Higher-order nonlinear effects in a Josephson parametric amplifier
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.; Fedorov, Arkady
2015-12-01
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.
Higher-order spectra for identification of nonlinear modal coupling
NASA Astrophysics Data System (ADS)
Hickey, Daryl; Worden, Keith; Platten, Michael F.; Wright, Jan R.; Cooper, Jonathan E.
2009-05-01
Over the past four decades considerable work has been done in the area of power spectrum estimation. The information contained within the power spectrum relates to a signal's autocorrelation or 'second-order statistics'. The power spectrum provides a complete statistical description of a Gaussian process; however, a problem with this information is that it is phase blind. This problem is addressed if one turns to a system's frequency response function (FRF). The FRF graphs the magnitude and phase of the frequency response of a system; in order to do this it requires information regarding the frequency content of the input and output signals. Situations arise in science and engineering whereby signal analysts are required to look beyond second-order statistics and analyse a signal's higher-order statistics (HOS). HOS or spectra give information on a signal's deviation from Gaussianity and consequently are a good indicator function for the presence of nonlinearity within a system. One of the main problems in nonlinear system identification is that of high modal density. Many modelling schemes involve making some expansion of the nonlinear restoring force in terms of polynomial or other basis terms. If more than one degree-of-freedom is involved this becomes a multivariate problem and the number of candidate terms in the expansion grows explosively with the order of nonlinearity and the number of degrees-of-freedom. This paper attempts to use HOS to detect and qualify nonlinear behaviour for a number of symmetrical and asymmetrical systems over a range of degrees-of-freedom. In doing so the paper also attempts to show that HOS are a more sensitive tool than the FRF in detecting nonlinearity. Furthermore, the object of this paper is to try and identify which modes couple in a nonlinear manner in order to reduce the number of candidate coupling terms, for a model, as much as possible. The bispectrum method has previously been applied to simple low-DOF systems with high
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.
Higher order harmonic detection for exploring nonlinear interactions
Vasudevan, Rama K; Okatan, M. B.; Rajapaksa, Indrajit; Kim, Yunseok; Marincel, Dan; Trolier-McKinstry, Susan; Jesse, Stephen; Nagarajan, Valanoor; Kalinin, Sergei V
2013-01-01
Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, decoupling the contributions of competing or co-existing mechanisms to the system response can be achieved through investigation of higher order harmonics. Here, a method using band excitation scanning probe microscopy to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The utility of the technique is demonstrated by probing the first three harmonics of strain for a well-known system, a model Pb(Zr1-xTix)O3 ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, nanoscale measurements of the second harmonic response with field reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of combining proximal probe techniques with nth harmonic detection methods in exploring and decoupling nonlinear dynamics in a wide variety of nanoscale materials.
NASA Astrophysics Data System (ADS)
Polyanskii, Peter V.; Felde, Christina V.; Konovchuk, Alexey V.; Oleksyuk, Maxim V.
2015-11-01
Recording nonlinearity is conventionally considered as the source of noise in holographic imaging. Important exclusion from this general statement is nonlinear holographic associative memory, where the quadratic recording nonlinearity causes true brightness rendering and the possibility for associative coupling and reconstructing optical signals of arbitrary complexity which are stored at the same carrier without interference. In this paper we discuss the role of nonlinearities of an amplitude response of a hologram of the orders higher than the quadratic one in implementing the second-ordered holographic associative memory. We show that higher-order nonlinearities are also involved in implementing this type of memory. This conclusion may be of importance for interpretation of biological/human memory also. The highlight of our study is the conclusion that reconstruction of the complex conjugate heteroassociative response is provided directly, viz. by the set of specified by us pseudogratings, rather than by the mechanism of sequential diffractions.
Nonlinear acoustics in higher-order approximation: Comment.
Mitri, Farid G
2010-08-01
Some useful expressions for the second- and third-order equations for harmonic generation of infinite plane acoustic waves in a nonlinear non-viscous fluid are corrected. The concern addressed in the present comment is to point out some typographical errors in the first-order velocity and pressure expressions intervening in the calculation of the secondorder nonlinear equations, as well as a miscalculation of the axial component of the third-order Lighthill tensor term and the resulting third-order velocity and pressure equations presented in that paper.
Nonlinear identification of the total baroreflex arc: higher-order nonlinearity.
Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna
2016-12-01
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 R(2) 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 R(2) values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R(2) 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.
NASA Astrophysics Data System (ADS)
Mohamadou, A.; Tatsing, P. H.; Latchio Tiofack, C. G.; Tabi, C. B.; Kofane, T. C.
2014-11-01
We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic-quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spectral region which are symmetric to the zero point. Moreover, some spectra have a high cut-off frequency but a narrow spectral width, which is obviously beneficial to the generation of high-repetition-rate pulse trains.
Higher-order nonlinear priors for surface reconstruction.
Tasdizen, Tolga; Whitaker, Ross
2004-07-01
For surface reconstruction problems with noisy and incomplete range data, a Bayesian estimation approach can improve the overall quality of the surfaces. The Bayesian approach to surface estimation relies on a likelihood term, which ties the surface estimate to the input data, and the prior, which ensures surface smoothness or continuity. This paper introduces a new high-order, nonlinear prior for surface reconstruction. The proposed prior can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion. An exact solution would require solving a fourth-order partial differential equation (PDE), which can be difficult with conventional numerical techniques. Our approach is to solve a cascade system of two second-order PDEs, which resembles the original fourth-order system. This strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals. We solve one PDE for processing the normals and one for refitting the surface to the normals. Furthermore, we implement the associated surface deformations using level sets. Hence, the algorithm can accommodate very complex shapes with arbitrary and changing topologies. This paper gives the mathematical formulation and describes the numerical algorithms. We also show results using range and medical data.
Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schrödinger Equations
NASA Astrophysics Data System (ADS)
Asad-uz-zaman, M.; Chachou Samet, H.; Khawaja, U. Al
2016-08-01
We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.
Higher-Order Spectral Analysis of a Nonlinear Pitch and Plunge Apparatus
NASA Technical Reports Server (NTRS)
Silva, Walter A.; Strganac, Thomas W.; Hajj, Muhammad R.
2005-01-01
Simulated aeroelastic responses of a nonlinear pitch and plunge apparatus are analyzed using various statistical signal processing techniques including higher-order spectral methods. A MATLAB version of the Nonlinear Aeroelastic Testbed Apparatus (NATA) at the Texas A&M University is used to generate various aeroelastic response data including limit cycle oscillations (LCO). Traditional and higher-order spectral (HOS) methods are applied to the simulated aeroelastic responses. Higher-order spectral methods are used to identify critical signatures that indicate the transition from linear to nonlinear (LCO) aeroelastic behavior.
Higher-order nonlinear Schrodinger equations for simulations of surface wavetrains
NASA Astrophysics Data System (ADS)
Slunyaev, Alexey
2016-04-01
Numerous recent results of numerical and laboratory simulations of waves on the water surface claim that solutions of the weakly nonlinear theory for weakly modulated waves in many cases allow a smooth generalization to the conditions of strong nonlinearity and dispersion, even when the 'envelope' is difficult to determine. The conditionally 'strongly nonlinear' high-order asymptotic equations still imply the smallness of the parameter employed in the asymptotic series. Thus at some (unknown a priori) level of nonlinearity and / or dispersion the asymptotic theory breaks down; then the higher-order corrections become useless and may even make the description worse. In this paper we use the higher-order nonlinear Schrodinger (NLS) equation, derived in [1] (the fifth-order NLS equation, or next-order beyond the classic Dysthe equation [2]), for simulations of modulated deep-water wave trains, which attain very large steepness (below or beyond the breaking limit) due to the Benjamin - Feir instability. The results are compared with fully nonlinear simulations of the potential Euler equations as well as with the weakly nonlinear theories represented by the nonlinear Schrodinger equation and the classic Dysthe equation with full linear dispersion [2]. We show that the next-order Dysthe equation can significantly improve the description of strongly nonlinear wave dynamics compared with the lower-order asymptotic models. [1] A.V. Slunyaev, A high-order nonlinear envelope equation for gravity waves in finite-depth water. JETP 101, 926-941 (2005). [2] K. Trulsen, K.B. Dysthe, A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281-289 (1996).
Higher order harmonic detection for exploring nonlinear interactions with nanoscale resolution.
Vasudevan, R K; Okatan, M Baris; Rajapaksa, I; Kim, Y; Marincel, D; Trolier-McKinstry, S; Jesse, S; Valanoor, N; Kalinin, S V
2013-01-01
Nonlinear dynamics underpin a vast array of physical phenomena ranging from interfacial motion to jamming transitions. In many cases, insight into the nonlinear behavior can be gleaned through exploration of higher order harmonics. Here, a method using band excitation scanning probe microscopy (SPM) to investigate higher order harmonics of the electromechanical response, with nanometer scale spatial resolution is presented. The technique is demonstrated by probing the first three harmonics of strain for a Pb(Zr(1-x)Ti(x))O₃ (PZT) ferroelectric capacitor. It is shown that the second order harmonic response is correlated with the first harmonic response, whereas the third harmonic is not. Additionally, measurements of the second harmonic reveal significant deviations from Rayleigh-type models in the form of a much more complicated field dependence than is observed in the spatially averaged data. These results illustrate the versatility of n(th) order harmonic SPM detection methods in exploring nonlinear phenomena in nanoscale materials.
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.
Collapse for the higher-order nonlinear Schrödinger equation
Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; ...
2016-02-01
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data,more » are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.« less
Collapse for the higher-order nonlinear Schrödinger equation
Achilleos, V.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G.
2016-02-01
We examine conditions for finite-time collapse of the solutions of the higher-order nonlinear Schr odinger (NLS) equation incorporating third-order dispersion, self-steepening, linear and nonlinear gain and loss, and Raman scattering; this is a system that appears in many physical contexts as a more realistic generalization of the integrable NLS. By using energy arguments, it is found that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. We identify a critical value of the linear gain, separating the possible decay of solutions to the trivial zero-state, from collapse. The numerical simulations, performed for a wide class of initial data, are found to be in very good agreement with the analytical results, and reveal long-time stability properties of localized solutions. The role of the higher-order effects to the transient dynamics is also revealed in these simulations.
Nonlinearity detection for condition monitoring utilizing higher-order spectral analysis diagnostics
NASA Astrophysics Data System (ADS)
Park, Hyeonsu
In this dissertation, we investigate the theory and application of higher-order spectral analysis techniques to condition monitoring in shipboard electrical power systems. Monitoring and early detection of faults in rotating machines, such as induction motors, are essential for both preventive maintenance and to avoid potentially severe damage. As machines degrade, they often tend to become more nonlinear. This increased nonlinearity results in the introduction of new frequencies which satisfy particular frequency selection rules; the exact selection rule depends on the order of the nonlinearity. In addition, the phases of the newly generated frequencies satisfy a similar phase selection rule. This results in a phase coherence, or phase coupling, between the "original" interacting frequencies and the "new" frequencies. This phase coupling is a true signature of nonlinearity. Since the classical auto-power spectrum contains no phase information, the phase coupling signature associated with nonlinear interactions is not available. However, various higher-order spectra (HOS) are capable of detecting such nonlinear-induced phase coupling. The efficacy of the various proposed HOS-based methodologies is investigated using real-world vibration time-series data from a faulted induction motor driving a dc generator. The fault is controlled by varying a resistor placed in one phase of the three-phase line to the induction motor. First, we propose a novel method using a bispectral change detection (BCD) for condition monitoring. Even though the bicoherence is dominant and powerful in the detection of phase coupling of nonlinearly interacting frequencies, it has some difficulties in its application to machine condition monitoring. Basically, the bicoherence may not be able to distinguish between intrinsic nonlinearities associated with healthy machines and fault-induced nonlinearities. Therefore, the ability to discriminate the fault-only nonlinearities from the intrinsic
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
Nonlinear and higher-order approaches to the encoding of natural scenes.
Zetzsche, Christoph; Nuding, Ulrich
2005-01-01
Linear operations can only partially exploit the statistical redundancies of natural scenes, and nonlinear operations are ubiquitous in visual cortex. However, neither the detailed function of the nonlinearities nor the higher-order image statistics are yet fully understood. We suggest that these complicated issues can not be tackled by one single approach, but require a range of methods, and the understanding of the crosslinks between the results. We consider three basic approaches: (i) State space descriptions can theoretically provide complete information about statistical properties and nonlinear operations, but their practical usage is confined to very low-dimensional settings. We discuss the use of representation-related state-space coordinates (multivariate wavelet statistics) and of basic nonlinear coordinate transformations of the state space (e.g., a polar transform). (ii) Indirect methods, like unsupervised learning in multi-layer networks, provide complete optimization results, but no direct information on the statistical properties, and no simple model structures. (iii) Approximation by lower-order terms of power-series expansions is a classical strategy that has not yet received broad attention. On the statistical side, this approximation amounts to cumulant functions and higher-order spectra (polyspectra), on the processing side to Volterra Wiener systems. In this context we suggest that an important concept for the understanding of natural scene statistics, of nonlinear neurons, and of biological pattern recognition can be found in AND-like combinations of frequency components. We investigate how the different approaches can be related to each other, how they can contribute to the understanding of cortical nonlinearities such as complex cells, cortical gain control, end-stopping and other extraclassical receptive field properties, and how we can obtain a nonlinear perspective on overcomplete representations and invariant coding in visual cortex.
Nonlinear Dynamic Stability of the Viscoelastic Plate Considering Higher Order Modes
NASA Astrophysics Data System (ADS)
Sun, Yuanxiang; Wang, Cheng
2016-11-01
-The dynamic stability of viscoelastic plates is investigated in this paper by using chaotic and fractal theory. The nonlinear integro-differential dynamic equation is changed into an autonomic 4-dimensional dynamical system. The numerical time integrations of equations are obtained by using the fourth order Runge-Kutta method. And the Lyapunov exponent spectrum, the fractal dimension of strange attractors and the time evolution of deflection are obtained. The influence of viscoelastic parameter on dynamic buckling of viscoelastic plates is discussed. The effect of higher order modes on dynamic stability of viscoelastic plate is obtained, the necessity of considering higher order modes is discussed.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Nonlinear optical higher-order effects in an optical lattice clock
NASA Astrophysics Data System (ADS)
Ovsyannikov, V. D.; Marmo, S. I.; Mokhnenko, S. N.; Pal'chikov, V. G.
2017-06-01
The development of optical frequency standards with a relative uncertainty of reproducing the time and frequency units at a level as low as 10-17-10-18 calls for an unprecedented accuracy in estimating the role of higher orders of optical nonlinearity, caused by the influence of the optical lattice on the frequency shift of the ‘clock transition’. This paper presents a systematic calculation of the contributions of multipole nonlinear anharmonic effects to the error of clocks based on optical lattices for alkaline-earth-like Sr, Yb, and Hg atoms.
Signal analysis applications of nonlinear dynamics and higher-order statistics
NASA Astrophysics Data System (ADS)
Solinsky, James C.; Feeney, John J.
1994-03-01
The use of higher-order statistics (HOS) in acoustic, and financial signal analysis applications is outlined in theory and followed with specific data examples. HOS analysis is used to identify data regions of interest, and nonlinear dynamics (ND) analysis is used in a 4D embedded space to show structural density changes resulting from the HOS regions. A second-order statistical comparison is made with the same data processed to have random Fourier phase, since the HOS information is contained in this nonrandom phase. These empirical results indicate that HOS data regions are structural distortions to a second-order planar disk in the 4D ND analysis space.
Higher-order nonlinear electromechanical effects in wurtzite GaN/AlN quantum dots.
Bahrami-Samani, Mehrdad; Patil, Sunil R; Melnik, Roderick
2010-12-15
As we demonstrated earlier, conventional mathematical models based on linear approximations may be inadequate in the analysis of properties of low-dimensional nanostructures and band structure calculations. In this work, a general three-dimensional axisymmetric coupled electromechanical model accounting for lattice mismatch, spontaneous polarization and higher-order nonlinear electrostriction effects has been applied to analyze properties of GaN/AlN quantum dots coupled with wetting layer. The generalized model that accounts for five independent electrostriction coefficients has been solved numerically via a finite-element implementation. The results, exemplified for truncated conical GaN/AlN quantum dots, demonstrate that the effect of nonlinear electrostriction in GaN/AlN nanoheterostructure quantum dots could be significant. In particular, the influence of nonlinear electromechanical effects on optoelectronic properties is highlighted by the results on band structure calculations based on a multiband effective mass theory.
Effects of higher-order nonlinear processes on harmonic-generation phase matching
NASA Astrophysics Data System (ADS)
Grynko, Rostislav I.; Weerawarne, Darshana L.; Shim, Bonggu
2017-07-01
We experimentally and theoretically reinvestigate the significant third-harmonic enhancement via plasma generation using time-resolved methods with two-color, copropagating femtosecond laser pulses. By measuring plasma densities with digital in-line holography and using carrier-resolved unidirectional pulse propagation equations to model the experiment, we show that a fifth-order nonlinearity contributes to third-harmonic generation mainly via phase matching. In particular, our study confirms that self- and cross-phase modulation including higher-order nonlinear processes can play a crucial role in harmonic-generation phase matching, which has recently been proposed by Weerawarne e t a l . [Phys. Rev. Lett. 114, 093901 (2015), 10.1103/PhysRevLett.114.093901] and should be potentially applicable to high-order harmonic generation.
Efficient nonlinear generation of high power, higher order, ultrafast "perfect" vortices in green.
Apurv Chaitanya, N; Jabir, M V; Samanta, G K
2016-04-01
We report on efficient nonlinear generation of ultrafast, higher order "perfect" vortices at the green wavelength. Based on Fourier transformation of the higher order Bessel-Gauss (BG) beam generated through the combination of the spiral phase plate and axicon, we have transformed the Gaussian beam of the ultrafast Yb-fiber laser at 1060 nm into perfect vortices of power 4.4 W and order up to 6. Using single-pass second-harmonic generation (SHG) of such vortices in 5 mm long chirped MgO-doped, periodically poled congruent LiNbO_{3} crystal, we have generated perfect vortices at green wavelength (530 nm) with output power of 1.2 W and vortex order up to 12 at a single-pass conversion efficiency of 27%, independent of the orders. This is the highest single-pass SHG efficiency of any optical beams other than Gaussian beams. Unlike the disintegration of higher order vortices due to spatial walk-off effect in birefringent crystals, here, the use of the quasi-phase-matching process enables generation of high-quality vortices, even at higher orders. The green perfect vortices of all orders have temporal and spectral widths of 507 fs and 1.9 nm, respectively, corresponding to a time-bandwidth product of 1.02.
NASA Astrophysics Data System (ADS)
Gelman, L.; Petrunin, I.; Komoda, J.
2010-02-01
The new chirp-Wigner higher order spectra (CWHOS) are proposed for transient signals with any known nonlinear polynomial variation of instantaneous frequency. The proposed technique is effective for nonlinearity detection for transient signals with nonlinear polynomial time variation of the instantaneous frequency.
Nonlinear optics in the LP(02) higher-order mode of a fiber.
Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A
2013-07-29
The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.
Higher order effects in non-linear evolution from a veto in rapidities
NASA Astrophysics Data System (ADS)
Chachamis, G.; Lublinsky, M.; Sabio Vera, A.
2005-02-01
Higher order corrections to the Balitsky-Kovchegov equation have been estimated by introducing a rapidity veto which forbids subsequent emissions to be very close in rapidity and is known to mimic higher order corrections to the linear BFKL equation. The rapidity veto constraint has been first introduced using analytical arguments obtaining a power growth with energy, Q(Y)˜e, of the saturation scale of λ˜0.45. Then a numerical analysis for the non-linear Balitsky-Kovchegov equation has been carried out for phenomenological rapidities: when a veto of about two units of rapidity is introduced for a fixed value of the coupling constant of α=0.2 the saturation scale λ decreases from ˜0.6 to ˜0.3, and when running coupling effects are taken into account it decreases from ˜0.4 to ˜0.3.
Nonlinear analysis of heart murmurs using wavelet-based higher-order spectral parameters.
Taplidou, Styliani A; Hadjileontiadis, Leontios J
2006-01-01
The aim of this study was to reveal and analyze the nonlinear characteristics of heart sounds, reflected in the quadrature phase coupling of the contained frequencies, as they evolve over time. To achieve this, the continuous wavelet transform was combined with third-order statistics/spectra in order to analyze their non Gaussian character, taking into account their non-stationarity. Heart sounds from patients with several pathologies that exhibit murmurs were drawn from a heart sound database and analyzed in the time-bi-frequency domain. The analysis results justified the efficient performance of this combinatory approach to reveal and quantify the evolution of heart murmurs nonlinearities with time.
NASA Astrophysics Data System (ADS)
Chin, Siu A.; Ashour, Omar A.; Nikolić, Stanko N.; Belić, Milivoj R.
2016-10-01
It is well known that Akhmediev breathers of the nonlinear cubic Schrödinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds linearly to form the peak height of the final breather. Using this peak-height formula, we show that at any given periodicity, there exists a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higher-order breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrödinger equation.
NASA Astrophysics Data System (ADS)
Kumar, Ratesh; Kaur, Harpreet; Arora, Geeta
2017-07-01
In this paper, Haar wavelet collocation mechanism (HWCM) is developed for obtaining the solution of higher order linear and nonlinear boundary value problems. Mechanism is based on approximation of solution by Haar wavelet family. To tackle the nonlinearity in the problems, Quasilinearization technique is applied. Many examples are considered to prove the successful application of the mechanism developed for getting the highly accurate result. By using the HWCM, an approximate solution for higher order boundary value problems (HOBVPs) are obtained and compared with exact and numerical solutions available in the literature.
Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail
2014-01-01
We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.
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.
NASA Astrophysics Data System (ADS)
Eskandar, S.; Hoseini, S. M.
2017-04-01
Using soliton perturbation theory, we analytically study weak interaction for a higher-order nonlinear Schrödinger equation. An ansatz consists of two well-separate single solitons is considered and slow variation of solitons parameters are found. Twelve different scenarios for when the initial velocities are zero are observed. A good comparison is found between numerical and analytical results.
Huang, T. W.; Zhou, C. T.; Zhang, H.; He, X. T.
2013-07-15
The effect of higher-order Kerr nonlinearity on channel formation by, and filamentation of, ultrashort laser pulses propagating in air is considered. Filament patterns originating from multiphoton ionization of the air molecules with and without the higher-order Kerr and molecular-rotation effects are investigated. It is found that diverging multiple filaments are formed if only the plasma-induced defocusing effect is included. In the presence of the higher-order Kerr effects, the light channel can exist for a long distance. The effect of noise on the filament patterns is also discussed.
NASA Astrophysics Data System (ADS)
Othman, N.; Shah, N. S. M.; Tay, K. G.; Pakarzadeh, H.; Cholan, N. A.; Talib, R.
2017-09-01
The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.
Weilnau, C; Denz, C; Ahles, M; Stepken, A; Motzek, K; Kaiser, F
2001-11-01
We investigate the generation of higher-order optical vector solitons in two transverse dimensions in anisotropic nonlinear media consisting of an incoherent superposition of a Gaussian beam and a higher-order laser mode with a complex internal modal structure. We demonstrate both numerically and experimentally various examples of these stable self-trapped light structures and show that vortex modes carrying topological charge always decay into multiple-humped structures that remain self trapped during propagation. Furthermore, we demonstrate the mutual stabilization of a triple- and a double-humped transverse light structure leading to the formation of a two-dimensional vector soliton without a stabilizing fundamental Gaussian mode.
NASA Astrophysics Data System (ADS)
Lee, C. T.; Lee, C. C.
2015-04-01
This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation.
Chin, Siu A; Ashour, Omar A; Nikolić, Stanko N; Belić, Milivoj R
2017-01-01
Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations, such as the Hirota equation, are indicated.
NASA Astrophysics Data System (ADS)
Chin, Siu A.; Ashour, Omar A.; Nikolić, Stanko N.; Belić, Milivoj R.
2017-01-01
Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations, such as the Hirota equation, are indicated.
Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model
NASA Astrophysics Data System (ADS)
Wang, Lei; Jiang, Dong-Yang; Qi, Feng-Hua; Shi, Yu-Ying; Zhao, Yin-Chuan
2017-01-01
Under investigation in this paper is a generalized mixed nonlinear Schrödinger equation (GMNLSE) which arises in several physical areas including the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. The linear stability analysis is performed and the instability zones as well as the modulational instability gain are obtained and discussed. Higher-order rogue waves (RWs) in terms of the determinants for the GMNLSE model are constructed by the N-fold Darboux transformation. Several patterns of the RWs are illustrated, such as the fundamental pattern, triangular pattern, circular pattern, pentagon pattern, circular-triangular pattern, and circular-fundamental pattern. Effects of the nonlinear parameters on the RWs are discussed. It is found that the nonlinear terms affect the widths and velocities of the RWs, although the amplitudes of these waves remain unchanged. The semirational RW solution, which is a combination of rational and exponential functions, is derived to describe the interaction between the RW and multi-breather.
NASA Astrophysics Data System (ADS)
Nuij, P. W. J. M.; Bosgra, O. H.; Steinbuch, M.
2006-11-01
For high-precision motion systems, modelling and control design specifically oriented at friction effects is instrumental. The sinusoidal input describing function theory represents an approximative mathematical framework for analysing non-linear system behaviour. This theory, however, limits the description of the non-linear system behaviour to a quasi-linear amplitude-dependent relation between sinusoidal excitation and sinusoidal response. In this paper, an extension to higher-order describing functions is realised by introducing the concept of the harmonics generator. The resulting higher-order sinusoidal input describing functions (HOSIDFs) relate the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude and phase of a sinusoidal excitation. Based on this extension two techniques to measure HOSIDFs are presented. The first technique is FFT based. The second technique is based on IQ (in-phase/quadrature-phase) demodulation. In a simulation, the measurement techniques have been tested by comparing the simulation results to analytically derived results from a known (backlash) non-linearity. In a subsequent practical case study both techniques are used to measure the changes in dynamic behaviour as a function of drive level due to friction in an electric motor. Both methods prove successful for measuring HOSIDFs.
Wang, Lei; Zhang, Jian-Hui; Wang, Zi-Qi; Liu, Chong; Li, Min; Qi, Feng-Hua; Guo, Rui
2016-01-01
We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.
Higher Order Residual Analysis for Nonlinear Time Series with Autoregressive Correlation Structures.
1984-09-25
ANALYSIS FOR NONLINEAR TIMEF SERIES WITH AI.OREGRESSIVE CORRELATION STRUVIURES BY P.A.W. Lewis & A. J. Lawrance September 1984 Approved for public release...of all or part of this report is authorized. P.A.W. Lewis A. J. Lawrance Professor of Operations Research University of Birmingham, England ’ Naval...J. Lawrance P. A. W. Lewis 9 PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK AREA G WORK UNIT NUMBERS Naval Postgraduate
NASA Astrophysics Data System (ADS)
Sahmani, S.; Bahrami, M.; Ansari, R.
2014-12-01
This investigation deals with the free vibration characteristics of circular higher-order shear deformable nanoplates around the postbuckling configuration incorporating surface effects. Using the Gurtin-Murdoch elasticity theory, a size-dependent higher-order shear deformable plate model is developed which takes account all surface effects including surface elasticity, surface stress and surface density. Geometrical nonlinearity is considered based on the von Karman type nonlinear strain-displacement relationships. Also, in order to satisfy the balance conditions between bulk and surfaces of nanoplate, it is assumed that the normal stress is distributed cubically through the thickness of nanoplate. Hamilton's principle is utilized to derive non-classical governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based on a generalized differential quadrature (GDQ) method is employed to solve numerically the problem so as to discretize the governing partial differential equations along various edge supports using Chebyshev-Gauss-Lobatto grid points and pseudo arc-length continuation technique. A comparison between the results of present non-classical model and those of the classical plate theory is conducted. It is demonstrated that in contrast to the prebuckling domain, for a specified value of axial load in the postbuckling domain, increasing the plate thickness leads to higher frequencies.
Horton, Rebecca B; McConico, Morgan; Landry, Currie; Tran, Tho; Vogt, Frank
2012-10-09
Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. 'Predictor Surfaces' were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables. As proof-of-principle for the Predictor Surfaces' capabilities, an application from environmental analytical chemistry was chosen. Microalgae cells are known to sensitively adapt to changes in environmental parameters such as pollution and/or nutrient availability and thus have potential as novel in situ sensors for environmental monitoring. These adaptations of the microalgae cells are reflected in their chemical signatures which were then acquired by means of FT-IR spectroscopy. In this study, the concentrations of three nutrients, namely inorganic carbon and two nitrogen containing ions, were chosen. Biological considerations predict that changes in nutrient availability produce a nonlinear response in the cells' biomass composition; it is also known that microalgae need certain nutrient mixes to thrive. The nonlinear Predictor Surfaces were demonstrated to be more accurate in predicting the values of these nutrients' concentrations than principal component regression. For qualitative chemical studies of biological systems, the Predictor Surfaces themselves are a novel tool as they visualize
NASA Astrophysics Data System (ADS)
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
Wang, Xiangyu; Li, Shihua; Chen, Michael Z Q
2017-07-27
This paper is devoted to solving the output consensus problem of leader-follower higher-order nonlinear multiagent systems subject to mismatched disturbances. The disturbances are allowed to be in higher-order forms. First, by constructing a generalized proportional-integral observer for each follower, estimates of the disturbances and their derivatives are obtained. At the same time, a distributed observer is also developed for the followers to estimate the leader state information. Second, based on the estimates of the disturbances and the leader state, together with the backstepping technique, a feedforward-feedback composite consensus control scheme is proposed. The designed distributed protocols guarantee asymptotic output consensus for the agents. Simulation results validate the effectiveness of the proposed composite control scheme.
NASA Astrophysics Data System (ADS)
Cole, Justin T.; Musslimani, Ziad H.
2015-12-01
Spectral transverse instabilities of one-dimensional solitary wave solutions to the two-dimensional nonlinear Schrödinger (NLS) equation with fourth-order dispersion/diffraction subject to higher-dimensional perturbations are studied. A linear boundary value problem governing the evolution of the transverse perturbations is derived. The eigenvalues of the perturbations are numerically computed using Fourier and finite difference differentiation matrices. It is found that for both signs of the higher-order dispersion coefficient there exists a finite band of unstable transverse modes. In the long wavelength limit we derive an asymptotic formula for the perturbation growth rate that agrees well with the numerical findings. Using a variational formulation based on Lagrangian model reduction, an approximate expression for the perturbation eigenvalues is obtained and its validity is compared with both the asymptotic and numerical results. The time dynamics of a one-dimensional soliton stripe in the presence of a transverse perturbation is studied using direct numerical simulations. Numerical nonlinear stability analysis is also addressed.
NASA Astrophysics Data System (ADS)
Erler, Norbert; Groß, Michael
2015-05-01
Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.
Han, Yaozhen; Liu, Xiangjie
2016-05-01
This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Gilson, C.; Hietarinta, J.; Nimmo, J.; Ohta, Y.
2003-07-01
Higher-order and multicomponent generalizations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately, the construction of multisoliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy. In the process, we also get bilinearizations and multisoliton formulas for a two-component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.
Fujioka, J; Espinosa, A
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
NASA Astrophysics Data System (ADS)
Fujioka, J.; Espinosa, A.
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
NASA Astrophysics Data System (ADS)
Liu, Ying; Xue, Yan Ling; Yu, Chuanxi
2015-03-01
Based on the dispersive Drude model in negative index materials (NIMs), nonlinear coupled Schodinger equations are derived for two copropagating optical waves with cubic-quintic nonlinearity and modulation instabilities induced by cross-phase modulation (XMI) are studied by using standard linear stability analysis and the Drude electromagnetic model. It is shown that the quintic nonlinearity strengthens the XMI with broader XMI spectra and higher peak gain. It is found that the XMI gain is obviously larger in the region with anomalous group velocity dispersion (GVD) than that in the region with normal GVD. It is also shown that the serious XMI occurs when two optical waves propagate simultaneously in the positive refractive index region or in different refractive index regions. The work provides a theoretical basis for the extinction or utilization of XMI in the propagation of high power and high speed signals in NIMs.
NASA Astrophysics Data System (ADS)
Honda, Koichiro; Cho, Yasuo
2012-12-01
Using scanning nonlinear dielectric microscopy with high-sensitivity capacitance variation detection capability, we succeeded in the high-resolution visualization of accumulated charges in metal-SiO2-SiN-SiO2-Si flash memory by detecting the higher-order (2-4 order) nonlinear permittivity. The obtained image contrast can be interpreted using a higher-order differential coefficient (dnC/dVn) of a quasi-static C-V curve of the SiO2-SiN-SiO2-Si interface capacitance as a function of externally applied voltage. Moreover, by using a higher-order nonlinear image, the charge concentration resolution can be improved. Thus, improved resolution of the spatial charge distribution is expected through improvement of the concentration resolution by the imaging of higher-order nonlinear dielectric terms.
Results on the higher order crossings approach to signal detection were obtained. In politicular, the earth:s polar notion was analyzed and new...periodicities were obtained. Another application was to online testing for white noise. It was also demonstrated that a higher order crossing sequence will converge to a frequency regardless of the signal to noise ratio. (kr)
1987-05-01
L AD-A199 489 HIGHER ORDER CROSSIMGSCU) MRRYLANDUUNIV COLLEGE PARK B KEDEN RAY 87 AFOSR-TR-87-1768 AFOSR-82-ai87 UNCLASSIFIED FVG 12/2 ML 6oi 132. @4...20332-6448 611027 2304 A5 MIt.rA TILsk~bbibl cankusd"i Higher Order Crossings M2 PAOWNAL AUTHORS1) B. Kedem all, TYP6 OF REPORT 1 136, TIME COVERED Lj...device that is useful as a diagnostic tool for higher order crossings was introduced. The graphical tool is also useful as a descriptive similarity
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Chen, Jian
2016-04-01
In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The Nth order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
NASA Astrophysics Data System (ADS)
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2017-03-01
Bound-state vector soliton solutions for the coupled variable-coefficient higher-order nonlinear Schrödinger equations, which describe the simultaneous propagation of nonlinear waves in the inhomogeneous optical fiber, are investigated. Introducing auxiliary functions, we derive the bilinear forms and corresponding constraints on the variable coefficients. Through symbolic computation, we construct the one- and two-soliton solutions. We see that the variable coefficients in the equations affect the soliton structures. With different choices of the variable coefficients, we obtain the cubic, periodic, and parabolic solitons. Bound-state solitons and interactions are analyzed graphically.
NASA Astrophysics Data System (ADS)
Chinone, N.; Yamasue, K.; Honda, K.; Cho, Y.
2013-11-01
Scanning nonlinear dielectric microscopy (SNDM) can evaluate carrier or charge distribution in semiconductor devices. High sensitivity to capacitance variation enables SNDM to measure the super-high-order (higher than 3rd) derivative of local capacitance-voltage (C-V) characteristics directly under the tip (dnC/dVn,n = 3, 4, ...). We demonstrate improvement of carrier density resolution by measurement of dnC/dVn,n = 1, 2, 3, 4 (super-higher-order method) in the cross-sectional observation of metal-oxide-semiconductor field-effect-transistor.
Singh Gill, Tarsem; Bedi, Chanchal; Saini, Nareshpal Singh
2011-04-15
The higher order solutions of dust acoustic wave in dusty plasma consisting of positively charged warm adiabatic dust, negatively charged cold dust, and nonisothermally distributed electrons are studied. The Schamel-KdV equation is derived using reductive perturbation method (RPM). RPM is further extended to include the contributions of higher order terms and a generalized KdV equation is derived to observe the deviation from isothermality. Effects of nonisothermal parameter, mass and charge ratio, ratio of ion to electron temperatures, and ratio of dust to ion temperatures have been thoroughly studied. By using the renormalization method of Kodama and Taniuti [J. Phys. Soc. Jpn. 45, 298 (1978)], authors have also discussed characteristics of the dressed solitons.
Wen, Xiao-Yong; Yan, Zhenya; Yang, Yunqing
2016-06-01
The integrable nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential [M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 110, 064105 (2013)] is investigated, which is an integrable extension of the standard nonlinear Schrödinger equation. Its novel higher-order rational solitons are found using the nonlocal version of the generalized perturbation (1,N-1)-fold Darboux transformation. These rational solitons illustrate abundant wave structures for the distinct choices of parameters (e.g., the strong and weak interactions of bright and dark rational solitons). Moreover, we also explore the dynamical behaviors of these higher-order rational solitons with some small noises on the basis of numerical simulations.
NASA Astrophysics Data System (ADS)
Cai, Yue-Jin; Bai, Cheng-Lin; Luo, Qing-Long
2017-03-01
In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higher-order nonlinear Schrödinger equations. In this paper, we will investigate the bright and dark soliton solutions of (2+1)-dimensional coupled higher-order nonlinear Schrödinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes. Supported by the National Natural Science Foundation of China under Grant No. 61671227 and the Natural Science Foundation of Shandong Province under Grant No. ZR2014AM018
NASA Astrophysics Data System (ADS)
Weerasekara, Gihan; Maruta, Akihiro
2017-01-01
The dynamics of the optical rogue wave phenomenon in the framework of integrable higher-order nonlinear Schrödinger equation (HNLSE) including the third order dispersion term is presented in this paper. When rogue waves generate through soliton collision, the colliding solitons' eigenvalues of the associated equation of HNLSE should be constant in the vicinity of rogue wave generation. Our results reveal that soliton collision is one of the generation mechanisms of optical rogue waves in anomalous dispersion fiber by taking the third order dispersion into consideration in the HNLSE based model.
Liu, Chuang; Lam, Hak-Keung; Fernando, Tyrone; Iu, Herbert Ho-Ching
2016-05-02
In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.
Liu, Chuang; Lam, Hak-Keung; Fernando, Tyrone; Iu, Herbert Ho-Ching
2016-05-02
In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.
NASA Astrophysics Data System (ADS)
Yomba, Emmanuel; Zakeri, Gholam-Ali
2013-12-01
We introduce an approach that combines a similarity method with several transformations to find analytical solitary wave solutions for a generalized space- and time-variable coefficients of nonlinear Schrödinger equation with higher-order terms with consideration of varying dispersion, higher nonlinearities, gain/loss and external potential. One of these transformations is constructed in such a way that allows study of the width of localized solutions. Solitary-like wave solutions for front, bright and dark are given. The precise expressions of the soliton's width, peak, and the trajectory of its mass center and the external potential which are symbol of dynamic behavior of these solutions, are investigated analytically. In addition, the dynamical behavior of moving, periodic, quasi-periodic of breathing, and resonant are discussed. Stability of the obtained solutions is analyzed both analytically and numerically.
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
Ordered Polymer Nonlinear Optical Materials.
1987-04-01
DC 20332-6448 LimtNO 140. NO. Pi. 1s. I I IsT6 dna/A II*EUS i fy CIewm.AAA Ordered Polymer Nonlinear Optical Materials 61102F 3005 Al 12. PERSONAL AUT...polymers as nonlinear optical materials . Table 1-2. Effect of Process Conditions on x(3 ) of PBT Sample Description x(3), esu 216.040.01 Biaxially... nonlinear optical materials and. as a result, optical transparency (homogeneity) and optical flatness must be greatly improved 9 * In order to enhance
Chitgarha, Mohammad Reza; Khaleghi, Salman; Bakhtiari, Zahra; Ziyadi, Morteza; Gerstel, Ori; Paraschis, Loukas; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2013-09-01
We demonstrate a reconfigurable optical transmitter of higher-order modulation formats including pulse-amplitude-modulation (PAM) signals and quadrature-amplitude-modulation (QAM) signals. We generated six different modulation formats by multiplexing 10 Gbit/s on-off-keying (OOK) signals (10 Gbaud binary phase-shift keying, 4-PAM, 8-PAM quadrature phase-shift keying (QPSK), 16-QAM and 16-star-QAM with error-vector magnitudes (EVMs) of 8.1%, 7.5%, 7.8%, 8.2%, 7.2%, and 6.9%, respectively) and 80 Gbit/s 16-QAM with an EVM of 8.5%, as well as 120 Gbit/s 64-QAM with an EVM of 7.1%, using two or three 40 Gbit/s QPSK signals, respectively. We also successfully transmitted the generated 16-QAM signals through a 100 km transmission line with negligible power penalty.
2007-08-01
convection dominated flows with particular emphasis on the incompressible Navier - Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32...Isogeometric fluid- structure interaction analysis with applications to arterial blood flow . Computational Mechanics, 38:310–322, 2006. [7] Y...for solution of two- and three-dimensional time dependent Navier - Stokes equations. In Europe-U.S. Conference on Finite Element Methods for Nonlinear
NASA Astrophysics Data System (ADS)
Cherednichenko, Kirill D.; Smyshlyaev, Valery P.
2004-12-01
We consider a scalar quasilinear equation in the divergence form with periodic rapid oscillations, which may be a model of, e.g., nonlinear conducting, dielectric, or deforming in a restricted way hardening elastic-plastic composites, with “outer” periodicity conditions of a fixed large period. Under some natural growth assumptions on the stored-energy function, we construct for uniformly elliptic problems a full two-scale asymptotic expansion, which has a precise “double-series” structure, separating the slow and the fast variables “in all orders”, so that its “slowly varying” part solves asymptotically an “infinite-order homogenised equation” (cf. Bakhvalov, N.S., Panasenko, G.P.: Homogenisation: Averaging Processes in Periodic Media. Nauka, Moscow, 1984 (in Russian); English translation: Kluwer, 1989), and whose higher-order terms depend on the higher gradients of the slowly varying part. We prove the error bound, i.e., that the truncated asymptotic expansion is “higher-order” close to the actual solution in appropriate norms. The approach is extended to a non-uniformly elliptic case: for two-dimensional power-law potentials we prove the “non-degeneracy” using topological index methods. Examples and explicit formulae for the higher-order terms are given. In particular, we prove that the first term in the higher-order homogenised equations is related to the first-order corrector to the “mean” flux, and has in general the form of a fully nonlinear operator which is quadratic with respect to its highest (second) derivative being a linear combination of the second minors of the Hessian with coefficients depending on the first gradient, and in dimension two is of Monge-Ampère type. We show that this term is present at least for some examples (three-phase power-law laminates).
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Yu, Xin
2015-10-01
Under investigation in this article is a higher-order nonlinear Schrödinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
NASA Astrophysics Data System (ADS)
Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan
2017-07-01
Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.
NASA Astrophysics Data System (ADS)
Mohammadimehr, M.; Mohammadi-Dehabadi, A. A.; Maraghi, Z. Khoddami
2017-04-01
In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W -shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W -shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
NASA Astrophysics Data System (ADS)
Rafat, A.; Rahman, M. M.; Alam, M. S.; Mamun, A. A.
2015-07-01
A precise theoretical investigation has been made on electron-acoustic (EA) Gardner solitons (GSs) and double layers (DLs) in a four-component plasma system consisting of nonextensive hot electrons and positrons, inertial cold electrons, and immobile positive ions. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations along with their solitary wave as well as double layer solutions. It has been found that depending on the plasma parameters, the K-dV solitons and GSs are either compressive or rarefactive, whereas the mK-dV solitons are only compressive, and Gardner DLs are only rarefactive. The analytical comparison among the K-dV solitons, mK-dV solitons, and GSs are also investigated. It has been identified that the basic properties of such EA solitons and EA DLs are significantly modified due to the effects of nonextensivity and other plasma parameters related to plasma particle number densities and to temperature of different plasma species. The results of our present investigation can be helpful for understanding the nonlinear electrostatic structures associated with EA waves in various interstellar space plasma environments and cosmological scenarios (viz. quark-gluon plasma, protoneutron stars, stellar polytropes, hadronic matter, dark-matter halos, etc.)
On nonlinear higher spin curvature
NASA Astrophysics Data System (ADS)
Manvelyan, Ruben; Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-05-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
Wang, Lei; Zhu, Yu-Jie; Qi, Feng-Hua; Li, Min; Guo, Rui
2015-06-01
In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2017-01-01
The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
Generalized structure of higher order nonclassicality
NASA Astrophysics Data System (ADS)
Verma, Amit; Pathak, Anirban
2010-02-01
A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering theorem introduced by us in [A. Pathak, J. Phys. A 33 (2000) 5607]. It is also generalized for multi-photon Bose operators of Brandt and Greenberg. Similarly, condition for higher order subpoissonian photon statistics is derived by normal ordering of higher powers of number operator. Further, with the help of simple density matrices, it is shown that the higher order antibunching (HOA) and higher order subpoissonian photon statistics (HOSPS) are not the manifestation of the same phenomenon and consequently it is incorrect to use the condition of HOA as a test of HOSPS. It is also shown that the HOA and HOSPS may exist even in absence of the corresponding lower order phenomenon. Binomial state, nonlinear first order excited squeezed state (NLESS) and nonlinear vacuum squeezed state (NLVSS) are used as examples of quantum state and it is shown that these states may show higher order nonclassical characteristics. It is observed that the Binomial state which is always antibunched, is not always higher order squeezed and NLVSS which shows higher order squeezing does not show HOSPS and HOA. The opposite is observed in NLESS and consequently it is established that the HOSPS and HOS are two independent signatures of higher order nonclassicality.
Hu, Erzhong; Nosato, Hirokazu; Sakanashi, Hidenori; Murakawa, Masahiro
2013-01-01
Capsule endoscopy is a patient-friendly endoscopy broadly utilized in gastrointestinal examination. However, the efficacy of diagnosis is restricted by the large quantity of images. This paper presents a modified anomaly detection method, by which both known and unknown anomalies in capsule endoscopy images of small intestine are expected to be detected. To achieve this goal, this paper introduces feature extraction using a non-linear color conversion and Higher-order Local Auto Correlation (HLAC) Features, and makes use of image partition and subspace method for anomaly detection. Experiments are implemented among several major anomalies with combinations of proposed techniques. As the result, the proposed method achieved 91.7% and 100% detection accuracy for swelling and bleeding respectively, so that the effectiveness of proposed method is demonstrated.
NASA Astrophysics Data System (ADS)
Liu, Lei; Tian, Bo; Chai, Jun; Chai, Han-Peng
2017-07-01
Studied in this paper are the interactions between bright-dark solitons for a generalized variable-coefficient coupled higher-order nonlinear Schrödinger system, which can be used to describe the simultaneous propagation of two ultrashort pulses in an inhomogeneous optical fiber. Under certain constraints, we obtain the analytic bright-dark one- and two-soliton solutions through the Hirota method and symbolic computation. With the help of this analytic treatment, properties of the single solitons, including the amplitudes, velocities, widths and central positions, are studied. Considering the amplification/absorption, group velocity and third-order dispersion effects, we study the interactions between two solitons with periodical variations of amplitudes and velocities. We find that the amplitudes of the two solitons depend solely on the amplification/absorption coefficient, while the velocities of the two solitons are related to the group velocity and third-order dispersion coefficients. Switches from the periodical interactions to head-on interactions and parallel propagation are presented.
Liu, Lei; Tian, Bo; Xie, Xi-Yang; Guan, Yue-Yang
2017-01-01
Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.
Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang
2017-04-01
We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.
Nonconservative higher-order hydrodynamic modulation instability
NASA Astrophysics Data System (ADS)
Kimmoun, O.; Hsu, H. C.; Kibler, B.; Chabchoub, A.
2017-08-01
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.
Complex higher order derivative theories
Margalli, Carlos A.; Vergara, J. David
2012-08-24
In this work is considered a complex scalar field theory with higher order derivative terms and interactions. A procedure is developed to quantize consistently this system avoiding the presence of negative norm states. In order to achieve this goal the original real scalar high order field theory is extended to a complex space attaching a complex total derivative to the theory. Next, by imposing reality conditions the complex theory is mapped to a pair of interacting real scalar field theories without the presence of higher derivative terms.
Higher-order uncertainty relations
NASA Astrophysics Data System (ADS)
Wünsche, A.
2006-07-01
Using the non-negativity of Gram determinants of arbitrary order, we derive higher-order uncertainty relations for the symmetric uncertainty matrices of corresponding order n?>?2 to n Hermitean operators (n?=?2 is the usual case). The special cases of third-order and fourth-order uncertainty relations are considered in detail. The obtained third-order uncertainty relations are applied to the Lie groups SU(1,1) with three Hermitean basis operators (K1,K2,K0) and SU(2) with three Hermitean basis operators (J1,J2,J3) where, in particular, the group-coherent states of Perelomov type and of Barut Girardello type for SU(1,1) and the spin or atomic coherent states for SU(2) are investigated. The uncertainty relations for the determinant of the third-order uncertainty matrix are satisfied with the equality sign for coherent states and this determinant becomes vanishing for the Perelomov type of coherent states for SU(1,1) and SU(2). As an example of the application of fourth-order uncertainty relations, we consider the canonical operators (Q1,P1,Q2,P2) of two boson modes and the corresponding uncertainty matrix formed by the operators of the corresponding mean deviations, taking into account the correlations between the two modes. In two mathematical appendices, we prove the non-negativity of the determinant of correlation matrices of arbitrary order and clarify the principal structure of higher-order uncertainty relations.
Second-order nonlinearity induced transparency.
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.
Electromagnetic cloaking in higher order spherical cloaks
NASA Astrophysics Data System (ADS)
Sidhwa, H. H.; Aiyar, R. P. R. C.; Kulkarni, S. V.
2017-06-01
The inception of transformation optics has led to the realisation of the invisibility devices for various applications, one of which is spherical cloaking. In this paper, a formulation for a higher-order spherical cloak has been proposed to reduce its physical thickness significantly by introducing a nonlinear relation between the original and transformed coordinate systems and it has been verified using the ray tracing approach. Analysis has been carried out to observe the anomalies in the variation of refractive index for higher order cloaks indicating the presence of poles in the relevant equations. Furthermore, a higher-order spherical cloak with predefined values of the material characteristics on its inner and outer surfaces has been designed for practical application.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong; Yan, Zhenya
2016-11-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1, N-1)-fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a>0 or a<0) into higher-order rational solitons (a = 0) in (x, t)-space with y=const. These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
NASA Astrophysics Data System (ADS)
Gudnason, Sven Bjarke; Nitta, Muneto
2017-09-01
We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However, we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally, we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.
NASA Astrophysics Data System (ADS)
Zhang, Xing-Hui; Xie, Xue-Jun
2014-03-01
This paper studies the state feedback control problem for a class of nonlinear systems with high-order and low-order nonlinearities. The introduction of the sign function together with the method of adding a power integrator and Lyapunov stability theorem makes the closed-loop system globally asymptotically stable. Exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work.
NASA Astrophysics Data System (ADS)
Kara, A. H.; Bokhari, Ashfaque H.
2011-11-01
In this paper, we study and classify the conservation laws of the combined nonlinear KdV, Camassa-Holm, Hunter-Saxton and the inviscid Burgers equation which arises in, inter alia, shallow water equations. It is shown that these can be obtained by variational methods but the main focus of the paper is the construction of the conservation laws as a consequence of the interplay between symmetry generators and 'multipliers', particularly, the higher-order ones.
Charges in nonlinear higher-spin theory
NASA Astrophysics Data System (ADS)
Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.
2017-03-01
Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4 d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.
Maimaiti, Aili; Holzmann, Daniela; Truong, Viet Giang; Ritsch, Helmut; Nic Chormaic, Síle
2016-07-25
Particles trapped in the evanescent field of an ultrathin optical fibre interact over very long distances via multiple scattering of the fibre-guided fields. In ultrathin fibres that support higher order modes, these interactions are stronger and exhibit qualitatively new behaviour due to the coupling of different fibre modes, which have different propagation wave-vectors, by the particles. Here, we study one dimensional longitudinal optical binding interactions of chains of 3 μm polystyrene spheres under the influence of the evanescent fields of a two-mode microfibre. The observation of long-range interactions, self-ordering and speed variation of particle chains reveals strong optical binding effects between the particles that can be modelled well by a tritter scattering-matrix approach. The optical forces, optical binding interactions and the velocity of bounded particle chains are calculated using this method. Results show good agreement with finite element numerical simulations. Experimental data and theoretical analysis show that higher order modes in a microfibre offer a promising method to not only obtain stable, multiple particle trapping or faster particle propulsion speeds, but that they also allow for better control over each individual trapped object in particle ensembles near the microfibre surface.
Maimaiti, Aili; Holzmann, Daniela; Truong, Viet Giang; Ritsch, Helmut; Nic Chormaic, Síle
2016-01-01
Particles trapped in the evanescent field of an ultrathin optical fibre interact over very long distances via multiple scattering of the fibre-guided fields. In ultrathin fibres that support higher order modes, these interactions are stronger and exhibit qualitatively new behaviour due to the coupling of different fibre modes, which have different propagation wave-vectors, by the particles. Here, we study one dimensional longitudinal optical binding interactions of chains of 3 μm polystyrene spheres under the influence of the evanescent fields of a two-mode microfibre. The observation of long-range interactions, self-ordering and speed variation of particle chains reveals strong optical binding effects between the particles that can be modelled well by a tritter scattering-matrix approach. The optical forces, optical binding interactions and the velocity of bounded particle chains are calculated using this method. Results show good agreement with finite element numerical simulations. Experimental data and theoretical analysis show that higher order modes in a microfibre offer a promising method to not only obtain stable, multiple particle trapping or faster particle propulsion speeds, but that they also allow for better control over each individual trapped object in particle ensembles near the microfibre surface. PMID:27451935
Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator
NASA Astrophysics Data System (ADS)
Fadly Nurullah Rasedee, Ahmad; Ishak, Norizarina; Raihana Hamzah, Siti; Ijam, Hazizah Mohd; Suleiman, Mohamed; Bibi Ibrahim, Zarina; Sathar, Mohammad Hasan Abdul; Ainna Ramli, Nur; Shuhada Kamaruddin, Nur
2017-09-01
Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy.
Higher order turbulence closure models
NASA Technical Reports Server (NTRS)
Amano, Ryoichi S.; Chai, John C.; Chen, Jau-Der
1988-01-01
Theoretical models are developed and numerical studies conducted on various types of flows including both elliptic and parabolic. The purpose of this study is to find better higher order closure models for the computations of complex flows. This report summarizes three new achievements: (1) completion of the Reynolds-stress closure by developing a new pressure-strain correlation; (2) development of a parabolic code to compute jets and wakes; and, (3) application to a flow through a 180 deg turnaround duct by adopting a boundary fitted coordinate system. In the above mentioned models near-wall models are developed for pressure-strain correlation and third-moment, and incorporated into the transport equations. This addition improved the results considerably and is recommended for future computations. A new parabolic code to solve shear flows without coordinate tranformations is developed and incorporated in this study. This code uses the structure of the finite volume method to solve the governing equations implicitly. The code was validated with the experimental results available in the literature.
NASA Astrophysics Data System (ADS)
Uzunov, Ivan M.; Arabadzhiev, Todor N.; Georgiev, Zhivko D.
2015-08-01
We have studied the impact of the higher-order effects: intrapulse Raman scattering (IRS), third-order of dispersion (TOD) and self-steepening (SS) on pulsating solutions, moving fronts and stationary solutions of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) found in Tsoy and Akhmediev (2005) as well as on the solutions presented in Uzunov et al. (2014). The applied basic equation generalizes the CCQGLE with the IRS, TOD and SS effects. A finite-dimensional dynamical system has been derived using the method of moments. Applying the derived dynamical system alongside with the numerical solution of the generalized CCQGLE performed by means of the fourth-order Runge-Kutta interaction picture method we have found that the influence of IRS and SS is stronger than the impact of TOD for the solutions of Tsoy and Akhmediev (2005). Perturbed pulsating solutions, moving fronts and stationary solutions in the presence of IRS, SS and TOD have been numerically observed. They exist up to some critical values of the parameters of perturbations. For the values of parameters larger than the critical ones the pulsating solutions are transformed into stable stationary solutions or unstable solutions. New localized fluctuating and stationary solutions have been obtained for fairly large values of parameters of IRS and TOD, respectively. The transformation of the stable stationary solution of Uzunov et al. (2014) under the influence of SS into pulsating solution has been numerically observed.
Higher-order Dirac solitons in binary waveguide arrays
Tran, Truong X.; Duong, Dũng C.
2015-10-15
We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range. - Highlights: • Higher-order Dirac solitons in nonlinear binary waveguide arrays are numerically demonstrated. • Amplitude profiles of higher-order Dirac solitons are periodic during propagation. • The period of higher-order Dirac solitons decreases when the soliton order increases.
Emamuddin, M.; Yasmin, S.; Mamun, A. A.
2013-04-15
The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for qq{sub c}) (where q{sub c} is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.
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.
Higher-Order Superposition for Dependent Types,
2007-11-02
Proofs for Higher-Order Rewrite Systems, J. Heering, K. Meinke , B. Moller, T. Nipkow ed., Higher Order Algebra, Logic and Term Rewriting, Lect. Notes in...Heering, K. Meinke , B. Moller, T. Nipkow ed., Higher Order Algebra, Logic and Term Rewriting, Lect. Notes in Comp. Sci., Vol 816, Springer Verlag, 1994, pp. 305-325
Cascaded Second-Order Nonlinearities in Waveguides.
NASA Astrophysics Data System (ADS)
Sundheimer, Michael Lee
The cascaded second-order nonlinearity arising from the second-harmonic generation process in noncentrosymmetric media is a novel approach to achieving the nonlinear phase shifts required for all-optical signal processing. The research presented in this dissertation demonstrated and measured the cascaded second-order nonlinearity for the first time in viable integrated optical waveguide formats. Cascaded self-phase modulation was measured in potassium titanyl phosphate (KTiOPO_4 or KTP) segmented quasi-phasematched waveguides at wavelengths near 855 nm and in the optical fiber telecommunications window near 1.585 μm using picosecond and femtosecond pulses, respectively. Spectral modulation and broadening were observed on the output fundamental spectrum and compared to predictions from pulsed second -harmonic generation theory under conditions of group-velocity mismatch (temporal walk-off) and group-velocity dispersion. Peak cascaded phase shifts of the fundamental of approximately pi at 855 nm were inferred with 690 W of peak guided power. Peak cascaded phase shifts of approximately pi/2 were inferred at 1.585 μm with 760 W of peak power in the guide. Direct interferometric measurements of the magnitude and sign of the cascaded nonlinear phase shift of the fundamental were performed in temperature-tuned lithium niobate (LiNbO _3) channel waveguides at 1.32 mum. The cascaded phase shift was shown to change sign upon passing through the phasematching condition, as required by theory. Peak cascaded phase shifts of +0.53 pi and -0.13 pi were measured for 86 W peak power in these waveguides. A non-uniform temperature profile along the waveguide led to a non-uniform wavevector-mismatch along the guide, resulting in an enhanced positive phase shift and an increased temperature bandwidth for the phase shift. The phase shifts achieved in this research are large enough to be suitable for some all-optical signal processing functions.
A new theorem on higher order derivatives of Lyapunov functions.
Meigoli, Vahid; Nikravesh, Seyyed Kamaleddin Yadavar
2009-04-01
The Lyapunov stability analysis method for nonlinear dynamic systems requires a non positive first derivative of the Lyapunov functions along the system's trajectories. In this paper, a new method is developed to relax this requirement. A new sufficient condition is developed for the stability analysis of nonlinear systems, introducing some inequalities for higher order derivatives of the Lyapunov function. The differential inequalities can be considered as a new controllable canonical form linear time invariant system with negative inputs. The stability analysis of a given nonlinear system is then reduced to check if the characteristic equation for the new linear time invariant system is Hurwitz. Some examples are presented to establish the approach.
Higher-order phase shift reconstruction approach
Cong Wenxiang; Wang Ge
2010-10-15
Purpose: Biological soft tissues encountered in clinical and preclinical imaging mainly consists of atoms of light elements with low atomic numbers and their elemental composition is nearly uniform with little density variation. Hence, x-ray attenuation contrast is relatively poor and cannot achieve satisfactory sensitivity and specificity. In contrast, x-ray phase-contrast provides a new mechanism for soft tissue imaging. The x-ray phase shift of soft tissues is about a thousand times greater than the x-ray absorption over the diagnostic x-ray energy range, yielding a higher signal-to-noise ratio than the attenuation contrast counterpart. Thus, phase-contrast imaging is a promising technique to reveal detailed structural variation in soft tissues, offering a high contrast resolution between healthy and malignant tissues. Here the authors develop a novel phase retrieval method to reconstruct the phase image on the object plane from the intensity measurements. The reconstructed phase image is a projection of the phase shift induced by an object and serves as input to reconstruct the 3D refractive index distribution inside the object using a tomographic reconstruction algorithm. Such x-ray refractive index images can reveal structural features in soft tissues, with excellent resolution differentiating healthy and malignant tissues. Methods: A novel phase retrieval approach is proposed to reconstruct an x-ray phase image of an object based on the paraxial Fresnel-Kirchhoff diffraction theory. A primary advantage of the authors' approach is higher-order accuracy over that with the conventional linear approximation models, relaxing the current restriction of slow phase variation. The nonlinear terms in the autocorrelation equation of the Fresnel diffraction pattern are eliminated using intensity images measured at different distances in the Fresnel diffraction region, simplifying the phase reconstruction to a linear inverse problem. Numerical experiments are performed
X Y model with higher-order exchange
NASA Astrophysics Data System (ADS)
Žukovič, Milan; Kalagov, Georgii
2017-08-01
An X Y model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range-order phase characterized by an algebraically decaying correlation function with the exponent η =T /[2 π J (p ,α )] , nonlinearly dependent on the parameters p and α that control the number of the higher-order terms and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of topological excitations (vortices) in changing the nature of the transition is discussed.
Higher order mechanics on graded bundles
NASA Astrophysics Data System (ADS)
Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz
2015-05-01
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for this higher order situation and derive in this framework the phase equations from an arbitrary (also singular) Lagrangian or Hamiltonian, as well as the Euler-Lagrange equations. As important examples, we geometrically derive the classical higher order Euler-Lagrange equations and analogous reduced equations for invariant higher order Lagrangians on Lie groupoids.
Higher-order organization of complex networks
Benson, Austin R.; Gleich, David F.; Leskovec, Jure
2016-01-01
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks—at the level of small network subgraphs—remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns. PMID:27387949
Nonlinear spectroscopic studies of interfacial molecular ordering
Superfine, R.
1991-07-01
The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface. 32 refs., 4 figs., 2 tabs.
Nonlinear spectroscopic studies of interfacial molecular ordering
NASA Astrophysics Data System (ADS)
Superfine, R.
1991-07-01
The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface.
Resonant radiation from oscillating higher order solitons
Driben, R.; Yulin, A. V.; Efimov, A.
2015-07-15
We present radiation mechanism exhibited by a higher order soliton. In a course of its evolution the higher-order soliton emits polychromatic radiation resulting in formation of multipeak frequency comb-like spectral band. The shape and spectral position of this band can be effectively controlled by the relative strength of the third order dispersion. An analytical description is corroborated by numerical simulations. Research showed that for longer pulses the described effect persists also under the action of higher order perturbations such as Raman and self-steepening.
Resonant radiation from oscillating higher order solitons
Driben, R.; Yulin, A. V.; Efimov, A.
2015-07-15
We present radiation mechanism exhibited by a higher order soliton. In a course of its evolution the higher-order soliton emits polychromatic radiation resulting in formation of multipeak frequency comb-like spectral band. Moreover, the shape and spectral position of this band can be effectively controlled by the relative strength of the third order dispersion. An analytical description is corroborated by numerical simulations. It is also shown that for longer pulses the described effect persists also under the action of higher order perturbations such as Raman and self-steepening.
Higher-order force gradient symplectic algorithms
NASA Astrophysics Data System (ADS)
Chin, Siu A.; Kidwell, Donald W.
2000-12-01
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.
Constructing higher-order hydrodynamics: The third order
NASA Astrophysics Data System (ADS)
Grozdanov, Sašo; Kaplis, Nikolaos
2016-03-01
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the N =4 supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.
Higher-Order Neural Networks Recognize Patterns
NASA Technical Reports Server (NTRS)
Reid, Max B.; Spirkovska, Lilly; Ochoa, Ellen
1996-01-01
Networks of higher order have enhanced capabilities to distinguish between different two-dimensional patterns and to recognize those patterns. Also enhanced capabilities to "learn" patterns to be recognized: "trained" with far fewer examples and, therefore, in less time than necessary to train comparable first-order neural networks.
Using Reflection to Develop Higher Order Processes
ERIC Educational Resources Information Center
Lerch, Carol; Bilics, Andrea; Colley, Binta
2006-01-01
The main purpose of this study was to look at how we used specific writing assignments in our courses to encourage metacognitive reflection in order to increase the learning that takes place. The study also aimed to aid in the development of higher order processing skills through the development of student reflection. The students involved in the…
Human motion perception: Higher-order organization
NASA Technical Reports Server (NTRS)
Kaiser, Mary K.; Proffitt, Dennis R.
1990-01-01
An overview is given of higher-order motion perception and organization. It is argued that motion is sufficient to fully specify a number of environmental properties, including: depth order, three-dimensional form, object displacement, and dynamics. A grammar of motion perception is proposed; applications of this work for display design are discussed.
Higher-order awareness, misrepresentation and function
Rosenthal, David
2012-01-01
Conscious mental states are states we are in some way aware of. I compare higher-order theories of consciousness, which explain consciousness by appeal to such higher-order awareness (HOA), and first-order theories, which do not, and I argue that higher-order theories have substantial explanatory advantages. The higher-order nature of our awareness of our conscious states suggests an analogy with the metacognition that figures in the regulation of psychological processes and behaviour. I argue that, although both consciousness and metacognition involve higher-order psychological states, they have little more in common. One thing they do share is the possibility of misrepresentation; just as metacognitive processing can misrepresent one's cognitive states and abilities, so the HOA in virtue of which one's mental states are conscious can, and sometimes does, misdescribe those states. A striking difference between the two, however, has to do with utility for psychological processing. Metacognition has considerable benefit for psychological processing; in contrast, it is unlikely that there is much, if any, utility to mental states' being conscious over and above the utility those states have when they are not conscious. PMID:22492758
Higher-order awareness, misrepresentation and function.
Rosenthal, David
2012-05-19
Conscious mental states are states we are in some way aware of. I compare higher-order theories of consciousness, which explain consciousness by appeal to such higher-order awareness (HOA), and first-order theories, which do not, and I argue that higher-order theories have substantial explanatory advantages. The higher-order nature of our awareness of our conscious states suggests an analogy with the metacognition that figures in the regulation of psychological processes and behaviour. I argue that, although both consciousness and metacognition involve higher-order psychological states, they have little more in common. One thing they do share is the possibility of misrepresentation; just as metacognitive processing can misrepresent one's cognitive states and abilities, so the HOA in virtue of which one's mental states are conscious can, and sometimes does, misdescribe those states. A striking difference between the two, however, has to do with utility for psychological processing. Metacognition has considerable benefit for psychological processing; in contrast, it is unlikely that there is much, if any, utility to mental states' being conscious over and above the utility those states have when they are not conscious.
Higher-order energy-conserving gyrokinetic theory
Mishchenko, Alexey; Brizard, Alain J.
2011-02-15
A higher-order self-consistent energy-conserving gyrokinetic system of equations is derived. It is shown that additional terms appear in the quasineutrality condition. These terms are nonlinear in the electric field. The derivation includes higher-order terms in the gyrokinetic Hamiltonian (needed for the energy conservation) and employs a variational principle that automatically provides all the conservation laws through the Noether theorem. The equations derived here can be applied in certain transition layers such as the stellarator transport barriers caused by the transition between the electron and ion root regimes. The theory may also be of interest for the edge plasma, where the nonlinear terms in the quasineutrality equation could be relevant. The equations derived are simple enough and can readily be used in gyrokinetic codes.
Entanglement equilibrium for higher order gravity
NASA Astrophysics Data System (ADS)
Bueno, Pablo; Min, Vincent S.; Speranza, Antony J.; Visser, Manus R.
2017-02-01
We show that the linearized higher derivative gravitational field equations are equivalent to an equilibrium condition on the entanglement entropy of small spherical regions in vacuum. This extends Jacobson's recent derivation of the Einstein equation using entanglement to include general higher derivative corrections. The corrections are naturally associated with the subleading divergences in the entanglement entropy, which take the form of a Wald entropy evaluated on the entangling surface. Variations of this Wald entropy are related to the field equations through an identity for causal diamonds in maximally symmetric spacetimes, which we derive for arbitrary higher derivative theories. If the variations are taken holding fixed a geometric functional that we call the generalized volume, the identity becomes an equivalence between the linearized constraints and the entanglement equilibrium condition. We note that the fully nonlinear higher curvature equations cannot be derived from the linearized equations applied to small balls, in contrast to the situation encountered in Einstein gravity. The generalized volume is a novel result of this work, and we speculate on its thermodynamic role in the first law of causal diamond mechanics, as well as its possible application to holographic complexity.
NASA Astrophysics Data System (ADS)
Gao, Fangzheng; Wu, Yuqiang; Yu, Xin
2016-12-01
In this paper, the problem of global stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with both high-order and low-order nonlinearities, to which the existing control methods are inapplicable. Based on the generalised stochastic Lyapunov theorem, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed, which can guarantee the global asymptotic stability in probability of the resulting closed-loop system in the sense of weak solution, and also is able to lead to an interesting result of finite-time stabilisation under appropriate conditions. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.
Assessing Higher Order Thinking in Mathematics.
ERIC Educational Resources Information Center
Kulm, Gerald, Ed.
This book explores current theory, research, practice, and policy in the assessment of higher order thinking in mathematics, focusing on the elementary and secondary grades. Current knowledge and research on mathematics learning and testing is synthesized. Examples of innovative test items for classroom use and state assessment programs are…
Higher Order Thinking in the Dance Studio
ERIC Educational Resources Information Center
Moffett, Ann-Thomas
2012-01-01
The author identifies higher order thinking as an essential component of dance training for students of all ages and abilities. Weaving together insights from interviews with experts in the field of dance education with practical pedagogical applications within an Improvisation and Composition class for talented and gifted youth, this article…
Higher Order Thinking in the Dance Studio
ERIC Educational Resources Information Center
Moffett, Ann-Thomas
2012-01-01
The author identifies higher order thinking as an essential component of dance training for students of all ages and abilities. Weaving together insights from interviews with experts in the field of dance education with practical pedagogical applications within an Improvisation and Composition class for talented and gifted youth, this article…
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.
Higher order cumulants in colorless partonic plasma
Cherif, S.; Ahmed, M. A. A.; Ladrem, M.
2016-06-10
Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to the thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.
Cosmological models in higher-order gravity
NASA Astrophysics Data System (ADS)
Cotsakis, Spiros
This thesis is divided into two parts. The first part deals with the conformal structure, inflationary regimes, and singularity theorems in the context of higher-order gravity theories. The second part focuses on the question of the nature of cosmological singularities and in particular on the occurrence of chaotic behavior in the framework of these theories. We begin part one by formulating and proving what we call the conformal equivalence theorem which states that higher order gravity theories which are derived from a lagrangian density that is an analytic function of the scalar curvature are conformally equivalent to general relativity plus a scalar field matter source with a particular self-interaction potential. The solution space of higher-order gravity theories is examined and the weak field limit of these theories is calculated. The role of conformal non-invariance and the associated particle production in these theories is discussed. Several interpretative issues concerning the physical equivalence of these theories to general relativity with scalar field matter source are given and the physical reality of the conformally related metric tensors is examined in detail. The existence and stability conditions of the de Sitter space in the context of these theories are established and several examples which lead to successful inflation are presented. Effective potentials are drawn for certain classes of these theories. Singularity theorems are proved in the context of higher-order gravity theories and the status of the cosmic no-hair conjectures in these theories is critically presented. In the second part we start by reviewing certain useful and powerful methods for the study of chaotic behavior near cosmological singularities in general relativity. Recent numerical evidence that concerns the genericity of such oscillatory solutions is critically presented and commented upon. A new method based on the analytic theory of ordinary differential equations is
Higher-order corrections to Coulomb fission
NASA Astrophysics Data System (ADS)
Wheeler, Raymond T.; Norbury, John W.
1995-03-01
Fission cross sections resulting from a 120 MeV/nucleon 238U beam incident upon Be, Al, Cu, Ag, and U targets have recently been measured by Justice et al. [Phys. Rev. C 49, R5 (1994)]. The electromagnetic contribution to these experimental cross sections have been compared to Weizsäcker-Williams theory which is based on first-order perturbation theory. The present work calculates the contribution to these cross sections due to higher-order excitations. Our results show that these corrections are insignificant in comparison to experimental error.
The regular state in higher order gravity
NASA Astrophysics Data System (ADS)
Cotsakis, Spiros; Kadry, Seifedine; Trachilis, Dimitrios
2016-08-01
We consider the higher-order gravity theory derived from the quadratic Lagrangian R + 𝜖R2 in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of the theory. We show that all such solutions, if analytic, contain the right number of free functions to qualify as general solutions of the theory. We further show that any regular analytic solution which satisfies the constraints and the evolution equations can be given in the form of an asymptotic formal power series expansion.
Performance assessment of higher order thinking.
Griffin, Patrick
2014-01-01
This article describes a study investigating the effect of intervention on student problem solving and higher order competency development using a series of complex numeracy performance tasks (Airasian and Russell, 2008). The tasks were sequenced to promote and monitor student development towards hypothetico-deductive reasoning. Using Rasch partial credit analysis (Wright and Masters, 1982) to calibrate the tasks and analysis of residual gain scores to examine the effect of class and school membership, the study illustrates how directed intervention can improve students' higher order competency skills. This paper demonstrates how the segmentation defined by Wright and Masters can offer a basis for interpreting the construct underlying a test and how segment definitions can deliver targeted interventions. Implications for teacher intervention and teaching mentor schemes are considered. The article also discusses multilevel regression models that differentiate class and school effects, and describes a process for generating, testing and using value added models.
Systems with Higher-order Modulation
NASA Astrophysics Data System (ADS)
Achiam, Yaakov; Kaplan, Arkady; Seimetz, Matthias
The chapter covers concepts, systems aspects, and key components for higher-order modulation. The introductory section presents relevant variants of higher-order modulation formats and includes coherent detection and coherent optical orthogonal frequency-division multiplexing as well. The next section is devoted to system configurations with particular emphasis on transmitter structures and receiver concepts, whereas the subsequent chapter focuses on key components. Included are LiNbO3-based quadrature modulators, integrated coherent receivers, in particular 90° hybrids, ranging from new concepts to proven implementations. A treatment of integrated balanced four-branch receivers ranges from theoretical analysis to the presentation of commercially available devices. The chapter concludes with a discussion of system trends and expected future developments.
Higher order structure in ribosomal RNA.
Gutell, R R; Noller, H F; Woese, C R
1986-05-01
The only reliable general method currently available for determining precise higher order structure in the large ribosomal RNAs is comparative sequence analysis. The method is here applied to reveal 'tertiary' structure in the 16S-like rRNAs, i.e. structure more complex than simple double-helical, secondary structure. From a list of computer-generated potential higher order interactions within 16S rRNA one such interaction considered likely was selected for experimental test. The putative interaction involves a Watson-Crick one to one correspondence between positions 570 and 866 in the molecule (E. coli numbering). Using existing oligonucleotide catalog information several organisms were selected whose 16S rRNA sequences might test the proposed co-variation. In all of the (phylogenetically independent) cases selected, full sequence evidence confirms the predicted one to one (Watson-Crick) correspondence. An interaction between positions 570 and 866 is, therefore, considered proven phylogenetically.
Random interactions in higher order neural networks
NASA Technical Reports Server (NTRS)
Baldi, Pierre; Venkatesh, Santosh S.
1993-01-01
Recurrent networks of polynomial threshold elements with random symmetric interactions are studied. Precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability. In particular, it is shown that there is a critical range of margins of stability (depending on the degree of polynomial interaction) such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network, while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network. The random energy model is also briefly examined and links with higher order neural networks and higher order spin glass models made explicit.
Higher-Order Mentalising and Executive Functioning.
2015-11-01
Higher-order mentalising is the ability to represent the beliefs and desires of other people at multiple, iterated levels - a capacity that sets humans apart from other species. However, there has not yet been a systematic attempt to determine what cognitive processes underlie this ability. Here we present three correlational studies assessing the extent to which performance on higher-order mentalising tasks relates to emotion recognition, self-reported empathy and self-inhibition. In Study 1a and 1b, examining emotion recognition and empathy, a relationship was identified between individual differences in the ability to mentalise and an emotion recognition task (the Reading the Mind in the Eyes task), but no correlation was found with the Empathy Quotient, a self-report scale of empathy. Study 2 investigated whether a relationship exists between individual mentalising abilities and four different forms of self-inhibition: motor inhibition, executive inhibition, automatic imitation and temporal discounting. Results demonstrate that only temporal discounting performance relates to mentalising ability; suggesting that cognitive skills relevant to representation of the minds of others' are not influenced by the ability to perform more basic inhibition. Higher-order mentalising appears to rely on the cognitive architecture that serves both low-level social cognition (emotion recognition), and complex forms of inhibition.
Higher-Order Mentalising and Executive Functioning
2015-01-01
Higher-order mentalising is the ability to represent the beliefs and desires of other people at multiple, iterated levels – a capacity that sets humans apart from other species. However, there has not yet been a systematic attempt to determine what cognitive processes underlie this ability. Here we present three correlational studies assessing the extent to which performance on higher-order mentalising tasks relates to emotion recognition, self-reported empathy and self-inhibition. In Study 1a and 1b, examining emotion recognition and empathy, a relationship was identified between individual differences in the ability to mentalise and an emotion recognition task (the Reading the Mind in the Eyes task), but no correlation was found with the Empathy Quotient, a self-report scale of empathy. Study 2 investigated whether a relationship exists between individual mentalising abilities and four different forms of self-inhibition: motor inhibition, executive inhibition, automatic imitation and temporal discounting. Results demonstrate that only temporal discounting performance relates to mentalising ability; suggesting that cognitive skills relevant to representation of the minds of others’ are not influenced by the ability to perform more basic inhibition. Higher-order mentalising appears to rely on the cognitive architecture that serves both low-level social cognition (emotion recognition), and complex forms of inhibition. PMID:26543298
Higher order modes in photonic crystal slabs.
Gansch, Roman; Kalchmair, Stefan; Detz, Hermann; Andrews, Aaron M; Klang, Pavel; Schrenk, Werner; Strasser, Gottfried
2011-08-15
We present a detailed investigation of higher order modes in photonic crystal slabs. In such structures the resonances exhibit a blue-shift compared to an ideal two-dimensional photonic crystal, which depends on the order of the slab mode and the polarization. By fabricating a series of photonic crystal slab photo detecting devices, with varying ratios of slab thickness to photonic crystal lattice constant, we are able to distinguish between 0th and 1st order slab modes as well as the polarization from the shift of resonances in the photocurrent spectra. This method complements the photonic band structure mapping technique for characterization of photonic crystal slabs. © 2011 Optical Society of America
Higher-order modulation theory for resonant flow over topography
NASA Astrophysics Data System (ADS)
Daher Albalwi, M.; Marchant, T. R.; Smyth, Noel F.
2017-07-01
The flow of a fluid over isolated topography in the long wavelength, weakly nonlinear limit is considered. The upstream flow velocity is assumed to be close to a linear long wave velocity of the unforced flow so that the flow is near resonant. Higher order nonlinear, dispersive and nonlinear-dispersive terms beyond the Korteweg-de Vries approximation are included so that the flow is governed by a forced extended Korteweg-de Vries equation. Modulation theory solutions for the undular bores generated upstream and downstream of the forcing are found and used to study the influence of the higher-order terms on the resonant flow, which increases for steeper waves. These modulation theory solutions are compared with numerical solutions of the forced extended Korteweg-de Vries equation for the case of surface water waves. Good comparison is obtained between theoretical and numerical solutions, for properties such as the upstream and downstream solitary wave amplitudes and the widths of the bores.
Representing higher-order dependencies in networks
Xu, Jian; Wickramarathne, Thanuka L.; Chawla, Nitesh V.
2016-01-01
To ensure the correctness of network analysis methods, the network (as the input) has to be a sufficiently accurate representation of the underlying data. However, when representing sequential data from complex systems, such as global shipping traffic or Web clickstream traffic as networks, conventional network representations that implicitly assume the Markov property (first-order dependency) can quickly become limiting. This assumption holds that, when movements are simulated on the network, the next movement depends only on the current node, discounting the fact that the movement may depend on several previous steps. However, we show that data derived from many complex systems can show up to fifth-order dependencies. In these cases, the oversimplifying assumption of the first-order network representation can lead to inaccurate network analysis results. To address this problem, we propose the higher-order network (HON) representation that can discover and embed variable orders of dependencies in a network representation. Through a comprehensive empirical evaluation and analysis, we establish several desirable characteristics of HON, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods. We illustrate how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking, and we demonstrate that, by using it as input, HON yields more accurate results without any modification to these tasks. PMID:27386539
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Liu, Zhi-Bo; Yan, Xiao-Qing; Tian, Jian-Guo; Zhou, Wen-Yuan; Zang, Wei-Ping
2007-10-01
We present a method that combines the Z-scan technique with nonlinear ellipse rotation (NER) to measure third-order nonlinear susceptibility components. The experimental details are demonstrated, and a comprehensive theoretical analysis is given. The validity of this method is verified by the measurements of the nonlinear susceptibility tensor of a well-characterized liquid, CS2.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
NASA Astrophysics Data System (ADS)
Alloatti, L.; Kieninger, C.; Froelich, A.; Lauermann, M.; Frenzel, T.; Köhnle, K.; Freude, W.; Leuthold, J.; Wegener, M.; Koos, C.
2015-09-01
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al2O3, B = TiO2, and C = HfO2. The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths.
Dynamics and control of higher-order nonholonomic systems
NASA Astrophysics Data System (ADS)
Rubio Hervas, Jaime
A theoretical framework is established for the control of higher-order nonholonomic systems, defined as systems that satisfy higher-order nonintegrable constraints. A model for such systems is developed in terms of differential-algebraic equations defined on a higher-order tangent bundle. A number of control-theoretic properties such as nonintegrability, controllability, and stabilizability are presented. Higher-order nonholonomic systems are shown to be strongly accessible and, under certain conditions, small time locally controllable at any equilibrium. There are important examples of higher-order nonholonomic systems that are asymptotically stabilizable via smooth feedback, including space vehicles with multiple slosh modes and Prismatic-Prismatic-Revolute (PPR) robots moving open liquid containers, as well as an interesting class of systems that do not admit asymptotically stabilizing continuous static or dynamic state feedback. Specific assumptions are introduced to define this class, which includes important examples of robotic systems. A discontinuous nonlinear feedback control algorithm is developed to steer any initial state to the equilibrium at the origin. The applicability of the theoretical development is illustrated through two examples: control of a planar PPR robot manipulator subject to a jerk constraint and control of a point mass moving on a constant torsion curve in a three dimensional space.
Higher-order brane gravity models
Dabrowski, Mariusz P.; Balcerzak, Adam
2010-06-23
We discuss a very general theory of gravity, of which Lagrangian is an arbitrary function of the curvature invariants, on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second order theory by introducing extra scalar and tensor fields: the scalaron and the tensoron. In order to obtain junction conditions we apply two methods: the application of the Gauss-Codazzi formalism and the application of the generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. In the most general case we derive junction conditions without assuming the continuity of the scalaron and the tensoron on the brane. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.
Higher order time integration methods for two-phase flow
NASA Astrophysics Data System (ADS)
Kees, Christopher E.; Miller, Cass T.
Time integration methods that adapt in both the order of approximation and time step have been shown to provide efficient solutions to Richards' equation. In this work, we extend the same method of lines approach to solve a set of two-phase flow formulations and address some mass conservation issues from the previous work. We analyze these formulations and the nonlinear systems that result from applying the integration methods, placing particular emphasis on their index, range of applicability, and mass conservation characteristics. We conduct numerical experiments to study the behavior of the numerical models for three test problems. We demonstrate that higher order integration in time is more efficient than standard low-order methods for a variety of practical grids and integration tolerances, that the adaptive scheme successfully varies the step size in response to changing conditions, and that mass balance can be maintained efficiently using variable-order integration and an appropriately chosen numerical model formulation.
Second order parametric processes in nonlinear silica microspheres.
Xu, Yong; Han, Ming; Wang, Anbo; Liu, Zhiwen; Heflin, James R
2008-04-25
We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-Q nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally generate quantum entangled photon pairs. Practical issues regarding implementation of the nonlinear microsphere are also discussed.
Higher Order Equations and Constituent Fields
NASA Astrophysics Data System (ADS)
Barci, D. G.; Bollini, C. G.; Oxman, L. E.; Rocca, M.
We consider a simple wave equation of fourth degree in the D'Alembertian operator. It contains the main ingredients of a general Lorentz-invariant higher order equation, namely, a normal bradyonic sector, a tachyonic state and a pair of complex conjugate modes. The propagators are respectively the Feynman causal function and three Wheeler-Green functions (half-advanced and half-retarded). The latter are Lorentz-invariant and consistent with the elimination of tachyons and complex modes from free asymptotic states. We also verify the absence of absorptive parts from convolutions involving Wheeler propagators.
A Novel Higher Order Artificial Neural Networks
NASA Astrophysics Data System (ADS)
Xu, Shuxiang
2010-05-01
In this paper a new Higher Order Neural Network (HONN) model is introduced and applied in several data mining tasks. Data Mining extracts hidden patterns and valuable information from large databases. A hyperbolic tangent function is used as the neuron activation function for the new HONN model. Experiments are conducted to demonstrate the advantages and disadvantages of the new HONN model, when compared with several conventional Artificial Neural Network (ANN) models: Feedforward ANN with the sigmoid activation function; Feedforward ANN with the hyperbolic tangent activation function; and Radial Basis Function (RBF) ANN with the Gaussian activation function. The experimental results seem to suggest that the new HONN holds higher generalization capability as well as abilities in handling missing data.
Optimal second order sliding mode control for nonlinear uncertain systems.
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.
The minimal power spectrum: Higher order contributions
NASA Technical Reports Server (NTRS)
Fry, J. N.
1994-01-01
It has been an accepted belief for some time that gravity induces a minimal tail P(k) approximately k(exp 4) in the power spectrum as k approaches 0 for distributions with no initial power on large scales. In a recent numerical experiment with initial power confined to a restricted range in k, Shandarin and Melott (1990) found a k approaches 0 tail that at early stages of evolution behaves as k(exp 4) and grows with time as a(exp 4)(t), where a(t) is the cosmological expansion factor, and at late times depends on scale as k(exp 3) and grows with time as a(exp 2)(t). I compute analytically several contributions to the power spectrum of higher order than those included in earlier work, and I apply the results to the particular case of initial power restricted to a finite range of k. As expected, in the perturbative regime P(k) approximately a(exp 4)k(exp 4) from the first correction to linear perturbation theory is the dominant term as k approaches 0. Numerical investigations show that the higher order contributions go as k(exp 4) also. However, perturbation theory alone cannot tell whether the P approximately a(exp 2)k(exp 3) result is 'nonperturbative' or a numerical artifact.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Numerical modeling of higher order magnetic moments in UXO discrimination
Sanchez, V.; Yaoguo, L.; Nabighian, M.N.; Wright, D.L.
2008-01-01
The surface magnetic anomaly observed in unexploded ordnance (UXO) clearance is mainly dipolar, and consequently, the dipole is the only magnetic moment regularly recovered in UXO discrimination. The dipole moment contains information about the intensity of magnetization but lacks information about the shape of the target. In contrast, higher order moments, such as quadrupole and octupole, encode asymmetry properties of the magnetization distribution within the buried targets. In order to improve our understanding of magnetization distribution within UXO and non-UXO objects and to show its potential utility in UXO clearance, we present a numerical modeling study of UXO and related metallic objects. The tool for the modeling is a nonlinear integral equation describing magnetization within isolated compact objects of high susceptibility. A solution for magnetization distribution then allows us to compute the magnetic multipole moments of the object, analyze their relationships, and provide a depiction of the anomaly produced by different moments within the object. Our modeling results show the presence of significant higher order moments for more asymmetric objects, and the fields of these higher order moments are well above the noise level of magnetic gradient data. The contribution from higher order moments may provide a practical tool for improved UXO discrimination. ?? 2008 IEEE.
Broadband frequency tripling in locally ordered nonlinear photonic crystal.
Sheng, Yan; Krolikowski, Wieslaw
2013-02-25
We propose and fabricate a LiNbO₃-based nonlinear photonic crystal with locally ordered ferroelectric domains. The nonlinearity modulation provides sets of uniformly distributed reciprocal lattice vectors, ensuring broadband high frequency conversion efficiency. Frequency tripling via cascading is demonstrated in the range of 1400-1830 nm, with energy conversion efficiency up to ∼15%.
Optimization of microscopic and macroscopic second order optical nonlinearities
NASA Technical Reports Server (NTRS)
Marder, Seth R.; Perry, Joseph W.
1993-01-01
Nonlinear optical materials (NLO) can be used to extend the useful frequency range of lasers. Frequency generation is important for laser-based remote sensing and optical data storage. Another NLO effect, the electro-optic effect, can be used to modulate the amplitude, phase, or polarization state of an optical beam. Applications of this effect in telecommunications and in integrated optics include the impression of information on an optical carrier signal or routing of optical signals between fiber optic channels. In order to utilize these effects most effectively, it is necessary to synthesize materials which respond to applied fields very efficiently. In this talk, it will be shown how the development of a fundamental understanding of the science of nonlinear optics can lead to a rational approach to organic molecules and materials with optimized properties. In some cases, figures of merit for newly developed materials are more than an order of magnitude higher than those of currently employed materials. Some of these materials are being examined for phased-array radar and other electro-optic switching applications.
Analysis of wheezes using wavelet higher order spectral features.
Taplidou, Styliani A; Hadjileontiadis, Leontios J
2010-07-01
Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
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 nonlinear 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.
Higher-order harmonics in bleached silver halide holograms
NASA Astrophysics Data System (ADS)
Bányász, I.
2006-09-01
A large number of plane wave holograms were recorded in Agfa-Gevaert 8E75HD holographic plates, at a wide range of bias exposures and fringe visibilities. The plates were processed by various combinations of developers (AAC, Pyrogallol and Catechol) and bleaching agents (R-9 and EDTA). The phase gratings were studied by phase-contrast microscopy, using a high-power immersion (100×) objective. The phase-contrast photomicrographs were Fourier analysed. Thus, first-, second-, and third-order modulations of the refractive index as a function of bias exposure and visibility of the recording interference pattern could be determined. The ratio of the amplitudes of higher-order modulations to that of the first-order can serve as a measure of the nonlinearity of the holographic recording.
Higher order correlations of IRAS galaxies
NASA Technical Reports Server (NTRS)
Meiksin, Avery; Szapudi, Istvan; Szalay, Alexander
1992-01-01
The higher order irreducible angular correlation functions are derived up to the eight-point function, for a sample of 4654 IRAS galaxies, flux-limited at 1.2 Jy in the 60 microns band. The correlations are generally found to be somewhat weaker than those for the optically selected galaxies, consistent with the visual impression of looser clusters in the IRAS sample. It is found that the N-point correlation functions can be expressed as the symmetric sum of products of N - 1 two-point functions, although the correlations above the four-point function are consistent with zero. The coefficients are consistent with the hierarchical clustering scenario as modeled by Hamilton and by Schaeffer.
Aspects of general higher-order gravities
NASA Astrophysics Data System (ADS)
Bueno, Pablo; Cano, Pablo A.; Min, Vincent S.; Visser, Manus R.
2017-02-01
We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in [P. Bueno and P. A. Cano, arXiv:1607.06463] to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify L (Riemann ) theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity. In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghostlike spin-2 mode (but can propagate the scalar) is a linear combination of f (Lovelock ) invariants, plus the Einsteinian cubic gravity term, plus a new ghost-free gravity term. Next, we construct the generalized Newton potential and the post-Newtonian parameter γ for general L (Riemann ) gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald's formalism for general L (Riemann ) theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.
Reduced order models for nonlinear aerodynamics
NASA Technical Reports Server (NTRS)
Mahajan, Aparajit J.; Dowell, Earl H.; Bliss, Donald B.
1988-01-01
Reduced order models are needed for reliable, efficient and accurate prediction of aerodynamic forces to analyze fluid structure interaction problems in turbomachinery, including propfans. Here, a finite difference, time marching Navier-Stokes code is validated for unsteady airfoil motion by comparing results with those from classical potential flow. The Navier-Stokes code is then analyzed for calculation of primitive and exact estimates of eigenvalues and eigenvectors associated with fluid-airfoil interaction. A variational formulation for the Euler equations and Navier-Stokes equations will be the basis for reduction of order through an eigenvector transformation.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
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
Giant fifth-order nonlinearity via tunneling induced quantum interference in triple quantum dots
Tian, Si-Cong Tong, Cun-Zhu Ning, Yong-Qiang; Wan, Ren-Gang
2015-02-15
Schemes for giant fifth-order nonlinearity via tunneling in both linear and triangular triple quantum dots are proposed. In both configurations, the real part of the fifth-order nonlinearity can be greatly enhanced, and simultaneously the absorption is suppressed. The analytical expression and the dressed states of the system show that the two tunnelings between the neighboring quantum dots can induce quantum interference, resulting in the giant higher-order nonlinearity. The scheme proposed here may have important applications in quantum information processing at low light level.
Higher order organization of human placental aromatase.
Ghosh, Debashis; Jiang, Wenhua; Lo, Jessica; Egbuta, Chinaza
2011-07-01
Aromatase (CYP19A1) is an integral membrane enzyme that catalyzes the removal of the 19-methyl group and aromatization of the A-ring of androgens. All human estrogens are synthesized from their androgenic precursors by this unique cytochrome P450. The crystal structure of active aromatase purified from human placenta has recently been determined in complex with its natural substrate androstenedione in the high-spin ferric state of heme. Hydrogen bond forming interactions and tight packing hydrophobic side chains closely complement puckering of the steroid backbone, thereby providing the molecular basis for the androgenic specificity of aromatase. In the crystal, aromatase molecules are linked by a head-to-tail intermolecular interaction via a surface loop between helix D and helix E of one aromatase molecule that penetrates the heme-proximal cavity of the neighboring, crystallographically related molecule, thus forming in tandem a polymeric aromatase chain. This intermolecular interaction is similar to the aromatase-cytochrome P450 reductase coupling and is driven by electrostatics between the negative potential surface of the D-E loop region and the positively charged heme-proximal cavity. This loop-to-proximal site link in aromatase is rather unique--there are only a few of examples of somewhat similar intermolecular interactions in the entire P450 structure database. Furthermore, the amino acids involved in the intermolecular contact appear to be specific for aromatase. Higher order organization of aromatase monomers may have implications in lipid integration and catalysis.
Higher order structure of aquaporin-4.
Nicchia, G P; Rossi, A; Mola, M G; Pisani, F; Stigliano, C; Basco, D; Mastrototaro, M; Svelto, M; Frigeri, A
2010-07-28
Unlike other mammalian AQPs, multiple tetramers of AQP4 associate in the plasma membrane to form peculiar structures called Orthogonal Arrays of Particles (OAPs), that are observable by freeze-fracture electron microscopy (FFEM). However, FFEM cannot give information about the composition of OAPs of different sizes, and due to its technical complexity is not easily applicable as a routine technique. Recently, we employed the 2D gel electrophoresis BN-SDS/PAGE that for the first time enabled the biochemical isolation of AQP4-OAPs from several tissues. We found that AQP4 protein is present in several higher-order complexes (membrane pools of supra-structures) which contain different ratios of M1/M23 isoforms corresponding to AQP4-OAPs of different size. In this paper, we illustrate in detail the potentiality of 2D BN/SDS-PAGE for analyzing AQP4 supra-structures, their relationship with the dystrophin glycoprotein complex and other membrane proteins, and their role as a specific target of Neuromyelitis Optica autoantibodies.
Analysis of higher order harmonics with holographic reflection gratings
NASA Astrophysics Data System (ADS)
Mas-Abellan, P.; Madrigal, R.; Fimia, A.
2017-05-01
Silver halide emulsions have been considered one of the most energetic sensitive materials for holographic applications. Nonlinear recording effects on holographic reflection gratings recorded on silver halide emulsions have been studied by different authors obtaining excellent experimental results. In this communication specifically we focused our investigation on the effects of refractive index modulation, trying to get high levels of overmodulation that will produce high order harmonics. We studied the influence of the overmodulation and its effects on the transmission spectra for a wide exposure range by use of 9 μm thickness films of ultrafine grain emulsion BB640, exposed to single collimated beams using a red He-Ne laser (wavelength 632.8 nm) with Denisyuk configuration obtaining a spatial frequency of 4990 l/mm recorded on the emulsion. The experimental results show that high overmodulation levels of refractive index produce second order harmonics with high diffraction efficiency (higher than 75%) and a narrow grating bandwidth (12.5 nm). Results also show that overmodulation produce diffraction spectra deformation of the second order harmonic, transforming the spectrum from sinusoidal to approximation of square shape due to very high overmodulation. Increasing the levels of overmodulation of refractive index, we have obtained higher order harmonics, obtaining third order harmonic with diffraction efficiency (up to 23%) and narrowing grating bandwidth (5 nm). This study is the first step to develop a new easy technique to obtain narrow spectral filters based on the use of high index modulation reflection gratings.
Evaluation of expressions involving higher order derivations
NASA Technical Reports Server (NTRS)
Grossman, Robert
1990-01-01
The local geometric properties of a nonlinear control system defined by vector fields E(sub 1),..., E(sub M) are determined by the algebraic properties of the iterated Lie brackets of the E(sub j)'s. The problem of rewriting expressions is examined involving the E(sub j)'s in terms of the D(sub mu)'s in such a way as to handle effectively any cancellation occurring due to commuting of the D(sub mu)'s. A data structure is introduced which allows us to organize the computation to take advantage of the symmetries in the expression and reduce the operation count.
Growth and characterization of third order nonlinear optical material: Isatin
NASA Astrophysics Data System (ADS)
Thirumalaiselvam, B.; Kanagadurai, R.; Jayaraman, D.; Natarajan, V.
2013-10-01
Isatin, an indole derivative, is a bioactive and nonlinear active material with broad range of applications in synthetic, biological and clinical activity and optoelectronics and photonics. Isatin single crystals were grown by the solution growth method. The grown crystals were characterized by single crystal XRD, UV-vis-NIR, FTIR spectral analysis, dielectric and thermal studies. Kurtz and Perry powder technique reveals the absence of second harmonic generation. The estimations of third order non-linear optical properties like non-linear absorption co-efficient (β), non-linear refractive index (n2) and susceptibility [χ(3)] using Z-scan technique confirm the third order NLO behaviour of the material and these results indicate that the crystal exhibits saturation absorption and self-focusing performance.
NASA Astrophysics Data System (ADS)
Chinone, N.; Cho, Y.
2017-09-01
We propose a new technique called local deep level transient spectroscopy (local-DLTS), which utilizes scanning nonlinear dielectric microscopy to analyze oxide/semiconductor interface traps, and validate the method by investigating thermally oxidized silicon carbide wafers. Measurements of C-t curves demonstrate the capability of distinguishing sample-to-sample differences in the trap density. Furthermore, the DC bias dependence of the time constant and the local-DLTS signal intensity are investigated, and the results agree to characteristic of interface traps. In addition, the Dit values for the examined samples are estimated from the local-DLTS signals and compared with results obtained using the conventional high-low method. The comparison reveals that the Dit values obtained by the two methods are of the same order of magnitude. Finally, two-dimensional (2D) distributions of local-DLTS signals are obtained, which show substantial intensity variations resulting in random 2D patterns. The 2D distribution of the local-DLTS signal depends on the time constant, which may be due to the coexistence of multiple types of traps with different capture cross sections.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
Alloatti, L. Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.
2015-09-21
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al{sub 2}O{sub 3}, B = TiO{sub 2}, and C = HfO{sub 2}. The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths.
Investigation of odd-order nonlinear susceptibilities in atomic vapors
Yan, Yaqi; Wu, Zhenkun; Si, Jinhai; Yan, Lihe; Zhang, Yiqi; Yuan, Chenzhi; Sun, Jia; Zhang, Yanpeng
2013-06-15
We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations. -- Highlights: •The macroscopic symmetry constraints are deduced for homogeneous media including atomic vapors. •We demonstrate that odd-order nonlinear susceptibilities satisfy the constraints. •We experimentally demonstrate the deduction in part.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively.
Higher order vortex methods with rezoning
NASA Astrophysics Data System (ADS)
Nordmark, H. O.
1988-05-01
The vortex method is a numerical method for approximating the flow of an incompressible, inviscid fluid. We consider the two-dimensional case. The accuracy depends on the choice of the cutoff function which approximates the delta function, on the cutoff parameter delta and on the smoothness of the initial data. We derive a class of infinite-order cutoff functions with arbitrarily high rates of decay at infinity. We also derive an eighth order cutoff function with compact support. We test two versions of rezoning. Version 1 has been suggested and tested by Beale and Majda, while version 2 is new. Using rezoning, we test the eighth order cutoff function and one infinite-order cutoff function on three test problems for which the solution of Euler's equation is known analytically. The accuracies of the two methods are comparable. We also compute the evolution of two circular vorticity patches and the evolution of one square vorticity patch over long time intervals. Finally, we make a comparison between the direct method of velocity evaluation and the Rokhlin-Greengard algorithm. The numerical experiments indicate that for smooth flows, high-order cutoffs combined with rezoning give high accuracy for long time integrations.
First and Higher Order Effects on Zero Order Radiative Transfer Model
NASA Astrophysics Data System (ADS)
Neelam, M.; Mohanty, B.
2014-12-01
Microwave radiative transfer model are valuable tool in understanding the complex land surface interactions. Past literature has largely focused on local sensitivity analysis for factor priotization and ignoring the interactions between the variables and uncertainties around them. Since land surface interactions are largely nonlinear, there always exist uncertainties, heterogeneities and interactions thus it is important to quantify them to draw accurate conclusions. In this effort, we used global sensitivity analysis to address the issues of variable uncertainty, higher order interactions, factor priotization and factor fixing for zero-order radiative transfer (ZRT) model. With the to-be-launched Soil Moisture Active Passive (SMAP) mission of NASA, it is very important to have a complete understanding of ZRT for soil moisture retrieval to direct future research and cal/val field campaigns. This is a first attempt to use GSA technique to quantify first order and higher order effects on brightness temperature from ZRT model. Our analyses reflect conditions observed during the growing agricultural season for corn and soybeans in two different regions in - Iowa, U.S.A and Winnipeg, Canada. We found that for corn fields in Iowa, there exist significant second order interactions between soil moisture, surface roughness parameters (RMS height and correlation length) and vegetation parameters (vegetation water content, structure and scattering albedo), whereas in Winnipeg, second order interactions are mainly due to soil moisture and vegetation parameters. But for soybean fields in both Iowa and Winnipeg, we found significant interactions only to exist between soil moisture and surface roughness parameters.
Higher-order theory of gravitation
Pandey, S.N.
1988-06-01
The field equation obtained by introducing a correction in the Hilbert Lagrangian in the form of a series of finite terms is R (triple bond g/sub ..mu..v/R/sup ..mu..v/) are considered in order to study the implications for the cosmological singularity.
Tachyons and Higher Order Wave Equations
NASA Astrophysics Data System (ADS)
Barci, D. G.; Bollini, C. G.; Rocca, M. C.
We consider a fourth order wave equation having normal as well as tachyonic solutions. The propagators are, respectively, the Feynman causal function and the Wheeler-Green function (half advanced and half retarded). The latter is consistent with the elimination of tachyons from free asymptotic states. We verify the absence of absorptive parts from convolutions involving the tachyon propagator.
Simulation Higher Order Language Requirements Study.
ERIC Educational Resources Information Center
Goodenough, John B.; Braun, Christine L.
The definitions provided for high order language (HOL) requirements for programming flight training simulators are based on the analysis of programs written for a variety of simulators. Examples drawn from these programs are used to justify the need for certain HOL capabilities. A description of the general structure and organization of the…
Third-Order Optical Nonlinear Properties of Polymers.
NASA Astrophysics Data System (ADS)
Yang, Lina
The development of polymers as nonlinear optical materials coincide with a renewed interest in the field of nonlinear optics, and its applications for the future photonic devices. Large nonresonant susceptibilities, fast electronic responses, and ease of processing make polymers one of the best candidates for the applications. This thesis describes the study of the third order optical nonlinear properties in polymers. The studies have been focused on two classes of conjugated polymers: the pi-electron system and the sigma-electron system. Important parameters which fully characterize the nonlinearities of materials, such as magnitude, response time, and the sign of chi^{(3)} have been measured. Various mechanisms responsible for the observed nonlinearities have also been investigated. The thesis consists of twelve chapters. The first two chapters provide an overview of the fundamental aspects of nonlinear optics, optical properties of polymers, and the experimental techniques, apparatus which can be used to investigate the third order optical nonlinearities of polymers, such as the degenerate four wave mixing and the single beam Z-scan technique. The pi-electron polymer systems are studied in Chapters III to VII. We have investigated the nonlinearities in polyacetylene, polydiacetylene, as well as in a relatively new material-polythiophenes. Most of the work has been concentrated on polythiophenes. For the first time, the spectrum of the nonlinear coefficient chi^3 covering the single photon transition band has been measured in polythiophene. The experimental results show that chi^3 is large (>10^{ -9}esu) and fast (<15ps) above gap. The real part of chi^3 has also been found to be negative at both 532 and 1064 nm. The single photon resonance is responsible for the negative chi^3 at 532 nm, while two photon resonant absorption is responsible for the negative chi^3 at 1064 nm. For the first time, the enhancement of chi ^{(3)} was observed about photoinduced
Small Schools and Higher Order Thinking Skills.
ERIC Educational Resources Information Center
Haller, Emil J.; And Others
A review of the literature indicates that, compared to larger, urban schools, small, rural secondary schools have limited course offerings in mathematics and science; the review also indicates, however, that the achievement of students in small, rural schools is equivalent to or even higher than, that of students in larger, urban schools. Such an…
Higher-order graph wavelets and sparsity on circulant graphs
NASA Astrophysics Data System (ADS)
Kotzagiannidis, Madeleine S.; Dragotti, Pier Luigi
2015-08-01
The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.
Higher order diffractions from a circular disk
NASA Technical Reports Server (NTRS)
Marsland, Diane P.; Balanis, Constantine A.; Brumley, Stephen A.
1987-01-01
The backscattering from a circular disk is analyzed using the geometrical theory of diffraction. First-, second-, and third-order diffractions are included in the hard polarization analysis, while first-, second-, and third-order slope diffractions are included for soft polarization. Improvements in the prediction of the monostatic radar cross section over previous works are noted. For hard polarization, an excellent agreement is exhibited between experimental and theoretical results, while a very good agreement is noted for soft polarization. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk is obtained and used to find an additional component of the backscattered field. The addition of this component significantly improves the results for wide angles, leading to excellent agreement for soft polarization also. An axial-caustic correction method using equivalent currents is also included in the analysis.
Higher order diffractions from a circular disk
NASA Technical Reports Server (NTRS)
Marsland, Diane P.; Balanis, Constantine A.; Brumley, Stephen A.
1987-01-01
The backscattering from a circular disk is analyzed using the geometrical theory of diffraction. First-, second-, and third-order diffractions are included in the hard polarization analysis, while first-, second-, and third-order slope diffractions are included for soft polarization. Improvements in the prediction of the monostatic radar cross section over previous works are noted. For hard polarization, an excellent agreement is exhibited between experimental and theoretical results, while a very good agreement is noted for soft polarization. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk is obtained and used to find an additional component of the backscattered field. The addition of this component significantly improves the results for wide angles, leading to excellent agreement for soft polarization also. An axial-caustic correction method using equivalent currents is also included in the analysis.
Invariant Higher-Order Variational Problems II
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier
2012-08-01
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesic on the group of transformations project to cubics. Finally, we apply second-order Lagrange-Poincaré reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.
Measurement of third order nonlinear susceptibilities by surface plasmons
NASA Astrophysics Data System (ADS)
Chen, Y. J.; Carter, G. M.
1982-08-01
A simple technique of measuring both the magnitude and the sign of the degenerate third order nonlinear susceptibility is demonstrated. It is pointed out that since the nonlinear interaction takes place at the interface, the technique can be used to study both bulk and thin film materials, in particular those of technological importance (such as epilayers and thin-film materials overcoated on the metal grating surface). What is more, the Si results demonstrate that the technique can be used in the wavelength region where the nonlinear medium is absorbing. This suggests the possibility of using this technique to study the resonant enhancement of the third-order nonlinear susceptibility near an absorption edge. It is pointed out that although the experiments described here use only a single laser beam, it is possible to explore the nondegenerate chi-3 (omega-1, omega-2, omega-3) by this technique using laser beams at different frequencies. It is also noted that, in principle, this nonlinear coupling effect could also be observed in a similar fashion in waveguide systems.
Asymptotic stability of distributed order nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Fernández-Anaya, G.; Nava-Antonio, G.; Jamous-Galante, J.; Muñoz-Vega, R.; Hernández-Martínez, E. G.
2017-07-01
In this article we present a generalization of the Lyapunov direct method for distributed order nonlinear time-varying systems. By extending recently introduced properties of the Caputo fractional derivative to the distributed order case, we provide various ways to determine the stability or asymptotic stability of certain systems. The fractional results that inspired this work are recovered if an appropriate distribution function is chosen. Some examples are given to validate the obtained results.
Adaptive control for a class of second-order nonlinear systems with unknown input nonlinearities.
Zhang, T; Guay, M
2003-01-01
An adaptive controller is developed for a class of second-order nonlinear dynamic systems with input nonlinearities using artificial neural networks (ANN). The unknown input nonlinearities are continuous and monotone and satisfy a sector constraint. In contrast to conventional Lyapunov-based design techniques, an alternative Lyapunov function, which depends on both system states and control input variable, is used for the development of a control law and a learning algorithm. The proposed adaptive controller guarantees the stability of the closed-loop system and convergence of the output tracking error to an adjustable neighbour of the origin.
Chromatin Higher-order Structure and Dynamics
Woodcock, Christopher L.; Ghosh, Rajarshi P.
2010-01-01
The primary role of the nucleus as an information storage, retrieval, and replication site requires the physical organization and compaction of meters of DNA. Although it has been clear for many years that nucleosomes constitute the first level of chromatin compaction, this contributes a relatively small fraction of the condensation needed to fit the typical genome into an interphase nucleus or set of metaphase chromosomes, indicating that there are additional “higher order” levels of chromatin condensation. Identifying these levels, their interrelationships, and the principles that govern their occurrence has been a challenging and much discussed problem. In this article, we focus on recent experimental advances and the emerging evidence indicating that structural plasticity and chromatin dynamics play dominant roles in genome organization. We also discuss novel approaches likely to yield important insights in the near future, and suggest research areas that merit further study. PMID:20452954
Nonlinear reduced-order modeling with monotonicity property
NASA Astrophysics Data System (ADS)
Chaturantabut, Saifon
2016-10-01
This work proposes a general form of nonlinear model reduction approach that preserves the monotonicity property of the original full-order model, which can be used to guarantee the existence and uniqueness of the solution. The derivation of the proposed methodology is based on using basis from proper orthogonal decomposition method and modifying an interpolatory projection approach, called discrete empirical interpolation method, by enforcing a symmetric structure of the approximation. The efficiency and accuracy of the proposed method are illustrated through the numerical tests on a nonlinear model describing reaction diffusion problems.
Nonlinear diffraction from high-order Hermite-Gauss beams.
Kalinowski, Ksawery; Shapira, Asia; Libster-Hershko, Ana; Arie, Ady
2015-01-01
We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall.
Visualising higher order Brillouin zones with applications
NASA Astrophysics Data System (ADS)
Andrew, R. C.; Salagaram, T.; Chetty, N.
2017-05-01
A key concept in material science is the relationship between the Bravais lattice, the reciprocal lattice and the resulting Brillouin zones (BZ). These zones are often complicated shapes that are hard to construct and visualise without the use of sophisticated software, even by professional scientists. We have used a simple sorting algorithm to construct BZ of any order for a chosen Bravais lattice that is easy to implement in any scientific programming language. The resulting zones can then be visualised using freely available plotting software. This method has pedagogical value for upper-level undergraduate students since, along with other computational methods, it can be used to illustrate how constant-energy surfaces combine with these zones to create van Hove singularities in the density of states. In this paper we apply our algorithm along with the empirical pseudopotential method and the 2D equivalent of the tetrahedron method to show how they can be used in a simple software project to investigate this interaction for a 2D crystal. This project not only enhances students’ fundamental understanding of the principles involved but also improves transferable coding skills.
Developing Higher-Order Materials Knowledge Systems
NASA Astrophysics Data System (ADS)
Fast, Anthony Nathan
2011-12-01
Advances in computational materials science and novel characterization techniques have allowed scientists to probe deeply into a diverse range of materials phenomena. These activities are producing enormous amounts of information regarding the roles of various hierarchical material features in the overall performance characteristics displayed by the material. Connecting the hierarchical information over disparate domains is at the crux of multiscale modeling. The inherent challenge of performing multiscale simulations is developing scale bridging relationships to couple material information between well separated length scales. Much progress has been made in the development of homogenization relationships which replace heterogeneous material features with effective homogenous descriptions. These relationships facilitate the flow of information from lower length scales to higher length scales. Meanwhile, most localization relationships that link the information from a from a higher length scale to a lower length scale are plagued by computationally intensive techniques which are not readily integrated into multiscale simulations. The challenge of executing fully coupled multiscale simulations is augmented by the need to incorporate the evolution of the material structure that may occur under conditions such as material processing. To address these challenges with multiscale simulation, a novel framework called the Materials Knowledge System (MKS) has been developed. This methodology efficiently extracts, stores, and recalls microstructure-property-processing localization relationships. This approach is built on the statistical continuum theories developed by Kroner that express the localization of the response field at the microscale using a series of highly complex convolution integrals, which have historically been evaluated analytically. The MKS approach dramatically improves the accuracy of these expressions by calibrating the convolution kernels in these
Higher order solutions to ion-acoustic solitons in a weakly relativistic two-fluid plasma
Gill, Tarsem Singh; Bala, Parveen; Kaur, Harvinder
2008-12-15
The nonlinear wave structure of small amplitude ion-acoustic solitary waves (IASs) is investigated in a two-fluid plasma consisting of weakly relativistic streaming ions and electrons. Using the reductive perturbation theory, the basic set of governing equations is reduced to the Korteweg-de Vries (KdV) equation for the lowest order perturbation. This analysis is further extended using the renormalization technique for the inclusion of higher order nonlinear and dispersive effects for better accuracy. The effect of higher order correction and various parameters on the soliton characteristics is investigated and also discussed.
Spacecraft attitude determination using a second-order nonlinear filter
NASA Technical Reports Server (NTRS)
Vathsal, S.
1987-01-01
The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.
Developing High-Order Weighted Compact Nonlinear Schemes
NASA Astrophysics Data System (ADS)
Deng, Xiaogang; Zhang, Hanxin
2000-11-01
The weighted technique is introduced in the compact high-order nonlinear schemes (CNS) and three fourth- and fifth-order weighted compact nonlinear schemes (WCNS) are developed in this paper. By Fourier analysis, the dissipative and dispersive features of WCNS are discussed. In view of the modified wave number, the WCNS are equivalent to fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the properties of WCNS. Both flux difference splitting and flux vector splitting methods can be applied in WCNS, though they are finite difference schemes. Boundary and near boundary schemes are developed and the asymptotic stability of WCNS is analyzed. Several numerical results are given which show the good performances of WCNS for discontinuity capture high accuracy for boundary layer calculation, and good convergent rate. We also compare WCNS with MUSCL scheme and spectral solutions. WCNS are more accurate than MUSCL, as expected, especially for heat transfer calculations.
Kim, T; Pasciak, J E; Vassilevski, P S
2004-09-20
In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
A Nonlinear Reduced Order Method for Prediction of Acoustic Fatigue
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2006-01-01
The goal of this investigation is to assess the quality of high-cycle-fatigue life estimation via a reduced order method, for structures undergoing geometrically nonlinear random vibrations. Modal reduction is performed with several different suites of basis functions. After numerically solving the reduced order system equations of motion, the physical displacement time history is obtained by an inverse transformation and stresses are recovered. Stress ranges obtained through the rainflow counting procedure are used in a linear damage accumulation method to yield fatigue estimates. Fatigue life estimates obtained using various basis functions in the reduced order method are compared with those obtained from numerical simulation in physical degrees-of-freedom.
Third order nonlinear optical properties of bismuth zinc borate glasses
Shanmugavelu, B.; Ravi Kanth Kumar, V. V.; Kuladeep, R.; Narayana Rao, D.
2013-12-28
Third order nonlinear optical characterization of bismuth zinc borate glasses are reported here using different laser pulse durations. Bismuth zinc borate glasses with compositions xBi{sub 2}O{sub 3}-30ZnO-(70-x) B{sub 2}O{sub 3} (where x = 30, 35, 40, and 45 mol. %) have been prepared by melt quenching method. These glasses were characterized by Raman, UV-Vis absorption, and Z scan measurements. Raman and UV-Vis spectroscopic results indicate that non-bridging oxygens increase with increase of bismuth content in the glass. Nonlinear absorption and refraction behavior in the nanosecond (ns), picosecond (ps), and femtosecond (fs) time domains were studied in detail. Strong reverse saturable absorption due to dominant two-photon absorption (TPA) was observed with both ps and fs excitations. In the case of ns pulse excitations, TPA and free-carrier absorption processes contribute for the nonlinear absorption. Two-photon absorption coefficient (β) and the absorption cross section due to free carriers (σ{sub e}) are estimated by theoretical fit of the open aperture Z-scan measurements and found to be dependent on the amount of bismuth oxide in the glass composition. In both ns and fs regimes the sign and magnitude of the third order nonlinearity are evaluated, and the optical limiting characteristics are also reported.
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.
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
Third- and fifth-order optical nonlinearities in organic materials
NASA Astrophysics Data System (ADS)
Said, A. A.; Wamsley, C.; Hagan, D. J.; Van Stryland, E. W.; Reinhardt, Bruce A.; Roderer, Paul; Dillard, Ann G.
1994-10-01
We measure the nonlinear optical properties of solutions of a bisbenzethiozole-substituted thiophene compound (BBTDOT) and didecyloxy substituted polyphenyl (DDOS) using the Z-scan technique with 532 nm picosecond pulses. Both compounds exhibit two-photon absorption (2PA) and excited-state absorption (ESA) from the 2PA generated excited states. We measure the magnitude and sign of the real (refractive) and imaginary (2PA) parts of the third-order hyperpolarizability, and the excited-state absorptive and refractive cross sections. We observe third-order self-focusing in BBTDOT and self-defocusing in DDOS while both show excited-state defocusing. All these effects were previously observed and modeled in semiconductors giving insight into the nonlinearities occurring in these organic materials.
Stabilisation of second-order nonlinear equations with variable delay
NASA Astrophysics Data System (ADS)
Berezansky, Leonid; Braverman, Elena; Idels, Lev
2015-08-01
For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilisation by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.
Software Contracts in a Higher-order World
2012-02-01
02-2012 final 01 March 2009 -01 February 2012 Software Contracts in a Higher -order World FA9550-09-1-0110 Matthias Felleisen Northeastern...contracts in a higher -order world of programming. The primary thrust of the work explored the meaning of contracts. We focused on three questions. First...contracts higher -order programming U U U UU 4 Matthias Felleisen 617-363-2085 Software Contracts in a Higher -Order World Matthias Felleisen matthias
Skinner-Rusk unified formalism for higher-order systems
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2012-07-01
The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, first-order and higher-order field theories, and higher-order autonomous systems. In this work we present a generalization of this formalism for higher-order non-autonomous mechanical systems.
Conceptualizing and Assessing Higher-Order Thinking in Reading
ERIC Educational Resources Information Center
Afflerbach, Peter; Cho, Byeong-Young; Kim, Jong-Yun
2015-01-01
Students engage in higher-order thinking as they read complex texts and perform complex reading-related tasks. However, the most consequential assessments, high-stakes tests, are currently limited in providing information about students' higher-order thinking. In this article, we describe higher-order thinking in relation to reading. We provide a…
Conceptualizing and Assessing Higher-Order Thinking in Reading
ERIC Educational Resources Information Center
Afflerbach, Peter; Cho, Byeong-Young; Kim, Jong-Yun
2015-01-01
Students engage in higher-order thinking as they read complex texts and perform complex reading-related tasks. However, the most consequential assessments, high-stakes tests, are currently limited in providing information about students' higher-order thinking. In this article, we describe higher-order thinking in relation to reading. We provide a…
NASA Astrophysics Data System (ADS)
Song, Pengchao
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
Second order optical nonlinearity in silicon by symmetry breaking
Cazzanelli, Massimo; Schilling, Joerg
2016-03-15
Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.
Geng, Lingling; Yu, Yongguang; Zhang, Shuo
2016-09-01
In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.
Third-order optical nonlinearities of PVP/Pd nanohybrids
NASA Astrophysics Data System (ADS)
Papagiannouli, I.; Potamianos, D.; Krasia-Christoforou, T.; Couris, S.
2017-10-01
Pd nanoparticles stabilized by polyvinylpyrrolidone were synthesized following mild reduction of palladium ion complexes. Their morphology and optical properties were characterized using Transmission Electron Microscopy, Dynamic Light Scattering and UV-Vis absorption spectroscopy to confirm the existence of monodispersed, low-dimensional single nanoparticles. Furthermore, their third-order nonlinear optical properties were investigated by means of the Z-scan technique, using 35 ps and 4 ns laser pulses, both in the visible (532 nm) and in the infrared (1064 nm). These results denote that the surface plasmon resonance is not significantly contributing to the nonlinear optical response of Pd nanoparticles. In contrast, a two photon absorption process was found to contribute to the observed response. The present results are discussed and compared with previous literature findings.
Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form
NASA Astrophysics Data System (ADS)
Kim, Sunghan; Lee, Ki-Ahm
2016-03-01
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.
Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
LaBryer, Allen
Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time
Fourth order wave equations with nonlinear strain and source terms
NASA Astrophysics Data System (ADS)
Liu, Yacheng; Xu, Runzhang
2007-07-01
In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I(u0)[greater-or-equal, slanted]0, E(0)=d. So the Esquivel-Avila's results are generalized and improved.
NASA Astrophysics Data System (ADS)
Chen, Feifei; Dai, Shixun; Xu, Tiefeng; Shen, Xiang; Lin, Changgui; Nie, Qiuhua; Liu, Chao; Heo, Jong
2011-09-01
Ellipsoidal gold nanoparticles embedded bismuthate glasses have been prepared via a facile melt-annealing approach. Femtosecond Z-scan measurement shows that the nanocomposites exhibit a maximum third-order nonlinear susceptibility χ(3) of 4.88 × 10-10 esu at 800 nm, which is two orders higher than that of the host glass. Optical Kerr shutter measurement demonstrates ultrafast response time (in scale of sub-picosecond) of the intraband transition enhanced third-order nonlinearities.
NASA Technical Reports Server (NTRS)
Sanghadasa, Mohan; Shin, In-Seek; Barr, Thomas A.; Clark, Ronald D.; Guo, Huai-Song; Martinez, Angela; Penn, Benjamin G.
1998-01-01
In recent years, there has been a growing interest in the development of passive optical power limiters for the protection of the human eye and solid-state sensors from damage caused by energetic light pulses and also for other switching applications. One of the key issues involved is the search for appropriate materials that show effective reverse saturable absorption. Phthalocyanines seem to be good candidates for such applications because of their higher third order nonlinearity and the unique electronic absorption characteristics. A series of 1,4,8,11,15, 18,22,25-octa-alkoxy metallophthalocyanines containing various central metal atoms such as zinc, copper, palladium, cobalt and nickel were characterized for their third order nonlinearity and for their nonlinear absorptive properties to evaluate their suitability to function as reverse saturable absorbers.
NASA Astrophysics Data System (ADS)
Surekha, R.; Sagayaraj, P.; Ambujam, K.
2014-03-01
Optical quality bis glycine hydrobromide (BGHB) single crystal was grown by slow evaporation technique. The third order nonlinear refractive index and nonlinear absorption coefficient of the grown crystal were measured by Z-scan studies. The third order nonlinear susceptibility was found to be 9.612 × 10-4 esu which is fairly higher than the other glycine compounds. The Photoluminescence spectra reveal the emission bands for BGHB crystals. The band gap energy was calculated to be 3.1 eV. The Photoconductivity studies were employed to determine the dependence of photocurrent on the applied electric field. Negative photoconductivity was exhibited by the sample. The d.c. conductivity of the grown crystal was measured by the complex impedance analysis wherein the obtained plot in the form of semicircle finds application in Debye relaxation for materials having large dc conductivity.
NASA Technical Reports Server (NTRS)
Sanghadasa, Mohan; Shin, In-Seek; Barr, Thomas A.; Clark, Ronald D.; Guo, Huai-Song; Martinez, Angela; Penn, Benjamin G.
1998-01-01
In recent years, there has been a growing interest in the development of passive optical power limiters for the protection of the human eye and solid-state sensors from damage caused by energetic light pulses and also for other switching applications. One of the key issues involved is the search for appropriate materials that show effective reverse saturable absorption. Phthalocyanines seem to be good candidates for such applications because of their higher third order nonlinearity and the unique electronic absorption characteristics. A series of 1,4,8,11,15, 18,22,25-octa-alkoxy metallophthalocyanines containing various central metal atoms such as zinc, copper, palladium, cobalt and nickel were characterized for their third order nonlinearity and for their nonlinear absorptive properties to evaluate their suitability to function as reverse saturable absorbers.
Higher-order effects in bandwidth-limited soliton propagation in optical fibers
Aceves, A.B.; De Angelis, C. ); Nalesso, G.; Santagiustina, M. )
1994-12-15
By means of numerical studies and soliton perturbation theory we examine the effects of higher-order linear and nonlinear terms in bandwidth-limited amplified soliton propagation. We show that these effects are responsible for strong reductions of soliton--soliton interaction in such systems.
Higher Order Crossings from a Parametric Family of Linear Filters
1989-09-01
HIGHER ORDER CROSSINGS FROM A PARAMETRIC FAMILY OF LINEAR FILTERS DTIC DTC Benjamin Kedem and Ta-hsin Li E! U 4C99 Department of MathematicsS4 9...NUMBER 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED Higher order crossings from a parametric family Technical Report of linear filters...corresponding family of zero-crossing counts. The resulting family of counts is referred to as higher order crossings or HOC. Thus, HOC are zero-crossing
NASA Astrophysics Data System (ADS)
Dakova, D.; Dakova, A.; Slavchev, V.; Staykov, P.; Kovachev, L.
2016-01-01
In last two decades the phenomena resulting from the evolution of ultra-short laser pulses in nonlinear dispersive medium actively are being studied. The most commonly used equation for describing the dynamics of optical pulses in one-dimensional and planar waveguides is the standard nonlinear Schrodinger equation (NSE). It works very well for nanosecond and picosecond laser pulses, but in the frames of femtosecond optics, it is necessary two additional terms to be included. They are responsible for higher order of linear dispersion and dispersion of nonlinearity. These effects are significant in the range of ultra-short light pulses. In the present paper, it is presented a theoretical model of the propagation of optical solitons. We found an exact analytical soliton solution of the modified NSE, including third order of linear dispersion and dispersion of nonlinearity. It is possible to observe a soliton as a result of the dynamic balance between effects of higher order of dispersion and nonlinearity.
Second-Order Nonlinear Optical Imaging of Chiral Crystals
Kissick, David J.; Wanapun, Debbie; Simpson, Garth J.
2012-01-01
Second-order nonlinear optical imaging of chiral crystals (SONICC) is an emerging technique for crystal imaging and characterization. We provide a brief overview of the origin of second harmonic generation signals in SONICC and discuss recent studies using SONICC for biological applications. Given that they provide near-complete suppression of any background, SONICC images can be used to determine the presence or absence of protein crystals through both manual inspection and automated analysis. Because SONICC creates high-resolution images, nucleation and growth kinetics can also be observed. SONICC can detect metastable, homochiral crystalline forms of amino acids crystallizing from racemic solutions, which confirms Ostwald’s rule of stages for crystal growth. SONICC’s selectivity, based on order, and sensitivity, based on background suppression, make it a promising technique for numerous fields concerned with chiral crystal formation. PMID:21469954
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide.
De Leonardis, Francesco; Soref, Richard A; Passaro, Vittorio M N
2017-01-18
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
NASA Astrophysics Data System (ADS)
de Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
De Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region. PMID:28098223
Promoting Higher Order Thinking Skills Using Inquiry-Based Learning
ERIC Educational Resources Information Center
Madhuri, G. V.; Kantamreddi, V. S. S. N; Prakash Goteti, L. N. S.
2012-01-01
Active learning pedagogies play an important role in enhancing higher order cognitive skills among the student community. In this work, a laboratory course for first year engineering chemistry is designed and executed using an inquiry-based learning pedagogical approach. The goal of this module is to promote higher order thinking skills in…
Planning a Telelearning Environment To Foster Higher Order Thinking.
ERIC Educational Resources Information Center
McLoughlin, Catherine; Oliver, Ron
1998-01-01
Discusses audiographic conferencing in Western Australia and describes research that investigated telematics classrooms, with a focus on changing the teaching/learning environment to develop higher-order thinking skills. Results indicate that higher-order thinking increased with the scaffolding role of the teacher and social interaction and…
Promoting Higher Order Thinking Skills Using Inquiry-Based Learning
ERIC Educational Resources Information Center
Madhuri, G. V.; Kantamreddi, V. S. S. N; Prakash Goteti, L. N. S.
2012-01-01
Active learning pedagogies play an important role in enhancing higher order cognitive skills among the student community. In this work, a laboratory course for first year engineering chemistry is designed and executed using an inquiry-based learning pedagogical approach. The goal of this module is to promote higher order thinking skills in…
Higher Order Thinking: Definition, Meaning and Instructional Approaches.
ERIC Educational Resources Information Center
Thomas, Ruth G., Ed.
This publication shares current thinking, research, and practice in the area of higher order thinking skills with home economics educators, including teachers, supervisors, and teacher educators. The first three articles provide general discussions of thinking skills. They are "Introduction" (Ruth Pestle); "Can Higher Order Thinking…
Higher Order Modeling In the BEM/FEM Hybrid Formulation
NASA Technical Reports Server (NTRS)
Fink, Patrick W.; Wilton, Don R.
2000-01-01
Hybrid formulations using low order curl-conforming bases to represent the total electric field within a finite element region and low order divergence-conforming bases to represent equivalent electric and magnetic currents on the boundary are well known. However, higher-order divergence and curl-conforming bases have been shown to provide significant benefits in convergence rates and accuracy when employed in strictly integral equation and strictly finite element formulations. In this paper, a hybrid electric field formulation employing higher order bases is presented. The paper addresses benefits and issues associated with using higher order divergence-and curl-conforming bases in the hybrid finite element/boundary element electric field formulation. The method of singularity subtraction may be used to compute the self terms of the boundary integral when the bases are of low order. But this method becomes laborious and requires great care when the divergence conforming bases are of higher order. In order to handle these singularities simply and accurately, a generalized Gaussian quadrature method is employed in which the expansion functions account for the singularity. In preliminary tests of the higher order hybrid formulation, the equivalent electric current induced by scattering of a plane wave from a square dielectric cylinder is examined. Accurate results are obtained using only a two-triangle mesh when the current basis is of order 4 or 5. Additional results are presented comparing the error obtained using higher order bases to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained with higher order bases are compared to those obtained with lower order bases for selected sample problems.
A robot architecture based on higher order perception loop.
Chella, Antonio
2010-01-01
The paper discusses the self-consciousness of a robot as based on higher order perceptions of the robot itself. In this sense, the first order perceptions of the robot are the immediate perceptions of the outer world of the robot, while higher order perceptions are the robot perceptions of its own inner world. The resulting architecture based on higher order perceptions has been implemented and tested in a project regarding a robotic touristic guide acting in the Botanical Garden of the University of Palermo.
Higher-order theories from the minimal length
NASA Astrophysics Data System (ADS)
Dias, M.; Hoff da Silva, J. M.; Scatena, E.
2016-06-01
We show that the introduction of a minimal length in the context of noncommutative space-time gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a generalization of the standard electromagnetism and general relativity by applying a consistent procedure that modifies the original Maxwell and Einstein-Hilbert actions. In order to set a bound on the minimal length, we compare the deviations from the inverse-square law with the potentials obtained in the higher-order theories and discuss the validity of the results. The introduction of a quantum bound for the minimal length parameter β in the higher-order QED allows us to lower the actual limits on the parameters of higher-derivative gravity by almost half of their order of magnitude.
Higher order factors of personality: do they exist?
Ashton, Michael C; Lee, Kibeom; Goldberg, Lewis R; de Vries, Reinout E
2009-05-01
Scales that measure the Big Five personality factors are often substantially intercorrelated. These correlations are sometimes interpreted as implying the existence of two higher order factors of personality. The authors show that correlations between measures of broad personality factors do not necessarily imply the existence of higher order factors and might instead be due to variables that represent same-signed blends of orthogonal factors. Therefore, the hypotheses of higher order factors and blended variables can only be tested with data on lower level personality variables that define the personality factors. The authors compared the higher order factor model and the blended variable model in three participant samples using the Big Five Aspect Scales, and found better fit for the latter model. In other analyses using the HEXACO Personality Inventory, they identified mutually uncorrelated markers of six personality factors. The authors conclude that correlations between personality factor scales can be explained without postulating any higher order dimensions of personality.
Higher-order mode photonic crystal based nanofluidic sensor
NASA Astrophysics Data System (ADS)
Peng, Wang; Chen, Youping; Ai, Wu
2017-01-01
A higher-order photonic crystal (PC) based nanofluidic sensor, which worked at 532 nm, was designed and demonstrated. A systematical and detailed method for sculpturing a PC sensor for a given peak wavelength value (PWV) and specified materials was illuminated. It was the first time that the higher order mode was used to design PC based nanofluidic sensor, and the refractive index (RI) sensitivity of this sensor had been verified with FDTD simulation software from Lumerical. The enhanced electrical field of higher order mode structure was mostly confined in the channel area, where the enhance field is wholly interacting with the analytes in the channels. The comparison of RI sensitivity between fundamental mode and higher order mode shows the RI variation of higher order mode is 124.5 nm/RIU which is much larger than the fundamental mode. The proposed PC based nanofluidic structure pioneering a novel style for future optofluidic design.
Symplectic structures related with higher order variational problems
NASA Astrophysics Data System (ADS)
Kijowski, Jerzy; Moreno, Giovanni
2015-06-01
In this paper, we derive the symplectic framework for field theories defined by higher order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher order system of partial differential equations to a constrained first-order one, the symplectic structures naturally arising in the dynamics of a first-order Lagrangian theory, and the importance of the Poincaré-Cartan form for variational problems, are all well-established facts. However, their adequate combination corresponding to higher order theories is missing in the literature. Here we obtain a consistent and truly finite-dimensional canonical formalism, as well as a higher order version of the Poincaré-Cartan form. In our exposition, the rigorous global proofs of the main results are always accompanied by their local coordinate descriptions, indispensable to work out practical examples.
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
Higher-Order Modes in Free Electron Lasers
2005-09-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Higher -Order Modes in Free Electron Lasers by B. W. Williams September 2005 Thesis Advisor: W...AGENCY USE ONLY (Leave blank) 2. REPORT DATE September 2005 3. REPORT TYPE AND DATES COVERED Master’s Thesis 4. TITLE AND SUBTITLE: Higher ...for the fundamental Gaussian mode, and higher -order modes in Cartesian and cylindrical coordinate spaces, yielding expressions for the complete and
Gravitational-wave tail effects to quartic non-linear order
NASA Astrophysics Data System (ADS)
Marchand, Tanguy; Blanchet, Luc; Faye, Guillaume
2016-12-01
Gravitational-wave tails are due to the backscattering of linear waves onto the space-time curvature generated by the total mass of the matter source. The dominant tails correspond to quadratic non-linear interactions and arise at the one-and-a-half post-Newtonian (1.5 PN) order in the gravitational waveform. The ‘tails-of-tails’, which are cubic non-linear effects appearing at the 3 PN order in the waveform, are also known. We derive here higher non-linear tail effects, namely those associated with quartic non-linear interactions or ‘tails-of-tails-of-tails’, which are shown to arise at the 4.5 PN order. As an application, we obtain at that order the complete coefficient in the total gravitational-wave energy flux of compact binary systems moving on circular orbits. Our result perfectly agrees with black-hole perturbation calculations in the limit of extreme mass ratio of the two compact objects.
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.
Second-order nonlinear optical effects of spin currents.
Wang, Jing; Zhu, Bang-Fen; Liu, Ren-Bao
2010-06-25
Pure spin currents carry information in spintronics and signify novel quantum spin phenomena such as topological insulators. Measuring pure spin currents, however, is difficult since they have no direct electromagnetic induction. Noticing that a longitudinal spin current, in which electrons move along their spin directions, is a chiral quantity, we envisage that it has a chiral sum-frequency optical effect. A systematic symmetry analysis confirms this idea and reveals the second-order optical effects of general spin currents with unique polarization dependence. Microscopic calculations based on the eight-band model of III-V compound semiconductors show that the susceptibility is sizable under realistic conditions. These findings form a basis for "seeing" spin currents where and while they flow with standard nonlinear optical spectroscopy, providing a toolbox to explore a wealth of physics connecting spins and photons.
Higher-order intersections in low-dimensional topology
Conant, Jim; Schneiderman, Rob; Teichner, Peter
2011-01-01
We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato–Levine, and Arf invariants. We also define higher-order Sato–Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described. PMID:21518909
Systematic Optimization of Second Order Nonlinear Optical Materials
1994-06-14
nonlinear optical materials and 2) to develop advanced electrooptic and photonic materials for enhanced...Nonlinear Optics, Val Thorens, (France), January 9-13, 1994. 7. Marder. S.R." A Chemists View of the Science and Technology of Organic Nonlinear Optical Materials ." Presented...DC, August 22-26, 1994. (Invited Lecture). 5. Marder. S. R." Nonlinear Optical Materials Design Criteria" To be presented at American Chemical
John, Fritz
1976-01-01
Strict solutions u of genuinely nonlinear homogeneous hyperbolic equations in two independent variables with initial data f(x) of compact support become singular after a time interval of order ∥f∥-1. In higher dimensions solutions initially of compact support are likely to have life expectancies of orders ∥f∥-2+ε at least. This is proved for the special case of solutions u(x1,..., xn, t) of a second order equation utt = Σi,jaijuxixj, where n ≥ 3 and where the coefficients aij are C∞-functions in the first derivatives of u, forming a symmetric positive definite matrix. PMID:16578737
Observation of Third-order Nonlinearities in Graphene Oxide Film at Telecommunication Wavelengths.
Xu, Xiaochuan; Zheng, Xiaorui; He, Feng; Wang, Zheng; Subbaraman, Harish; Wang, Yaguo; Jia, Baohua; Chen, Ray T
2017-08-29
All-optical switches have been considered as a promising solution to overcome the fundamental speed limit of the current electronic switches. However, the lack of a suitable third-order nonlinear material greatly hinders the development of this technology. Here we report the observation of ultrahigh third-order nonlinearity about 0.45 cm(2)/GW in graphene oxide thin films at the telecommunication wavelength region, which is four orders of magnitude higher than that of single crystalline silicon. Besides, graphene oxide is water soluble and thus easy to process due to the existence of oxygen containing groups. These unique properties can potentially significantly advance the performance of all-optical switches.
NASA Astrophysics Data System (ADS)
Almeida, Juliana M. P.; da Silva, Diego S.; Kassab, Luciana R. P.; Zilio, Sergio C.; Mendonça, Cleber R.; De Boni, Leonardo
2014-02-01
This work reports on the third-order nonlinear properties and the response time of GeO2-Bi2O3 glass, as well as the effect of gold nanoparticles on these properties. The nonlinear refractive index spectrum and the nonlinear absorption coefficient were determined by the Z-scan technique, and the response time was obtained through Kerr gate measurements, using femtosecond pulses. The results show that the presence of gold nanoparticles causes a saturable absorption effect that is overcome by the two-photon absorption process at higher light intensities, for wavelengths within the plasmon band. We measured a constant value for the nonlinear refractive index (n2) for the visible and infrared regions, which was not affected by the presence of gold nanoparticles in the sample. However, the n2 value is one order of magnitude higher than the one for fused silica and 1.5 times better than PGO (PbO-GeO2) glasses. In addition, the response time of the induced birefringence for the samples with and without gold nanoparticles is faster than the pulse duration (220 fs), indicating an ultra-fast electronic process.
NASA Astrophysics Data System (ADS)
Li, Jinsha; Li, Junmin
2016-07-01
In this paper, the adaptive fuzzy iterative learning control scheme is proposed for coordination problems of Mth order (M ≥ 2) distributed multi-agent systems. Every follower agent has a higher order integrator with unknown nonlinear dynamics and input disturbance. The dynamics of the leader are a higher order nonlinear systems and only available to a portion of the follower agents. With distributed initial state learning, the unified distributed protocols combined time-domain and iteration-domain adaptive laws guarantee that the follower agents track the leader uniformly on [0, T]. Then, the proposed algorithm extends to achieve the formation control. A numerical example and a multiple robotic system are provided to demonstrate the performance of the proposed approach.
On the Higher Power Sums of Reciprocal Higher-Order Sequences
Zhang, Jin
2014-01-01
Let {un} be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher-order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums. PMID:24741351
Intermodal Čerenkov radiation in a higher-order-mode fiber.
Cheng, Ji; Pedersen, Martin E V; Charan, Kriti; Wang, Ke; Xu, Chris; Grüner-Nielsen, Lars; Jakobsen, Dan
2012-11-01
We demonstrate an intermodal Čerenkov radiation effect in a higher-order-mode (HOM) fiber with a mode crossing (i.e., two guided modes having the same propagation constant at the same wavelength). A frequency-shifted soliton in the vicinity of the mode-crossing wavelength emits a phase-matched dispersive wave in a different propagation mode. We develop a theoretical explanation for this nonlinear optical effect and demonstrate that the mode crossing in HOM fibers can be utilized to achieve simultaneous wavelength and mode conversion; the strength of this intermodal nonlinear interaction can be tuned by controlled fiber bending.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Higher Order Lagrange Finite Elements In M3D
J. Chen; H.R. Strauss; S.C. Jardin; W. Park; L.E. Sugiyama; G. Fu; J. Breslau
2004-12-17
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Determination of higher order accelerations by a functional method
NASA Astrophysics Data System (ADS)
Tudosie, C.
A functional method is developed for the simultaneous determination of all the linear accelerations which exist in the differential equation of a material system dynamics. The method introduces variable angular accelerations of different orders, called direct connection functions, which allow the passing from a linear acceleration of a certain order to that of a higher order. Feedback functions are also introduced which allow the passing from a linear acceleration of a certain order to that of lower orders. This method is applicable to accelerations which occur when passenger trains move rapidly around a curve and at the vertical vibrations of trucks and tractors.
A Model for the National Assessment of Higher Order Thinking.
ERIC Educational Resources Information Center
Paul, Richard; Nosich, Gerald M.
This document provides a model for the national assessment of higher order thinking and consists of a preface and four main sections. The preface discusses the problem of lower order learning, summarizes the state of research into critical thinking and instructional reform, and explains the structure of the paper. Section 1 of the paper describes…
Higher order relativistic galaxy number counts: dominating terms
NASA Astrophysics Data System (ADS)
TrØst Nielsen, Jeppe; Durrer, Ruth
2017-03-01
We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our derivation to higher order terms, especially the third order number counts which are needed to compute the 1-loop contribution to the power spectrum.
Nonlinear pulsations of a Hamiltonian system of the fourth order by a nonlinear trigonometric series
NASA Astrophysics Data System (ADS)
Miroshnikov, George
2011-11-01
Dynamics of Hamiltonian systems is the key issue of solitary waves since the initial-value problems on free surfaces and interfaces are reduced to Hamiltonian problems in the reference frame moving with the wave. The Hamiltonian approach covers applications at high Reynolds numbers, which range from the famous irrotational Boussinesq-Rayleigh solitary wave to the rotational waves with a uniform vorticity. The Hamiltonian system with a polynomial potential of the fourth order is studied in the asymmetric case of subcritical periodic pulsations by using a nonlinear trigonometric series in even powers of cosine. The series solutions are computed symbolically and compared with the numerical solution using the Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant. It is shown that the series solutions with uniform convergence are superior to the numeric solutions with local convergence. The qualitative comparison of the theoretical solutions with the experimental profiles of the Geminga pulsar is also provided.
Z-scan: A simple technique for determination of third-order optical nonlinearity
Singh, Vijender; Aghamkar, Praveen
2015-08-28
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 be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.
NASA Astrophysics Data System (ADS)
Wang, Gang; Wang, Chaoli; Du, Qinghui; Cai, Xuan
2016-10-01
In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.
Third-order optical nonlinearity studies of bilayer Au/Ag metallic films
NASA Astrophysics Data System (ADS)
Mezher, M. H.; Chong, W. Y.; Zakaria, R.
2016-05-01
This paper presents nonlinear optical studies of bilayer metallic films of gold (Au) and silver (Ag) on glass substrate prepared using electron beam evaporation. The preparation of Au and Ag nanoparticles (NPs) on the substrate involved the use of electron beam deposition, then thermal annealing at 600 °C and 270 °C, respectively, to produce a randomly distributed layer of Au and a layer of Ag NPs. Observation of field-effect scanning electron microscope images indicated the size of the NPs. Details of the optical properties related to peak absorption of surface plasmon resonance of the nanoparticle were revealed by use of UV-Vis spectroscopy. The Z-scan technique was used to measure the nonlinear absorption and nonlinear refraction of the fabricated NP layers. The third-order nonlinear refractive index coefficients for Au and Ag are (-9.34 and -1.61) × 10-11 cm2 W-1 given lower n 2, in comparison with bilayer (Au and Ag) NPs at -1.24 × 10-10 cm2 W-1. The results show bilayer NPs have higher refractive index coefficients thus enhance the nonlinearity effects.
Higher-order figure discrimination in fly and human vision.
Aptekar, Jacob W; Frye, Mark A
2013-08-19
Visually-guided animals rely on their ability to stabilize the panorama and simultaneously track salient objects, or figures, that are distinct from the background in order to avoid predators, pursue food resources and mates, and navigate spatially. Visual figures are distinguished by luminance signals that produce coherent motion cues as well as more enigmatic 'higher-order' statistical features. Figure discrimination is thus a complex form of motion vision requiring specialized neural processing. In this minireview, we will highlight recent advances in understanding the perceptual, behavioral, and neurophysiological basis of higher-order figure detection in flies, much of which is grounded in the historical perspective and mechanistic underpinnings of human psychophysics.
Unified formalism for higher order non-autonomous dynamical systems
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2012-03-01
This work is devoted to giving a geometric framework for describing higher order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.
Chaos in the fractional order nonlinear Bloch equation with delay
NASA Astrophysics Data System (ADS)
Baleanu, Dumitru; Magin, Richard L.; Bhalekar, Sachin; Daftardar-Gejji, Varsha
2015-08-01
The Bloch equation describes the dynamics of nuclear magnetization in the presence of static and time-varying magnetic fields. In this paper we extend a nonlinear model of the Bloch equation to include both fractional derivatives and time delays. The Caputo fractional time derivative (α) in the range from 0.85 to 1.00 is introduced on the left side of the Bloch equation in a commensurate manner in increments of 0.01 to provide an adjustable degree of system memory. Time delays for the z component of magnetization are inserted on the right side of the Bloch equation with values of 0, 10 and 100 ms to balance the fractional derivative with delay terms that also express the history of an earlier state. In the absence of delay, τ = 0 , we obtained results consistent with the previously published bifurcation diagram, with two cycles appearing at α = 0.8548 with subsequent period doubling that leads to chaos at α = 0.9436 . A periodic window is observed for the range 0.962 < α < 0.9858 , with chaos arising again as α nears 1.00. The bifurcation diagram for the case with a 10 ms delay is similar: two cycles appear at the value α = 0.8532 , and the transition from two to four cycles at α = 0.9259 . With further increases in the fractional order, period doubling continues until at α = 0.9449 chaos ensues. In the case of a 100 millisecond delay the transitions from one cycle to two cycles and two cycles to four cycles are observed at α = 0.8441 , and α = 0.8635 , respectively. However, the system exhibits chaos at much lower values of α (α = 0.8635). A periodic window is observed in the interval 0.897 < α < 0.9341 , with chaos again appearing for larger values of α . In general, as the value of α decreased the system showed transitions from chaos to transient chaos, and then to stability. Delays naturally appear in many NMR systems, and pulse programming allows the user control over the process. By including both the fractional derivative and time delays in
Tensor Spectral Clustering for Partitioning Higher-order Network Structures.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2015-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Benson, Austin R.; Gleich, David F.; Leskovec, Jure
2016-01-01
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms. PMID:27812399
Higher order annular Gaussian laser beam propagation in free space
NASA Astrophysics Data System (ADS)
Eyyuboglu, Halil T.; Yenice, Yusuf E.; Baykal, Yahya K.
2006-03-01
Propagation of higher order annular Gaussian (HOAG) laser beams in free space is examined. HOAG beams are defined as the difference of two Hermite-Gaussian (HG) beams; thus, they can be produced by subtracting a smaller beam from a larger beam, that are cocentered and both possess HG mode field distributions. Such beams can be considered as a generalization of the well-known annular Gaussian beams. We formulate the source and receiver plane characteristics and kurtosis parameter of HOAG beams propagating in free space and evaluate them numerically. In comparison to HG beams, HOAG beams have a broader beam size with outer lobes of kidney shape. The amount of received power within the same receiver aperture size, that is, power in bucket, is generally lower for higher order beams. The convergence of the kurtosis parameter to an asymptotic value for higher order beams takes much longer propagation distances compared to zero-order beams.
Modeling Higher-Order Correlations within Cortical Microcolumns
Köster, Urs; Sohl-Dickstein, Jascha; Gray, Charles M.; Olshausen, Bruno A.
2014-01-01
We statistically characterize the population spiking activity obtained from simultaneous recordings of neurons across all layers of a cortical microcolumn. Three types of models are compared: an Ising model which captures pairwise correlations between units, a Restricted Boltzmann Machine (RBM) which allows for modeling of higher-order correlations, and a semi-Restricted Boltzmann Machine which is a combination of Ising and RBM models. Model parameters were estimated in a fast and efficient manner using minimum probability flow, and log likelihoods were compared using annealed importance sampling. The higher-order models reveal localized activity patterns which reflect the laminar organization of neurons within a cortical column. The higher-order models also outperformed the Ising model in log-likelihood: On populations of 20 cells, the RBM had 10% higher log-likelihood (relative to an independent model) than a pairwise model, increasing to 45% gain in a larger network with 100 spatiotemporal elements, consisting of 10 neurons over 10 time steps. We further removed the need to model stimulus-induced correlations by incorporating a peri-stimulus time histogram term, in which case the higher order models continued to perform best. These results demonstrate the importance of higher-order interactions to describe the structure of correlated activity in cortical networks. Boltzmann Machines with hidden units provide a succinct and effective way to capture these dependencies without increasing the difficulty of model estimation and evaluation. PMID:24991969
Modeling higher-order correlations within cortical microcolumns.
Köster, Urs; Sohl-Dickstein, Jascha; Gray, Charles M; Olshausen, Bruno A
2014-07-01
We statistically characterize the population spiking activity obtained from simultaneous recordings of neurons across all layers of a cortical microcolumn. Three types of models are compared: an Ising model which captures pairwise correlations between units, a Restricted Boltzmann Machine (RBM) which allows for modeling of higher-order correlations, and a semi-Restricted Boltzmann Machine which is a combination of Ising and RBM models. Model parameters were estimated in a fast and efficient manner using minimum probability flow, and log likelihoods were compared using annealed importance sampling. The higher-order models reveal localized activity patterns which reflect the laminar organization of neurons within a cortical column. The higher-order models also outperformed the Ising model in log-likelihood: On populations of 20 cells, the RBM had 10% higher log-likelihood (relative to an independent model) than a pairwise model, increasing to 45% gain in a larger network with 100 spatiotemporal elements, consisting of 10 neurons over 10 time steps. We further removed the need to model stimulus-induced correlations by incorporating a peri-stimulus time histogram term, in which case the higher order models continued to perform best. These results demonstrate the importance of higher-order interactions to describe the structure of correlated activity in cortical networks. Boltzmann Machines with hidden units provide a succinct and effective way to capture these dependencies without increasing the difficulty of model estimation and evaluation.
Higher order language competence and adolescent mental health.
Cohen, Nancy J; Farnia, Fataneh; Im-Bolter, Nancie
2013-07-01
Clinic and community-based epidemiological studies have shown an association between child psychopathology and language impairment. The demands on language for social and academic adjustment shift dramatically during adolescence and the ability to understand the nonliteral meaning in language represented by higher order language becomes essential. : This article reports on the association between difficulties in higher order language skills, reading, cognition, and social-emotional adjustment in adolescents. : 144 clinic-referred and 186 comparison youth aged 12-18 years were administered a battery of standardized tests of intelligence, working memory, structural and higher order language, and reading achievement. Parent ratings on the Child Behavior Checklist were used as a measure of severity of social-emotional problems. : Clinic-referred youth scored significantly lower than comparison youth on measures of structural and higher order language, working memory, and reading. Of the clinic-referred youth, 45% had some type of higher order language impairment, whereas this was the case for 15% of youth in the comparison group. Lower levels of nonverbal ability and working memory as well as lower level of mothers' education were associated with greater risk of having higher order language impairment. : Findings have implications for practitioners' seeking to understand and treat adolescents since therapeutic techniques rely on skills where higher order language is at play including the ability to discuss opinions flexibly and to weigh interpretations. Therapists must be aware that there are areas that have potential for miscommunication with some adolescents and where inaccurate inferences may be made about their behavior. Furthermore, educators must consider resources for youth who may increasingly struggle in high school because of such difficulties. © 2013 The Authors. Journal of Child Psychology and Psychiatry © 2013 Association for Child and
NASA Astrophysics Data System (ADS)
Gill, Tarsem Singh; Kaur, Ravinder; Mahajan, Ranju
2010-09-01
This paper presents an analysis of self-consistent, steady-state, theoretical model, which explains the ring formation in a Gaussian electromagnetic beam propagating in a magnetoplasma, characterized by relativistic nonlinearity. Higher order terms (up to r4) in the expansion of the dielectric function and the eikonal have been taken into account. The condition for the formation of a dark and bright ring derived earlier by Misra and Mishra [J. Plasma Phys. 75, 769 (2009)] has been used to study focusing/defocusing of the beam. It is seen that inclusion of higher order terms does significantly affect the dependence of the beam width on the distance of propagation. Further, the effect of the magnetic field and the nature of nonlinearity on the ring formation and self-focusing of the beam have been explored.
Nonlinear high-order mode locking in stochastic sensory neurons
NASA Astrophysics Data System (ADS)
Rowe, Michael; Afghan, Muhammad; Neiman, Alexander
2004-03-01
Excitable systems demonstrate various mode locking regimes when driven by periodic external signals. With noise taken into account, such regimes represent complex nonlinear responses which depend crucially on the frequency and amplitude of the periodic drive as well as on the noise intensity. We study this using a computational model of a stochastic Hodgkin-Huxley neuron in combination with the turtle vestibular sensory system as an experimental model. A bifurcation analysis of the model is performed. Extracellular recordings from primary vestibular afferent neurons with two types of stimuli are used in the experimental study. First, mechanical stimuli applied to the labyrinth allow us to study the responses of the entire system, including transduction by the hair cells and spike generation in the primary afferents. Second, a galvanic stimuli applied directly to an afferent are used to study the responses of afferent spike generator directly. The responses to galvanic stimuli reveal multiple high-order mode locking regimes which are well reproduced in numerical simulation. Responses to mechanical stimulation are characterized by larger variability so that fewer mode-locking regimes can be observed.
Higher-dimensional catastrophes in nonlinear Compton scattering
NASA Astrophysics Data System (ADS)
Kharin, Vasily; Seipt, Daniel; Rykovanov, Sergey
2016-10-01
The Compton scattering of the light on the accelerated electron beam is a valuable tool for generating tunable wide range X- and γ-radiation.However, the cross-section of the scattering is relatively low. That is, in order to obtain bright X-rays one naturally may consider increasing the intensity of the incident light. Passing to relativistic values of laser intensity significantly changes scattering mechanism. Precise QED analysis of the scattered spectra leads to the study of the corresponding elements of S-matrix. Evaluation is usually performed numerically (except cases of specific pulse shapes and scattering angles). We argue that the problem of extracting the scattered spectra in nonlinear Compton scattering of the pulse can be reformulated in terms of studying properties of projection map of specific surfaces associated to the pulse. They are stable with respect to initial conditions, and the brightest regions of the spectrum appear to be in correspondence with the singularities of the projection map, also known as caustics in pure mathematics, diffraction optics and cosmology. Work was supported by the Helmholtz Association (Helmholtz Young Investigators group VH-NG-1037).
Higher-Order Factors of Personality: Do They Exist?
Ashton, Michael C.; Lee, Kibeom; Goldberg, Lewis R.; de Vries, Reinout E.
2010-01-01
Scales that measure the Big Five personality factors are often substantially intercorrelated. These correlations are sometimes interpreted as implying the existence of two higher-order factors of personality. We show that correlations between measures of broad personality factors do not necessarily imply the existence of higher-order factors, and might instead be due to variables that represent same-signed blends of orthogonal factors. Therefore, the hypotheses of higher-order factors and blended variables can only be tested with data on lower-level personality variables that define the personality factors. We compared the higher-order factor model and the blended variable model in three participant samples using the Big Five Aspect Scales, and found better fit for the latter model. In other analyses using the HEXACO Personality Inventory, we identified mutually uncorrelated markers of six personality factors. We conclude that correlations between personality factor scales can be explained without postulating any higher-order dimensions of personality. PMID:19458345
Conical emission from laser filaments and higher-order Kerr effect in air.
Béjot, P; Kasparian, J
2011-12-15
We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the nonlinear focus and of the modulational instability over the whole filament length.
Existence of solutions of higher order Sturm-Liouville boundary value problems
NASA Astrophysics Data System (ADS)
Wong, Patricia J. Y.
2017-07-01
We consider a higher order Sturm-Liouville boundary value problem (BVP) where the nonlinear term involves derivatives - such cases are seldom investigated in the literature due to the complexity introduced by the derivatives. A new technique is used to obtain existence criteria for at least one positive solution of the BVP. We demonstrate the usefulness of the results obtained by an example with known positive solutions.
Nonlinear response theory for Markov processes. II. Fifth-order response functions
NASA Astrophysics Data System (ADS)
Diezemann, Gregor
2017-08-01
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012), 10.1103/PhysRevE.85.051502]. For sinusoidal fields the 5 ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.
Higher-order discrete variational problems with constraints
NASA Astrophysics Data System (ADS)
Colombo, Leonardo; Martín de Diego, David; Zuccalli, Marcela
2013-09-01
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this paper, we derive new variational integrators for higher-order Lagrangian mechanical system subjected to higher-order constraints. From the discretization of the variational principles, we show that our methods are automatically symplectic and, in consequence, with a very good energy behavior. Additionally, the symmetries of the discrete Lagrangian imply that momentum is conserved by the integrator. Moreover, we extend our construction to variational integrators where the Lagrangian is explicitly time-dependent. Finally, some motivating applications of higher-order problems are considered; in particular, optimal control problems for explicitly time-dependent underactuated systems and an interpolation problem on Riemannian manifolds.
New, higher-order, elasticity-based micromechanics model
Williams, T. O.
2003-01-01
The formulation for a new homogenization theory is presented. The theory utilizes a higher-order, elasticity-based cell analysis of a periodic array of unit cells. The unit cell is discretized into subregions or subcells. The displacement field within each subcell is approximated by an (truncated) eigenfunction function expansion of up to fifth order. The governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields. The specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in a subcell. The fifth order theory is subsequently reduced to a third order theory. The appropriate reduction of the fifth and third order theories to the first order theory (which corresponds to a variant of the original method of cells (MOC) (Aboudi, 1991) theory) is outlined. The 3D ECM theory correctly reduces to the 2D ECM theory microstructures and the exact 1D theory for bilaminated structures. Comparison of the predicted bulk and local responses with published results indicates that the theory accurately predicts both types of responses. Furthermore, it is shown that the higher order fields introduced coupling effects between the local fields that can result in substantial changes in the predicted bulk inelastic response of a composite.
Stable static structures in models with higher-order derivatives
Bazeia, D.; Lobão, A.S.; Menezes, R.
2015-09-15
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that the zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.
Higher order matrix differential equations with singular coefficient matrices
Fragkoulis, V. C.; Kougioumtzoglou, I. A.; Pantelous, A. A.; Pirrotta, A.
2015-03-10
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
Improvements to local projective noise reduction through higher order and multiscale refinements.
Moore, Jack Murdoch; Small, Michael; Karrech, Ali
2015-06-01
The broad spectrum characteristic of signals from nonlinear systems obstructs noise reduction techniques developed for linear systems. Local projection was developed to reduce noise while preserving nonlinear deterministic structures, and a second order refinement to local projection which was proposed ten years ago does so particularly effectively. It involves adjusting the origin of the projection subspace to better accommodate the geometry of the attractor. This paper describes an analytic motivation for the enhancement from which follows further higher order and multiple scale refinements. However, the established enhancement is frequently as or more effective than the new filters arising from solely geometric considerations. Investigation of the way that measurement errors reinforce or cancel throughout the refined local projection procedure explains the special efficacy of the existing enhancement, and leads to a new second order refinement offering widespread gains. Different local projective filters are found to be best suited to different noise levels. At low noise levels, the optimal order increases as noise increases. At intermediate levels second order tends to be optimal, while at high noise levels prototypical local projection is most effective. The new higher order filters perform better relative to established filters for longer signals or signals corresponding to higher dimensional attractors.
Improvements to local projective noise reduction through higher order and multiscale refinements
NASA Astrophysics Data System (ADS)
Moore, Jack Murdoch; Small, Michael; Karrech, Ali
2015-06-01
The broad spectrum characteristic of signals from nonlinear systems obstructs noise reduction techniques developed for linear systems. Local projection was developed to reduce noise while preserving nonlinear deterministic structures, and a second order refinement to local projection which was proposed ten years ago does so particularly effectively. It involves adjusting the origin of the projection subspace to better accommodate the geometry of the attractor. This paper describes an analytic motivation for the enhancement from which follows further higher order and multiple scale refinements. However, the established enhancement is frequently as or more effective than the new filters arising from solely geometric considerations. Investigation of the way that measurement errors reinforce or cancel throughout the refined local projection procedure explains the special efficacy of the existing enhancement, and leads to a new second order refinement offering widespread gains. Different local projective filters are found to be best suited to different noise levels. At low noise levels, the optimal order increases as noise increases. At intermediate levels second order tends to be optimal, while at high noise levels prototypical local projection is most effective. The new higher order filters perform better relative to established filters for longer signals or signals corresponding to higher dimensional attractors.
Higher Order Mode Coupler Heating in Continuous Wave Operation
NASA Astrophysics Data System (ADS)
Solyak, N.; Awida, M.; Hocker, A.; Khabibobulline, T.; Lunin, A.
Electromagnetic heating due to higher order modes (HOM) propagation is particularly a concern for continuous wave (CW) particle accelerator machines. Power on the order of several watts could flow out of the cavity's HOM ports in CW operations. The upgrade of the Linac Coherent Light Source (LCLS-II) at SLAC requires a major modification of the design of the higher order mode (HOM) antenna and feed through of the conventional ILC elliptical 9-cell cavity in order to utilize it for LCLS-II. The HOM antenna is required to bear higher RF losses, while relatively maintaining the coupling level of the higher order modes. In this paper, we present a detailed analysis of the heating expected in the HOM coupler with a thorough thermal quench study in comparison with the conventional ILC design. We discuss also how the heat will be removed from the cavity through RF cables with specially designed cooling straps. Finally, we report on the latest experimental results of cavity testing in vertical and horizontal cryostats.
Detection of small target using recursive higher order statistics
NASA Astrophysics Data System (ADS)
Hou, Wang; Sun, Hongyuan; Lei, Zhihui
2014-02-01
In this paper, a recursive higher order statistics algorithm is proposed for small target detection in temporal domain. Firstly, the background of image sequence is normalized. Then, the higher order statistics are recursively solved in image sequence to obtain the feature image. Finally, the feature image is segmented with threshold to detect the small target. To validate the algorithm proposed in this paper, five simulated and one semi-simulation image sequences are created. The ROC curves are employed for evaluation of experimental results. Experiment results show that our method is very effective for small target detection.
Higher-Order Airy Scaling in Deformed Dyck Paths
NASA Astrophysics Data System (ADS)
Haug, Nils; Olde Daalhuis, Adri; Prellberg, Thomas
2017-03-01
We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, `jumps' orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their half-length, area and number of jumps. This represents the first example of an exactly solvable two-dimensional lattice vesicle model showing a higher-order multicritical point. Applying the generalized method of steepest descents, we see that the associated two-variable scaling function is given by the logarithmic derivative of a generalized (higher-order) Airy integral.
Vakonomic Constraints in Higher-Order Classical Field Theory
NASA Astrophysics Data System (ADS)
Campos, Cédric M.
2010-07-01
We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.
Higher-order dynamical effects in Coulomb dissociation
Esbensen, H.; Bertsch, G.F.; Bertulani, C.A.
1995-08-01
Coulomb dissociation is a technique commonly used to extract the dipole response of nuclei far from stability. This technique is applicable if the dissociation is dominated by dipole transitions and if first-order perturbation theory is valid. In order to assess the significance of higher-order processes we solve numerically the time evolution of the wave function for a two-body breakup in the Coulomb field from a high Z target. We applied this method to the breakup reactions: {sup 11}Be {yields} {sup 10}Be + n and {sup 11}Li {yields} +2n. The latter is treated as a two-body breakup, using a di-neutron model.
Prominent Higher-Order Contributions to Electronic Recombination
Beilmann, C.; Mokler, P. H.; Bernitt, S.; Keitel, C. H.; Ullrich, J.; Lopez-Urrutia, J. R. Crespo; Harman, Z.
2011-09-30
Intershell higher-order (HO) electronic recombination is reported for highly charged Ar, Fe, and Kr ions, where simultaneous excitation of one K-shell electron and one or two additional L-shell electrons occurs upon resonant capture of a free electron. For the mid-Z region, HO resonance strengths grow unexpectedly strong with decreasing atomic number Z ({proportional_to}Z{sup -4}), such that, for Ar ions the 2nd-order overwhelms the 1st-order resonant recombination considerably. The experimental findings are confirmed by multiconfiguration Dirac-Fock calculations including hitherto neglected excitation pathways.
Study of thermally induced higher order microcantilever modes
NASA Astrophysics Data System (ADS)
Kadam, Ashwini
Microcantilevers have been widely studied for sensing tiny quantities of chemical and biological analytes in both vapor and liquid media. They have been shown to respond to changes in chemical, biological, thermal and physical processes. The primary sensing mechanisms are static bending due to induced differential surface stress and changes in the fundamental resonant frequency upon mass uptake. Although the possibility of using thermally induced higher order modes has been suggested for sensing and for understanding the mechanical behavior of microcantilevers, experimental demonstrations have not been given in the literature. Studies of thermally induced spectra provide an alternate in-situ detection technique for microcantilever sensing that is attractive in that no external excitation mechanism is required. However, thermally induced higher order modes have smaller amplitudes than what is obtained with external excitation. This dissertation examines the use of thermally induced higher order microcantilever modes both for sensing and studying adsorption induced interfacial changes between the Au coated microcantilever surface and Hg. The use of a thermally induced spectrum takes advantage of the fact that no additional external components are necessary to study them when using the optical lever (AFM style) detection technique. A process to microfabricate rectangular microcantilever is optimized and demonstrated. Thermally induced higher order flexural modes are demonstrated for Hg sensing with Au coated microcantilevers. Furthermore Hg sensing is carried out with microcantilevers having different Au coverage to investigate the use of thermally induced higher order modes for sensing. Two different types of Au surfaces are employed for Hg sensing with microcantilevers, one obtained by thermally evaporating Au, and the other by sputtering Au. Although the conventionally used deflection signal showed similar trend to Hg with both these films, exactly the opposite
Higher order multiple births: natural wonder or failure of therapy?
Grützner-Könnecke, H; Grützner, P; Grützner, B; Grützner, U; Spalding-Grützner, A; Spalding, P
1990-01-01
Data of 601 families with triplets and higher multiples have been collected. Since about nine years the number of higher-order births has been increasing enormously. The average pregnancy duration and the average birthweight of these mostly premature children have been declining from year to year. Despite the progress in neonatology, the death rate and the rate of handicapped children is very high. To prevent such disastrous outcomes, treatments for infertility should be performed only by physicians in centers with strong controls. Selective abortions are no regular solution to the problem of higher multiple gestation.
NASA Astrophysics Data System (ADS)
Panourgias, Konstantinos T.; Ekaterinaris, John A.
2016-12-01
The nonlinear filter introduced by Yee et al. (1999) [27] and extensively used in the development of low dissipative well-balanced high order accurate finite-difference schemes is adapted to the finite element context of discontinuous Galerkin (DG) discretizations. The filter operator is constructed in the canonical computational domain for the standard cubical element where it is applied to the computed conservative variables in a direction per direction basis. Filtering becomes possible for all element types in unstructured meshes using collapsed coordinate transformations. The performance of the proposed nonlinear filter for DG discretizations is demonstrated and evaluated for different orders of expansions for one-dimensional and multidimensional problems with exact solutions. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter is applied for a number of standard inviscid flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the total variation bounded (TVB) limiter and high-order hierarchical limiting. The proposed approach is suitable for p-adaptivity in order to locally enhance resolution of three-dimensional flow simulations that include discontinuities and complex flow features.
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.
Computer-Mediated Assessment of Higher-Order Thinking Development
ERIC Educational Resources Information Center
Tilchin, Oleg; Raiyn, Jamal
2015-01-01
Solving complicated problems in a contemporary knowledge-based society requires higher-order thinking (HOT). The most productive way to encourage development of HOT in students is through use of the Problem-based Learning (PBL) model. This model organizes learning by solving corresponding problems relative to study courses. Students are directed…
Using Higher Order Computer Tasks with Disadvantaged Students.
ERIC Educational Resources Information Center
Anderson, Neil
A pilot program initially designed for a 12-year-old girl with mild to moderate intellectual disabilities in higher order computer tasks was developed for a larger group of students with similar disabilities enrolled in fifth and sixth grades (ages 9-12) at three different schools. An examination of the original pilot study was undertaken to…
Higher order microfibre modes for dielectric particle trapping and propulsion
NASA Astrophysics Data System (ADS)
Maimaiti, Aili; Truong, Viet Giang; Sergides, Marios; Gusachenko, Ivan; Nic Chormaic, Síle
2015-03-01
Optical manipulation in the vicinity of optical micro- and nanofibres has shown potential across several fields in recent years, including microparticle control, and cold atom probing and trapping. To date, most work has focussed on the propagation of the fundamental mode through the fibre. However, along the maximum mode intensity axis, higher order modes have a longer evanescent field extension and larger field amplitude at the fibre waist compared to the fundamental mode, opening up new possibilities for optical manipulation and particle trapping. We demonstrate a microfibre/optical tweezers compact system for trapping and propelling dielectric particles based on the excitation of the first group of higher order modes at the fibre waist. Speed enhancement of polystyrene particle propulsion was observed for the higher order modes compared to the fundamental mode for particles ranging from 1 μm to 5 μm in diameter. The optical propelling velocity of a single, 3 μm polystyrene particle was found to be 8 times faster under the higher order mode than the fundamental mode field for a waist power of 25 mW. Experimental data are supported by theoretical calculations. This work can be extended to trapping and manipulation of laser-cooled atoms with potential for quantum networks.
Higher order microfibre modes for dielectric particle trapping and propulsion
Maimaiti, Aili; Truong, Viet Giang; Sergides, Marios; Gusachenko, Ivan; Nic Chormaic, Síle
2015-01-01
Optical manipulation in the vicinity of optical micro- and nanofibres has shown potential across several fields in recent years, including microparticle control, and cold atom probing and trapping. To date, most work has focussed on the propagation of the fundamental mode through the fibre. However, along the maximum mode intensity axis, higher order modes have a longer evanescent field extension and larger field amplitude at the fibre waist compared to the fundamental mode, opening up new possibilities for optical manipulation and particle trapping. We demonstrate a microfibre/optical tweezers compact system for trapping and propelling dielectric particles based on the excitation of the first group of higher order modes at the fibre waist. Speed enhancement of polystyrene particle propulsion was observed for the higher order modes compared to the fundamental mode for particles ranging from 1 μm to 5 μm in diameter. The optical propelling velocity of a single, 3 μm polystyrene particle was found to be 8 times faster under the higher order mode than the fundamental mode field for a waist power of 25 mW. Experimental data are supported by theoretical calculations. This work can be extended to trapping and manipulation of laser-cooled atoms with potential for quantum networks. PMID:25766925
Higher-order structure of rRNA
NASA Technical Reports Server (NTRS)
Gutell, R. R.; Woese, C. R.
1986-01-01
A comparative search for phylogenetically covarying basepair replacements within potential helices has been the only reliable method to determine the correct secondary structure of the 3 rRNAs, 5S, 16S, and 23S. The analysis of 16S from a wide phylogenetic spectrum, that includes various branches of the eubacteria, archaebacteria, eucaryotes, in addition to the mitochondria and chloroplast, is beginning to reveal the constraints on the secondary structures of these rRNAs. Based on the success of this analysis, and the assumption that higher order structure will also be phylogenetically conserved, a comparative search was initiated for positions that show co-variation not involved in secondary structure helices. From a list of potential higher order interactions within 16S rRNA, two higher-order interactions are presented. The first of these interactions involves positions 570 and 866. Based on the extent of phylogenetic covariation between these positions while maintaining Watson-Crick pairing, this higher-order interaction is considered proven. The other interaction involves a minimum of six positions between the 1400 and 1500 regions of the 16S rRNA. Although these patterns of covariation are not as striking as the 570/866 interaction, the fact that they all exist in an anti-parallel fashion and that experimental methods previously implicated these two regions of the molecule in tRNA function suggests that these interactions be given serious consideration.
Building Higher-Order Markov Chain Models with EXCEL
ERIC Educational Resources Information Center
Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K.
2004-01-01
Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…
Improving Reading Comprehension through Higher-Order Thinking Skills
ERIC Educational Resources Information Center
McKown, Brigitte A.; Barnett, Cynthia L.
2007-01-01
This action research project report documents the action research project that was conducted to improve reading comprehension with second grade and third grade students. The teacher researchers intended to improve reading comprehension by using higher-order thinking skills such as predicting, making connections, visualizing, inferring,…
Recent Advances in Higher-Order, Multimodal, Biomedical Imaging Agents.
Rieffel, James; Chitgupi, Upendra; Lovell, Jonathan F
2015-09-16
Advances in biomedical imaging have spurred the development of integrated multimodal scanners, usually capable of two simultaneous imaging modes. The long-term vision of higher-order multimodality is to improve diagnostics or guidance through the analysis of complementary, data-rich, co-registered images. Synergies achieved through combined modalities could enable researchers to better track diverse physiological and structural events, analyze biodistribution and treatment efficacy, and compare established and emerging modalities. Higher-order multimodal approaches stand to benefit from molecular imaging probes and, in recent years, contrast agents that have hypermodal characteristics have increasingly been reported in preclinical studies. Given the chemical requirements for contrast agents representing various modalities to be integrated into a single entity, the higher-order multimodal agents reported so far tend to be of nanoparticulate form. To date, the majority of reported nanoparticles have included components that are active for magnetic resonance. Herein, recent progress in higher-order multimodal imaging agents is reviewed, spanning a range of material and structural classes, and demonstrating utility in three (or more) imaging modalities.
An Analysis of Higher Order Thinking in Online Discussions
ERIC Educational Resources Information Center
McLoughlin, D.; Mynard, J.
2009-01-01
This paper describes a study of online discussion forums as tools for promoting higher-order thinking. The study was carried out in a women's university in the United Arab Emirates. Data, in the form of online discussion forum transcripts, were collected over a 20-week semester and were analysed according to a model developed by Garrison,…
Addition of higher order plate elements to NASTRAN
NASA Technical Reports Server (NTRS)
Narayanaswami, R.; Mei, C.
1976-01-01
Two plate elements, the linear strain triangular membrane element CTRIM6 and the higher order plate bending element CTRPLT1, were added to NASTRAN Level 16.0. The theoretical formulation, programming details, and bulk data information pertaining to the addition of these elements are discussed. Sample problems illustrating the use of these elements are presented.
Higher order Fano graphene metamaterials for nanoscale optical sensing.
Guo, Xiangdong; Hu, Hai; Zhu, Xing; Yang, Xiaoxia; Dai, Qing
2017-10-12
Plasmonic Fano metamaterials provide a unique platform for optical sensing applications due to their sharp spectral response and the ability to confine light to nanoscale regions that make them a strong prospect for refractive-index sensing. Higher order Fano resonance modes in noble metal plasmonic structures can further improve the sensitivity, but their applications are heavily limited by crosstalk between different modes due to the large damping rates and broadband spectral responses of the metal plasmon modes. Here, we create pure higher order Fano modes by designing asymmetric metamaterials comprised of a split-ring resonator and disk with a low-loss graphene plasmon. These higher order modes are highly sensitive to the nanoscale analyte (8 nm thick) both in refractive-index and in infrared vibrational fingerprint sensing, as demonstrated by the numerical calculation. The frequency sensitivity and figure-of-merit of the hexacontatetrapolar mode can reach 289 cm(-1) per RIU and 29, respectively, and it can probe the weak infrared vibrational modes of the analyte with more than 400 times enhancement. The enhanced sensitivity and tunability of higher order Fano graphene metamaterials promise a high-performance nanoscale optical sensor.
Enhancing Higher Order Thinking Skills through Clinical Simulation
ERIC Educational Resources Information Center
Varutharaju, Elengovan; Ratnavadivel, Nagendralingan
2014-01-01
Purpose: The study aimed to explore, describe and analyse the design and implementation of clinical simulation as a pedagogical tool in bridging the deficiency of higher order thinking skills among para-medical students, and to make recommendations on incorporating clinical simulation as a pedagogical tool to enhance thinking skills and align the…
Higher order microfibre modes for dielectric particle trapping and propulsion.
Maimaiti, Aili; Truong, Viet Giang; Sergides, Marios; Gusachenko, Ivan; Nic Chormaic, Síle
2015-03-13
Optical manipulation in the vicinity of optical micro- and nanofibres has shown potential across several fields in recent years, including microparticle control, and cold atom probing and trapping. To date, most work has focussed on the propagation of the fundamental mode through the fibre. However, along the maximum mode intensity axis, higher order modes have a longer evanescent field extension and larger field amplitude at the fibre waist compared to the fundamental mode, opening up new possibilities for optical manipulation and particle trapping. We demonstrate a microfibre/optical tweezers compact system for trapping and propelling dielectric particles based on the excitation of the first group of higher order modes at the fibre waist. Speed enhancement of polystyrene particle propulsion was observed for the higher order modes compared to the fundamental mode for particles ranging from 1 μm to 5 μm in diameter. The optical propelling velocity of a single, 3 μm polystyrene particle was found to be 8 times faster under the higher order mode than the fundamental mode field for a waist power of 25 mW. Experimental data are supported by theoretical calculations. This work can be extended to trapping and manipulation of laser-cooled atoms with potential for quantum networks.
[Higher order aberrations in physiological optical system--own experience].
Zelichowska, Beata; Rekas, Marek; Krix-Jachym, Karolina; Rubajczyk, Marcin
2007-01-01
To assess higher order aberrations in the physiological optical system in relation to pupil diameter and age of people studied. The study comprised 235 eyes of 122 subjects (67 women and 55 men) (mean age 43.8 +/- 15.5 years). Aberrations of the optical system were assessed using a LADARWave aberrometer (Alcon Laboratories). Aberration finding analysis included age, the pupil diameter, and their interrelations. ANOVA, Kruskal-Wallistest, multiple comparison and Ch2 tests were used to establish the statistical significance, and the correlation coefficient was calculated according to Spearman test. Basing on the studies performed, we found that the older subjects were the more statistically significant was the increase in the prevalence of higher order aberrations, including coma and spherical aberrations, at the same pupil diameter of 5-6.5 mm. When the relationship between aberrations and the pupil diameter was analyzed in a group of subjects aged 20-40 yrs, it turned out that the bigger the pupil diameter was the more statistically significant was the increase of higher order aberrations, including coma. While assessing the whole group studied we found a statistically significant reverse correlation between the pupil diameter and the subjects' age. Aberrations parameters between age groups 20-40, 40-60 and over 60 y. did not differ significantly. In the optical system an age-related increase of higher order aberrations is compensated by miosis, which reduces disadvantages of these aberrations and maintains the best optical quality of retinal image.
Higher-order structure of rRNA
NASA Technical Reports Server (NTRS)
Gutell, R. R.; Woese, C. R.
1986-01-01
A comparative search for phylogenetically covarying basepair replacements within potential helices has been the only reliable method to determine the correct secondary structure of the 3 rRNAs, 5S, 16S, and 23S. The analysis of 16S from a wide phylogenetic spectrum, that includes various branches of the eubacteria, archaebacteria, eucaryotes, in addition to the mitochondria and chloroplast, is beginning to reveal the constraints on the secondary structures of these rRNAs. Based on the success of this analysis, and the assumption that higher order structure will also be phylogenetically conserved, a comparative search was initiated for positions that show co-variation not involved in secondary structure helices. From a list of potential higher order interactions within 16S rRNA, two higher-order interactions are presented. The first of these interactions involves positions 570 and 866. Based on the extent of phylogenetic covariation between these positions while maintaining Watson-Crick pairing, this higher-order interaction is considered proven. The other interaction involves a minimum of six positions between the 1400 and 1500 regions of the 16S rRNA. Although these patterns of covariation are not as striking as the 570/866 interaction, the fact that they all exist in an anti-parallel fashion and that experimental methods previously implicated these two regions of the molecule in tRNA function suggests that these interactions be given serious consideration.
Developing Higher-Order Thinking Skills through WebQuests
ERIC Educational Resources Information Center
Polly, Drew; Ausband, Leigh
2009-01-01
In this study, 32 teachers participated in a year-long professional development project related to technology integration in which they designed and implemented a WebQuest. This paper describes the extent to which higher-order thinking skills (HOTS) and levels of technology implementation (LoTI) occur in the WebQuests that participants designed.…
Higher Order Language Competence and Adolescent Mental Health
ERIC Educational Resources Information Center
Cohen, Nancy J.; Farnia, Fataneh; Im-Bolter, Nancie
2013-01-01
Background: Clinic and community-based epidemiological studies have shown an association between child psychopathology and language impairment. The demands on language for social and academic adjustment shift dramatically during adolescence and the ability to understand the nonliteral meaning in language represented by higher order language…
Higher-Order Item Response Models for Hierarchical Latent Traits
ERIC Educational Resources Information Center
Huang, Hung-Yu; Wang, Wen-Chung; Chen, Po-Hsi; Su, Chi-Ming
2013-01-01
Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…
Multimedia: A Gateway to Higher-Order Thinking Skills.
ERIC Educational Resources Information Center
Fontana, Lynn A.; And Others
In June 1990, the research group at George Mason University (Virginia) Center for Interactive Educational Technology began designing a multimedia prototype to foster higher-order thinking skills in social studies. As an initial step, the Civil War Interactive Project using the Ken Burns documentary, "The Civil War," was used in a design…
Higher-Order Item Response Models for Hierarchical Latent Traits
ERIC Educational Resources Information Center
Huang, Hung-Yu; Wang, Wen-Chung; Chen, Po-Hsi; Su, Chi-Ming
2013-01-01
Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…
Higher-Order Latent Trait Models for Cognitive Diagnosis
ERIC Educational Resources Information Center
de la Torre, Jimmy; Douglas, Jeffrey A.
2004-01-01
Higher-order latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a high-dimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative…
Higher Order Language Competence and Adolescent Mental Health
ERIC Educational Resources Information Center
Cohen, Nancy J.; Farnia, Fataneh; Im-Bolter, Nancie
2013-01-01
Background: Clinic and community-based epidemiological studies have shown an association between child psychopathology and language impairment. The demands on language for social and academic adjustment shift dramatically during adolescence and the ability to understand the nonliteral meaning in language represented by higher order language…
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Third order nonlinear optical response exhibited by mono- and few-layers of WS2
Torres-Torres, Carlos; Perea-López, Néstor; Elías, Ana Laura; ...
2016-04-13
In this work, strong third order nonlinear optical properties exhibited by WS2 layers are presented. Optical Kerr effect was identified as the dominant physical mechanism responsible for these third order optical nonlinearities. An extraordinary nonlinear refractive index together with an important contribution of a saturated absorptive response was observed to depend on the atomic layer stacking. Comparative experiments performed in mono- and few-layer samples of WS2 revealed that this material is potentially capable of modulating nonlinear optical processes by selective near resonant induced birefringence. In conclusion, we envision applications for developing all-optical bidimensional nonlinear optical devices.
Speckle reduction via higher order total variation approach.
Wensen Feng; Hong Lei; Yang Gao
2014-04-01
Multiplicative noise (also known as speckle) reduction is a prerequisite for many image-processing tasks in coherent imaging systems, such as the synthetic aperture radar. One approach extensively used in this area is based on total variation (TV) regularization, which can recover significantly sharp edges of an image, but suffers from the staircase-like artifacts. In order to overcome the undesirable deficiency, we propose two novel models for removing multiplicative noise based on total generalized variation (TGV) penalty. The TGV regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness. Furthermore, an efficient algorithm is developed for solving the TGV-based optimization problems. Numerical experiments demonstrate that our proposed methods achieve state-of-the-art results, both visually and quantitatively. In particular, when the image has some higher order smoothness, our methods outperform the TV-based algorithms.
Self-similarity of higher-order moving averages
NASA Astrophysics Data System (ADS)
Arianos, Sergio; Carbone, Anna; Türk, Christian
2011-10-01
In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis).
NASA Technical Reports Server (NTRS)
Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.
Higher order correlation beams in atmosphere under strong turbulence conditions.
Avetisyan, H; Monken, C H
2016-02-08
Higher order correlation beams, that is, two-photon beams obtained from the process of spontaneous parametric down-conversion pumped by Hermite-Gauss or Laguerre-Gauss beams of any order, can be used to encode information in many modes, opening the possibility of quantum communication with large alphabets. In this paper we calculate, analytically, the fourth-order correlation function for the Hermite-Gauss and Laguerre-Gauss coherent and partially coherent correlation beams propagating through a strong turbulent medium. We show that fourth-order correlation functions for correlation beams have, under certain conditions, expressions similar to those of intensities of classical beams and are degraded by turbulence in a similar way as the classical beams. Our results can be useful in establishing limits for the use of two-photon beams in quantum communications with larger alphabets under atmospheric turbulence.
Role of spatial higher order derivatives in momentum space entanglement
NASA Astrophysics Data System (ADS)
Kumar, S. Santhosh; Shankaranarayanan, S.
2017-03-01
We study the momentum space entanglement between different energy modes of interacting scalar fields propagating in general (D +1 )-dimensional flat space-time. As opposed to some of the recent works [V. Balasubramanian et al., Phys. Rev. D 86, 045014 (2012), 10.1103/PhysRevD.86.045014], we use a Lorentz invariant normalized ground state to obtain the momentum space entanglement entropy. We show that the Lorenz invariant definition removes the spurious power-law behavior obtained in the earlier works. More specifically, we show that the cubic interacting scalar field in (1 +1 ) dimensions leads to logarithmic divergence of the entanglement entropy and is consistent with the results from real space entanglement calculations. We study the effects of the introduction of the Lorentz violating higher derivative terms in the presence of a nonlinear self-interacting scalar field potential and show that the divergence structure of the entanglement entropy is improved in the presence of spatial higher derivative terms.
Transversely isotropic higher-order averaged structure tensors
NASA Astrophysics Data System (ADS)
Hashlamoun, Kotaybah; Federico, Salvatore
2017-08-01
For composites or biological tissues reinforced by statistically oriented fibres, a probability distribution function is often used to describe the orientation of the fibres. The overall effect of the fibres on the material response is accounted for by evaluating averaging integrals over all possible directions in space. The directional average of the structure tensor (tensor product of the unit vector describing the fibre direction by itself) is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, their evaluation has a quite high computational cost. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher-order averaged structure tensors, for the case of a transversely isotropic probability distribution of orientation. A component expression is first introduced, using which a general tensor expression is obtained, in terms of an orthonormal basis in which one of the vectors coincides with the axis of symmetry of transverse isotropy. Then, a higher-order transversely isotropic averaged structure tensor is written in an appropriate basis, constructed starting from the basis of the space of second-order transversely isotropic tensors, which is constituted by the structure tensor and its complement to the identity.
A family of solutions of a higher order PVI equation near a regular singularity
NASA Astrophysics Data System (ADS)
Shimomura, Shun
2006-09-01
Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N = 2.
Lipkin method of particle-number restoration to higher orders
NASA Astrophysics Data System (ADS)
Wang, X. B.; Dobaczewski, J.; Kortelainen, M.; Yu, L. F.; Stoitsov, M. V.
2014-07-01
Background: On the mean-field level, pairing correlations are incorporated through the Bogoliubov-Valatin transformation, whereby the particle degrees of freedom are replaced by quasiparticles. This approach leads to a spontaneous breaking of the particle-number symmetry and mixing of states with different particle numbers. In order to restore the particle number, various methods have been employed, which are based on projection approaches before or after variation. Approximate variation-after-projection (VAP) schemes, utilizing the Lipkin method, have mostly been used within the Lipkin-Nogami prescription. Purpose: Without employing the Lipkin-Nogami prescription, and using, instead, states rotated in the gauge space, we derive the Lipkin method of particle-number restoration up to sixth order and we test the convergence and accuracy of the obtained expansion. Methods: We perform self-consistent calculations using the higher-order Lipkin method to restore the particle-number symmetry in the framework of superfluid nuclear energy-density functional theory. We also apply the Lipkin method to a schematic exactly solvable two-level pairing model. Results: Calculations performed in open-shell tin and lead isotopes show that the Lipkin method converges at fourth order and satisfactorily reproduces the VAP ground-state energies and energy kernels. Near closed shells, the higher-order Lipkin method cannot be applied because of a nonanalytic kink in the ground-state energies as a function of the particle number. Conclusions: In open-shell nuclei, the higher-order Lipkin method provides a good approximation to the exact VAP energies. The method is computationally inexpensive, making it particularly suitable, for example, for future optimizations of the nuclear energy density functionals and simultaneous restoration of different symmetries.
Resonant-type third-order optical nonlinearity and optical bandgap in multicomponent oxide glasses
El-Diasty, Fouad; Abdel-Baki, Manal; Bakry, Assem M.
2009-05-01
Optical nonlinearity or the nonlinear hyperpolarizability of amorphous materials (e.g., glasses) is related directly to the complex third-order susceptibility. The imaginary part of third-order susceptibility affects negatively the maximum data rate in telecommunication systems. In addition, many transition metals containing glasses have bandgaps with semiconductor-like behavior. So, due to the necessity of operation near the absorption band edge, the study of optical nonlinearity and band structure in glasses is very essential. In this work, we investigated the relationship between the imaginary third-order nonlinear susceptibility and the bandgap of some different series of prepared oxide glasses. A universal empirical formula is given to correlate the imaginary part of the third-order nonlinear susceptibility of the glasses and their optical bandgaps. The obtained nonlinearity is discussed in view of available theories and mechanisms.
Resonant-type third-order optical nonlinearity and optical bandgap in multicomponent oxide glasses.
el-Diasty, Fouad; Abdel-Baki, Manal; Bakry, Assem M
2009-05-01
Optical nonlinearity or the nonlinear hyperpolarizability of amorphous materials (e.g., glasses) is related directly to the complex third-order susceptibility. The imaginary part of third-order susceptibility affects negatively the maximum data rate in telecommunication systems. In addition, many transition metals containing glasses have bandgaps with semiconductor-like behavior. So, due to the necessity of operation near the absorption band edge, the study of optical nonlinearity and band structure in glasses is very essential. In this work, we investigated the relationship between the imaginary third-order nonlinear susceptibility and the bandgap of some different series of prepared oxide glasses. A universal empirical formula is given to correlate the imaginary part of the third-order nonlinear susceptibility of the glasses and their optical bandgaps. The obtained nonlinearity is discussed in view of available theories and mechanisms.
Analytical formulas for gravitational lensing: Higher order calculation
Amore, Paolo; Arceo, Santiago; Fernandez, Francisco M.
2006-10-15
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. We have tested our method on the metric of Schwarzschild and Reissner-Nordstroem black holes, on the metric of a charged black hole coupled to Born-Infeld electrodynamics and on the metric of Weyl gravity. Since our method is geometrically convergent, as proved in our previous work, our analytical formulas obtained working to fourth order are sufficient to reach errors of few percents even in proximity of the photon sphere.
A higher order theory of laminated composite cylindrical shells
NASA Technical Reports Server (NTRS)
Krishna Murthy, A. V.; Reddy, T. S. R.
1986-01-01
A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.
Higher-order photon correlations in pulsed photonic crystal nanolasers
Elvira, D.; Hachair, X.; Braive, R.; Beaudoin, G.; Robert-Philip, I.; Sagnes, I.; Abram, I.; Beveratos, A.; Verma, V. B.; Baek, B.; Nam, S. W.; Stevens, M. J.; Dauler, E. A.
2011-12-15
We report on the higher-order photon correlations of a high-{beta} nanolaser under pulsed excitation at room temperature. Using a multiplexed four-element superconducting single-photon detector we measured g{sup (n)}(0-vector) with n=2,3,4. All orders of correlation display partially chaotic statistics, even at four times the threshold excitation power. We show that this departure from coherence and Poisson statistics is due to the quantum fluctuations associated with the small number of photons at the lasing threshold.
Higher-order polarization singularitites in tailored vector beams
NASA Astrophysics Data System (ADS)
Otte, E.; Alpmann, C.; Denz, C.
2016-07-01
Higher-order polarization singularities embedded in tailored vector beams are introduced and experimentally realized. As holographic modulation allows to define order and location of any vectorial singularity, the surrounding vector field can be dynamically shaped. We demonstrate light fields associated with flowers or spider webs due to regular and even irregular patterns of the orientation of polarization ellipses. Beyond that, not yet investigated hybrid structures are introduced that allow generating networks of flowers and webs in very close vicinity. Our results pave the way to applications of singular optics in spatially extended, optimized optical tweezing and high-resolution imaging.
Sandia Higher Order Elements (SHOE) v 0.5 alpha
2013-09-24
SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likely exist.
Learning in higher order Boltzmann machines using linear response.
Leisink, M A; Kappen, H J
2000-04-01
We introduce an efficient method for learning and inference in higher order Boltzmann machines. The method is based on mean field theory with the linear response correction. We compute the correlations using the exact and the approximated method for a fully connected third order network of ten neurons. In addition, we compare the results of the exact and approximate learning algorithm. Finally we use the presented method to solve the shifter problem. We conclude that the linear response approximation gives good results as long as the couplings are not too large.
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.
Higher-order-mode fiber optimized for energetic soliton propagation.
Pedersen, Martin E V; Cheng, Ji; Charan, Kriti; Wang, Ke; Xu, Chris; Grüner-Nielsen, Lars; Jakobsen, Dan
2012-08-15
We describe the design optimization of a higher-order-mode (HOM) fiber for energetic soliton propagation at wavelengths below 1300 nm. A new HOM fiber is fabricated according to our design criteria. The HOM fiber is pumped at 1045 nm by an energetic femtosecond fiber laser. The soliton self-frequency shift process shifts the center wavelength of the soliton to 1085 nm. The soliton has a temporal duration of 216 fs and a pulse energy of 6.3 nJ. The demonstrated pulse energy is approximately six times higher than the previous record in a solid core fiber at wavelengths below 1300 nm.
Organometallic Compounds and Polymers with Second and Third Order Nonlinear Optical Properties
1993-05-06
Nonlinear Optical Properties of Inorganic Coordination Polymers . William Chiang, Mark E. Thompson, Donna Van Engen , "Organic Materials for Nonlinear...Organometallic Compounds and Polymers with Second and Third Order Nonlinear Optical Pro. -c.AUTHOR(S) 61102F 2303 All Mark E. Thompson, PI 7. PERFORMING...scale Sc -Cr $5 Fe > Co. Polar coordination polymers were prepared in which excellent polar order was found in the polyermic chains. however, the
Higher Order Mode Damping Simulation and Multipacting Analysis
NASA Astrophysics Data System (ADS)
Xiao, Liling
2015-10-01
When the beam is passing through an accelerator, it will generate higher order modes (HOM), which will affect to the beam quality especially in high energy accelerators such as International Linear accelerator Collider (ILC). In order to preserve the beam quality, HOM couplers are required to be installed to extract HOM power. Most of HOM couplers are 3D complex structures including small features. In addition, many physics process are involved in HOM coupler design such as RF heating and multipacting. Numerical modeling and simulation are essential for HOM coupler design and optimization for successful operation of high energy accelerators. SLAC developed 3D finite element parallel electromagnetics code suite ACE3P can be used to accelerator modeling with higher accuracy in fast turnaround time. In this paper, ACE3P application for HOM damping simulation and multipating analysis is presented for ILC 3.9 GHz crab cavity.
Second order higher-derivative corrections in Double Field Theory
NASA Astrophysics Data System (ADS)
Lescano, Eric; Marqués, Diego
2017-06-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives O({α}^' 2}) for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
Toddlers infer higher-order relational principles in causal learning.
Walker, Caren M; Gopnik, Alison
2014-01-01
Children make inductive inferences about the causal properties of individual objects from a very young age. When can they infer higher-order relational properties? In three experiments, we examined 18- to 30-month-olds' relational inferences in a causal task. Results suggest that at this age, children are able to infer a higher-order relational causal principle from just a few observations and use this inference to guide their own subsequent actions and bring about a novel causal outcome. Moreover, the children passed a revised version of the relational match-to-sample task that has proven very difficult for nonhuman primates. The findings are considered in light of their implications for understanding the nature of relational and causal reasoning, and their evolutionary origins.
Promoting higher order thinking skills using inquiry-based learning
NASA Astrophysics Data System (ADS)
Madhuri, G. V.; S. S. N Kantamreddi, V.; Goteti, L. N. S. Prakash
2012-05-01
Active learning pedagogies play an important role in enhancing higher order cognitive skills among the student community. In this work, a laboratory course for first year engineering chemistry is designed and executed using an inquiry-based learning pedagogical approach. The goal of this module is to promote higher order thinking skills in chemistry. Laboratory exercises are designed based on Bloom's taxonomy and a just-in-time facilitation approach is used. A pre-laboratory discussion outlining the theory of the experiment and its relevance is carried out to enable the students to analyse real-life problems. The performance of the students is assessed based on their ability to perform the experiment, design new experiments and correlate practical utility of the course module with real life. The novelty of the present approach lies in the fact that the learning outcomes of the existing experiments are achieved through establishing a relationship with real-world problems.
Higher order interactions in magneto-inductive waveguides
NASA Astrophysics Data System (ADS)
Syms, R. R. A.; Sydoruk, O.; Shamonina, E.; Solymar, L.
2007-03-01
The properties of periodic chains of magnetically coupled L-C resonators supporting magneto-inductive (MI) waves are examined in the case when non-nearest neighbour interactions are significant. The variation of the coupling coefficient with separation is measured using resonant elements based on printed circuit board inductors and surface mount capacitors, and used to predict the S-parameters and dispersion characteristics of magnetoinductive waveguides. Good agreement with experimental measurements is obtained when higher order interactions are included. The significance of non-nearest neighbour interactions in more general MI wave devices is then highlighted in an example problem involving reflection from a waveguide discontinuity, and the influence of higher order evanescent waves is discussed.
A higher-order-statistics-based approach to face detection
NASA Astrophysics Data System (ADS)
Li, Chunming; Li, Yushan; Wu, Ruihong; Li, Qiuming; Zhuang, Qingde; Zhang, Zhan
2005-02-01
A face detection method based on higher order statistics is proposed in this paper. Firstly, the object model and noise model are established to extract moving object from the background according to the fact that higher order statistics is nonsense to Gaussian noise. Secondly, the improved Sobel operator is used to extract the edge image of moving object. And a projection function is used to detect the face in the edge image. Lastly, PCA(Principle Component Analysis) method is used to do face recognition. The performance of the system is evaluated on the real video sequences. It is shown that the proposed method is simple and robust to the detection of human faces in the video sequences.
Higher Order Aberrations after Femtosecond LASIK Flap Creation
2016-03-03
such as corneal refractive surgery . While studies have previously compared HOA in microkeratome vs. femtosecond corneal flap creation, no studies... surgery . Higher order aberrations · after LASIK with femtosecond flap creation Jason Croskrey, Matthew Caldwell. J . Richard Townley, Douglas Apsey...and post- surgery between iFS and Z04 eyes, (P>0.05) No statistical difference in the change in spherical equivalent pre and post- surgery between
Enhanced sensitivity at higher-order exceptional points
NASA Astrophysics Data System (ADS)
Hodaei, Hossein; Hassan, Absar U.; Wittek, Steffen; Garcia-Gracia, Hipolito; El-Ganainy, Ramy; Christodoulides, Demetrios N.; Khajavikhan, Mercedeh
2017-08-01
Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement—specifically, a ternary, parity-time-symmetric photonic laser molecule—with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.
Enhanced sensitivity at higher-order exceptional points.
Hodaei, Hossein; Hassan, Absar U; Wittek, Steffen; Garcia-Gracia, Hipolito; El-Ganainy, Ramy; Christodoulides, Demetrios N; Khajavikhan, Mercedeh
2017-08-09
Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce. In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency, unidirectional invisibility, band merging, topological chirality and laser mode selectivity. Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations. Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies, their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement-specifically, a ternary, parity-time-symmetric photonic laser molecule-with a carefully tailored gain-loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics, microwaves and atomic physics.
Higher order spin effects in inspiralling compact objects binaries
NASA Astrophysics Data System (ADS)
Marsat, Sylvain
2015-04-01
We present recent progress on higher order spin effects in the post-Newtonian dynamics of compact objects binaries. We present first an extension of a Lagrangian formalism for point particle with spins, where finite size effects are represented by an additional multipolar structure. When applied to the case of a spin-induced octupole, the formalism allows for the computation of the cubic-in-spin effects that enter at the order 3.5PN. We also report on results obtained for quadratic-in-spin effects at the next-to-leading order 3PN. In both cases, we recover existing results for the dynamics, and derive for the first time the gravitational wave energy flux and orbital phasing. These results will be useful for the data analysis of the upcoming generation of advanced detectors of gravitational waves. NASA Grant 11-ATP-046.
Higher order parabolic approximations of the reduced wave equation
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.
1986-01-01
Asymptotic solutions of order k to the nth are developed for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory, and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.
A higher-order Robert-Asselin type time filter
NASA Astrophysics Data System (ADS)
Li, Yong; Trenchea, Catalin
2014-02-01
The Robert-Asselin (RA) time filter combined with leapfrog scheme is widely used in numerical models of weather and climate. It successfully suppresses the spurious computational mode associated with the leapfrog method, but it also weakly dampens the physical mode and degrades the numerical accuracy. The Robert-Asselin-Williams (RAW) time filter is a modification of the RA filter that reduces the undesired numerical damping of RA filter and increases the accuracy. We propose a higher-order Robert-Asselin (hoRA) type time filter which effectively suppresses the computational modes and achieves third-order accuracy with the same storage requirement as RAW filter. Like RA and RAW filters, the hoRA filter is non-intrusive, and so it would be easily implementable. The leapfrog scheme with hoRA filter is almost as accurate, stable and efficient as the intrusive third-order Adams-Bashforth (AB3) method.
Higher-Order Hurst Signatures: Dynamical Information in Time Series
NASA Astrophysics Data System (ADS)
Ferenbaugh, Willis
2005-10-01
Understanding and comparing time series from different systems requires characteristic measures of the dynamics embedded in the series. The Hurst exponent is a second-order dynamical measure of a time series which grew up within the blossoming fractal world of Mandelbrot. This characteristic measure is directly related to the behavior of the autocorrelation, the power-spectrum, and other second-order things. And as with these other measures, the Hurst exponent captures and quantifies some but not all of the intrinsic nature of a series. The more elusive characteristics live in the phase spectrum and the higher-order spectra. This research is a continuing quest to (more) fully characterize the dynamical information in time series produced by plasma experiments or models. The goal is to supplement the series information which can be represented by a Hurst exponent, and we would like to develop supplemental techniques in analogy with Hurst's original R/S analysis. These techniques should be another way to plumb the higher-order dynamics.
Bayati, Basil S; Eckhoff, Philip A
2012-12-01
We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.
Third order nonlinearity in pulsed laser deposited LiNbO{sub 3} thin films
Tumuluri, Anil; Rapolu, Mounika; Rao, S. Venugopal E-mail: svrsp@uohyd.ernet.in; Raju, K. C. James 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.
Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite
Sharma, Mamta; Tripathi, S. K. E-mail: surya-tr@yahoo.com
2015-06-24
CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n{sub 2}) and nonlinear susceptibility (χ{sup 3}) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n{sub 2} and β and is found to be of the order of 10{sup −7} – 10{sup −8} m{sup 2}/V{sup 2}. The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect.
Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
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
Higher-Order Corrections to Earthʼs Ionosphere Shocks
NASA Astrophysics Data System (ADS)
Abdelwahed, H. G.; El-Shewy, E. K.
2017-01-01
Nonlinear shock wave structures in unmagnetized collisionless viscous plasmas composed fluid of positive (negative) ions and nonthermally electron distribution are examined. For ion shock formation, a reductive perturbation technique applied to derive Burgers equation for lowest-order potential. As the shock amplitude decreasing or enlarging, its steepness and velocity deviate from Burger equation. Burgers type equation with higher order dissipation must be obtained to avoid this deviation. Solution for the compined two equations has been derived using renormalization analysis. Effects of higher-order, positive- negative mass ratio Q, electron nonthermal parameter δ and kinematic viscosities coefficient of positive (negative) ions {η }1 and {η }2 on the electrostatic shocks in Earth’s ionosphere are also argued. Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under the Research Project No. 2015/01/4787
The importance of nonlinearity on the higher harmonic control of helicopter vibration
NASA Technical Reports Server (NTRS)
Molusis, J. A.
1984-01-01
The effect of nonlinearity on the higher harmonic control (HHC) of helicopter vibration is investigated using a nonlinear aeroelastic simulation. A nonlinear solution is proposed which relates the HHC inputs to vibration outputs on the basis of a Volterra functional series. The Volterra series solution is shown to reduce to a vector polynomial equation relating HHC inputs to vibration outputs at any harmonic frequency. The nonlinear transfer relationship is identified from a nonlinear vibration analysis computer program, and the identification model is examined in detail. Improvements to current HHC algorithms are presented, and several Kalman filter divergence problems are quantified.
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.
NASA Astrophysics Data System (ADS)
Zhou, Yunshan; Shi, Zonghai; Zhang, Lijuan; ul Hassan, Sadaf; Qu, Ningning
2013-11-01
The third-order nonlinear optical properties of a Keplerate-type polyoxometalate (NH4)18[(Bu4N]24[Mo132O372(H2O)72(CH3COO)30]ṡ ca.7NH4CH3COOṡ ca.173H2O (denoted Bu4N-{Mo132}) in solution and in films of poly(methylmethacrylate) (denoted PMMA) matrix have been studied by the Z-scan method at 532 nm with a pulse duration of 20 ps. Experimental results show that both the solution and the solid films of Bu4N-{Mo132} have nonlinear self-defocusing effects and notable nonlinear reverse saturable absorption. Embedding Bu4N-{Mo132} as inclusion into PMMA host significantly improves the nonlinear absorption coefficient β, while it reduces the nonlinear refractive coefficient as a result of the higher concentration of Bu4N-{Mo132} in PMMA matrix than in solution. The magnitude of β for solid-state Bu4N-{Mo132} in films increases with the increasing amount of incorporated Bu4N-{Mo132}, while the third-order nonlinear refractive index n 2 decreases. Experimental results prove the high stability of Bu4N-{Mo132} in PMMA films in inorganic acidic and basic solutions. These studies indicate that Bu4N-{Mo132} in thin solid films of PMMA are potential candidates for fabricating nonlinear optical devices.
Estimation on nonlinear damping in second order distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1989-01-01
An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.
Orchestration of Molecular Information through Higher Order Chemical Recognition
NASA Astrophysics Data System (ADS)
Frezza, Brian M.
Broadly defined, higher order chemical recognition is the process whereby discrete chemical building blocks capable of specifically binding to cognate moieties are covalently linked into oligomeric chains. These chains, or sequences, are then able to recognize and bind to their cognate sequences with a high degree of cooperativity. Principally speaking, DNA and RNA are the most readily obtained examples of this chemical phenomenon, and function via Watson-Crick cognate pairing: guanine pairs with cytosine and adenine with thymine (DNA) or uracil (RNA), in an anti-parallel manner. While the theoretical principles, techniques, and equations derived herein apply generally to any higher-order chemical recognition system, in practice we utilize DNA oligomers as a model-building material to experimentally investigate and validate our hypotheses. Historically, general purpose information processing has been a task limited to semiconductor electronics. Molecular computing on the other hand has been limited to ad hoc approaches designed to solve highly specific and unique computation problems, often involving components or techniques that cannot be applied generally in a manner suitable for precise and predictable engineering. Herein, we provide a fundamental framework for harnessing high-order recognition in a modular and programmable fashion to synthesize molecular information process networks of arbitrary construction and complexity. This document provides a solid foundation for routinely embedding computational capability into chemical and biological systems where semiconductor electronics are unsuitable for practical application.
Higher-order ionosphere modeling for CODE's next reprocessing activities
NASA Astrophysics Data System (ADS)
Lutz, S.; Schaer, S.; Meindl, M.; Dach, R.; Steigenberger, P.
2009-12-01
CODE (the Center for Orbit Determination in Europe) is a joint venture between the Astronomical Institute of the University of Bern (AIUB, Bern, Switzerland), the Federal Office of Topography (swisstopo, Wabern, Switzerland), the Federal Agency for Cartography and Geodesy (BKG, Frankfurt am Main, Germany), and the Institut für Astronomische und Phsyikalische Geodäsie of the Technische Universität München (IAPG/TUM, Munich, Germany). It acts as one of the global analysis centers of the International GNSS Service (IGS) and participates in the first IGS reprocessing campaign, a full reanalysis of GPS data collected since 1994. For a future reanalyis of the IGS data it is planned to consider not only first-order but also higher-order ionosphere terms in the space geodetic observations. There are several works (e.g. Fritsche et al. 2005), which showed a significant and systematic influence of these effects on the analysis results. The development version of the Bernese Software used at CODE is expanded by the ability to assign additional (scaling) parameters to each considered higher-order ionosphere term. By this, each correction term can be switched on and off on normal-equation level and, moreover, the significance of each correction term may be verified on observation level for different ionosphere conditions.
Higher-order massive neutrino perturbations in large-scale structure
NASA Astrophysics Data System (ADS)
Führer, Florian; Wong, Yvonne Y. Y.
2015-03-01
We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlasov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at lesssim 1% accuracy, we find that the total matter bispectrum with a low neutrino mass m = 0.046 eV can be reproduced by all but the fluid approximation, while for larger neutrino masses m=0.46 → 0.93 eV only the hybrid approach has the desired accuracy on a large range of scales. This result serves as a cautionary note that approximate nonlinear models of neutrino clustering that reproduce the gross features of some observables may not suffice for precision calculations, nor are they guaranteed to apply to other observables. All of the approximation schemes fail to reproduce the bispectrum of the neutrino density perturbations at better than 20% accuracy across all scales, indicating that an exact treatment of nonlinear neutrino perturbations is necessary.
Higher-order massive neutrino perturbations in large-scale structure
Führer, Florian; Wong, Yvonne Y.Y. E-mail: yvonne.y.wong@unsw.edu.au
2015-03-01
We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlasov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at ∼< 1% accuracy, we find that the total matter bispectrum with a low neutrino mass m = 0.046 eV can be reproduced by all but the fluid approximation, while for larger neutrino masses m=0.46 → 0.93 eV only the hybrid approach has the desired accuracy on a large range of scales. This result serves as a cautionary note that approximate nonlinear models of neutrino clustering that reproduce the gross features of some observables may not suffice for precision calculations, nor are they guaranteed to apply to other observables. All of the approximation schemes fail to reproduce the bispectrum of the neutrino density perturbations at better than 20% accuracy across all scales, indicating that an exact treatment of nonlinear neutrino perturbations is necessary.
Application of higher order statistics/spectra in biomedical signals--a review.
Chua, Kuang Chua; Chandran, Vinod; Acharya, U Rajendra; Lim, Choo Min
2010-09-01
For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second-order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.
Higher-order automatic differentiation of mathematical functions
NASA Astrophysics Data System (ADS)
Charpentier, Isabelle; Dal Cappello, Claude
2015-04-01
Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.
Polymer quantization, stability and higher-order time derivative terms
NASA Astrophysics Data System (ADS)
Cumsille, Patricio; Reyes, Carlos M.; Ossandon, Sebastian; Reyes, Camilo
2016-03-01
The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.
Higher order mode damping in an ALS test cavity
Jacob, A.F.; Lamberston, G.R. ); Barry, W. )
1990-06-01
The higher order mode attenuation scheme proposed for the Advanced Light Source accelerating cavities consists of two broad-band dampers placed 90{degrees} apart on the outer edge. In order to assess the damping efficiency a test assembly was built. The HOM damping was obtained by comparing the peak values of the transmission through the cavity for both the damped and the undamped case. Because of the high number of modes and frequency shifts due to the damping gear, the damping was assessed statistically, by averaging over several modes. In the frequency range from 1.5 to 5.5 GHz, average damping greater than 100 was obtained. 1 ref., 6 figs.
Higher-Order Theory for Functionally Graded Materials
NASA Technical Reports Server (NTRS)
Aboudi, Jacob; Pindera, Marek-Jerzy; Arnold, Steven M.
1999-01-01
This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.
An improved higher order panel method for linearized supersonic flow
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Epton, M. A.; Johnson, F. T.; Magnus, A. E.; Rubbert, P. E.
1978-01-01
An improved higher order panel method for linearized supersonic flow is described. Each panel, defined by four points on the surface, is divided into eight subpanels in such a way that all subpanel and panel edges are contiguous. By prescribing a quadratic distribution of the doublet on each subpanel, the doublet strength is made strictly continuous on the paneled surface. A linear source distribution is also used. Numerical results are smoother and in better agreement with experiment than the previous method with less strict continuity. A brief discussion of superinclined panels used to eliminate interior interference in nacelles is included.
Higher order temporal finite element methods through mixed formalisms.
Kim, Jinkyu
2014-01-01
The extended framework of Hamilton's principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.
Programming real-time executives in higher order language
NASA Technical Reports Server (NTRS)
Foudriat, E. C.
1982-01-01
Methods by which real-time executive programs can be implemented in a higher order language are discussed, using HAL/S and Path Pascal languages as program examples. Techniques are presented by which noncyclic tasks can readily be incorporated into the executive system. Situations are shown where the executive system can fail to meet its task scheduling and yet be able to recover either by rephasing the clock or stacking the information for later processing. The concept of deadline processing is shown to enable more effective mixing of time and information synchronized systems.
Extension of MINOTAUR to higher-order spatial functions
Pevey, R.E.
1999-09-01
MINOTAUR, a generalized multidimensional geometry discrete ordinates kernel that can be used to calculate the particle flow through a complicated geometrical arrangement of materials, has been extended to use higher-order within-node spatial flux expansions. MINOTAUR is an improved version of the CENTAUR code, which was developed at the Savannah River Site by DeHart, Pevey, and Parish for flat intranode flux distributions. CENTAUR was later extended to linear spatial flux shapes by Grove and Pevey. Both of these codes were limited to two-dimensional generalized geometries, for which the regions are bounded by arbitrarily oriented line segments.
Higher Order Mode Properties of Superconducting Two-Spoke Cavities
Hopper, C. S.; Delayen, J. R.; Olave, R. G.
2011-07-01
Multi-Spoke cavities lack the cylindrical symmetry that many other cavity types have, which leads to a more complex Higher Order Mode (HOM) spectrum. In addition, spoke cavities offer a large velocity acceptance which means we must perform a detailed analysis of the particle velocity dependence for each mode's R/Q. We present here a study of the HOM properties of two-spoke cavities designed for high-velocity applications. Frequencies, R/Q and field profiles of HOMs have been calculated and are reported.
Tight focusing of higher orders Laguerre-Gaussian modes
Savelyev, Dmitry A. Khonina, Svetlana N.; Golub, Ilya
2016-04-13
The spatial redistribution of the contribution of different electric field components provides a decrease in the size of the central focal spot for higher orders Laguerre-Gaussian modes. It was shown that when sharply focusing laser beams with vortex or special binary phase plate, a sub-wavelength light localization of separate vector field components is possible for any polarization type. This fact should be considered for the interaction of laser radiation with materials selectively sensitive to lateral and longitudinal components of the electromagnetic field.
Higher-order modes in the APS storage ring waveguides
Brauer, S.O.; Kustom, R.L.
1993-07-01
Twelve higher-order modes (HOMs) in the single-cell accelerating cavities for the Advanced Photon Source (APS) storage ring were calculated to have complex impedances that will cause coupled-bunched instabilities near or below the 300mA positron current which is the design goal. Some of these modes couple, through the coupling loop, from the storage ring cavity into the waveguide. This study investigates the transmission of these modes from the cavity into the waveguide. The standing wave ratio (VSWR) of a WR2300 hybrid waveguide component has been measured at each HOM frequency, and its effect on the transmitted modes in the waveguide is studied.
Higher order software - A methodology for defining software
NASA Technical Reports Server (NTRS)
Hamilton, M.; Zeldin, S.
1976-01-01
Higher order software (HOS) is concerned only with computable functions and relationships. The HOS methodology can be used for the definition of software for multiprogrammed, multiprocessor, or multicomputer systems. A description of HOS methodology is presented, giving attention to questions of formulation, interface correctness, specification language principles, and HOS analyzers. Aspects of system design are considered, and details of software management are discussed. Attention is given to modularity as defined by HOS, frozen module management, the assembly control supervisor, and aspects of reliability and efficiency.
An improved higher order panel method for linearized supersonic flow
NASA Technical Reports Server (NTRS)
Ehlers, F. E.; Epton, M. A.; Johnson, F. T.; Magnus, A. E.; Rubbert, P. E.
1978-01-01
An improved higher order panel method for linearized supersonic flow is described. Each panel, defined by four points on the surface, is divided into eight subpanels in such a way that all subpanel and panel edges are contiguous. By prescribing a quadratic distribution of the doublet on each subpanel, the doublet strength is made strictly continuous on the paneled surface. A linear source distribution is also used. Numerical results are smoother and in better agreement with experiment than the previous method with less strict continuity. A brief discussion of superinclined panels used to eliminate interior interference in nacelles is included.
Programming real-time executives in higher order language
NASA Technical Reports Server (NTRS)
Foudriat, E. C.
1982-01-01
Methods by which real-time executive programs can be implemented in a higher order language are discussed, using HAL/S and Path Pascal languages as program examples. Techniques are presented by which noncyclic tasks can readily be incorporated into the executive system. Situations are shown where the executive system can fail to meet its task scheduling and yet be able to recover either by rephasing the clock or stacking the information for later processing. The concept of deadline processing is shown to enable more effective mixing of time and information synchronized systems.
Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong
2014-02-01
Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.
Effects of time ordering in quantum nonlinear optics
NASA Astrophysics Data System (ADS)
Quesada, Nicolás; Sipe, J. E.
2014-12-01
We study time-ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four-wave mixing (SFWM), and frequency conversion using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase-matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in SPDC and SFWM are reduced to quadrature.
Higher Order Aberration and Astigmatism in Children with Hyperopic Amblyopia.
Choi, Seung Kwon; Chang, Ji Woong
2016-02-01
To investigate the changes in corneal higher-order aberration (HOA) during amblyopia treatment and the correlation between HOA and astigmatism in hyperopic amblyopia children. In this retrospective study, a total of 72 eyes from 72 patients ranging in age from 38 to 161 months were included. Patients were divided into two groups based on the degree of astigmatism. Corneal HOA was measured using a KR-1W aberrometer at the initial visit and at 3-, 6-, and 12-month follow-ups. Correlation analysis was performed to assess the association between HOA and astigmatism. A total of 72 patients were enrolled in this study, 37 of which were classified as belonging to the higher astigmatism group, while 35 were assigned to the lower astigmatism group. There was a statistically significant difference in success rate between the higher and lower astigmatism groups. In both groups, all corneal HOAs were significantly reduced during amblyopia treatment. When comparing the two groups, a significant difference in coma HOA at the 12-month follow-up was detected (p = 0.043). In the Pearson correlation test, coma HOA at the 12-month follow-up demonstrated a statistically significant correlation with astigmatism and a stronger correlation with astigmatism in the higher astigmatism group than in the lower astigmatism group (coefficient values, 0.383 and 0.284 as well as p = 0.021 and p = 0.038, respectively). HOA, particularly coma HOA, correlated with astigmatism and could exert effects in cases involving hyperopic amblyopia.
NASA Technical Reports Server (NTRS)
Melott, A. L.; Buchert, T.; Weib, A. G.
1995-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.
Spectral dependence of nonlinear absorption in ordered silver metallic nanoprism arrays.
Sánchez-Esquivel, Héctor; Raygoza-Sánchez, Karen Y; Rangel-Rojo, Raúl; Gemo, Emanuele; Michieli, Niccolò; Kalinic, Boris; Reyes-Esqueda, Jorge Alejandro; Cesca, Tiziana; Mattei, Giovanni
2017-07-13
Ordered metallic nanoprism arrays have been proposed as novel and versatile systems for the observation of nonlinear effects such as nonlinear absorption. The study of the effect of the local field reinforcement on the fast optical third order nonlinear response around the Surface Plasmon Resonance is of great interest for many plasmonic applications. In this work, silver nanoprism arrays have been synthesized by the nanosphere lithography method. A low repetition rate tunable picosecond laser source was used to study the irradiance and wavelength dependence of the nonlinear absorption properties around the dipolar and quadrupolar resonances of the nanoarray with the use of the z-scan technique. The irradiance dependence of the on-resonance nonlinearity was studied, and a spectral region where nonlinear absorption is negligible was identified. This is important for the possible application of these materials in optical information processing devices.
Third-order Nonlinear Optical Properties of Metallodielectric Stacks
2011-07-01
developed by Sheik- Bahae et al [7] a (Gaussian) laser beam is focused in free space; a sample is positioned along the propagation (Z) axis of the laser...transmittance and reflectance coefficients are defined for any angle of incidence as 22 0 ||,|| cos cos rRt n n T i tt ; (2) i and t are...nonlinear coefficient, 4 2 2 i n , has a complex value. The longitudinal component of the Poynting vector was used in Eq. (11). The Kerr
NASA Astrophysics Data System (ADS)
Schmauss, Bernhard; Asif, Rameez; Lin, Chien-Yu
2012-01-01
Recent numerical and experimental studies have shown that coherent transmission with advanced modulation formats i.e. DP-QPSK and QAM are the promising candidates for next-generation systems with data rates of 100Gbit/s and above. Coherent detection is considered efficient along with digital signal processing (DSP) to compensate many linear effects in fiber propagation i.e. chromatic dispersion (CD) and polarization-mode dispersion (PMD). Despite of fiber non-linearities (NL), which are the major limiting factors, next-generation optical systems are employing higher order modulation formats in order to fulfil the ever increasing demand of capacity requirements. However, the channel capacity is limited at higher signal input powers because the system is operating in the non-linear regime. Due to this phenomenon the compensation of non-linearities is a topic of great interest and research these days, especially for long-haul fiber transmission. Digital backward propagation (DBP) algorithm has emerged as a promising and potentially capable candidate, which can jointly compensate fiber dispersion and non-linearities along with the coherent receiver. In this paper we give a detailed overview on the advancements in DBP algorithm based on different types of mathematical models i.e. Wiener (Asymmetric Method) and Wiener Hammerstein models (Symmetric Method). We also discuss the importance of optimized step-size selection, i.e. constant step-size and logarithmic step-size based split step Fourier methods, for simplified and computationally efficient implementation of DBP algorithm. Moreover, by means of numerical investigations we refer to recent system investigations to further improve the performance of DBP algorithm.
NASA Technical Reports Server (NTRS)
Sirkis, James S. (Inventor); Sivanesan, Ponniah (Inventor); Venkat, Venki S. (Inventor)
2001-01-01
A Bragg grating sensor for measuring distributed strain and temperature at the same time comprises an optical fiber having a single mode operating wavelength region and below a cutoff wavelength of the fiber having a multimode operating wavelength region. A saturated, higher order Bragg grating having first and second order Bragg conditions is fabricated in the optical fiber. The first order of Bragg resonance wavelength of the Bragg grating is within the single mode operating wavelength region of the optical fiber and the second order of Bragg resonance wavelength is below the cutoff wavelength of the fiber within the multimode operating wavelength region. The reflectivities of the saturated Bragg grating at the first and second order Bragg conditions are less than two orders of magnitude of one another. In use, the first and second order Bragg conditions are simultaneously created in the sensor at the respective wavelengths and a signal from the sensor is demodulated with respect to each of the wavelengths corresponding to the first and second order Bragg conditions. Two Bragg conditions have different responsivities to strain and temperature, thus allowing two equations for axial strain and temperature to be found in terms of the measure shifts in the primary and second order Bragg wavelengths. This system of equations can be solved for strain and temperature.
Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers
Gershman, D. J.; Block, B. P.; Rubin, M.; Zurbuchen, T. H.; Benna, M.; Mahaffy, P. R.
2011-12-15
This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupole mass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and the ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.
Higher order parametric excitation modes for spaceborne quadrupole mass spectrometers
NASA Astrophysics Data System (ADS)
Gershman, D. J.; Block, B. P.; Rubin, M.; Benna, M.; Mahaffy, P. R.; Zurbuchen, T. H.
2011-12-01
This paper describes a technique to significantly improve upon the mass peak shape and mass resolution of spaceborne quadrupole mass spectrometers (QMSs) through higher order auxiliary excitation of the quadrupole field. Using a novel multiresonant tank circuit, additional frequency components can be used to drive modulating voltages on the quadrupole rods in a practical manner, suitable for both improved commercial applications and spaceflight instruments. Auxiliary excitation at frequencies near twice that of the fundamental quadrupole RF frequency provides the advantages of previously studied parametric excitation techniques, but with the added benefit of increased sensed excitation amplitude dynamic range and the ability to operate voltage scan lines through the center of upper stability islands. Using a field programmable gate array, the amplitudes and frequencies of all QMS signals are digitally generated and managed, providing a robust and stable voltage control system. These techniques are experimentally verified through an interface with a commercial Pfeiffer QMG422 quadrupole rod system. When operating through the center of a stability island formed from higher order auxiliary excitation, approximately 50% and 400% improvements in 1% mass resolution and peak stability were measured, respectively, when compared with traditional QMS operation. Although tested with a circular rod system, the presented techniques have the potential to improve the performance of both circular and hyperbolic rod geometry QMS sensors.
Temporal difference models describe higher-order learning in humans.
Seymour, Ben; O'Doherty, John P; Dayan, Peter; Koltzenburg, Martin; Jones, Anthony K; Dolan, Raymond J; Friston, Karl J; Frackowiak, Richard S
2004-06-10
The ability to use environmental stimuli to predict impending harm is critical for survival. Such predictions should be available as early as they are reliable. In pavlovian conditioning, chains of successively earlier predictors are studied in terms of higher-order relationships, and have inspired computational theories such as temporal difference learning. However, there is at present no adequate neurobiological account of how this learning occurs. Here, in a functional magnetic resonance imaging (fMRI) study of higher-order aversive conditioning, we describe a key computational strategy that humans use to learn predictions about pain. We show that neural activity in the ventral striatum and the anterior insula displays a marked correspondence to the signals for sequential learning predicted by temporal difference models. This result reveals a flexible aversive learning process ideally suited to the changing and uncertain nature of real-world environments. Taken with existing data on reward learning, our results suggest a critical role for the ventral striatum in integrating complex appetitive and aversive predictions to coordinate behaviour.
Laser-PlasmaWakefield Acceleration with Higher Order Laser Modes
Geddes, C.G.R.; Cormier-Michel, E.; Esarey, E.; Schroeder, C.B.; Mullowney, P.; Paul, K.; Cary, J.R.; Leemans, W.P.
2010-06-01
Laser-plasma collider designs point to staging of multiple accelerator stages at the 10 GeV level, which are to be developed on the upcoming BELLA laser, while Thomson Gamma source designs use GeV stages, both requiring efficiency and low emittance. Design and scaling of stages operating in the quasi-linear regime to address these needs are presented using simulations in the VORPAL framework. In addition to allowing symmetric acceleration of electrons and positrons, which is important for colliders, this regime has the property that the plasma wakefield is proportional to the transverse gradient of the laser intensity profile. We demonstrate use of higher order laser modes to tailor the laser pulse and hence the transverse focusing forces in the plasma. In particular, we show that by using higher order laser modes, we can reduce the focusing fields and hence increase the matched electron beam radius, which is important to increased charge and efficiency, while keeping the low bunch emittance required for applications.
Inhibitory control gains from higher-order cognitive strategy training.
Motes, Michael A; Gamino, Jacquelyn F; Chapman, Sandra B; Rao, Neena K; Maguire, Mandy J; Brier, Matthew R; Kraut, Michael A; Hart, John
2014-02-01
The present study examined the transfer of higher-order cognitive strategy training to inhibitory control. Middle school students enrolled in a comprehension- and reasoning-focused cognitive strategy training program and passive controls participated. The training program taught students a set of steps for inferring essential gist or themes from materials. Both before and after training or a comparable duration in the case of the passive controls, participants completed a semantically cued Go/No-Go task that was designed to assess the effects of depth of semantic processing on response inhibition and components of event-related potentials (ERP) related to response inhibition. Depth of semantic processing was manipulated by varying the level of semantic categorization required for response selection and inhibition. The SMART-trained group showed inhibitory control gains and changes in fronto-central P3 ERP amplitudes on inhibition trials; whereas, the control group did not. The results provide evidence of the transfer of higher-order cognitive strategy training to inhibitory control and modulation of ERPs associated with semantically cued inhibitory control. The findings are discussed in terms of implications for cognitive strategy training, models of cognitive abilities, and education. Published by Elsevier Inc.
Visualizing Higher Order Finite Elements: FY05 Yearly Report.
Thompson, David; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, simulations will typically fail to produce a valid approximation to the solution.Recent work has shown that increasing the number of degrees of freedom by increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were
Higher-Order Interference in Extensions of Quantum Theory
NASA Astrophysics Data System (ADS)
Lee, Ciarán M.; Selby, John H.
2016-10-01
Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined `foil' theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski's theory is argued not to be a genuine phenomenon, but to
Higher-Order Interference in Extensions of Quantum Theory
NASA Astrophysics Data System (ADS)
Lee, Ciarán M.; Selby, John H.
2017-01-01
Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined `foil' theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski's theory is argued not to be a genuine phenomenon, but to
Higher-order phase transitions on financial markets
NASA Astrophysics Data System (ADS)
Kasprzak, A.; Kutner, R.; Perelló, J.; Masoliver, J.
2010-08-01
Statistical and thermodynamic properties of the anomalous multifractal structure of random interevent (or intertransaction) times were thoroughly studied by using the extended continuous-time random walk (CTRW) formalism of Montroll, Weiss, Scher, and Lax. Although this formalism is quite general (and can be applied to any interhuman communication with nontrivial priority), we consider it in the context of a financial market where heterogeneous agent activities can occur within a wide spectrum of time scales. As the main general consequence, we found (by additionally using the Saddle-Point Approximation) the scaling or power-dependent form of the partition function, Z(q'). It diverges for any negative scaling powers q' (which justifies the name anomalous) while for positive ones it shows the scaling with the general exponent τ(q'). This exponent is the nonanalytic (singular) or noninteger power of q', which is one of the pilar of higher-order phase transitions. In definition of the partition function we used the pausing-time distribution (PTD) as the central one, which takes the form of convolution (or superstatistics used, e.g. for describing turbulence as well as the financial market). Its integral kernel is given by the stretched exponential distribution (often used in disordered systems). This kernel extends both the exponential distribution assumed in the original version of the CTRW formalism (for description of the transient photocurrent measured in amorphous glassy material) as well as the Gaussian one sometimes used in this context (e.g. for diffusion of hydrogen in amorphous metals or for aging effects in glasses). Our most important finding is the third- and higher-order phase transitions, which can be roughly interpreted as transitions between the phase where high frequency trading is most visible and the phase defined by low frequency trading. The specific order of the phase transition directly depends upon the shape exponent α defining the stretched
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.
Interaction Solutions for (1+1)-Dimensional Higher-Order Broer—Kaup System
NASA Astrophysics Data System (ADS)
Xin, Xiang-Peng; Liu, Xi-Qiang
2016-11-01
The (1+1)-dimensional higher-order Broer—Kaup (HBK) system is studied by consistent tanh expansion (CTE) method in this paper. It is proved that the HBK system is CTE solvable, and some exact interaction solutions among different nonlinear excitations such as solitons, rational waves, periodic waves, corresponding images are explicitly given. Supported by National Natural Science Foundation of China under Grant Nos. 11505090, 11171041, 11405103, 11447220, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009
NASA Technical Reports Server (NTRS)
Wang, K. S.; Vaidya, P. G.
1975-01-01
The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow.
Travelling wave solutions for higher-order wave equations of kdv type (iii).
Li, Jibin; Rui, Weigou; Long, Yao; He, Bin
2006-01-01
By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain.
NASA Technical Reports Server (NTRS)
Kim, Heung Soo; Zhu, Linfa; Chattopadhyay, Aditi; Goldberg, Robert K.
2004-01-01
A procedure has been developed to investigate the nonlinear response of composite plates under large strain and high strain rate loading. A recently developed strain dependent micromechanics model is extended to account for the shear effects during impact. Four different assumptions of shear deformation effects are investigated to improve the development strain rate dependent micromechanics model. A method to determine through the thickness strain and transverse Poisson's ratio is developed. The revised micromechanics model is implemented into higher order laminate theory. Parametric studies are conducted to investigate transverse shear effects during impact.
NASA Astrophysics Data System (ADS)
Abdulwahhab, Muhammad Alim; Jhangeer, Adil
Conservation laws of various systems have been studied for decades due to their unparalleled importance in unraveling systems’ intricacies without having to go into microscopic details of the physical process involved. Their association with symmetries has not only had a stupendous impact in the formulation of the fundamental laws of physics, but also open doors to further explorations and unifications of others. In this study, we present the Lie symmetries and nonlinearly self-adjoint classifications of the wave equation on Bianchi I spacetime. For different forms of the metric potentials, generalized higher order non-trivial conserved vectors are constructed. Some exact invariant solutions are also exhibited.
Higher order mode analysis of the APT superconducting cavities
Krawczyk, F.L.
1997-08-01
In another contribution to this conference the design of superconducting cavities for low velocity proton beams will be reported. Besides an optimization of the rf properties of the accelerating {pi}-mode, other modes, possibly excited by the traversing proton beam, need to be regarded. The full spectrum of modes in {beta} = 0.64 and {beta} = 0.82 5-cell cavities, as proposed for the Accelerator Production of Tritium (APT) facility, has been calculated up to frequencies higher than 2.0 GHz. These have been evaluated for their potential to affect the beam. The presence of {open_quotes}trapped{close_quotes} modes has also been investigated. In addition to the specific mode spectrum, the total power deposited into the cavities by the beam has been determined from the induced wake-fields. Due to the operation with beams below the velocity of light, extreme care was required to prevent incorrect results by wave reflections from the boundaries of the calculation volume. The simulations indicate that a power deposition of up to 17 W per cavity can be expected in the worst case. This power might have to be removed by higher order mode couplers, which is a technically feasible task. Transporting this power out to a room temperature dump does not even noticeably increase the requirements to the cryogenic system. Also for the prevention of beam break-up effects and for suppression of resonant excitation of specific higher order modes (HOMs) it is of interest to investigate the removal of this HOM-power. Different approaches to implement this removal technically are entertained.
Higher Order Mode Heating Analysis for the ILC Superconducting Linacs
Bane, K.L.F.; Nantista, C.; Adolphsen, C.; /SLAC
2010-10-27
The superconducting cavities and interconnects in the 11 km long linacs of the International Linear Collider (ILC) are designed to operate at 2K, where cooling costs are very expensive. It is thus important to minimize cryogenic heat loads. In addition to an unavoidable static load and the dynamic load of the fundamental 1.3 GHz accelerating rf, a further heat source is presented by the higher order mode (HOM) power deposited by the beam. Such modes will be damped by specially designed HOM couplers attached to the cavities (for trapped modes), and by ceramic dampers at 70K that are located between the eight or nine cavity cryomodules (for propagating modes). Brute force calculation of the higher frequency modes excited in a string of cryomodules is limited by computing capacity (see, e.g. [1]). M. Liepe has calculated {approx} 400 longitudinal TM modes in 3 superconducting cavities plus absorbers, up to 8 GHz [2]. Joestingmeier, et al., have used a ray tracing calculation to find the effect at higher frequencies, specifically in the range of tens of GHz and above [3]. In this report we present a scattering matrix approach, which we apply to an rf unit comprising 26 cavities and 3 absorbers. We perform calculations at sample frequencies (up to 20 GHz) to predict the effectiveness of the ceramic dampers in limiting HOM heat deposition at 2K.
Higher-order ice-sheet modelling accelerated by multigrid on graphics cards
NASA Astrophysics Data System (ADS)
Brædstrup, Christian; Egholm, David
2013-04-01
Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.
Analysis of warping deformation modes using higher order ANCF beam element
NASA Astrophysics Data System (ADS)
Orzechowski, Grzegorz; Shabana, Ahmed A.
2016-02-01
Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition. However, in the absolute nodal coordinate formulation (ANCF) continuum-based beams, this assumption can be relaxed allowing for capturing deformation modes that couple the cross-section deformation and beam bending, torsion, and/or elongation. The deformation modes captured by ANCF finite elements depend on the interpolating polynomials used. The most widely used spatial ANCF beam element employs linear approximation in the transverse direction, thereby restricting the cross section deformation and leading to locking problems. The objective of this investigation is to examine the behavior of a higher order ANCF beam element that includes quadratic interpolation in the transverse directions. This higher order element allows capturing warping and non-uniform stretching distribution. Furthermore, this higher order element allows for increasing the degree of continuity at the element interface. It is shown in this paper that the higher order ANCF beam element can be used effectively to capture warping and eliminate Poisson locking that characterizes lower order ANCF finite elements. It is also shown that increasing the degree of continuity requires a special attention in order to have acceptable results. Because higher order elements can be more computationally expensive than the lower order elements, the use of reduced integration for evaluating the stress forces and the use of explicit and implicit numerical integrations to solve the nonlinear dynamic equations of motion are investigated in this paper. It is shown that the use of some of these integration methods can be very effective in reducing the CPU time without adversely affecting the solution accuracy.
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; Mohammad Ali, Dastan Diznab; Saied, Mohajernasab; Saied, Seif Mohammad
2017-01-01
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.
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.
NASA Technical Reports Server (NTRS)
Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.
Fuzzy neural order robust of the non-linear systems
NASA Astrophysics Data System (ADS)
Madour, F.; Benmahammed, K.
2008-06-01
This article introduces a controller at structure of a network multi-layer neurons specified by the fuzzy reasoning of Takagi-Sugeno (TS) order one [1], the weights of the network represent the standard deviations of the membership function. This controller is applied to the ordering of a reversed pendulum. Changes in the entries and the exit, as of the environment changes of operation are introduced in order to test the robustness of the designed controller.
Fuzzy neural order robust of the non-linear systems
Madour, F.; Benmahammed, K.
2008-06-12
This article introduces a controller at structure of a network multi-layer neurons specified by the fuzzy reasoning of Takagi-Sugeno (TS) order one, the weights of the network represent the standard deviations of the membership function. This controller is applied to the ordering of a reversed pendulum. Changes in the entries and the exit, as of the environment changes of operation are introduced in order to test the robustness of the designed controller.
UV Curable Epoxy-Based Second Order Nonlinear Optical Materials; Synthesis and Characterization
1992-05-14
01JUN91 to 31MAY92 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS UV Curable Epoxy-Based Second Order Nonlinear Optical Materials ; C: N00014-90-J- 1148 Svnthesis... Nonlinear Optical Materials ; Synthesis and Characterization by R.J. Jeng, Y.M. Chen, B.K. Mandal, J. Kumar and S.K. Tripathy to be published in
Fuzzy fractional order sliding mode controller for nonlinear systems
NASA Astrophysics Data System (ADS)
Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.
2010-04-01
In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.
Higher order mode beams mitigate halos in high intensity proton linacs
NASA Astrophysics Data System (ADS)
Pathak, Abhishek; Krishnagopal, Srinivas
2017-01-01
High intensity proton linacs (HIPLs) for applications such as Accelerator Driven Reactor Systems (ADRS) have serious beam dynamics issues related to beam halo formation. This can lead to particle loss and radioactivation of the surroundings which consequently limit the beam current. Beam halos are largely driven by the nonlinear space-charge force of the beam, which depends strongly on the beam distribution and also on the initial beam mismatch. We propose here the use of a higher order mode beam (HOMB), that has a weaker nonlinear force, to mitigate beam halos. We first show how the nonlinear space-charge force can itself be exploited in the presence of nonlinear solenoid fields, to produce a HOMB in the low energy beam transport (LEBT) line. We then study the transport of such a beam through a radio frequency quadrupole (RFQ), and show that the HOMB has a significant advantage in terms of emittance blow-up, halo formation and beam loss, over a Gaussian beam, even with a finite initial mismatch. For example, for the transport of a 30 mA beam through the RFQ, with an initial beam mismatch of 45%, the Gaussian beam sees an emittance blow-up of 125%, while the HOMB sees a blow-up of only 35% (relative to the initial emittance of 0.2 π mm -mrad ). Similarly, the beam halo parameter and beam loss are 0.95 and 25% respectively for a Gaussian beam, but only 0.35 and 15% for a HOMB. The beam dynamics of the HOMB agrees quite well with the particle-core model, because of the more linear space-charge force, while for the Gaussian beam there are additional particle loss mechanisms arising from nonlinear resonances. Therefore, the HOMB suppresses emittance blow-up and halo formation, and can make high current ADRS systems more viable.
Vehicle track segmentation using higher order random fields
Quach, Tu -Thach
2017-01-09
Here, we present an approach to segment vehicle tracks in coherent change detection images, a product of combining two synthetic aperture radar images taken at different times. The approach uses multiscale higher order random field models to capture track statistics, such as curvatures and their parallel nature, that are not currently utilized in existing methods. These statistics are encoded as 3-by-3 patterns at different scales. The model can complete disconnected tracks often caused by sensor noise and various environmental effects. Coupling the model with a simple classifier, our approach is effective at segmenting salient tracks. We improve the F-measure onmore » a standard vehicle track data set to 0.963, up from 0.897 obtained by the current state-of-the-art method.« less
Dependable software through higher-order strategic programming.
Winter, Victor Lono; Fraij, Fares; Roach, Steve
2004-03-01
Program transformation is a restricted form of software construction that can be amenable to formal verification. When successful, the nature of the evidence provided by such a verification is considered strong and can constitute a major component of an argument that a high-consequence or safety-critical system meets its dependability requirements. This article explores the application of novel higher-order strategic programming techniques to the development of a portion of a class loader for a restricted implementation of the Java Virtual Machine (JVM). The implementation is called the SSP and is intended for use in high-consequence safety-critical embedded systems. Verification of the strategic program using ACL2 is also discussed.
Revealing Higher Order Protein Structure Using Mass Spectrometry
NASA Astrophysics Data System (ADS)
Chait, Brian T.; Cadene, Martine; Olinares, Paul Dominic; Rout, Michael P.; Shi, Yi
2016-06-01
The development of rapid, sensitive, and accurate mass spectrometric methods for measuring peptides, proteins, and even intact protein assemblies has made mass spectrometry (MS) an extraordinarily enabling tool for structural biology. Here, we provide a personal perspective of the increasingly useful role that mass spectrometric techniques are exerting during the elucidation of higher order protein structures. Areas covered in this brief perspective include MS as an enabling tool for the high resolution structural biologist, for compositional analysis of endogenous protein complexes, for stoichiometry determination, as well as for integrated approaches for the structural elucidation of protein complexes. We conclude with a vision for the future role of MS-based techniques in the development of a multi-scale molecular microscope.
Neutron scattering studies on chromatin higher-order structure
Graziano, V.; Gerchman, S.E.; Schneider, D.K.; Ramakrishnan, V.
1994-12-31
We have been engaged in studies of the structure and condensation of chromatin into the 30nm filament using small-angle neutron scattering. We have also used deuterated histone H1 to determine its location in the chromatin 30nm filament. Our studies indicate that chromatin condenses with increasing ionic strength to a limiting structure that has a mass per unit length of 6-7 nucleosomes/11 nm. They also show that the linker histone H1/H5 is located in the interior of the chromatin filament, in a position compatible with its binding to the inner face of the nucleosome. Analysis of the mass per unit length as a function of H5 stoichiometry suggests that 5-7 contiguous nucleosomes need to have H5 bound before a stable higher order structure can exist.
Higher order monochromatic aberrations of the human infant eye
Wang, Jingyun; Candy, T. Rowan
2009-01-01
The monochromatic optical aberrations of the eye degrade retinal image quality. Any significant aberrations during postnatal development could contribute to infants’ immature visual performance and provide signals for the control of eye growth. Aberrations of human infant eyes from 5 to 7 weeks old were compared with those of adult subjects using a model of an adultlike infant eye that accounted for differences in both eye and pupil size. Data were collected using the COAS Shack-Hartmann wavefront sensor. The results demonstrate that the higher order aberrations of the 5-to-7-week-old eye are less than a factor of 2 greater than predicted for an adultlike infant eye of this age. The data are discussed in the context of infants’ visual performance and the signals available for controlling growth of the eye. PMID:16097867
Higher order statistics of planetary gravities and topographies
NASA Technical Reports Server (NTRS)
Kaula, William M.
1993-01-01
The statistical properties of Earth, Venus, Mars, Moon, and a 3-D mantle convection model are compared. The higher order properties are expressed by third and fourth moments: i.e., as mean products over equilateral triangles (defined as coskewance) and equilateral quadrangles (defined as coexance). For point values, all the fields of real planets have positive skewness, ranging from slightly above zero for Lunar gravity to 2.6 sigma(exp 3) for Martian gravity (sigma is rms magnitude). Six of the eight excesses are greater than Gaussian (3 sigma(exp 4)), ranging from 2.0 sigma(exp 4) for Earth topography to 18.6 sigma(exp 4), for Martian topography. The coskewances and coexances drop off to zero within 20 deg arc in most cases. The mantle convective model has zero skewness and excess slightly less than Gaussian, probably arising from viscosity variations being only radial.
Inflationary scenarios in Starobinsky model with higher order corrections
NASA Astrophysics Data System (ADS)
Artymowski, Michał; Lalak, Zygmunt; Lewicki, Marek
2015-06-01
We consider the Starobinsky inflation with a set of higher order corrections parametrised by two real coefficients λ1 , λ2. In the Einstein frame we have found a potential with the Starobinsky plateau, steep slope and possibly with an additional minimum, local maximum or a saddle point. We have identified three types of inflationary behaviour that may be generated in this model: i) inflation on the plateau, ii) at the local maximum (topological inflation), iii) at the saddle point. We have found limits on parameters λi and initial conditions at the Planck scale which enable successful inflation and disable eternal inflation at the plateau. We have checked that the local minimum away from the GR vacuum is stable and that the field cannot leave it neither via quantum tunnelling nor via thermal corrections.
RNA Seeds Higher Order Assembly of FUS Protein
Schwartz, Jacob C.; Wang, Xueyin; Podell, Elaine R.; Cech, Thomas R.
2014-01-01
SUMMARY The abundant nuclear RNA-binding protein FUS binds the CTD of RNA polymerase II in an RNA-dependent manner, affecting Ser2 phosphorylation and transcription. Here we examine the mechanism of this process and find that RNA binding nucleates the formation of higher order FUS RNP assemblies that bind the CTD. Both the low-complexity domain and the RGG domain of FUS contribute to assembly. The assemblies appear fibrous by electron microscopy and have characteristics of beta-zipper structures. These results support the emerging view that the pathologic protein aggregation seen in neurodegenerative diseases such as ALS may occur by exaggeration of functionally important assemblies of RNA-binding proteins. PMID:24268778
Higher-order cellular information processing with synthetic RNA devices.
Win, Maung Nyan; Smolke, Christina D
2008-10-17
The engineering of biological systems is anticipated to provide effective solutions to challenges that include energy and food production, environmental quality, and health and medicine. Our ability to transmit information to and from living systems, and to process and act on information inside cells, is critical to advancing the scale and complexity at which we can engineer, manipulate, and probe biological systems. We developed a general approach for assembling RNA devices that can execute higher-order cellular information processing operations from standard components. The engineered devices can function as logic gates (AND, NOR, NAND, or OR gates) and signal filters, and exhibit cooperativity. RNA devices process and transmit molecular inputs to targeted protein outputs, linking computation to gene expression and thus the potential to control cellular function.
A higher-order-mode erbium-doped-fiber amplifier.
Nicholson, J W; Fini, J M; DeSantolo, A M; Monberg, E; DiMarcello, F; Fleming, J; Headley, C; DiGiovanni, D J; Ghalmi, S; Ramachandran, S
2010-08-16
We demonstrate the first erbium-doped fiber amplifier operating in a single, large-mode area, higher-order mode. A high-power, fundamental-mode, Raman fiber laser operating at 1480 nm was used as a pump source. Using a UV-written, long-period grating, both pump and 1564 nm signal were converted to the LP(0,10) mode, which had an effective area of 2700 microm(2) at 1550 nm. A maximum output power of 5.8 W at 1564 nm with more than 20 dB of gain in a 2.68 m long amplifier was obtained. The mode profile was undistorted at the highest output power.
Pulse transmission transmitter including a higher order time derivate filter
Dress, Jr., William B.; Smith, Stephen F.
2003-09-23
Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission transmitter includes: a clock; a pseudorandom polynomial generator coupled to the clock, the pseudorandom polynomial generator having a polynomial load input; an exclusive-OR gate coupled to the pseudorandom polynomial generator, the exclusive-OR gate having a serial data input; a programmable delay circuit coupled to both the clock and the exclusive-OR gate; a pulse generator coupled to the programmable delay circuit; and a higher order time derivative filter coupled to the pulse generator. The systems and methods significantly reduce lower-frequency emissions from pulse transmission spread-spectrum communication modes, which reduces potentially harmful interference to existing radio frequency services and users and also simultaneously permit transmission of multiple data bits by utilizing specific pulse shapes.
Higher order mode propagation in nonuniform circular ducts
NASA Technical Reports Server (NTRS)
Cho, Y. C.; Ingard, K. U.
1980-01-01
Higher order mode propagation in a nonuniform circular duct without mean flow was investigated. An approximate wave equation is derived on the assumptions that the duct cross section varies slowly and that mode conversion is negligible. Exact closed form solutions are obtained for a particular class of converging-diverging circular duct which referred to as 'circular cosh duct.' Numerical results are presented in terms of the transmission loss for the various duct shapes and frequencies. The results are applicable to multimodal propagation, single mode propagation, and sound radiation from certain types of contoured inlet ducts, or of sound propagation in a converging-diverging duct of somewhat different shape from a cosh duct.
Higher order mode propagation in nonuniform circular ducts
NASA Technical Reports Server (NTRS)
Cho, Y. C.; Ingard, K. U.
1980-01-01
This paper presents an analytical investigation of higher order mode propagation in a nonuniform circular duct without mean flow. An approximate wave equation is derived on the assumptions that the duct cross section varies slowly and that mode conversion is negligible. Exact closed form solutions are obtained for a particular class of converging-diverging circular duct which is here referred to as 'circular cosh duct'. Numerical results are presentd in terms of the transmission loss for the various duct shapes and frequencies. The results are applicable to studies of multimodal propagation as well as single mode propagation. The results are also applicable to studies of sound radiation from certain types of contoured inlet ducts, or of sound propagation in a converging-diverging duct of somewhat different shape from a cosh duct.
Higher order statistical moment application for solar PV potential analysis
NASA Astrophysics Data System (ADS)
Basri, Mohd Juhari Mat; Abdullah, Samizee; Azrulhisham, Engku Ahmad; Harun, Khairulezuan
2016-10-01
Solar photovoltaic energy could be as alternative energy to fossil fuel, which is depleting and posing a global warming problem. However, this renewable energy is so variable and intermittent to be relied on. Therefore the knowledge of energy potential is very important for any site to build this solar photovoltaic power generation system. Here, the application of higher order statistical moment model is being analyzed using data collected from 5MW grid-connected photovoltaic system. Due to the dynamic changes of skewness and kurtosis of AC power and solar irradiance distributions of the solar farm, Pearson system where the probability distribution is calculated by matching their theoretical moments with that of the empirical moments of a distribution could be suitable for this purpose. On the advantage of the Pearson system in MATLAB, a software programming has been developed to help in data processing for distribution fitting and potential analysis for future projection of amount of AC power and solar irradiance availability.
Higher Order Intentionality Tasks Are Cognitively More Demanding.
Lewis, Penelope A; Birch, Amy; Hall, Alexander; Dunbar, R I M
2017-03-13
A central assumption that underpins much of the discussion of the role played by social cognition in brain evolution is that social cognition is unusually cognitively demanding. This assumption has never been tested. Here, we use a task in which participants read stories and then answered questions about the stories in a behavioural experiment (39 participants) and an fMRI experiment (17 participants) to show that mentalising requires more time for responses than factual memory of a matched complexity and also that higher orders of mentalising is disproportionately more demanding and requires the recruitment of more neurons in brain regions known to be associated with theory of mind, including insula, posterior STS, temporal pole, and cerebellum. These results have significant implications both for models of brain function and for models of brain evolution.
A higher-order theory of emotional consciousness.
LeDoux, Joseph E; Brown, Richard
2017-03-07
Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programmed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system in the brain. In this view, what differs in emotional and nonemotional states are the kinds of inputs that are processed by a general cortical network of cognition, a network essential for conscious experiences. Although subcortical circuits are not directly responsible for conscious feelings, they provide nonconscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences. In building the case for this proposal, we defend a modified version of what is known as the higher-order theory of consciousness.
Inflationary scenarios in Starobinsky model with higher order corrections
Artymowski, Michał; Lalak, Zygmunt; Lewicki, Marek
2015-06-17
We consider the Starobinsky inflation with a set of higher order corrections parametrised by two real coefficients λ{sub 1} ,λ{sub 2}. In the Einstein frame we have found a potential with the Starobinsky plateau, steep slope and possibly with an additional minimum, local maximum or a saddle point. We have identified three types of inflationary behaviour that may be generated in this model: i) inflation on the plateau, ii) at the local maximum (topological inflation), iii) at the saddle point. We have found limits on parameters λ{sub i} and initial conditions at the Planck scale which enable successful inflation and disable eternal inflation at the plateau. We have checked that the local minimum away from the GR vacuum is stable and that the field cannot leave it neither via quantum tunnelling nor via thermal corrections.
Higher-order resonances in a Stark decelerator
Meerakker, Sebastiaan Y.T. van de; Bethlem, Hendrick L.; Vanhaecke, Nicolas; Meijer, Gerard
2005-05-15
The motion of polar molecules can be controlled by time-varying inhomogeneous electric fields. In a Stark decelerator, this is exploited to select a fraction of a molecular beam that is accelerated, transported, or decelerated. Phase stability ensures that the selected bunch of molecules is kept together throughout the deceleration process. In this paper an extended description of phase stability in a Stark decelerator is given, including higher-order effects. This analysis predicts a wide variety of resonances that originate from the spatial and temporal periodicity of the electric fields. These resonances are experimentally observed using a beam of OH ({sup 2}{pi}{sub 3/2},v=0,J=3/2) radicals passing through a Stark decelerator.
Efficient multiple time-stepping algorithms of higher order
NASA Astrophysics Data System (ADS)
Demirel, Abdullah; Niegemann, Jens; Busch, Kurt; Hochbruck, Marlis
2015-03-01
Multiple time-stepping (MTS) algorithms allow to efficiently integrate large systems of ordinary differential equations, where a few stiff terms restrict the timestep of an otherwise non-stiff system. In this work, we discuss a flexible class of MTS techniques, based on multistep methods. Our approach contains several popular methods as special cases and it allows for the easy construction of novel and efficient higher-order MTS schemes. In addition, we demonstrate how to adapt the stability contour of the non-stiff time-integration to the physical system at hand. This allows significantly larger timesteps when compared to previously known multistep MTS approaches. As an example, we derive novel predictor-corrector (PCMTS) schemes specifically optimized for the time-integration of damped wave equations on locally refined meshes. In a set of numerical experiments, we demonstrate the performance of our scheme on discontinuous Galerkin time-domain (DGTD) simulations of Maxwell's equations.
Chemical probes for higher-order structure in RNA.
Peattie, D A; Gilbert, W
1980-01-01
Three chemical reactions can probe the secondary and tertiary interactions of RNA molecules in solution. Dimethyl sulfate monitors the N-7 of guanosines and senses tertiary interactions there, diethyl pyrocarbonate detects stacking of adenosines, and an alternate dimethyl sulfate reaction examines the N-3 of cytidines and thus probes base pairing. The reactions work between 0 degrees C and 90 degrees C and at pH 4.5--8.5 in a variety of buffers. As an example we follow the progressive denaturation of yeast tRNAPhe terminally labeled with 32P as the tertiary and secondary structures sequentially melt out. A single autoradiograph of a terminally labeled molecule locates regions of higher-order structure and identifies the bases involved. Images PMID:6159633
A higher-order theory of emotional consciousness
LeDoux, Joseph E.; Brown, Richard
2017-01-01
Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programmed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system in the brain. In this view, what differs in emotional and nonemotional states are the kinds of inputs that are processed by a general cortical network of cognition, a network essential for conscious experiences. Although subcortical circuits are not directly responsible for conscious feelings, they provide nonconscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences. In building the case for this proposal, we defend a modified version of what is known as the higher-order theory of consciousness. PMID:28202735
Evidence for several higher order structural elements in ribosomal RNA.
Woese, C R; Gutell, R R
1989-05-01
Comparative analysis of small subunit ribosomal RNA sequences suggests the existence of two new higher order interactions: (i) a double-helical structure involving positions 505-507 and 524-526 (Escherichia coli numbering) and (ii) an interaction between the region of position 130 and the helix located approximately between positions 180 and 195. In the first of these, one of the strands of the helix exists in the bulge loop, and the other strand exists in the terminal loop of a previously recognized compound helix involving positions 500-545. Therefore, the new structure formally represents a pseudoknot. In the second, the insertion/deletion of a nucleotide in the vicinity of position 130 correlates with the length of the helix in the 180-195 region, the latter having a 3-base-pair stalk when the base in question is deleted and a stalk of approximately 10 pairs when it is inserted.
Evidence for several higher order structural elements in ribosomal RNA.
Woese, C R; Gutell, R R
1989-01-01
Comparative analysis of small subunit ribosomal RNA sequences suggests the existence of two new higher order interactions: (i) a double-helical structure involving positions 505-507 and 524-526 (Escherichia coli numbering) and (ii) an interaction between the region of position 130 and the helix located approximately between positions 180 and 195. In the first of these, one of the strands of the helix exists in the bulge loop, and the other strand exists in the terminal loop of a previously recognized compound helix involving positions 500-545. Therefore, the new structure formally represents a pseudoknot. In the second, the insertion/deletion of a nucleotide in the vicinity of position 130 correlates with the length of the helix in the 180-195 region, the latter having a 3-base-pair stalk when the base in question is deleted and a stalk of approximately 10 pairs when it is inserted. PMID:2654936
Dynamic facilitation picture of a higher-order glass singularity.
Sellitto, Mauro; De Martino, Daniele; Caccioli, Fabio; Arenzon, Jeferson J
2010-12-31
We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions.
Higher order corrections to asymptotic-de Sitter inflation
NASA Astrophysics Data System (ADS)
Mohsenzadeh, M.; Yusofi, E.
2017-08-01
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.
Inflationary scenarios in Starobinsky model with higher order corrections
Artymowski, Michał; Lalak, Zygmunt; Lewicki, Marek E-mail: Zygmunt.Lalak@fuw.edu.pl
2015-06-01
We consider the Starobinsky inflation with a set of higher order corrections parametrised by two real coefficients λ{sub 1} , λ{sub 2}. In the Einstein frame we have found a potential with the Starobinsky plateau, steep slope and possibly with an additional minimum, local maximum or a saddle point. We have identified three types of inflationary behaviour that may be generated in this model: i) inflation on the plateau, ii) at the local maximum (topological inflation), iii) at the saddle point. We have found limits on parameters λ{sub i} and initial conditions at the Planck scale which enable successful inflation and disable eternal inflation at the plateau. We have checked that the local minimum away from the GR vacuum is stable and that the field cannot leave it neither via quantum tunnelling nor via thermal corrections.
Intermediary LEO propagation including higher order zonal harmonics
NASA Astrophysics Data System (ADS)
Hautesserres, Denis; Lara, Martin
2017-04-01
Two new intermediary orbits of the artificial satellite problem are proposed. The analytical solutions include higher order effects of the geopotential, and are obtained by means of a torsion transformation applied to the quasi-Keplerian system resulting after the elimination of the parallax simplification, for the first intermediary, and after the elimination of the parallax and perigee simplifications, for the second one. The new intermediaries perform notably well for low Earth orbits propagation, are free from special functions, and result advantageous, both in accuracy and efficiency, when compared to the standard Cowell integration of the J_2 problem, thus providing appealing alternatives for onboard, short-term, orbit propagation under limited computational resources.
Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models
NASA Technical Reports Server (NTRS)
Buchert, T.; Melott, A. L.; Weiss, A. G.
1993-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the
Quantum theory of the third-order nonlinear electrodynamic effects of graphene
NASA Astrophysics Data System (ADS)
Mikhailov, S. A.
2016-02-01
The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene σα β γ δ(ω1,ω2,ω3) , which describes its nonlinear response to a uniform electromagnetic field. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third-harmonic generation, the four-wave mixing, the saturable absorption, the second-harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.
X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity
NASA Astrophysics Data System (ADS)
Balyan, M. K.
2016-12-01
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.
Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
Non-rigid registration using higher-order mutual information
NASA Astrophysics Data System (ADS)
Rueckert, D.; Clarkson, M. J.; Hill, D. L. G.; Hawkes, D. J.
2000-03-01
Non-rigid registration of multi-modality images is an important tool for assessing temporal and structural changesbetween images. For rigid registration, voxel similarity measures like mutual information have been shown to alignimages from different modalities accurately and robustly. For non-rigid registration, mutual information can besensitive to local variations of intensity which in MR images may be caused by RF inhomogeneity. The reasonfor the sensitivity of mutual information towards intensity variations stems from the fact that mutual informationignores any spatial information. In this paper we propose an extension of the mutual information framework whichincorporates spatial information about higher-order image structure into the registration process and has the potentialto improve the accuracy and robustness of non-rigid registration in the presence of intensity variations. We haveapplied the non-rigid registration algorithm to a number of simulated MR brain images of a digital phantom whichhave been degraded by a simulated intensity shading and a known deformation. In addition, we have applied thealgorithm for the non-rigid registration of eight pre- and post-operative brain MR images which were acquired withan interventional MR scanner and therefore have substantial intensity shading due to RF field inhomogeneities. Inall cases the second-order estimate of mutual information leads to robust and accurate registration.
Analytical higher-order model for flexible and stretchable sensors
NASA Astrophysics Data System (ADS)
Zhang, Yongfang; Zhu, Hongbin; Liu, Cheng; Liu, Xu; Liu, Fuxi; Lü, Yanjun
2015-03-01
The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil. The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil. According to the requirement of mechanical flexibility of the sensor, the combined use of a layered flexible structural formation and a strain isolation layer is implemented. An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors. The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model. The stress distribution in the structure is investigated when bending load is applied to the structures. The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation (polydimethylsiloxane) layer accurately. The results by the proposed model are in good agreement with the finite element method, in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer. The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.
Higher-order nonclassical effects in fluctuating-loss channels
NASA Astrophysics Data System (ADS)
Bohmann, M.; Sperling, J.; Semenov, A. A.; Vogel, W.
2017-01-01
We study the evolution of higher-order nonclassicality and entanglement criteria in atmospheric fluctuating-loss channels. By formulating input-output relations for the matrix of moments, we investigate the influence of such channels on the corresponding quantumness criteria. This generalization of our previous work on Gaussian entanglement [M. Bohmann et al., Phys. Rev. A 94, 010302(R) (2016), 10.1103/PhysRevA.94.010302] not only exploits second-order-based scenarios, but it also provides a detailed investigation of nonclassicality and entanglement in non-Gaussian and multimode radiation fields undergoing a fluctuating attenuation. That is, various examples of criteria and states are studied in detail, unexpected effects, e.g., the dependency of the squeezing transfer on the coherent displacement, are discovered, and it is demonstrated that non-Gaussian entanglement can be more robust against atmospheric losses than Gaussian one. Additionally, we propose a detection scheme for measuring the considered moments after propagation through the atmosphere. Therefore, our results may help to develop, improve, and optimize non-Gaussian sources of quantum light for applications in free-space quantum communication.
Correlated stopping, proton clusters and higher order proton cumulants
NASA Astrophysics Data System (ADS)
Bzdak, Adam; Koch, Volker; Skokov, Vladimir
2017-05-01
We investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons N_{part} lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at √{s}=7.7 GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce the preliminary experimental data. We speculate that this clustering may originate either from collective/multi-collision stopping which is expected to be effective at lower energies or from a possible first-order phase transition, or from (attractive) final state interactions. To test these ideas we propose to measure a mixed multi-particle correlation between stopped protons and a produced particle (e.g. pion, antiproton).
Certifiable higher order sliding mode control: Practical stability margins approach
NASA Astrophysics Data System (ADS)
Panathula, Chandrasekhara Bharath
The Higher Order Sliding Mode (HOSM) controllers are well known for their robustness/insensitivity to bounded perturbations and for handling any given arbitrary relative degree system. The HOSM controller is to be certified for robustness to unmodeled dynamics, before deploying the controller for practical applications. Phase Margin (PM) and Gain Margin ( GM) are the classical characteristics used in linear systems to quantify the linear controller robustness to unmodeled dynamics, and certain values of these margins are required to certify the controller. These conventional margins (PM and GM) are extended to Practical Stability Phase Margin (PSPM) and Practical Stability Gain Margin (PSGM) in this dissertation, and are used to quantify the HOSM control robustness to unmodeled dynamics, presiding the tool to close the gap for HOSM control certification. The proposed robustness metrics ( PSPM and PSGM) are identified by developing tools/algorithms based on Describing Function-Harmonic Balance method. In order for the HOSM controller to achieve the prescribed values on robustness metrics ( PSPM and PSGM), the HOSM controller is cascaded with a linear compensator. A case study of the application of the proposed metrics (PSPM and PSGM) for the certification of F-16 aircraft HOSM attitude control robustness to cascade unmodeled dynamics is presented. In addition, several simulation examples are presented to verify and to validate the proposed methodology.
SPHS: smoothed particle hydrodynamics with a higher order dissipation switch
NASA Astrophysics Data System (ADS)
Read, J. I.; Hayfield, T.
2012-06-01
We present a novel implementation of smoothed particle hydrodynamics that uses the spatial derivative of the velocity divergence as a higher order dissipation switch. Our switch - which is second order accurate - detects flow convergence before it occurs. If particle trajectories are going to cross, we switch on the usual SPH artificial viscosity, as well as conservative dissipation in all advected fluid quantities (e.g. the entropy). The viscosity and dissipation terms (that are numerical errors) are designed to ensure that all fluid quantities remain single valued as particles approach one another, to respect conservation laws, and to vanish on a given physical scale as the resolution is increased. SPHS alleviates a number of known problems with 'classic' SPH, successfully resolving mixing, and recovering numerical convergence with increasing resolution. An additional key advantage is that - treating the particle mass similarly to the entropy - we are able to use multimass particles, giving significantly improved control over the refinement strategy. We present a wide range of code tests including the Sod shock tube, Sedov-Taylor blast wave, Kelvin-Helmholtz Instability, the 'blob test' and some convergence tests. Our method performs well on all tests, giving good agreement with analytic expectations.
Correlated stopping, proton clusters and higher order proton cumulants
Bzdak, Adam; Koch, Volker; Skokov, Vladimir
2017-05-05
Here, we investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons Npart lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at √s = 7.7 GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce the preliminary experimental data. We speculate that this clustering may originate eithermore » from collective/multi-collision stopping which is expected to be effective at lower energies or from a possible first-order phase transition, or from (attractive) final state interactions. To test these ideas we propose to measure a mixed multi-particle correlation between stopped protons and a produced particle (e.g. pion, antiproton).« less
Higher-order approximations in stress analysis of submarine pipelines
Konuk, I.
1980-12-01
A unified three-dimensional formulation of the pipeline or riser problems is developed by following the rod theories. A rigorous singular perturbation technique is used to solve the associated two-dimensional nonlinear problem. The results can be used with a programmable calculator.
Cycles in finite samples and cumulative processes of higher orders
NASA Astrophysics Data System (ADS)
Klemeš, VíT.; Klemeš, Ivo
1988-01-01
The process formed by a sequence of cumulative departures from the mean or from some other constant (residual mass curve, cusum chart) is a popular tool for the representation and analysis of time series in many sciences, for example, in hydrology, climatology, economics, game theory. In these and other natural and social sciences, similar cumulative processes also often arise naturally; examples include fluctuations of storage in a dam with a constant release rate, lake levels, volume of glaciers, biomass, inventories, and bank accounts. Moreover, many natural economic and other phenomena may represent, or contain, components of cumulative processes of higher orders, i.e., cumulative processes of cumulative processes. In this paper we show that for a sample {yt(0)}≡{xt} of any finite size N, the pure cumulative process of nth order, yt(n)≡∑i=1t(yi(n-1) - μ(n-1)), where μ(n-1) is the sample mean of {yt(n-1)} and t=1, 2, …, N, converges for n→∞ to a sine wave with a period equal to an integral fraction of the sample size N. This happens for any initial sample {yt(0)} and the convergence is of an exponential order. For samples from most stochastic as well as deterministic processes, the period of the limiting sine wave is equal to the sample size N. This behavior is demonstrated by examples involving samples from various processes ranging from pure random series to various deterministic series and including time series of some natural processes such as streamflow, lake levels, and glacier volumes. The paper includes a demonstration of effects of noise superimposed on, and of error in the value of, sample mean on the rate of convergence, and a discussion of some practical implications of the phenomenon described; it brings together some aspects of the work of Slutzky (1937), Hurst (1951), and Yule (1926).
Emotion recognition from EEG using higher order crossings.
Petrantonakis, Panagiotis C; Hadjileontiadis, Leontios J
2010-03-01
Electroencephalogram (EEG)-based emotion recognition is a relatively new field in the affective computing area with challenging issues regarding the induction of the emotional states and the extraction of the features in order to achieve optimum classification performance. In this paper, a novel emotion evocation and EEG-based feature extraction technique is presented. In particular, the mirror neuron system concept was adapted to efficiently foster emotion induction by the process of imitation. In addition, higher order crossings (HOC) analysis was employed for the feature extraction scheme and a robust classification method, namely HOC-emotion classifier (HOC-EC), was implemented testing four different classifiers [quadratic discriminant analysis (QDA), k-nearest neighbor, Mahalanobis distance, and support vector machines (SVMs)], in order to accomplish efficient emotion recognition. Through a series of facial expression image projection, EEG data have been collected by 16 healthy subjects using only 3 EEG channels, namely Fp1, Fp2, and a bipolar channel of F3 and F4 positions according to 10-20 system. Two scenarios were examined using EEG data from a single-channel and from combined-channels, respectively. Compared with other feature extraction methods, HOC-EC appears to outperform them, achieving a 62.3% (using QDA) and 83.33% (using SVM) classification accuracy for the single-channel and combined-channel cases, respectively, differentiating among the six basic emotions, i.e., happiness, surprise, anger, fear, disgust, and sadness. As the emotion class-set reduces its dimension, the HOC-EC converges toward maximum classification rate (100% for five or less emotions), justifying the efficiency of the proposed approach. This could facilitate the integration of HOC-EC in human machine interfaces, such as pervasive healthcare systems, enhancing their affective character and providing information about the user's emotional status (e.g., identifying user's emotion
Predicting perceptual learning from higher-order cortical processing.
Wang, Fang; Huang, Jing; Lv, Yaping; Ma, Xiaoli; Yang, Bin; Wang, Encong; Du, Boqi; Li, Wu; Song, Yan
2016-01-01
Visual perceptual learning has been shown to be highly specific to the retinotopic location and attributes of the trained stimulus. Recent psychophysical studies suggest that these specificities, which have been associated with early retinotopic visual cortex, may in fact not be inherent in perceptual learning and could be related to higher-order brain functions. Here we provide direct electrophysiological evidence in support of this proposition. In a series of event-related potential (ERP) experiments, we recorded high-density electroencephalography (EEG) from human adults over the course of learning in a texture discrimination task (TDT). The results consistently showed that the earliest C1 component (68-84ms), known to reflect V1 activity driven by feedforward inputs, was not modulated by learning regardless of whether the behavioral improvement is location specific or not. In contrast, two later posterior ERP components (posterior P1 and P160-350) over the occipital cortex and one anterior ERP component (anterior P160-350) over the prefrontal cortex were progressively modified day by day. Moreover, the change of the anterior component was closely correlated with improved behavioral performance on a daily basis. Consistent with recent psychophysical and imaging observations, our results indicate that perceptual learning can mainly involve changes in higher-level visual cortex as well as in the neural networks responsible for cognitive functions such as attention and decision making.
Higher order acoustoelastic Lamb wave propagation in stressed plates.
Pei, Ning; Bond, Leonard J
2016-11-01
Modeling and experiments are used to investigate Lamb wave propagation in the direction perpendicular to an applied stress. Sensitivity, in terms of changes in velocity, for both symmetrical and anti-symmetrical modes was determined. Codes were developed based on analytical expressions for waves in loaded plates and they were used to give wave dispersion curves. The experimental system used a pair of compression wave transducers on variable angle wedges, with set separation, and variable frequency tone burst excitation, on an aluminum plate 0.16 cm thick with uniaxial applied loads. The loads, which were up to 600 με, were measured using strain gages. Model results and experimental data are in good agreement. It was found that the change in Lamb wave velocity, due to the acoustoelastic effect, for the S1 mode exhibits about ten times more sensitive, in terms of velocity change, than the traditional bulk wave measurements, and those performed using the fundamental Lamb modes. The data presented demonstrate the potential for the use of higher order Lamb modes for online industrial stress measurement in plate, and that the higher sensitivity seen offers potential for improved measurement systems.
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.
Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps.
Sailer, Zachary R; Harms, Michael J
2017-03-01
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the "scale" of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.
Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps
Sailer, Zachary R.; Harms, Michael J.
2017-01-01
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the “scale” of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this article, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2 to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps. PMID:28100592
Nonresonant high-order nonlinear optical properties of silver nanoparticles in aqueous solution.
Rativa, Diego; de Araujo, R E; Gomes, A S L
2008-11-10
In this work we determine the third, fifth- and seventh-order nonresonant nonlinear optical properties of silver nanoparticles (9 nm average diameter) colloids in aqueous solution under high intensity excitation. The nonlinear optical response and its dependence with the nanoparticles filling factor was measured and theoretically described. We show that for low inclusion concentration, the third order nonlinearity of the colloid can be described by the generalized Maxwell-Garnett model. With the increase of the nanoparticle concentration, changes in the medium nonlinearities was observed leading to high order effects. The fifth- and seventh- order susceptibilities were obtained for highly concentrated silver nanoparticle colloid and the data was supported by a theoretical model. The conventional Z-scan technique was employed, using 80 f s laser pulses at 800 nm, in a regime of high pulse energy (microJ) and low repetition rate (1 kHz).
Regular solutions to higher order curvature Einstein Yang Mills systems in higher dimensions
NASA Astrophysics Data System (ADS)
Breitenlohner, Peter; Maison, Dieter; Tchrakian, D. H.
2005-12-01
We study regular, static, spherically symmetric solutions of Yang Mills theories employing higher order invariants of the field strength coupled to gravity in d dimensions. We consider models with only two such invariants characterized by integers p and q. These models depend on one dimensionless parameter α leading to one-parameter families of regular solutions, obtainable by numerical solution of the corresponding boundary value problem. Much emphasis is put on an analytical understanding of the numerical results.
Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2012-01-01
A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.
NASA Astrophysics Data System (ADS)
Pandian, Muthu Senthil; Karuppasamy, P.; Ramasamy, P.
2017-05-01
The semi-organic nonlinear optical single crystals of potassium 3,5-dinitrobenzoate (KDNB) were grown by slow evaporation solution technique (SEST). The lattice parameters of the grown crystal were confirmed by single crystal X-ray diffraction analysis. The optical transmittance, cut-off wavelength and band gap of the KDNB crystal were obtained by UV-Vis NIR spectrum analysis. Vickers microhardness analysis was carried out to identify mechanical stability and work hardening co-efficient of the grown crystal. The crystalline perfection of the grown crystal was identified by chemical etching study using water as etchant. The third-order nonlinear optical properties such as nonlinear refractive index (n2), nonlinear absorption co-efficient (β) and third order nonlinear susceptibility (χ(3)) of KDNB crystal were evaluated using Z-scan technique at the wavelength of 632.8 nm.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States.
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-21
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects' affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain's motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States
NASA Astrophysics Data System (ADS)
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-01
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-01-01
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states. PMID:26996254
Higher-order Fourier analysis over finite fields and applications
NASA Astrophysics Data System (ADS)
Hatami, Pooya
Higher-order Fourier analysis is a powerful tool in the study of problems in additive and extremal combinatorics, for instance the study of arithmetic progressions in primes, where the traditional Fourier analysis comes short. In recent years, higher-order Fourier analysis has found multiple applications in computer science in fields such as property testing and coding theory. In this thesis, we develop new tools within this theory with several new applications such as a characterization theorem in algebraic property testing. One of our main contributions is a strong near-equidistribution result for regular collections of polynomials. The densities of small linear structures in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by approximating the indicator function of a subset by a function of bounded number of polynomials. Then, to approximate the average, it suffices to know the joint distribution of the polynomials applied to the linear forms. We prove a near-equidistribution theorem that describes these distributions for the group F(n/p) when p is a fixed prime. This fundamental fact was previously known only under various extra assumptions about the linear forms or the field size. We use this near-equidistribution theorem to settle a conjecture of Gowers and Wolf on the true complexity of systems of linear forms. Our next application is towards a characterization of testable algebraic properties. We prove that every locally characterized affine-invariant property of functions f : F(n/p) → R with n∈ N, is testable. In fact, we prove that any such property P is proximity-obliviously testable. More generally, we show that any affine-invariant property that is closed under subspace restrictions and has "bounded complexity" is testable. We also prove that any property that can be described as the property of decomposing into a known structure of low
Ultra-high speed optical signal processing through third-order fiber nonlinearity (Invited Paper)
NASA Astrophysics Data System (ADS)
Kikuchi, Kazuro
2005-04-01
Third-order optical nonlinearity in optical fibers has many attractive applications to all-optical signal processing that will be employed in future large-capacity photonic networks. After reviewing the third-order nonlinear optical property of optical fibers, we describe our recent experimental results on all-optical signal processing functions such as wideband wavelength conversion, ultrafast gate switching, and ultrafast pulse reshaping. These functions are based on self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in nonlinear fibers.
NASA Astrophysics Data System (ADS)
Sudheesh, P.; Rao, D. Mallikharjuna; Chandrasekharan, K.
2014-01-01
The third-order nonlinear optical properties of newly synthesized phenylhydrazone derivatives and the influence of noble metal nanoparticles (Ag & Au) on their nonlinear optical responses were investigated by employing Degenerate Four wave Mixing (DFWM) technique with a 7 nanosecond, 10Hz Nd: YAG laser pulses at 532nm. Metal nanoparticles were prepared by laser ablation and the particle formation was confirmed using UV-Visible spectroscopy, Transmission Electron Microscopy (TEM). The nonlinear optical susceptibility were measured and found to be of the order 10-13esu. The results are encouraging and conclude that the materials are promising candidate for future optical device applications.
Sudheesh, P.; Chandrasekharan, K.; Rao, D. Mallikharjuna
2014-01-28
The third-order nonlinear optical properties of newly synthesized phenylhydrazone derivatives and the influence of noble metal nanoparticles (Ag and Au) on their nonlinear optical responses were investigated by employing Degenerate Four wave Mixing (DFWM) technique with a 7 nanosecond, 10Hz Nd: YAG laser pulses at 532nm. Metal nanoparticles were prepared by laser ablation and the particle formation was confirmed using UV-Visible spectroscopy, Transmission Electron Microscopy (TEM). The nonlinear optical susceptibility were measured and found to be of the order 10{sup −13}esu. The results are encouraging and conclude that the materials are promising candidate for future optical device applications.
Weiss, William F; Gabrielson, John P; Al-Azzam, Wasfi; Chen, Guodong; Davis, Darryl L; Das, Tapan K; Hayes, David B; Houde, Damian; Singh, Satish K
2016-12-01
Characterization of the higher order structure (HOS) of protein-based biopharmaceutical products is an important aspect of their development. Opinions vary about how best to apply biophysical methods, in which contexts to use these methods, and how to use the resulting data to make technical decisions as drug candidates are commercialized [Gabrielson JP, Weiss WF IV. J Pharm Sci. 2015;104(4):1240-1245]. The aim of this commentary is to provide guidance for the development and implementation of a robust and comprehensive HOS characterization strategy. We first consider important concepts involved in developing a strategy that is appropriately suited to a particular biologic, and then discuss ways industry can partner with academia, technology companies, government laboratories, and regulatory agencies to improve the consistency with which HOS characterization is applied across the biopharmaceutical industry. Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.
A viscoelastic higher-order beam finite element
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tressler, Alexander
1996-01-01
A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
The third-order nonlinear optical properties in polymer ferroelectrics
NASA Astrophysics Data System (ADS)
Verkhovskaya, K. A.; Grishina, A. D.; Krivenko, T. V.; Savel'ev, V. V.; Laryushkin, A. S.; Vannikov, A. V.
2017-04-01
The third-order susceptibility of vinylidene fluoride-trifluoroethylene (VDF-TrFE) copolymer are analyzed by using the z-scan technique with a nanosecond laser as an excitation source. It is established that optical transmittance of the VDF-TrFE samples decreases after their polarization in an electric field.
Nonlinear Programming Approach to Optimal Scaling of Partially Ordered Categories
ERIC Educational Resources Information Center
Nishisato, Shizuhiko; Arri, P. S.
1975-01-01
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…
A Higher-Order Neural Network Design for Improving Segmentation Performance in Medical Image Series
NASA Astrophysics Data System (ADS)
Selvi, Eşref; Selver, M. Alper; Güzeliş, Cüneyt; Dicle, Oǧuz
2014-03-01
Segmentation of anatomical structures from medical image series is an ongoing field of research. Although, organs of interest are three-dimensional in nature, slice-by-slice approaches are widely used in clinical applications because of their ease of integration with the current manual segmentation scheme. To be able to use slice-by-slice techniques effectively, adjacent slice information, which represents likelihood of a region to be the structure of interest, plays critical role. Recent studies focus on using distance transform directly as a feature or to increase the feature values at the vicinity of the search area. This study presents a novel approach by constructing a higher order neural network, the input layer of which receives features together with their multiplications with the distance transform. This allows higher-order interactions between features through the non-linearity introduced by the multiplication. The application of the proposed method to 9 CT datasets for segmentation of the liver shows higher performance than well-known higher order classification neural networks.
Higher-order web link analysis using multilinear algebra.
Kenny, Joseph P.; Bader, Brett William; Kolda, Tamara Gibson
2005-07-01
Linear algebra is a powerful and proven tool in web search. Techniques, such as the PageRank algorithm of Brin and Page and the HITS algorithm of Kleinberg, score web pages based on the principal eigenvector (or singular vector) of a particular non-negative matrix that captures the hyperlink structure of the web graph. We propose and test a new methodology that uses multilinear algebra to elicit more information from a higher-order representation of the hyperlink graph. We start by labeling the edges in our graph with the anchor text of the hyperlinks so that the associated linear algebra representation is a sparse, three-way tensor. The first two dimensions of the tensor represent the web pages while the third dimension adds the anchor text. We then use the rank-1 factors of a multilinear PARAFAC tensor decomposition, which are akin to singular vectors of the SVD, to automatically identify topics in the collection along with the associated authoritative web pages.
Higher order SVD analysis for dynamic texture synthesis.
Costantini, Roberto; Sbaiz, Luciano; Süsstrunk, Sabine
2008-01-01
Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.
Higher order statistical frequency domain decomposition for operational modal analysis
NASA Astrophysics Data System (ADS)
Nita, G. M.; Mahgoub, M. A.; Sharyatpanahi, S. G.; Cretu, N. C.; El-Fouly, T. M.
2017-02-01
Experimental methods based on modal analysis under ambient vibrational excitation are often employed to detect structural damages of mechanical systems. Many of such frequency domain methods, such as Basic Frequency Domain (BFD), Frequency Domain Decomposition (FFD), or Enhanced Frequency Domain Decomposition (EFFD), use as first step a Fast Fourier Transform (FFT) estimate of the power spectral density (PSD) associated with the response of the system. In this study it is shown that higher order statistical estimators such as Spectral Kurtosis (SK) and Sample to Model Ratio (SMR) may be successfully employed not only to more reliably discriminate the response of the system against the ambient noise fluctuations, but also to better identify and separate contributions from closely spaced individual modes. It is shown that a SMR-based Maximum Likelihood curve fitting algorithm may improve the accuracy of the spectral shape and location of the individual modes and, when combined with the SK analysis, it provides efficient means to categorize such individual spectral components according to their temporal dynamics as coherent or incoherent system responses to unknown ambient excitations.
Effective description of higher-order scalar-tensor theories
NASA Astrophysics Data System (ADS)
Langlois, David; Mancarella, Michele; Noui, Karim; Vernizzi, Filippo
2017-05-01
Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called "beyond Horndeski" theories. We also discuss Lorentz-breaking models inspired by Horava gravity.
Generation of Higher Order Modes in a Rectangular Duct
NASA Technical Reports Server (NTRS)
Gerhold, Carl H.; Cabell, Randolph H.; Brown, Donald E.
2004-01-01
Advanced noise control methodologies to reduce sound emission from aircraft engines take advantage of the modal structure of the noise in the duct. This noise is caused by the interaction of rotor wakes with downstream obstructions such as exit guide vanes. Mode synthesis has been accomplished in circular ducts and current active noise control work has made use of this capability to cancel fan noise. The goal of the current effort is to examine the fundamental process of higher order mode propagation through an acoustically treated, curved duct. The duct cross-section is rectangular to permit greater flexibility in representation of a range of duct curvatures. The work presented is the development of a feedforward control system to generate a user-specified modal pattern in the duct. The multiple-error, filtered-x LMS algorithm is used to determine the magnitude and phase of signal input to the loudspeakers to produce a desired modal pattern at a set of error microphones. Implementation issues, including loudspeaker placement and error microphone placement, are discussed. Preliminary results from a 9-3/8 inch by 21 inch duct, using 12 loudspeakers and 24 microphones, are presented. These results demonstrate the ability of the control system to generate a user-specified mode while suppressing undesired modes.
Degree of musical expertise modulates higher order brain functioning.
Oechslin, Mathias S; Van De Ville, Dimitri; Lazeyras, François; Hauert, Claude-Alain; James, Clara E
2013-09-01
Using functional magnetic resonance imaging, we show for the first time that levels of musical expertise stepwise modulate higher order brain functioning. This suggests that degree of training intensity drives such cerebral plasticity. Participants (non-musicians, amateurs, and expert musicians) listened to a comprehensive set of specifically composed string quartets with hierarchically manipulated endings. In particular, we implemented 2 irregularities at musical closure that differed in salience but were both within the tonality of the piece (in-key). Behavioral sensitivity scores (d') of both transgressions perfectly separated participants according to their level of musical expertise. By contrasting brain responses to harmonic transgressions against regular endings, functional brain imaging data showed compelling evidence for stepwise modulation of brain responses by both violation strength and expertise level in a fronto-temporal network hosting universal functions of working memory and attention. Additional independent testing evidenced an advantage in visual working memory for the professionals, which could be predicted by musical training intensity. The here introduced findings of brain plasticity demonstrate the progressive impact of musical training on cognitive brain functions that may manifest well beyond the field of music processing.
A general higher-order remap algorithm for ALE calculations
Chiravalle, Vincent P
2011-01-05
A numerical technique for solving the equations of fluid dynamics with arbitrary mesh motion is presented. The three phases of the Arbitrary Lagrangian Eulerian (ALE) methodology are outlined: the Lagrangian phase, grid relaxation phase and remap phase. The Lagrangian phase follows a well known approach from the HEMP code; in addition the strain rate andflow divergence are calculated in a consistent manner according to Margolin. A donor cell method from the SALE code forms the basis of the remap step, but unlike SALE a higher order correction based on monotone gradients is also added to the remap. Four test problems were explored to evaluate the fidelity of these numerical techniques, as implemented in a simple test code, written in the C programming language, called Cercion. Novel cell-centered data structures are used in Cercion to reduce the complexity of the programming and maximize the efficiency of memory usage. The locations of the shock and contact discontinuity in the Riemann shock tube problem are well captured. Cercion demonstrates a high degree of symmetry when calculating the Sedov blast wave solution, with a peak density at the shock front that is similar to the value determined by the RAGE code. For a flyer plate test problem both Cercion and FLAG give virtually the same velocity temporal profile at the target-vacuum interface. When calculating a cylindrical implosion of a steel shell, Cercion and FLAG agree well and the Cercion results are insensitive to the use of ALE.
Image denoising using the higher order singular value decomposition.
Rajwade, Ajit; Rangarajan, Anand; Banerjee, Arunava
2013-04-01
In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented.
Pressure and higher-order spectra for homogeneous isotropic turbulence
NASA Technical Reports Server (NTRS)
Pullin, D. I.; Rogallo, R. S.
1994-01-01
The spectra of the pressure, and other higher-order quantities including the dissipation, the enstrophy, and the square of the longitudinal velocity derivative are computed using data obtained from direct numerical simulation of homogeneous isotropic turbulence at Taylor-Reynolds numbers R(sub lambda) in the range 38 - 170. For the pressure spectra we find reasonable collapse in the dissipation range (of the velocity spectrum) when scaled in Kolmogorov variables and some evidence, which is not conclusive, for the existence of a k(exp -7/3) inertial range where k = absolute value of K, is the modulus of the wavenumber. The power spectra of the dissipation, the enstrophy, and the square of the longitudinal velocity derivative separate in the dissipation range, but appear to converge together in the short inertial range of the simulations. A least-squares curve-fit in the dissipation range for one value of R(sub lambda) = 96 gives a form for the spectrum of the dissipation as k(exp 0)exp(-Ck eta), for k(eta) greater than 0.2, where eta is the Kolmogorov length and C is approximately equal to 2.5.
Higher-Order Synaptic Interactions Coordinate Dynamics in Recurrent Networks
Chambers, Brendan; MacLean, Jason N.
2016-01-01
Linking synaptic connectivity to dynamics is key to understanding information processing in neocortex. Circuit dynamics emerge from complex interactions of interconnected neurons, necessitating that links between connectivity and dynamics be evaluated at the network level. Here we map propagating activity in large neuronal ensembles from mouse neocortex and compare it to a recurrent network model, where connectivity can be precisely measured and manipulated. We find that a dynamical feature dominates statistical descriptions of propagating activity for both neocortex and the model: convergent clusters comprised of fan-in triangle motifs, where two input neurons are themselves connected. Fan-in triangles coordinate the timing of presynaptic inputs during ongoing activity to effectively generate postsynaptic spiking. As a result, paradoxically, fan-in triangles dominate the statistics of spike propagation even in randomly connected recurrent networks. Interplay between higher-order synaptic connectivity and the integrative properties of neurons constrains the structure of network dynamics and shapes the routing of information in neocortex. PMID:27542093
The Weak Field Limit of Higher Order Gravity
NASA Astrophysics Data System (ADS)
Stabile, Arturo
2008-09-01
The Higher Order Theories of Gravity - f(R, R_{alphabeta}R(alphabeta) ) - theory, where R is the Ricci scalar, R_{alphabeta} is the Ricci tensor and f is any analytic function - have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration, the flatness of the rotation curves of spiral galaxies and other relevant astrophysical phenomena. It is a crucial point testing these alternative theories in the so called weak field and newtonian limit of a f(R, R_{alphabeta}R(alphabeta) ) - theory. With this "perturbation technique" it is possible to find spherically symmetric solutions and compare them with the ones of General Relativity. On both approaches we found a modification of General Relativity: the behaviour of gravitational potential presents a modification Yukawa - like in the newtonian case and a massive propagation in the weak field case. When the modification of the theory is removed (i.e. f(R, R_{alphabeta}R(alphabeta) ) = R, Hilbert - Einstein lagrangian) we find the usual outcomes of General Relativity. Also the Noether symmetries technique has been investigated to find some time independent spherically symmetric solutions.
Huang, T W; Zhou, C T; He, X T
2013-05-01
Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared.
Communications: Ab initio second-order nonlinear optics in solids.
Luppi, Eleonora; Hübener, Hannes; Véniard, Valérie
2010-06-28
We present a first-principles theory for the calculation of the macroscopic second-order susceptibility chi((2)), based on the time-dependent density-functional theory approach. Our method allows to include straightforwardly the many-body effects, such as crystal local fields and excitons. We apply the theory to the computation of the second-harmonic generation spectroscopy. In order to demonstrate the accuracy of this approach we present spectra for the cubic semiconductor GaAs for which we obtain a very good agreement with the experimental results. We point out that crystal local fields are not sufficient to reproduce the experimental results. Only when we account for the excitonic effects we obtain a very good agreement with the experimental second-harmonic generation spectrum.
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.
NASA Astrophysics Data System (ADS)
Lan, Jun; Li, Yifeng; Yu, Huiyang; Li, Baoshun; Liu, Xiaozhou
2017-04-01
We theoretically investigate the nonlinear effects of acoustic wave propagation and dispersion in a cylindrical pipe with periodically arranged Helmholtz resonators. By using the classical perturbation method in nonlinear acoustics and considering a nonlinear response up to the third-order at the fundamental frequency, the expressions of the nonlinear impedance ZNHR of the Helmholtz resonator and effective nonlinear bulk modulus Bneff of the composite structure are derived. In order to confirm the nonlinear properties of the acoustic metamaterial, the transmission spectra have been studied by means of the acoustic transmission line method. Moreover, we calculate the effective acoustic impedance and dispersion relation of the system using the acoustic impedance theory and Bloch theory, respectively. It is found that with the increment of the incident acoustic pressure level, owing to the nonlinearity of the Helmholtz resonators, the resonant frequency ω0 shifts toward the lower frequency side and the forbidden bandgap of the transmission spectrum is shown to be broadened. The perturbation method employed in this paper extends the general analytical framework for a nonlinear acoustic metamaterial.
Identification of Nonlinear Times Series from First Order Cumulative Characteristics.
1991-08-01
Jj by Aj. It can be checked that A = (Aj) converges in distribution to a Gaussian random vector with mean zero and covariance matrix having rl th...and order determination. Biometrika 77 669-687. Bartlett, M. S. (1954). Probl~mes de l’analyse spectrale des series temporelles stationnaires. Pub... series . Stoch. Process. Appl. 36 85-106. Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and its Applications. Academic Press, New York. Hall
Chaos and Order in Weakly Coupled Systems of Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Bruhn, B.
1987-01-01
We consider in this paper perturbations of two degree of freedom Hamiltonian systems which contain periodic and heteroclinic orbits. The Melnikov-Keener condition is used to proof the existence of horseshoes in the dynamics. The same condition is applied to prove a high degree of order in the motion of the swinging Atwood's machine. For some selected parameter values the theoretical predictions are checked by numerical calculations.
New Developments in Second-Order Nonlinear Optical Polymeric Materials
1994-03-17
spectrophotometer. SHG measurements were carried out according to the method reported earlier[151. RESULTS AND DISCUSSION SHG in spin coated film An...monolayers of poly(4-BCMU) were obtained by similar method . Fiber formation was not observed even at higher surface pressure and no measurable SH...1984). 12. W. H. Kim, N. B. Kodali , J. Kumar, and S. K. Tripathy, To be published in Macromolecules. 13. T. P. Russel, H. Gugger, and J. D. Swalen
Rodrigues, Clóves G; Silva, Carlos A B; Ramos, José G; Luzzi, Roberto
2017-02-01
A family of what can be so-called Maxwell times which arises in the context of higher-order generalized hydrodynamics (HOGH; also called mesoscopic hydrothermodynamics) is evidenced. This is done in the framework of a HOGH built within a statistical formalism in terms of a nonequilibrium statistical ensemble formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them. These Maxwell times have a fundamental role in determining the type of hydrodynamic motion that the system would display in the given conditions and constraints. They determine a Maxwell viscous force not present in the usual hydrodynamic equations, for example, in Navier-Stokes equation.
NASA Astrophysics Data System (ADS)
Rodrigues, Clóves G.; Silva, Carlos A. B.; Ramos, José G.; Luzzi, Roberto
2017-02-01
A family of what can be so-called Maxwell times which arises in the context of higher-order generalized hydrodynamics (HOGH; also called mesoscopic hydrothermodynamics) is evidenced. This is done in the framework of a HOGH built within a statistical formalism in terms of a nonequilibrium statistical ensemble formalism. It consists in a description in terms of the densities of particles and energy and their fluxes of all orders, with the motion described by a set of coupled nonlinear integro-differential equations involving them. These Maxwell times have a fundamental role in determining the type of hydrodynamic motion that the system would display in the given conditions and constraints. They determine a Maxwell viscous force not present in the usual hydrodynamic equations, for example, in Navier-Stokes equation.
Simultaneous silence organizes structured higher-order interactions in neural populations
Shimazaki, Hideaki; Sadeghi, Kolia; Ishikawa, Tomoe; Ikegaya, Yuji; Toyoizumi, Taro
2015-01-01
Activity patterns of neural population are constrained by underlying biological mechanisms. These patterns are characterized not only by individual activity rates and pairwise correlations but also by statistical dependencies among groups of neurons larger than two, known as higher-order interactions (HOIs). While HOIs are ubiquitous in neural activity, primary characteristics of HOIs remain unknown. Here, we report that simultaneous silence (SS) of neurons concisely summarizes neural HOIs. Spontaneously active neurons in cultured hippocampal slices express SS that is more frequent than predicted by their individual activity rates and pairwise correlations. The SS explains structured HOIs seen in the data, namely, alternating signs at successive interaction orders. Inhibitory neurons are necessary to maintain significant SS. The structured HOIs predicted by SS were observed in a simple neural population model characterized by spiking nonlinearity and correlated input. These results suggest that SS is a ubiquitous feature of HOIs that constrain neural activity patterns and can influence information processing. PMID:25919985
NASA Astrophysics Data System (ADS)
Ikuta, Akira; Orimoto, Hisako; Ogawa, Hitoshi
In this study, a stochastic detection method of failure of machines based on the changing information of not only a linear correlation but also the higher order nonlinear correlation is proposed in a form suitable for on-line signal processing in time domain by using a personal computer, especially in order to find minutely the mutual relationship between sound and vibration emitted from rotational machines. More specifically, a conditional probability hierarchically reflecting various types of correlation information is theoretically derived by introducing an expression on the multi-dimensional probability distribution in orthogonal expansion series form. The effectiveness of the proposed theory is experimentally confirmed by applying it to the observed data emitted from a rotational machine driven by an electric motor.
Solutions to higher-order anisotropic parabolic equations in unbounded domains
NASA Astrophysics Data System (ADS)
Kozhevnikova, L. M.; Leont'ev, A. A.
2014-01-01
The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder D=(0,\\infty)\\times\\Omega, where \\Omega\\subset R^n, n\\geq 3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t\\to \\infty is found. An upper estimate characterizing the decay of the solution is established, which is close to the lower estimate if the domain is sufficiently 'narrow'. The same authors have previously obtained results of this type for second order anisotropic parabolic equations. Bibliography: 29 titles.