has been devoted in the last 10years to the fundamental aspects of quantumconfined structures, which have properties somewhat intermediate between the bulk crystals and atoms or molecules. From this point of view, SDGs represent an easily available test system, and optical techniques have been a major diagnostic tool. Luminescence and absorption spectroscopy were extensively used to characterize the electronic states. The experiments aimed at the measurement of the real and imaginary parts of the third-order optical susceptibility of SDGs below the bandgap are described in some detail, and the results obtained with different techniques are compared. Besides the intrinsic fast nonlinearity due to bound electrons, SDGs may present a larger but much slower nonlinearity due to the free carriers generated by two-photon absorption. This implies that experiments have to be properly designed for separation of the two effects. In this article we stress the importance of a detailed structural characterization of the samples. Knowledge of the volume fraction occupied by the nanocrystals is necessary in order to derive from the experimental data the intrinsic nonlinearity and to compare it with the bulk nonlinearity. We discuss recent experiments in which the dependence of the intrinsic nonlinearity on the crystal size is derived by performing, on the samples, measurements of the real part and imaginary part of the nonlinear optical susceptibility and measurements of crystal size and volume fraction. Structural characterization is of interest also for a better understanding of the physical processes underlying the growth of crystallites in SDGs. The average size of nanocrystals can be tailored by controlling the temperature or time of the treatment. The major problem is the size dispersion of the crystallites, which is intrinsic to the diffusion process. At present, this is the major source of the undesired inhomogeneous broadening of the optical transition lines of the SDGs. Efforts are at present being made to fabricate materials, SDGs included, which embed nanocrystals with a reduced spread of sizes. The interest in the nonlinear optical properties is due not only to fundamental reasons but also to possible applications for optical devices. Generally speaking, resonant nonlinearities are much larger than non-resonant nonlinearities, but they are not necessarily the most interesting for applications because materials at resonance absorb the incident radiation and also present long response times. The studies below the bandgap seem to indicate that the values of the intrinsic nonlinearities of nanocrystals in the structures which are at present available are similar to those of the bulk. New and better controlled structures are now under development and have to be tested from the viewpoint of optical nonlinearities. In several situations SDGs cannot be modelled as an ensemble of freely standing nanocrystals, with the glass matrix playing the role of an inert support. Phenomena such as trapping and darkening, which are very probably connected with electronic states at the glasssemiconductor interface, may play a role in determining the optical response. They might give rise to an extrinsic optical nonlinearity which can be even larger than the intrinsic nonlinearity. The physical processes which are involved in these extrinsic nonlinearities are poorly understood and at present being investigated.

Analytical and Computational Modeling of Mechanical Waves in Microscale Granular Crystals: Nonlinearity and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Wallen, Samuel P.

Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing, shock and vibration mitigation, and powder processing.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

Quantification of loading in biomechanical testing: the influence of dissection sequence.

PubMed

Funabashi, Martha; El-Rich, Marwan; Prasad, Narasimha; Kawchuk, Gregory N

2015-09-18

Sequential dissection is a technique used to investigate loads experienced by articular tissues. When the joint of interest is tested in an unconstrained manner, its kinematics change with each tissue removal. To address this limitation, sufficiently rigid robots are used to constrain joint kinematics. While this approach can quantify loads experienced by each tissue, it does not assure similar results when removal order is changed. Specifically, structure loading is assumed to be independent of removal order if the structure behaves linearly (i.e. principle of superposition applies), but dependent on removal order when response is affected by material and/or geometry nonlinearities and/or viscoelasticiy (e.g. biological tissues). Therefore, this experiment was conducted to evaluate if structure loading created through robotic testing is dependent on the order in which connectors are removed. Six identical models were 3D printed. Each model was composed of 2 rigid bodies and 3 connecting structures with nonlinear time-dependent behavior. To these models, pure rotations were applied about a predefined static center of rotation using a parallel robot. A unique dissection sequence was used for each of the six models and the same movements applied robotically after each dissection. When comparing the moments experienced by each structure between different removal sequences, a statistically significant difference (p<0.05) was observed. These results suggest that even in an optimized environment, the sequence in which nonlinear viscoelastic structures are removed influence model loading. These findings support prior work suggesting that tissue loads obtained from robotic testing are specific to removal order. Copyright © 2015 Elsevier Ltd. All rights reserved.

Complete super-sample lensing covariance in the response approach

NASA Astrophysics Data System (ADS)

Barreira, Alexandre; Krause, Elisabeth; Schmidt, Fabian

2018-06-01

We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky ≈ 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by ≈ 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles l1,l2 gtrsim 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

Third-order nonlinear optical properties of acid green 25 dye by Z-scan method

NASA Astrophysics Data System (ADS)

Jeyaram, S.; Geethakrishnan, T.

2017-03-01

Third-order nonlinear optical (NLO) properties of aqueous solutions of an anthraquinone dye (Acid green 25 dye, color index: 61570) have been studied by Z-scan method with a 5 mW continuous wave (CW) diode laser operating at 635 nm. The nonlinear refractive index (n2) and the absorption coefficient (β) have been evaluated respectively from the closed and open aperture Z-scan data and the values of these parameters are found to increase with increase in concentration of the dye solution. The negative sign of the observed nonlinear refractive index (n2) indicates that the aqueous solution of acid green 25 dye exhibits self-defocusing type optical nonlinearity. The mechanism of the observed nonlinear absorption (NLA) and nonlinear refraction (NLR) is attributed respectively to reverse saturable absorption (RSA) and thermal nonlinear effects. The magnitudes of n2 and β are found to be of the order of 10-7 cm2/W and 10-3 cm/W respectively. With these experimental results, the authors suggest that acid green 25 dye may have potential applications in nonlinear optics.

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

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.

An alternative approach to characterize nonlinear site effects

USGS Publications Warehouse

Zhang, R.R.; Hartzell, S.; Liang, J.; Hu, Y.

2005-01-01

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Short Time Impulse Response Function (STIRF) for automatic evaluation of the variation of the dynamic parameters of reinforced concrete framed structures during strong earthquakes.

NASA Astrophysics Data System (ADS)

Carlo Ponzo, Felice; Ditommaso, Rocco

2015-04-01

This study presents an innovative strategy for automatic evaluation of the variable fundamental frequency and related damping factor of nonlinear structures during strong motion phases. Most of methods for damage detection are based on the assessment of the variations of the dynamic parameters characterizing the monitored structure. A crucial aspect of these methods is the automatic and accurate estimation of both structural eigen-frequencies and related damping factors also during the nonlinear behaviour. A new method, named STIRF (Short-Time Impulse Response Function - STIRF), based on the nonlinear interferometric analysis combined with the Fourier Transform (FT) here is proposed in order to allow scientists and engineers to characterize frequencies and damping variations of a monitored structure. The STIRF approach helps to overcome some limitation derived from the use of techniques based on simple Fourier Transform. These latter techniques provide good results when the response of the monitored system is stationary, but fails when the system exhibits a non-stationary, time-varying behaviour: even non-stationary input, soil-foundation and/or adjacent structures interaction phenomena can show the inadequacy of classic techniques to analysing the nonlinear and/or non-stationary behaviour of structures. In fact, using this kind of approach it is possible to improve some of the existing methods for the automatic damage detection providing stable results also during the strong motion phase. Results are consistent with those expected if compared with other techniques. The main advantage derived from the use of the proposed approach (STIRF) for Structural Health Monitoring is based on the simplicity of the interpretation of the nonlinear variations of the fundamental frequency and the related equivalent viscous damping factor. The proposed methodology has been tested on both numerical and experimental models also using data retrieved from shaking table tests. Based on the results provided in this study, the methodology seems to be able to evaluate fast variations (over time) of dynamic parameters of a generic reinforced concrete framed structure. Further analyses are necessary to better calibrate the length of the moving time-window (in order to minimize the spurious frequency within each Interferometric Response Function evaluated on both weak and strong motion phases) and to verify the possibility to use the STIRF to analyse the nonlinear behaviour of general systems. Acknowledgements This study was partially funded by the Italian Civil Protection Department within the project DPC-RELUIS 2014 - RS4 ''Seismic observatory of structures and health monitoring''. References R. Ditommaso, F.C. Ponzo (2015). Automatic evaluation of the fundamental frequency variations and related damping factor of reinforced concrete framed structures using the Short Time Impulse Response Function (STIRF). Engineering Structures, 82 (2015), 104-112. http://dx.doi.org/10.1016/j.engstruct.2014.10.023.

Technique for Very High Order Nonlinear Simulation and Validation

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2001-01-01

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

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.

Plasmon resonance enhanced mid-infrared generation by graphene on gold gratings through difference frequency mixing

NASA Astrophysics Data System (ADS)

Cao, Jianjun; Kong, Yan; Gao, Shumei; liu, Cheng

2018-01-01

Graphene has been demonstrated to have extraordinary large second order nonlinear susceptibility that can be applied in generating mid-infrared (MIR) and terahertz waves through the difference frequency process. In this study, we exploit the highly localized electric fields caused by plasmon resonances to increase the nonlinear response from graphene. The proposed structure contains a graphene sheet on a gold grating substrate that sustains both surface plasmons at the near-infrared on the gold surface and plasmons at the MIR on the graphene surface. Based on finite difference time domain (FDTD) numerical simulations, more than 3 orders of magnitude improvement of the MIR generation efficiency is obtained by placing graphene sheets on a gold grating substrate under resonance conditions instead of placing them on a flat substrate. With the same gold grating substrate, MIR waves tunable from 30 to 55 THz are generated by tuning the gate voltage of the graphene sheet.

Ultrafast third-order nonlinear optical response of pyrene derivatives

NASA Astrophysics Data System (ADS)

Shi, Yufang; Li, Zhongguo; Fang, Yu; Sun, Jinyu; Zhao, Minggen; Song, Yinglin

2017-05-01

Two mono-substituted pyrene derivatives with delocalized electron system 1-(pyren-1-yl)-3-(4-Methyl thiophene-2-yl) acrylic ketone (13#) and 1-(pyren-1-yl)-3-(4-bromo thiophene-2-yl) acrylic ketone (15#) were successfully synthesized. The resultant compounds were characterized by nuclear magnetic resonance (NMR), infrared spectroscopy (IR), high resolution mass spectrum (HR-MS), and UV-vis spectra. The third-order nonlinear optical properties of the compounds were investigated using Z-scan technique with femtosecond laser pulses at 500 nm and 700 nm, respectively. Both of the compounds showed a decrease in transmittance about the focus, which are typical of two-photon absorption. It was found that the two-photon absorption behavior of the pyrene derivatives were modified by substituents on thiophene ring. These results indicate that both compounds can be promising candidates for future optoelectronic and bio-imaging applications.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Enhanced third-order nonlinear optical properties determined in thin films using the Z-scan technique: bis(μ-4,4'-oxydibenzoato)bis[(4'-phenyl-2,2':6',2''-terpyridine)cobalt(II)].

PubMed

Liu, Runqiang; Zhao, Ning; Liu, Ping; An, Caixia; Lian, Zhaoxun

2016-05-01

π-Conjugated organic materials exhibit high and tunable nonlinear optical (NLO) properties, and fast response times. 4'-Phenyl-2,2':6',2''-terpyridine (PTP) is an important N-heterocyclic ligand involving π-conjugated systems, however, studies concerning the third-order NLO properties of terpyridine transition metal complexes are limited. The title binuclear terpyridine Co(II) complex, bis(μ-4,4'-oxydibenzoato)-κ(3)O,O':O'';κ(3)O'':O,O'-bis[(4'-phenyl-2,2':6',2''-terpyridine-κ(3)N,N',N'')cobalt(II)], [Co2(C14H8O5)2(C21H15N3)2], (1), has been synthesized under hydrothermal conditions. In the crystal structure, each Co(II) cation is surrounded by three N atoms of a PTP ligand and three O atoms, two from a bidentate and one from a symmetry-related monodentate 4,4'-oxydibenzoate (ODA(2-)) ligand, completing a distorted octahedral coordination geometry. Neighbouring [Co(PTP)](2+) units are bridged by ODA(2-) ligands to form a ring-like structure. The third-order nonlinear optical (NLO) properties of (1) and PTP were determined in thin films using the Z-scan technique. The title compound shows a strong third-order NLO saturable absorption (SA), while PTP exhibits a third-order NLO reverse saturable absorption (RSA). The absorptive coefficient β of (1) is -37.3 × 10(-7) m W(-1), which is larger than that (8.96 × 10(-7) m W(-1)) of PTP. The third-order NLO susceptibility χ((3)) values are calculated as 6.01 × 10(-8) e.s.u. for (1) and 1.44 × 10(-8) e.s.u. for PTP.

Nonlinear optical studies of curcumin metal derivatives with cw laser

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

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S.

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition modelmore » with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.« less

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.

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.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads are developed. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratcheting. Thus, geometric as well as material type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies are being developed for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which were associated with these load conditions, were thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution process.

Enhanced third-harmonic generation in silicon nanoparticles driven by magnetic response.

PubMed

Shcherbakov, Maxim R; Neshev, Dragomir N; Hopkins, Ben; Shorokhov, Alexander S; Staude, Isabelle; Melik-Gaykazyan, Elizaveta V; Decker, Manuel; Ezhov, Alexander A; Miroshnichenko, Andrey E; Brener, Igal; Fedyanin, Andrey A; Kivshar, Yuri S

2014-11-12

We observe enhanced third-harmonic generation from silicon nanodisks exhibiting both electric and magnetic dipolar resonances. Experimental characterization of the nonlinear optical response through third-harmonic microscopy and spectroscopy reveals that the third-harmonic generation is significantly enhanced in the vicinity of the magnetic dipole resonances. The field localization at the magnetic resonance results in two orders of magnitude enhancement of the harmonic intensity with respect to unstructured bulk silicon with the conversion efficiency limited only by the two-photon absorption in the substrate.

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.

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.

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.

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.

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

NASA Technical Reports Server (NTRS)

Erickson, Gary E.

2010-01-01

Response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration at supersonic speeds in the NASA LaRC Unitary Plan Wind Tunnel. The Mach 3 staging was dominated by shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. The inference space was partitioned into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using central composite designs capable of fitting full second-order response functions. The underlying aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle were estimated using piecewise-continuous lower-order polynomial functions. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. Augmenting the central composite designs to full third-order using computer-generated D-optimality criteria was evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting lower-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Exposure-lag-response in Longitudinal Studies: Application of Distributed Lag Non-linear Models in an Occupational Cohort.

PubMed

Neophytou, Andreas M; Picciotto, Sally; Brown, Daniel M; Gallagher, Lisa E; Checkoway, Harvey; Eisen, Ellen A; Costello, Sadie

2018-02-13

Prolonged exposures can have complex relationships with health outcomes, as timing, duration, and intensity of exposure are all potentially relevant. Summary measures such as cumulative exposure or average intensity of exposure may not fully capture these relationships. We applied penalized and unpenalized distributed lag non-linear models (DLNMs) with flexible exposure-response and lag-response functions in order to examine the association between crystalline silica exposure and mortality from lung cancer and non-malignant respiratory disease in a cohort study of 2,342 California diatomaceous earth workers, followed 1942-2011. We also assessed associations using simple measures of cumulative exposure assuming linear exposure-response and constant lag-response. Measures of association from DLNMs were generally higher than from simpler models. Rate ratios from penalized DLNMs corresponding to average daily exposures of 0.4 mg/m3 during lag years 31-50 prior to the age of observed cases were 1.47 (95% confidence interval (CI) 0.92, 2.35) for lung cancer and 1.80 (95% CI: 1.14, 2.85) for non-malignant respiratory disease. Rate ratios from the simpler models for the same exposure scenario were 1.15 (95% CI: 0.89-1.48) and 1.23 (95% CI: 1.03-1.46) respectively. Longitudinal cohort studies of prolonged exposures and chronic health outcomes should explore methods allowing for flexibility and non-linearities in the exposure-lag-response. © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.

A simple model of mechanotransduction in primate glabrous skin

PubMed Central

Dong, Yi; Mihalas, Stefan; Kim, Sung Soo; Yoshioka, Takashi; Niebur, Ernst

2013-01-01

Tactile stimulation of the hand evokes highly precise and repeatable patterns of activity in mechanoreceptive afferents; the strength (i.e., firing rate) and timing of these responses have been shown to convey stimulus information. To achieve an understanding of the mechanisms underlying the representation of tactile stimuli in the nerve, we developed a two-stage computational model consisting of a nonlinear mechanical transduction stage followed by a generalized integrate-and-fire mechanism. The model improves upon a recently published counterpart in two important ways. First, complexity is dramatically reduced (at least one order of magnitude fewer parameters). Second, the model comprises a saturating nonlinearity and therefore can be applied to a much wider range of stimuli. We show that both the rate and timing of afferent responses are predicted with remarkable precision and that observed adaptation patterns and threshold behavior are well captured. We conclude that the responses of mechanoreceptive afferents can be understood using a very parsimonious mechanistic model, which can then be used to accurately simulate the responses of afferent populations. PMID:23236001

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.

A direct method for synthesizing low-order optimal feedback control laws with application to flutter suppression

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.; Abel, I.

1980-01-01

A direct method of synthesizing a low-order optimal feedback control law for a high order system is presented. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean square steady state responses and control inputs. The controller is shown to be equivalent to a partial state estimator. The method is applied to the problem of active flutter suppression. Numerical results are presented for a 20th order system representing an aeroelastic wind-tunnel wing model. Low-order controllers (fourth and sixth order) are compared with a full order (20th order) optimal controller and found to provide near optimal performance with adequate stability margins.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

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.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

PubMed

Pashaei, Shabnam; Badamchizadeh, Mohammadali

2016-07-01

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Linear and nonlinear winter atmospheric responses to extreme phases of low frequency Pacific sea surface temperature variability

NASA Astrophysics Data System (ADS)

Cao, Dandan; Wu, Qigang; Hu, Aixue; Yao, Yonghong; Liu, Shizuo; Schroeder, Steven R.; Yang, Fucheng

2018-02-01

This study examines Northern Hemisphere winter (DJFM) atmospheric responses to opposite strong phases of interdecadal (low frequency, LF) Pacific sea surface temperature (SST) forcing, which resembles El Niño-Southern Oscillation (ENSO) on a longer time scale, in observations and GFDL and CAM4 model simulations. Over the Pacific-North America (PNA) sector, linear observed responses of 500-hPa height (Z500) anomalies resemble the PNA teleconnection pattern, but show a PNA-like nonlinear response because of a westward Z500 shift in the negative (LF-) relative to the positive LF (LF+) phase. Significant extratropical linear responses include a North Atlantic Oscillation (NAO)-like Z500 anomaly, a dipole-like Z500 anomaly over northern Eurasia associated with warming over mid-high latitude Eurasia, and a Southern Annular anomaly pattern associated with warming in southern land areas. Significant nonlinear Z500 responses also include a NAO-like anomaly pattern. Models forced by LF+ and LF- SST anomalies reproduce many aspects of observed linear and nonlinear responses over the Pacific-North America sector, and linear responses over southern land, but not in the North Atlantic-European sector and Eurasia. Both models simulate PNA-like linear responses in the North Pacific-North America region similar to observed, but show larger PNA-like LF+ responses, resulting in a PNA nonlinear response. The nonlinear PNA responses result from both nonlinear western tropical Pacific rainfall changes and extratropical transient eddy feedbacks. With LF tropical Pacific forcing only (LFTP+ and LFTP-, climatological SST elsewhere), CAM4 simulates a significant NAO response to LFTP-, including a linear negative and nonlinear positive NAO response.

Nonlinear magnetoelectric effects at high magnetic field amplitudes in composite multiferroics

NASA Astrophysics Data System (ADS)

Fetisov, L. Y.; Burdin, D. A.; Ekonomov, N. A.; Chashin, D. V.; Zhang, J.; Srinivasan, G.; Fetisov, Y. K.

2018-04-01

Magnetoelectric effects (ME) in ferromagnetic-ferroelectric layered composites arise due to magnetostriction and piezoelectric effect in the ferroic phases and are mediated by mechanical strain. The ME coupling strength in such composites could be measured by electrical response to an applied ac magnetic field h and a bias magnetic field H. The coupling, in general, is linear for small ac field amplitudes, but one expects nonlinear ME interactions for high field strengths since the dependence of magnetostriction λ on magnetic fields is nonlinear. Here we report on nonlinear voltage response of a composite of ferromagnetic Metglas and piezoelectric lanthanum gallium tantalate (langatate) subjected to an ac and a bias magnetic fields, resulting in the generation of voltages at harmonics of the frequency of h. The dependences of the ME voltage of the first four harmonics on the magnetic fields for H  =  0–20 Oe and h  =  0–50 Oe were measured. Up to a hundred harmonics were observed in the voltage versus frequency spectra and was indicative of high nonlinearity of the ME coupling in the multiferroic structure. It is shown that for h smaller than the saturation magnetic field H S for magnetostriction in the ferromagnetic layer, the amplitudes of the ME voltages are proportional to the derivatives of λ with respect to H and show a power-law dependence on the pumping field amplitude A n (H) ~ λ (n)(H)h n . We discuss a procedure for estimating the amplitudes of the harmonics for large pumping fields h, on the order of H S. The nonlinear ME effects in the composites are of interest for application in signal processing devices and highly sensitive magnetic field sensors.

Thiophene-based terpyridine and its zinc halide complexes: third-order nonlinear optical properties in the near-infrared region.

PubMed

Tan, Jingyun; Li, Rui; Li, Dandan; Zhang, Qiong; Li, Shengli; Zhou, Hongping; Yang, Jiaxiang; Wu, Jieying; Tian, Yupeng

2015-01-21

A novel 4'-(4-(diphenylamino)thienyl)-2,2':6',2''-terpyridine ligand () based on thiophene and its complexes (X = Cl, Br, I, SCN) was designed, synthesized and characterized by elemental analysis, far-IR, MALDI-TOF-MS, and single crystal X-ray diffraction analysis. Structural studies revealed that the central zinc(ii) atom adopted a distorted trigonal bipyramidal coordination model. However, there were different hydrogen bonds and stacking models with different counter anions in the crystals. The absorption properties of the compounds were investigated with the aid of TD-DFT computational methods. Furthermore, the third-order nonlinear optical (NLO) properties were systematically studied via open-aperture Z-scan methods using a tunable wavelength femtosecond laser. The results from photophysical property investigations suggested that the complexation of the thiophene-based terpyridine ligand with zinc halides resulted in strong ICT/LLCT bands of about 450 nm, and the complexes exhibited strong nonlinear optical response in the near-infrared range around 850 nm. Above all, the two-photon absorption (2PA) cross-section values (σ) were enhanced by coordination with zinc and influenced by halide ions, reaching up to 2583 GM (X = Br).

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.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Correlation between piezoresponse nonlinearity and hysteresis in ferroelectric crystals at nanoscale

DOE PAGES

Kalinin, Sergei V.; Jesse, Stephen; Yang, Yaodong; ...

2016-04-27

Here, the nonlinear response of a ferroic to external fields has been studied for decades, garnering interest for both understanding fundamental physics, as well as technological applications such as memory devices. Yet, the behavior of ferroelectrics at mesoscopic regimes remains poorly understood, and the scale limits of theories developed for macroscopic regimes are not well tested experimentally. Here, we test the link between piezo-nonlinearity and local piezoelectric strain hysteresis, via AC-field dependent measurements in conjunction with first order reversal curve (FORC) measurements on (K,Na)NbO 3 crystals with band-excitation piezoelectric force microscopy. The correlation coefficient between nonlinearity amplitude and the FORCmore » of the polarization switching shows a clear decrease in correlation with increasing AC bias, suggesting the impact of domain wall clamping on the DC measurement case. Further, correlation of polynomial fitting terms from the nonlinear measurements with the hysteresis loop area reveals that the largest correlations are reserved for the quadratic terms, which is expected for irreversible domain wall motion contributions that impact both piezoelectric behavior as well as minor loop formation. These confirm the link between local piezoelectric nonlinearity, domain wall motion and minor loop formation, and suggest that existing theories (such as Preisach) are applicable at these length scales, with associated implications for future nanoscale devices.« less

The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion

PubMed Central

Massot, Corentin; Schneider, Adam D.; Chacron, Maurice J.; Cullen, Kathleen E.

2012-01-01

Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways. PMID:22911113

Constrained State Estimation for Individual Localization in Wireless Body Sensor Networks

PubMed Central

Feng, Xiaoxue; Snoussi, Hichem; Liang, Yan; Jiao, Lianmeng

2014-01-01

Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF) show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS), which gets better filtering performance than NILS without constraint. PMID:25390408

fNL‑gNL mixing in the matter density field at higher orders

NASA Astrophysics Data System (ADS)

Gressel, Hedda A.; Bruni, Marco

2018-06-01

In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of fNL, gNL, hNL\\ldots , we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.

Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

PubMed

Kohlgraf-Owens, Dana C; Kik, Pieter G

2008-07-07

Maxwell Garnett effective medium theory is used to study the influence of silver nanoparticle induced field enhancement on the nonlinear response of a Kerr-type nonlinear host. We show that the composite nonlinear absorption coefficient, beta(c), can be enhanced relative to the host nonlinear absorption coefficient near the surface plasmon resonance of silver nanoparticles. This enhancement is not due to a resonant enhancement of the host nonlinear absorption, but rather due to a phase shifted enhancement of the host nonlinear refractive response. The enhancement occurs at the expense of introducing linear absorption, alpha(c), which leads to an overall reduced figure of merit beta(c)/alpha(c) for nonlinear absorption. For thin (< 1 microm) composites, the use of surface plasmons is found to result in an increased nonlinear absorption response compared to that of the host material.

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

PubMed

Chen, Yong; Yan, Zhenya

2016-03-22

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

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

PubMed Central

Chen, Yong; Yan, Zhenya

2016-01-01

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543

Enhanced Broadband Vibration Energy Harvesting Using a Multimodal Nonlinear Magnetoelectric Converter

NASA Astrophysics Data System (ADS)

Lin, Zhiming; Yang, Jin; Zhao, Jiangxin; Zhao, Nian; Liu, Jun; Wen, Yumei; Li, Ping

2016-07-01

In this work, we present a multimodal wideband vibration energy harvester designed to scavenge energy from ambient vibrations over a wide frequency range. The harvester consists of a folded cantilever, three magnetoelectric (ME) transducers, and two magnetic circuits. The folded cantilever enables multi-resonant response formed by bending of each stage, and the nonlinear magnetic forces acting on the folded cantilever beam allow further broadening of the frequency response. We also investigate the effects of the position of the ME transducer on the electrical output in order to achieve optimal performance. The experimental results show that the vibration energy harvester exhibited three resonance peaks in a range of 5 Hz to 30 Hz, a wider working bandwidth of 10.1 Hz, and a maximum average power value of 31.58 μW at an acceleration of 0.6 g (with g = 9.8 m/s2).

Nuclear counting filter based on a centered Skellam test and a double exponential smoothing

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

Coulon, Romain; Kondrasovs, Vladimir; Dumazert, Jonathan

2015-07-01

Online nuclear counting represents a challenge due to the stochastic nature of radioactivity. The count data have to be filtered in order to provide a precise and accurate estimation of the count rate, this with a response time compatible with the application in view. An innovative filter is presented in this paper addressing this issue. It is a nonlinear filter based on a Centered Skellam Test (CST) giving a local maximum likelihood estimation of the signal based on a Poisson distribution assumption. This nonlinear approach allows to smooth the counting signal while maintaining a fast response when brutal change activitymore » occur. The filter has been improved by the implementation of a Brown's double Exponential Smoothing (BES). The filter has been validated and compared to other state of the art smoothing filters. The CST-BES filter shows a significant improvement compared to all tested smoothing filters. (authors)« less

The dynamics of current carriers in standing Alfvén waves: Parallel electric fields in the auroral acceleration region

NASA Astrophysics Data System (ADS)

Wright, Andrew N.; Allan, W.; Ruderman, Michael S.; Elphic, R. C.

2002-07-01

The acceleration of current carriers in an Alfvén wave current system is considered. The model incorporates a dipole magnetic field geometry, and we present an analytical solution of the two-fluid equations by successive approximations. The leading solution corresponds to the familiar single-fluid toroidal oscillations. The next order describes the nonlinear dynamics of electrons responsible for carrying a few μAm-2 field aligned current into the ionosphere. The solution shows how most of the electron acceleration in the magnetosphere occurs within 1 RE of the ionosphere, and that a parallel electric field of the order of 1 mVm-1 is responsible for energising the electrons to 1 keV. The limitations of the electron fluid approximation are considered, and a qualitative solution including electron beams and a modified E∥ is developed in accord with observations. We find that the electron acceleration can be nonlinear, (ve∥∇∥)ve∥ > ωve∥, as a result of our nonuniform equilibrium field geometry even when ve∥ is less than the Alfvén speed. Our calculation also elucidates the processes through which E∥ is generated and supported.

A nonlinear macromodel of the bipolar integrated circuit operational amplifier for electromagnetic interference analysis

NASA Astrophysics Data System (ADS)

Chen, G. K. C.

1981-06-01

A nonlinear macromodel for the bipolar transistor integrated circuit operational amplifier is derived from the macromodel proposed by Boyle. The nonlinear macromodel contains only two nonlinear transistors in the input stage in a differential amplifier configuration. Parasitic capacitance effects are represented by capacitors placed at the collectors and emitters of the input transistors. The nonlinear macromodel is effective in predicting the second order intermodulation effect of operational amplifiers in a unity gain buffer amplifier configuration. The nonlinear analysis computer program NCAP is used for the analysis. Accurate prediction of demodulation of amplitude modulated RF signals with RF carrier frequencies in the 0.05 to 100 MHz range is achieved. The macromodel predicted results, presented in the form of second order nonlinear transfer function, come to within 6 dB of the full model predictions for the 741 type of operational amplifiers for values of the second order transfer function greater than -40 dB.

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.

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.

Investigation of the Flutter Suppression by Fuzzy Logic Control for Hypersonic Wing

NASA Astrophysics Data System (ADS)

Li, Dongxu; Luo, Qing; Xu, Rui

This paper presents a fundamental study of flutter characteristics and control performance of an aeroelastic system based on a two-dimensional double wedge wing in the hypersonic regime. Dynamic equations were established based on the modified third order nonlinear piston theory and some nonlinear structural effects are also included. A set of important parameters are observed. And then aeroelastic control law is designed to suppress the amplitude of the LCOs for the system in the sub/supercritical speed range by applying fuzzy logic control on the input of the deflection of the flap. The overall effects of the parameters on the aeroelastic system were outlined. Nonlinear aeroelastic responses in the open- and closed-loop system are obtained through numerical methods. The simulations show fuzzy logic control methods are effective in suppressing flutter and provide a smart approach for this complicated system.

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

NASA Astrophysics Data System (ADS)

Haim, L.; Gedalin, M.; Spitkovsky, A.; Krasnoselskikh, V.; Balikhin, M.

2012-06-01

Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ<<1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron-ion shock front. This potential is responsible for electron energization.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

NASA Astrophysics Data System (ADS)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

NASA Astrophysics Data System (ADS)

Scoccimarro, Román; Frieman, Joshua A.

1999-07-01

We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly nonlinear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated Ansatz that yields the strongly nonlinear behavior of the skewness, S3, starting from leading-order perturbation theory. When generalized to higher order (p>3) polyspectra or correlation functions, this Ansatz leads to a good description of nonlinear amplitudes in the strongly nonlinear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly nonlinear regimes, analogous to previous expressions for the power spectrum.

A Solar Cycle Dependence of Nonlinearity in Magnetospheric Activity

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

Johnson, Jay R; Wing, Simon

2005-03-08

The nonlinear dependencies inherent to the historical K(sub)p data stream (1932-2003) are examined using mutual information and cumulant based cost as discriminating statistics. The discriminating statistics are compared with surrogate data streams that are constructed using the corrected amplitude adjustment Fourier transform (CAAFT) method and capture the linear properties of the original K(sub)p data. Differences are regularly seen in the discriminating statistics a few years prior to solar minima, while no differences are apparent at the time of solar maximum. These results suggest that the dynamics of the magnetosphere tend to be more linear at solar maximum than at solarmore » minimum. The strong nonlinear dependencies tend to peak on a timescale around 40-50 hours and are statistically significant up to one week. Because the solar wind driver variables, VB(sub)s and dynamical pressure exhibit a much shorter decorrelation time for nonlinearities, the results seem to indicate that the nonlinearity is related to internal magnetospheric dynamics. Moreover, the timescales for the nonlinearity seem to be on the same order as that for storm/ring current relaxation. We suggest that the strong solar wind driving that occurs around solar maximum dominates the magnetospheric dynamics suppressing the internal magnetospheric nonlinearity. On the other hand, in the descending phase of the solar cycle just prior to solar minimum, when magnetospheric activity is weaker, the dynamics exhibit a significant nonlinear internal magnetospheric response that may be related to increased solar wind speed.« less

Can we detect a nonlinear response to temperature in European plant phenology?

PubMed

Jochner, Susanne; Sparks, Tim H; Laube, Julia; Menzel, Annette

2016-10-01

Over a large temperature range, the statistical association between spring phenology and temperature is often regarded and treated as a linear function. There are suggestions that a sigmoidal relationship with definite upper and lower limits to leaf unfolding and flowering onset dates might be more realistic. We utilised European plant phenological records provided by the European phenology database PEP725 and gridded monthly mean temperature data for 1951-2012 calculated from the ENSEMBLES data set E-OBS (version 7.0). We analysed 568,456 observations of ten spring flowering or leafing phenophases derived from 3657 stations in 22 European countries in order to detect possible nonlinear responses to temperature. Linear response rates averaged for all stations ranged between -7.7 (flowering of hazel) and -2.7 days °C -1 (leaf unfolding of beech and oak). A lower sensitivity at the cooler end of the temperature range was detected for most phenophases. However, a similar lower sensitivity at the warmer end was not that evident. For only ∼14 % of the station time series (where a comparison between linear and nonlinear model was possible), nonlinear models described the relationship significantly better than linear models. Although in most cases simple linear models might be still sufficient to predict future changes, this linear relationship between phenology and temperature might not be appropriate when incorporating phenological data of very cold (and possibly very warm) environments. For these cases, extrapolations on the basis of linear models would introduce uncertainty in expected ecosystem changes.

Third order nonlinearity in pulsed laser deposited LiNbO{sub 3} thin films

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

Tumuluri, Anil; Rapolu, Mounika; Rao, S. Venugopal, E-mail: kcjrsp@uohyd.ernet.in, E-mail: svrsp@uohyd.ernet.in

2016-05-06

Lithium niobate (LiNbO{sub 3}) thin films were prepared using pulsed laser deposition technique. Structural properties of the same were examined from XRD and optical band gap of the thin films were measured from transmittance spectra recorded using UV-Visible spectrophotometer. Nonlinear optical properties of the thin films were recorded using Z-Scan technique. The films were exhibiting third order nonlinearity and their corresponding two photon absorption, nonlinear refractive index, real and imaginary part of nonlinear susceptibility were calculated from open aperture and closed aperture transmission curves. From these studies, it suggests that these films have potential applications in nonlinear optical devices.

Non-Uniformity Correction Using Nonlinear Characteristic Performance Curves for Calibration

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna Roberts

Infrared imaging is an expansive field with many applications. Advances in infrared technology have lead to a greater demand from both commercial and military sectors. However, a known problem with infrared imaging is its non-uniformity. This non-uniformity stems from the fact that each pixel in an infrared focal plane array has its own photoresponse. Many factors such as exposure time, temperature, and amplifier choice affect how the pixels respond to incoming illumination and thus impact image uniformity. To improve performance non-uniformity correction (NUC) techniques are applied. Standard calibration based techniques commonly use a linear model to approximate the nonlinear response. This often leaves unacceptable levels of residual non-uniformity. Calibration techniques often have to be repeated during use to continually correct the image. In this dissertation alternates to linear NUC algorithms are investigated. The goal of this dissertation is to determine and compare nonlinear non-uniformity correction algorithms. Ideally the results will provide better NUC performance resulting in less residual non-uniformity as well as reduce the need for recalibration. This dissertation will consider new approaches to nonlinear NUC such as higher order polynomials and exponentials. More specifically, a new gain equalization algorithm has been developed. The various nonlinear non-uniformity correction algorithms will be compared with common linear non-uniformity correction algorithms. Performance will be compared based on RMS errors, residual non-uniformity, and the impact quantization has on correction. Performance will be improved by identifying and replacing bad pixels prior to correction. Two bad pixel identification and replacement techniques will be investigated and compared. Performance will be presented in the form of simulation results as well as before and after images taken with short wave infrared cameras. The initial results show, using a third order polynomial with 16-bit precision, significant improvement over the one and two-point correction algorithms. All algorithm have been implemented in software with satisfactory results and the third order gain equalization non-uniformity correction algorithm has been implemented in hardware.

Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

PubMed

Xie, Xue-Jun; Zhang, Xing-Hui

2014-03-01

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Optimal second order sliding mode control for nonlinear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-07-01

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

NASA Astrophysics Data System (ADS)

Chouvion, B.; McWilliam, S.; Popov, A. A.

2018-06-01

This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼ 60 % , it is found that three ring modes of vibration (1 θ, 2 θ and 3 θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2 θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping.

Modeling of the Through-the-Thickness Electric Potentials of a Piezoelectric Bimorph Using the Spectral Element Method

PubMed Central

Dong, Xingjian; Peng, Zhike; Hua, Hongxing; Meng, Guang

2014-01-01

An efficient spectral element (SE) with electric potential degrees of freedom (DOF) is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL) model based on first-order shear deformation theory (FSDT) is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE) analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator. PMID:24561399

Time and frequency domain characteristics of detrending-operation-based scaling analysis: Exact DFA and DMA frequency responses

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Tsujimoto, Yutaka

2016-07-01

We develop a general framework to study the time and frequency domain characteristics of detrending-operation-based scaling analysis methods, such as detrended fluctuation analysis (DFA) and detrending moving average (DMA) analysis. In this framework, using either the time or frequency domain approach, the frequency responses of detrending operations are calculated analytically. Although the frequency domain approach based on conventional linear analysis techniques is only applicable to linear detrending operations, the time domain approach presented here is applicable to both linear and nonlinear detrending operations. Furthermore, using the relationship between the time and frequency domain representations of the frequency responses, the frequency domain characteristics of nonlinear detrending operations can be obtained. Based on the calculated frequency responses, it is possible to establish a direct connection between the root-mean-square deviation of the detrending-operation-based scaling analysis and the power spectrum for linear stochastic processes. Here, by applying our methods to DFA and DMA, including higher-order cases, exact frequency responses are calculated. In addition, we analytically investigate the cutoff frequencies of DFA and DMA detrending operations and show that these frequencies are not optimally adjusted to coincide with the corresponding time scale.

Time and frequency domain characteristics of detrending-operation-based scaling analysis: Exact DFA and DMA frequency responses.

PubMed

Kiyono, Ken; Tsujimoto, Yutaka

2016-07-01

We develop a general framework to study the time and frequency domain characteristics of detrending-operation-based scaling analysis methods, such as detrended fluctuation analysis (DFA) and detrending moving average (DMA) analysis. In this framework, using either the time or frequency domain approach, the frequency responses of detrending operations are calculated analytically. Although the frequency domain approach based on conventional linear analysis techniques is only applicable to linear detrending operations, the time domain approach presented here is applicable to both linear and nonlinear detrending operations. Furthermore, using the relationship between the time and frequency domain representations of the frequency responses, the frequency domain characteristics of nonlinear detrending operations can be obtained. Based on the calculated frequency responses, it is possible to establish a direct connection between the root-mean-square deviation of the detrending-operation-based scaling analysis and the power spectrum for linear stochastic processes. Here, by applying our methods to DFA and DMA, including higher-order cases, exact frequency responses are calculated. In addition, we analytically investigate the cutoff frequencies of DFA and DMA detrending operations and show that these frequencies are not optimally adjusted to coincide with the corresponding time scale.

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

Differences between direct current and alternating current capacitance nonlinearities in high-k dielectrics and their relation to hopping conduction

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

Khaldi, O.; Kassmi, M.; El Manar University, LMOP, 2092 Tunis

2014-08-28

Capacitance nonlinearities were studied in atomic layer deposited HfO{sub 2} films using two types of signals: a pure ac voltage of large magnitude (ac nonlinearities) and a small ac voltage superimposed to a large dc voltage (dc nonlinearities). In theory, ac and dc nonlinearities should be of the same order of magnitude. However, in practice, ac nonlinearities are found to be an order of magnitude higher than dc nonlinearities. Besides capacitance nonlinearities, hopping conduction is studied using low-frequency impedance measurements and is discussed through the correlated barrier hopping model. The link between hopping and nonlinearity is established. The ac nonlinearitiesmore » are ascribed to the polarization of isolated defect pairs, while dc nonlinearities are attributed to electrode polarization which originates from defect percolation paths. Both the ac and dc capacitance nonlinearities display an exponential variation with voltage, which results from field-induced lowering of the hopping barrier energy.« less

Neural activation in the "reward circuit" shows a nonlinear response to facial attractiveness.

PubMed

Liang, Xiaoyun; Zebrowitz, Leslie A; Zhang, Yi

2010-01-01

Positive behavioral responses to attractive faces have led neuroscientists to investigate underlying neural mechanisms in a "reward circuit" that includes brain regions innervated by dopamine pathways. Using male faces ranging from attractive to extremely unattractive, disfigured ones, this study is the first to demonstrate heightened responses to both rewarding and aversive faces in numerous areas of this putative reward circuit. Parametric analyses employing orthogonal linear and nonlinear regressors revealed positive nonlinear effects in anterior cingulate cortex, lateral orbital frontal cortex (LOFC), striatum (nucleus accumbens, caudate, putamen), and ventral tegmental area, in addition to replicating previously documented linear effects in medial orbital frontal cortex (MOFC) and LOFC and nonlinear effects in amygdala and MOFC. The widespread nonlinear responses are consistent with single cell recordings in animals showing responses to both rewarding and aversive stimuli, and with some human fMRI investigations of non-face stimuli. They indicate that the reward circuit does not process face valence with any simple dissociation of function across structures. Perceiver gender modulated some responses to our male faces: Women showed stronger linear effects, and men showed stronger nonlinear effects, which may have functional implications. Our discovery of nonlinear responses to attractiveness throughout the reward circuit echoes the history of amygdala research: Early work indicated a linear response to threatening stimuli, including faces; later work also revealed a nonlinear response with heightened activation to affectively salient stimuli regardless of valence. The challenge remains to determine how such dual coding influences feelings, such as pleasure and pain, and guides goal-related behavioral responses, such as approach and avoidance.

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.

Non-linear dynamic analysis of geared systems. Final Report Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

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

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Development of control strategies for safe microburst penetration: A progress report

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1987-01-01

A single-engine, propeller-driven, general-aviation model was incorporated into the nonlinear simulation and into the linear analysis of root loci and frequency response. Full-scale wind tunnel data provided its aerodynamic model, and the thrust model included the airspeed dependent effects of power and propeller efficiency. Also, the parameters of the Jet Transport model were changed to correspond more closely to the Boeing 727. In order to study their effects on steady-state repsonse to vertical wind inputs, altitude and total specific energy (air-relative and inertial) feedback capabilities were added to the nonlinear and linear models. Multiloop system design goals were defined. Attempts were made to develop controllers which achieved these goals.

Probing the nuclear susceptibility of mesoionic compounds using two-beam coupling with chirp-controlled pulses

NASA Astrophysics Data System (ADS)

Bosco, Carlos A. C.; Maciel, Glauco S.; Rakov, Nikifor; de Araújo, Cid B.; Acioli, Lúcio H.; Simas, Alfredo M.; Athayde-Filho, Petrônio F.; Miller, Joseph

2007-11-01

The third-order non-linear optical response of mesoionic compounds (MIC) in dimethylsulfoxide (DMSO) and methanol solutions was investigated by use of collinear pump and probe technique with chirp-controlled femtosecond pulses. The experiments allowed the investigation of non-instantaneous nuclear processes and thermal effects induced by two-photon absorption (TPA). We found that the nuclear non-linearity of MIC in DMSO is ˜1/5 the benzene, which was used as a reference material. This result is attributed to the large inertia of MIC to rotation, compared to benzene. The results for MIC in methanol indicate the influence of thermal effects due to TPA.

Four wave mixing as a probe of the vacuum

NASA Astrophysics Data System (ADS)

Tennant, Daniel M.

2016-06-01

Much attention has been paid to the quantum structure of the vacuum. Higher order processes in quantum electrodynamics are strongly believed to cause polarization and even breakdown of the vacuum in the presence of strong fields soon to be accessible in high intensity laser experiments. Less explored consequences of strong field electrodynamics include effects from Born-Infeld type of electromagnetic theories, a nonlinear electrodynamics that follows from classical considerations as opposed to coupling to virtual fluctuations. In this article, I will demonstrate how vacuum four wave mixing has the possibility to differentiate between these two types of vacuum responses: quantum effects on one hand and nonlinear classical extensions on the other.

Nonlinear Optical Response of Polar Semiconductors in the Terahertz Range

NASA Astrophysics Data System (ADS)

Roman, Eric; Yates, Jonathan; Veithen, Marek; Vanderbilt, David; Souza, Ivo

2006-03-01

Using the Berry-phase finite-field method, we compute from first-principles the recently measured infrared (IR) dispersion of the nonlinear susceptibility (2)circ in III-V zincblende semiconductors. At far-IR (terahertz) frequencies, in addition to the purely electronic response (2)circ∞, the total (2)circ depends on three other parameters, C1, C2, and C3, describing the contributions from ionic motion. They relate to the TO Raman polarizability and the second-order displacement-induced dielectric polarization and forces, respectively. Contrary to a widely-accepted model, but in agreement with the recent experiments on GaAs, ^1 we find that the contribution from mechanical anharmonicity dominates over electrical anharmonicity. By using Richardson extrapolation to evaluate the Berry's phase in k-space by finite differences, we are able to improve the convergence of the nonlinear susceptibility from the usual O[(δk)^2] to O[(δk)^4], dramatically reducing the computational cost. T. Dekorsy, V. A. Yakovlev, W. Seidel, M. Helm, and F. Keilmann, Phys. Rev. Lett. 90, 055508 (2003). C. Flytzanis, Phys. Rev. B 6, 1264 (1972). R. Umari and A. Pasquarello, Phys. Rev. B 68, 085114 (2003).

Nonlinear optical memory for manipulation of orbital angular momentum of light.

PubMed

de Oliveira, R A; Borba, G C; Martins, W S; Barreiro, S; Felinto, D; Tabosa, J W R

2015-11-01

We report on the demonstration of a nonlinear optical memory (NOM) for storage and on-demand manipulation of orbital angular momentum (OAM) of light via higher-order nonlinear processes in cold cesium atoms. A spatially resolved phase-matching technique is used to select each order of the nonlinear susceptibility associated, respectively, with time-delayed four-, six-, and eight-wave mixing processes. For a specific configuration of the stored OAM of the incident beams, we demonstrated that the OAM of the retrieved beam can be manipulated according to the order of the nonlinear process chosen by the operator for reading out the NOM. This demonstration indicates new pathways for applications in classical and quantum information processing where OAM of light is used to encode optical information.

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

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

Lidorikis, Elefterios

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model inmore » which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.« less

Investigation of the spatial distribution of second-order nonlinearity in thermally poled optical fibers.

PubMed

An, Honglin; Fleming, Simon

2005-05-02

The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1996-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1999-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high-order characteristics of the system. In this paper only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles of attack: 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of the identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the estimated closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Nonlinear Y-Like Receptive Fields in the Early Visual Cortex: An Intermediate Stage for Building Cue-Invariant Receptive Fields from Subcortical Y Cells.

PubMed

Gharat, Amol; Baker, Curtis L

2017-01-25

Many of the neurons in early visual cortex are selective for the orientation of boundaries defined by first-order cues (luminance) as well as second-order cues (contrast, texture). The neural circuit mechanism underlying this selectivity is still unclear, but some studies have proposed that it emerges from spatial nonlinearities of subcortical Y cells. To understand how inputs from the Y-cell pathway might be pooled to generate cue-invariant receptive fields, we recorded visual responses from single neurons in cat Area 18 using linear multielectrode arrays. We measured responses to drifting and contrast-reversing luminance gratings as well as contrast modulation gratings. We found that a large fraction of these neurons have nonoriented responses to gratings, similar to those of subcortical Y cells: they respond at the second harmonic (F2) to high-spatial frequency contrast-reversing gratings and at the first harmonic (F1) to low-spatial frequency drifting gratings ("Y-cell signature"). For a given neuron, spatial frequency tuning for linear (F1) and nonlinear (F2) responses is quite distinct, similar to orientation-selective cue-invariant neurons. Also, these neurons respond to contrast modulation gratings with selectivity for the carrier (texture) spatial frequency and, in some cases, orientation. Their receptive field properties suggest that they could serve as building blocks for orientation-selective cue-invariant neurons. We propose a circuit model that combines ON- and OFF-center cortical Y-like cells in an unbalanced push-pull manner to generate orientation-selective, cue-invariant receptive fields. A significant fraction of neurons in early visual cortex have specialized receptive fields that allow them to selectively respond to the orientation of boundaries that are invariant to the cue (luminance, contrast, texture, motion) that defines them. However, the neural mechanism to construct such versatile receptive fields remains unclear. Using multielectrode recording, we found a large fraction of neurons in early visual cortex with receptive fields not selective for orientation that have spatial nonlinearities like those of subcortical Y cells. These are strong candidates for building cue-invariant orientation-selective neurons; we present a neural circuit model that pools such neurons in an imbalanced "push-pull" manner, to generate orientation-selective cue-invariant receptive fields. Copyright © 2017 the authors 0270-6474/17/370998-16$15.00/0.

Third-order nonlinear optical properties of organic azo dyes by using strength of nonlinearity parameter and Z-scan technique

NASA Astrophysics Data System (ADS)

Motiei, H.; Jafari, A.; Naderali, R.

2017-02-01

In this paper, two chemically synthesized organic azo dyes, 2-(2,5-Dichloro-phenyazo)-5,5-dimethyl-cyclohexane-1,3-dione (azo dye (i)) and 5,5-Dimethyl-2-tolylazo-cyclohexane-1,3-dione (azo dye (ii)), have been studied from optical Kerr nonlinearity point of view. These materials were characterized by Ultraviolet-visible spectroscopy. Experiments were performed using a continous wave diode-pumped laser at 532 nm wavelength in three intensities of the laser beam. Nonlinear absorption (β), refractive index (n2) and third-order susceptibility (χ (3)) of dyes, were calculated. Nonlinear absorption coefficient of dyes have been calculated from two methods; 1) using theoretical fits and experimental data in the Z-scan technique, 2) using the strength of nonlinearity curves. The values of β obtained from both of the methods were approximately the same. The results demonstrated that azo dye (ii) displays better nonlinearity and has a lower two-photon absorption threshold than azo dye (i). Calculated parameter related to strength of nonlinearity for azo dye (ii) was higher than azo dye (i), It may be due to presence of methyl in azo dye (ii) instead of chlorine in azo dye (i). Furthermore, The measured values of third order susceptibility of azo dyes were from the order of 10-9 esu . These azo dyes can be suitable candidate for optical switching devices.

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

NASA Astrophysics Data System (ADS)

Ma, Tiedong; Li, Teng; Cui, Bing

2018-01-01

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

PubMed

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons

PubMed Central

Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system. PMID:29304173

Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft

NASA Astrophysics Data System (ADS)

Su, Weihua

This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation of the framework. Gust responses of the Flying-Wing configuration subject to stall effects are investigated. A bilinear torsional stiffness model is introduced to study the skin wrinkling due to large bending curvature of the Flying-Wing. The numerical studies illustrate the improvements of the existing reduced-order formulation with new capabilities of both structural modeling and coupled aeroelastic and flight dynamic analysis of fully flexible aircraft.