Synthesis of higher order nonlinear circuit elements
NASA Astrophysics Data System (ADS)
Chua, L. O.; Szeto, E. W.
1984-02-01
Higher and mixed-order n-port circuit elements were introduced recently to provide a logically complete formulation for nonlinear circuit theory. In this paper, higher order mutators are defined and used to synthesize these elements. The class of all higher order mutators is shown to form a group under cascade interconnections. Each mutator is realized using only linear capacitors, linear inductors and linear controlled sources. An upper bound on each type of element needed to realize a mutator is also given. Each higher or mixed-order n-port element is realized by cascading approprimate mutators across each port of a nonlinear n-port resistor. The main theorem shows that any higher or mixed-order nonlinear n-port element with a constitutive relation defined on a compact set can be realized using linear capacitors, inductors, and controlled sources, and 2-terminal nonlinear resistors.
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 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.
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.
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(Zr1-xTix)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 nth order harmonic SPM detection methods in exploring nonlinear phenomena in nanoscale materials. PMID:24045269
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.; 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,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
Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion
NASA Astrophysics Data System (ADS)
Latchio Tiofack, C. G.; Mohamadou, Alidou; HASH(0x2fc74c8), Alim; Porsezian, K.; Kofane, Timoleon C.
2012-06-01
Modulational instability (MI) in negative refractive metamaterials with saturable nonlinearity, fourth-order dispersion (FOD), and second-order nonlinear dispersion (SOND) is investigated by using standard linear stability analysis and the Drude electromagnetic model. The expression for the MI gain spectrum is obtained, which clearly reveals the influence of the saturation of the nonlinearity, FOD, and SOND parameters on the temporal MI. The evolution of the MI in negative refractive metamaterials is numerically investigated. Special attention is paid to study the effects of the higher-order dispersion terms on the formation and evolution of the solitons induced by MI. It is shown that as the third-order dispersion term increases, the solitons travel toward the right. Moreover, the magnitude of the FOD term influences considerably the number of wave trains induced by MI.
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
Nonlinear optomechanics with gain and loss: amplifying higher-order sideband and group delay
NASA Astrophysics Data System (ADS)
Jiao, Y.; Lü, H.; Qian, J.; Li, Y.; Jing, H.
2016-08-01
We study the nonlinear optomechanically induced transparency (OMIT) with gain and loss. We find that (i) for a single active cavity, significant enhancement can be achieved for the higher-order sidebands, including the transmission rate and the group delay; (ii) for active-passive-coupled cavities, hundreds of microsecond of optical delay or advance are attainable for the nonlinear sideband pulses in the parity-time-symmetric regime. The active higher-order OMIT effects, as firstly revealed here, open up the way to make a low-power optomechaical amplifier, which can amplify both the strength and group delay of not only the probe light but also its higher-order sidebands.
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).
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. PMID:25277626
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.
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. PMID:27192233
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.
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.
Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Zai-Dong, Li; Xuan, Wu; Qiu-Yan, Li; P, B. He
2016-01-01
In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schrödinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability (MI) process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov-Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schrödinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton’s peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses. Project supported by the Key Project of Scientific and Technological Research in Hebei Province, China (Grant No. ZD2015133).
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.
Lump solitons in a higher-order nonlinear equation in 2 +1 dimensions
NASA Astrophysics Data System (ADS)
Estévez, P. G.; Díaz, E.; Domínguez-Adame, F.; Cerveró, Jose M.; Diez, E.
2016-06-01
We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrödinger equation to 2 +1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.
Lump solitons in a higher-order nonlinear equation in 2+1 dimensions.
Estévez, P G; Díaz, E; Domínguez-Adame, F; Cerveró, Jose M; Diez, E
2016-06-01
We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrödinger equation to 2+1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed. PMID:27415266
Effects of static equilibrium and higher-order nonlinearities on rotor blade stability in hover
NASA Technical Reports Server (NTRS)
Crespodasilva, Marcelo R. M.; Hodges, Dewey H.
1988-01-01
The equilibrium and stability of the coupled elastic lead/lag, flap, and torsion motion of a cantilever rotor blade in hover are addressed, and the influence of several higher-order terms in the equations of motion of the blade is determined for a range of values of collective pitch. The blade is assumed to be untwisted and to have uniform properties along its span. In addition, chordwise offsets between its elastic, tension, mass, and aerodynamic centers are assumed to be negligible for simplicity. The aerodynamic forces acting on the blade are modeled using a quasi-steady, strip-theory approximation.
NASA Astrophysics Data System (ADS)
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.
From the Fermi-Pasta-Ulam Model to Higher-Order Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.
2016-02-01
We consider generalizations of the Korteweg-de Vries equation of the fifth and seventh order obtained from the Fermi-Pasta-Ulam problem. Analytical properties of the equation are investigated taking into account the Painlevé test. It is shown that the equations of the fifth and seventh order do not have the Painlevé property. We demonstrate that there are expansions of the solution in the Laurent series and as a consequence we can find exact solutions of the equations. Solitary wave and elliptic solutions of the fifth and seventh order equations are presented.
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. PMID:26920085
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.
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.
Stone, Joanne; Kohari, Katherine S
2015-09-01
Higher-order multiple gestations have increased since the advent of advanced reproductive technologies. These pregnancies present unique risks to both mothers and fetuses. It is imperative that early diagnosis of chronicity be determined and that proper counseling is performed, so patients understand the risks, evaluation, and management needed.
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.
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.
NASA Technical Reports Server (NTRS)
Chou, Jin
1993-01-01
Rational Bezier and B-spline representations of circles have been heavily publicized. However, all the literature assumes the rational Bezier segments in the homogeneous space are both planar and (equivalent to) quadratic. This creates the illusion that circles can only be achieved by planar and quadratic curves. Circles that are formed by higher order rational Bezier curves which are nonplanar in the homogeneous space are shown. The problem of whether it is possible to represent a complete circle with one Bezier curve is investigated. In addition, some other interesting properties of cubic Bezier arcs are discussed.
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
NASA Astrophysics Data System (ADS)
Wang, Qi-Min; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei
2015-10-01
In this paper, a higher-order nonlinear Schrödinger-Maxwell-Bloch system with quintic terms is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. Multi-soliton, breather and rogue-wave solutions are derived by virtue of the Darboux transformation and the limiting procedure. Features and interaction patterns of the solitons, breathers and rogue waves are discussed. (i) The solitonic amplitudes, widths and velocities are exhibited, and solitonic amplitudes and widths are proved to have nothing to do with the higher-order terms. (ii) The higher-order terms and frequency detuning affect the growth rate of periodic modulation and skewing angle for the breathers, except for the range of the frequency of modulation. (iii) The quintic terms and frequency detuning have the effects on the temporal duration for the rogue waves. (iv) Breathers are classified into two types, according to the range of the modulation instability. (v) Interaction between the two solitons is elastic. When the two solitons interact with each other, the periodic structure occurs, which is affected by the higher-order terms and frequency detuning. (vi) Interaction between the two Akhmediev-like breathers or two Kuznetsov-Ma-like solitons shows the different patterns with different ratios of the relative modulation frequencies, while the interaction area induced by the two breathers looks like a higher-order rogue wave.
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.
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. PMID:27415265
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.
Higher dimensional nonlinear massive gravity
NASA Astrophysics Data System (ADS)
Do, Tuan Q.
2016-05-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constantlike behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini (anti-) de Sitter metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity are figured out consistently.
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.
NASA Astrophysics Data System (ADS)
Boyd, John P.; Xu, Zhengjie
2012-02-01
Computation of solitons of the cubically-nonlinear Benjamin-Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣ x∣ 2). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H( uXX) - c u + (1 - δ) u2 + δu3 = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin-Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin-Ono equations are also computed and compared to their Korteweg-deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.
NASA Astrophysics Data System (ADS)
Fernández, Leandro; Onorato, Miguel; Monbaliu, Jaak; Toffoli, Alessandro
2015-04-01
This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing laboratory experiments, field measurements and numerical simulations. It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics and second order based statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh = 1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if kh < 1.36. In this regard, the aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, laboratory experiments in a large wave basin, numerical experiments solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and field experiments at the Lake George experimental site (Australia) have been compared to assess the role of third order nonlinearity, and particularly modulational instability, on wave statistics. Herein, we present a comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between laboratory experiments, simulations and in-situ data which provides a confrontation between the numerical results and real observations in laboratory and field conditions.
Lagrangian systems with higher order constraints
NASA Astrophysics Data System (ADS)
Cendra, H.; Grillo, S. D.
2007-05-01
A class of mechanical systems subject to higher order constraints (i.e., constraints involving higher order derivatives of the position of the system) are studied. We call them higher order constrained systems (HOCSs). They include simplified models of elastic rolling bodies, and also the so-called generalized nonholonomic systems (GNHSs), whose constraints only involve the velocities of the system (i.e., first order derivatives in the position of the system). One of the features of this kind of systems is that D'Alembert's principle (or its nonlinear higher order generalization, the Chetaev's principle) is not necessarily satisfied. We present here, as another interesting example of HOCS, systems subjected to friction forces, showing that those forces can be encoded in a second order kinematic constraint. The main aim of the paper is to show that every HOCS is equivalent to a GNHS with linear constraints, in a canonical way. That is to say, systems with higher order constraints can be described in terms of one with linear constraints in velocities. We illustrate this fact with a system with friction and with Rocard's model [Dynamique Générale des Vibrations (1949), Chap. XV, p. 246 and L'instabilité en Mécanique; Automobiles, Avions, Ponts Suspendus (1954)] of a pneumatic tire. As a by-product, we introduce some applications on higher order tangent bundles, which we expect to be useful for the study of intrinsic aspects of the geometry of such bundles.
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
NASA Astrophysics Data System (ADS)
Maimaiti, Aili; Holzmann, Daniela; Truong, Viet Giang; Ritsch, Helmut; Nic Chormaic, Síle
2016-07-01
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.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Chinone, N.; Nakamura, T.; Cho, Y.
2014-08-01
The dopant distribution and depletion layer in a cross-section of a SiC double diffused MOSFET (DMOSFET) is visualized using super-higher-order scanning nonlinear dielectric microscopy (SHO-SNDM), which is a form of scanning probe microscopy. Analysis of the data acquired by SHO-SNDM clarifies the dopant distribution in great detail, which is otherwise difficult to detect using conventional scanning capacitance microscopy or scanning microwave microscopy. Moreover, the newly developed SHO-SNDM method enables us to distinguish the n-type, p-type, and depletion layer regions very clearly, and they are found to be consistent with the general DMOSFET structure.
NASA Astrophysics Data System (ADS)
Zhang, Jiefang; Dai, Chaoqing
2005-05-01
By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schrodinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic terms, self-steepening, and nonlinear dispersive terms. Moreover, we give the formation condition of the bright and dark solitons for this higher-order NLSE.
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.
Second-order cascading in third-order nonlinear optical processes
NASA Astrophysics Data System (ADS)
Meredith, Gerald R.
1982-12-01
Because cascaded second-order processes make substantial qualitative and quanitative differences to the results of third-order nonlinear optical experiments, a formalism for their treatment is presented. The symmetry dictates concerning the occurrence and relationships of magnitudes of cascading are tabulated for the higher symmetry crystal classes. Angular momentum considerations are applied to the situations allowing circularly polarized light waves.
Higher-order organization of complex networks.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2016-07-01
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.
Higher-order organization of complex networks.
Benson, Austin R; Gleich, David F; Leskovec, Jure
2016-07-01
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
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.
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.
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.
Higher-order generic functions for CLOS
Hernandez, J.E.
1992-03-01
This paper presents a framework for developing higher-order generic functions within the Common Lisp Object System similar to the ones in Common Lisp for processing sequences. The framework consist of several CLOS classes which define a protocol that allows other classes to inherit default methods for many higher-order generic functions. These generic functions provide an elegant and uniform framework for processing CLOS objects that primarily represent collections of other objects.
Higher order equations of motion and gravity
NASA Astrophysics Data System (ADS)
Lämmerzahl, Claus; Rademaker, Patricia
2012-12-01
Standard fundamental equations of motion for point particles are of second order in the time derivative. Here we are exploring the consequences of fundamental equations of motion with an additional small even higher order term to the standard formulation. This is related to two issues: (i) higher order equations of motion will have influence on the definition of the structure of possible interactions and in particular of the gravitational interaction, and (ii) such equations of motion provide a framework to test the validity of Newton’s second law which is the basis for the definition of forces but which assumes from the very beginning that the fundamental equations of motion are of second order. We will show that starting with our generalized equations of motions it is possible to introduce the space-time metric describing the gravitational interaction by means of a standard gauge principle. Another main result within our model of even higher order derivatives is that for slowly varying and smooth fields the higher order derivatives either lead to runaway solutions or induces a zitterbewegung. We confront this higher order scheme with experimental data.
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 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.
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 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. PMID:22492758
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
Breastfeeding twins and higher-order multiples.
Gromada, K K; Spangler, A K
1998-01-01
The benefits of breastfeeding for pre-term and full-term infants are well documented. Breastfeeding facilitates maternal-infant attachment, provides optimal infant nutrition and immunologic protection, and minimizes economic impact. These benefits are multiplied with twins and higher-order multiples, who often are born at risk. Supporting a mother as she initiates and continues to breastfeed one infant requires specific knowledge and skills. Health professionals need additional knowledge and skills if they are to provide appropriate assessment, intervention, and support when a mother breastfeeds twins or higher-order multiples.
Breastfeeding twins and higher-order multiples.
Gromada, K K; Spangler, A K
1998-01-01
The benefits of breastfeeding for pre-term and full-term infants are well documented. Breastfeeding facilitates maternal-infant attachment, provides optimal infant nutrition and immunologic protection, and minimizes economic impact. These benefits are multiplied with twins and higher-order multiples, who often are born at risk. Supporting a mother as she initiates and continues to breastfeed one infant requires specific knowledge and skills. Health professionals need additional knowledge and skills if they are to provide appropriate assessment, intervention, and support when a mother breastfeeds twins or higher-order multiples. PMID:9684207
Higher-order dielectrophoresis of nonspherical particles
NASA Astrophysics Data System (ADS)
Nili, Hossein; Green, Nicolas G.
2014-06-01
Higher-order terms of dielectrophoretic (DEP) force are commonly ignored by invoking the simplifying dipole approximation. Concurrently, the trend towards micro- and nano-electrode structures in DEP design is bringing about an increasing number of instances where the approximation is expected to lose reliability. The case is severe for nonspherical particles (the shape of many biological particles) due to the shape-dependent nature of dielectric polarization. However, there is a lack of analytical means to determine multipole moments of nonspherical particles, numerical calculations of the same are regarded as unreliable, and there is a prevalence for higher-order force considerations to be ignored. As a result, the dipole approximation is used and/or nonspherical particles are approximated as spheres. This work proves the inefficacy of current qualitative criteria for the reliability of the dipole approximation and presents a quantitative substitute, with verified accuracy, that enables precise determination of the extent to which the dipole approximation would be reliable, and if found unreliable, corrects the approximation by adding second- and third-order terms of the DEP force. The effects of field nonuniformity, electrode design, and particle shape and aspect ratio on the significance of higher-order DEP forces is quantitatively analyzed. The results show that higher-order DEP forces are indeed of substantially increased significance for nonspherical particles; in the cases examined in this work, multipolar terms are seen to constitute more than 40% of the total force on ellipsoidal and cylindrical particles. It is further shown that approximating nonspherical particles as spheres of similar dimensions is subject to substantial error. Last, the substantial importance of the electrode design in influencing higher-order forces is shown.
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.
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. PMID:26263071
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…
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.
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.
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
2015-01-01
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
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
Representing higher-order dependencies in networks.
Xu, Jian; Wickramarathne, Thanuka L; Chawla, Nitesh V
2016-05-01
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
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.
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.
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.
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.
The fundamental skills of higher order thinking.
Grossen, B
1991-01-01
It may be possible to teach reasoning strategies to subjects with poor reasoning, including many subjects with learning disabilities (LD), using curriculum designed around a sameness analysis. The higher order thinking skills of analogical and logical reasoning are defined using the sameness analysis methodology. The sameness in the strategy for forming a generalization from experience is called "reasoning by analogy," while the sameness in the strategy for applying generalizations is described by the syllogism (logical reasoning). The research base for effective instruction in analogical and logical reasoning, particularly with subjects with LD, is summarized. The wide applicability of reasoning by analogy and by syllogism as complementary strategies is illustrated through their use in a critical review of the editorial page of a daily newspaper, and in linking content material in several domains.
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.
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.
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.
Nonlinear waves in second order conformal hydrodynamics
NASA Astrophysics Data System (ADS)
Fogaça, D. A.; Marrochio, H.; Navarra, F. S.; Noronha, J.
2015-02-01
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.
Higher-order artificial neural networks
Bengtsson, M.
1990-12-01
The report investigates the storage capacity of an artificial neural network where the state of each neuron depends on quadratic correlations of all other neurons, i.e. a third order network. This is in contrast to a standard Hopfield network where the state of each single neuron depends on the state on every other neuron, without any correlations. The storage capacity of a third order network is larger than that for standard Hopfield by one order of N. However, the number of connections is also larger by an order of N. It is shown that the storage capacity per connection is identical for standard Hopfield and for this third order network.
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.
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 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
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.
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
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.
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.
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.
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.
High-order nonlinear differentiator and application to aircraft control
NASA Astrophysics Data System (ADS)
Wang, Xinhua; Shirinzadeh, Bijan
2014-06-01
In this paper, a high-order continuous nonlinear differentiator with lead compensation is presented based on finite-time stability. Not only the proposed high-order nonlinear differentiator can obtain the high-order derivatives of a signal, but also the chattering phenomenon can be reduced sufficiently. The parameters regulation is only required to be satisfied with Routh-Hurwitz Stability Criterion. The presented differentiator is a generalization of sliding mode differentiator and linear high-gain differentiator. The merits of the continuous differentiator include its simplicity, selecting parameters easily, restraining noises sufficiently, decreasing the phase shift and avoiding the chattering phenomenon. The theoretical results are confirmed by computer simulations and an experiment on a quadrotor aircraft: (i) the estimation of flying velocity and acceleration from the position measurement; (ii) a control law is designed based on the presented nonlinear differentiator to track a reference trajectory.
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.
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
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.
Global attractors for a third order in time nonlinear dynamics
NASA Astrophysics Data System (ADS)
Caixeta, Arthur H.; Lasiecka, Irena; Cavalcanti, Valéria N. D.
2016-07-01
Long time behavior of a third order (in time) nonlinear PDE equation is considered. This type of equations arises in the context of nonlinear acoustics [12,20,22,24] where modeling accounts for a finite speed of propagation paradox, the latter results in hyperbolic nature of the dynamics. It will be proved that the underlying PDE generates a well-posed dynamical system which admits a global and finite dimensional attractor. The main difficulty associated with the problem studied is the lack of Lyapunov function along with the lack of compactness of trajectories, which fact prevents applicability of standard tools in the area of dynamical systems.
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.
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…
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.
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.
Cascaded second-order contribution to the third-order nonlinear susceptibility
NASA Astrophysics Data System (ADS)
Kolleck, Christian
2004-05-01
Cascading of second-order nonlinear effects leads to an effective third-order nonlinearity. In addition to the macroscopic electric field at the intermediate frequencies another term has to be taken into account which is due to the locality of the intermediate polarization sources. Combining the correction terms at the three intermediate frequencies gives rise to a third-order susceptibility tensor, which exhibits the same symmetry properties as an intrinsic susceptibility. This particularly applies to the contributions from the rectified and the second-harmonic fields to the degenerate susceptibility.
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. PMID:26671817
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.
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.
Quenching phenomena for fourth-order nonlinear parabolic equations
NASA Astrophysics Data System (ADS)
Yi, Niu; Xiaotong, Qiu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the initial boundary value problem for the fourth-order nonlinear parabolic equation in bounded domain. By some assumptions on the exponents and initial data for a class of equations with the general source term, we not only obtain the quenching phenomena in finite time but also estimate the quenching time. Our main tools are maximum principle, comparison principle and eigenfunction method.
Ablation and optical third-order nonlinearities in Ag nanoparticles
Torres-Torres, Carlos; Peréa-López, Néstor; Reyes-Esqueda, Jorge Alejandro; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; Oliver, Alicia
2010-01-01
The optical damage associated with high intensity laser excitation of silver nanoparticles (NPs) was studied. In order to investigate the mechanisms of optical nonlinearity of a nanocomposite and their relation with its ablation threshold, a high-purity silica sample implanted with Ag ions was exposed to different nanosecond and picosecond laser irradiations. The magnitude and sign of picosecond refractive and absorptive nonlinearities were measured near and far from the surface plasmon resonance (SPR) of the Ag NPs with a self-diffraction technique. Saturable optical absorption and electronic polarization related to self-focusing were identified. Linear absorption is the main process involved in nanosecond laser ablation, but non-linearities are important for ultrashort picosecond pulses when the absorptive process become significantly dependent on the irradiance. We estimated that near the resonance, picosecond intraband transitions allow an expanded distribution of energy among the NPs, in comparison to the energy distribution resulting in a case of far from resonance, when the most important absorption takes place in silica. We measured important differences in the ablation threshold and we estimated that the high selectiveness of the SPR of Ag NPs as well as their corresponding optical nonlinearities can be strongly significant for laser-induced controlled explosions, with potential applications for biomedical photothermal processes. PMID:21187944
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.
Proper orthogonal decomposition-based spectral higher-order stochastic estimation
Baars, Woutijn J.; Tinney, Charles E.
2014-05-15
A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.
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.
Third Order Nonlinear Optical Effects in Some Polybenzidines
NASA Astrophysics Data System (ADS)
Cheng, Chi Fai
Third order nonlinear optical properties of organic compounds with pi electron delocalization are currently receiving much attention in view of potential applications in switching and optical information processing. Polymers of Benzidine were synthesized by hydrogen peroxide reaction catalyzed by horseradish peroxidase enzyme. The polymerization reaction was carried out at room temperature in a monophasic organic solvent with a small amount of water at pH 7.5. The technique of Degenerate Four Wave Mixing with picosecond and nanosecond pulses was employed to measure the third order susceptibility chi^{(3) } of polybenzidine. The observed values for chi^{(3)} are of order 10^{-9} to 10 ^{-8} esu. In order to understand the origin of these high values of chi^ {(3)}, we measured the real and imaginary components of chi^{(3)} . Investigation of total energy transmission as a function of incident intensity and fluence at 532 nm for picosecond and nanosecond laser pulses using a frequency doubled Nd:YAG laser indicates reverse saturable absorption. The experiments are carried out for the sample in solution in Dimethyl Sulfoxide and Methanol (DMSO:MeOH) 4:1 ratio. As we observe the nanosecond and picosecond curves to be superimposed for intensity dependence and not for fluence, we conclude that the third order nonlinearity is predominantly due to two photon absorption. Values for Im chi ^{(3)} determined by our experiments are of order 10^{-9} to 10^{-8} esu. We measure the real part of chi^{(3)} by optical Kerr gate technique. The value is about one order lower compared to the imaginary component. In view of the reverse saturable absorption characteristics observed for the samples, the material is a good candidate for applications in optical power limiting.
Existence of solutions for some higher order boundary value problems
NASA Astrophysics Data System (ADS)
Charkrit, Sita; Kananthai, Amnuay
2007-05-01
In this paper, we are concerned with the existence of solutions for the higher order boundary value problem in the form where m is a given positive integer and is continuous. We introduce a new maximum principle of higher order equations and develop a monotone method in the presence of lower and upper solutions for this problem.
Assessing Higher Order Thinking and Communication Skills: Literacy.
ERIC Educational Resources Information Center
Venezky, Richard L.
Assessment of higher order literacy skills encounters three initial problems aside from assessment methods: (1) definition of literacy; (2) range of skills to assess; and (3) whether or not higher order literacy can be assessed independently of a particular content area. Regardless of definitions, the general performance areas to be covered must…
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.
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.
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system. PMID:27586626
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation
NASA Astrophysics Data System (ADS)
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.
Exact solutions for two nonlinear wave equations with nonlinear terms of any order
NASA Astrophysics Data System (ADS)
Chen, Yong; Li, Biao; Zhang, Hongqing
2005-03-01
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin-Bona-Mahony (BBM) equation and the generalized Burgers-Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported.
[Corneal higher order aberrations and their changes with aging].
Cermáková, S; Skorkovská, S
2010-12-01
Cornea is the most important refractive medium of the eye and affects its total aberration state. This paper deals with corneal higher order aberrations in healthy humans and evaluates their changes with aging and corneal curvature. The influence of the corneal anterior and posterior surfaces on aberrations of the whole cornea was also investigated. The examination was performed with a Scheimpflug camera which enables to examine the anterior and posterior corneal surface separately. The results show that higher order aberrations of the whole cornea are influenced mainly by the anterior surface aberrations. The main corneal higher order aberration is the Z (4,0) spherical aberration which has a positive value and increases with age. Also, 3rd order aberration values are of importance, especially coma which also increases with age. As a consequence, the root-mean-square of the 3rd and 4th order aberrations in elderly people has a higher value.
Higher Order Fractional Stable Motion: Hyperdiffusion with Heavy Tails
NASA Astrophysics Data System (ADS)
Kawai, Reiichiro
2016-08-01
We introduce the class of higher order fractional stable motions that can exhibit hyperdiffusive spreading with heavy tails. We define the class as a generalization of higher order fractional Brownian motion as well as a generalization of linear fractional stable motions. Higher order fractional stable motions are self-similar with Hurst index larger than one and non-Gaussian stable marginals with infinite variance and have stationary higher order increments. We investigate their sample path properties and asymptotic dependence structure on the basis of codifference. In particular, by incrementing or decrementing sample paths once under suitable conditions, the diffusion rate can be accelerated or decelerated by one order. With a view towards simulation study, we provide a ready-for-use sample path simulation recipe at discrete times along with error analysis. The proposed simulation scheme requires only elementary numerical operations and is robust to high frequency sampling, irregular spacing and super-sampling.
Higher Order Fractional Stable Motion: Hyperdiffusion with Heavy Tails
NASA Astrophysics Data System (ADS)
Kawai, Reiichiro
2016-10-01
We introduce the class of higher order fractional stable motions that can exhibit hyperdiffusive spreading with heavy tails. We define the class as a generalization of higher order fractional Brownian motion as well as a generalization of linear fractional stable motions. Higher order fractional stable motions are self-similar with Hurst index larger than one and non-Gaussian stable marginals with infinite variance and have stationary higher order increments. We investigate their sample path properties and asymptotic dependence structure on the basis of codifference. In particular, by incrementing or decrementing sample paths once under suitable conditions, the diffusion rate can be accelerated or decelerated by one order. With a view towards simulation study, we provide a ready-for-use sample path simulation recipe at discrete times along with error analysis. The proposed simulation scheme requires only elementary numerical operations and is robust to high frequency sampling, irregular spacing and super-sampling.
A Testing Theory for a Higher-Order Cryptographic Language
NASA Astrophysics Data System (ADS)
Koutavas, Vasileios; Hennessy, Matthew
We study a higher-order concurrent language with cryptographic primitives, for which we develop a sound and complete, first-order testing theory for the preservation of safety properties. Our theory is based on co-inductive set simulations over transitions in a first-order Labelled Transition System. This keeps track of the knowledge of the observer, and treats transmitted higher-order values in a symbolic manner, thus obviating the quantification over functional contexts. Our characterisation provides an attractive proof technique, and we illustrate its usefulness in proofs of equivalence, including cases where bisimulation theory does not apply.
Superposition rules for higher order systems and their applications
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Grabowski, J.; de Lucas, J.
2012-05-01
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work, we extend this notion and other related ones to systems of higher order differential equations and analyse their properties. Several results concerning the existence of various types of superposition rules for higher order systems are proved and illustrated with examples extracted from the physics and mathematics literature. In particular, two new superposition rules for the second- and third-order Kummer-Schwarz equations are derived.
Higher order methods for convection-diffusion problems
NASA Astrophysics Data System (ADS)
Murphy, J. D.; Prenter, P. M.
This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.
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.
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.
On the Evaluation of Higher-Order Science Instructional Objectives
ERIC Educational Resources Information Center
Hambleton, Ronald K.; Sheehan, Daniel S.
1977-01-01
Advocates the use of a free-sort categorization technique for evaluation of higher-order science instructional objectives. An explanation and demonstration of the use of the evaluation technique with 284 ninth-grade science students is provided. (CP)
Development of a core confidence-higher order construct.
Stajkovic, Alexander D
2006-11-01
The author develops core confidence as a higher order construct and suggests that a core confidence-higher order construct--not addressed by extant work motivation theories--is helpful in better understanding employee motivation in today's rapidly changing organizations. Drawing from psychology (social, clinical, and developmental) and social anthropology, the author develops propositions regarding the relationships between core confidence and performance, attitudes, and subjective well-being. The core confidence-higher order construct is proposed to be manifested by hope, self-efficacy, optimism, and resilience. The author reasons that these four variables share a common confidence core (a higher order construct) and may be considered as its manifestations. Suggestions for future research and implications of the work are discussed. PMID:17100479
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.
Feynman rules of higher-order poles in CHY construction
NASA Astrophysics Data System (ADS)
Huang, Rijun; Feng, Bo; Luo, Ming-xing; Zhu, Chuan-Jie
2016-06-01
In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.
Higher-order Lagrangian perturbative theory for the Cosmic Web
NASA Astrophysics Data System (ADS)
Tatekawa, Takayuki; Mizuno, Shuntaro
2016-10-01
Zel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.
NASA Astrophysics Data System (ADS)
Ito, Kazuma; Sato, Yasuaki; Takasu, Ryosuke; Mase, Nobuyuki; Kawata, Yoshimasa; Tasaka, Shigeru; Sugita, Atsushi
2014-01-01
In this manuscript, we describe the current manuscript describes the second-order nonlinear optical susceptibility of guest-host polymers possessing chromophores with strongly electron-accepting tricyanofuran (TCF). Chromophores substituted with different numbers of hydroxyl groups were prepared. Our experimental results demonstrated that the guest-host polymers exhibited nonlinear optical susceptibilities simply upon annealing at temperatures higher than the glass transition point of the host polymers even in the absence of applied external DC electric fields. Nonelectrical poling behaviors were only available for the materials possessing hydroxyl-group-functionalized chromophores. The results indicate that chemisorption of the hydroxyl groups on the substrate led to the orientation order of the guest chromophores. The orientation order of the chromophores was reproduced well by the model of poled polymers in previous studies.
Higher-order conditioning and the retrosplenial cortex.
Todd, Travis P; Huszár, Roman; DeAngeli, Nicole E; Bucci, David J
2016-09-01
The retrosplenial cortex (RSC) is known to contribute to contextual and spatial learning and memory. This is consistent with its well-established connectivity; the RSC is located at the interface of visuo-spatial association areas and the parahippocampal-hippocampal memory system. However, the RSC also contributes to learning and memory for discrete cues. For example, both permanent lesions and temporary inactivation of the RSC have been shown to impair sensory preconditioning, a form of higher-order conditioning. The purpose of the present experiment was to examine the role of the RSC in a closely related higher-order conditioning paradigm: second-order conditioning. Sham and RSC lesioned rats received first-order conditioning in which one visual stimulus (V1) was paired with footshock and one visual stimulus (V2) was not. Following first-order conditioning, one auditory stimulus (A1) was then paired with V1 and a second auditory stimulus (A2) was paired with V2. Although lesions of the RSC impaired the first-order discrimination, they had no impact on the acquisition of second-order conditioning. Thus, the RSC does not appear necessary for acquisition/expression of second-order fear conditioning. The role of the RSC in higher-order conditioning, as well as a possible dissociation from the hippocampus, is discussed.
Higher-order conditioning and the retrosplenial cortex.
Todd, Travis P; Huszár, Roman; DeAngeli, Nicole E; Bucci, David J
2016-09-01
The retrosplenial cortex (RSC) is known to contribute to contextual and spatial learning and memory. This is consistent with its well-established connectivity; the RSC is located at the interface of visuo-spatial association areas and the parahippocampal-hippocampal memory system. However, the RSC also contributes to learning and memory for discrete cues. For example, both permanent lesions and temporary inactivation of the RSC have been shown to impair sensory preconditioning, a form of higher-order conditioning. The purpose of the present experiment was to examine the role of the RSC in a closely related higher-order conditioning paradigm: second-order conditioning. Sham and RSC lesioned rats received first-order conditioning in which one visual stimulus (V1) was paired with footshock and one visual stimulus (V2) was not. Following first-order conditioning, one auditory stimulus (A1) was then paired with V1 and a second auditory stimulus (A2) was paired with V2. Although lesions of the RSC impaired the first-order discrimination, they had no impact on the acquisition of second-order conditioning. Thus, the RSC does not appear necessary for acquisition/expression of second-order fear conditioning. The role of the RSC in higher-order conditioning, as well as a possible dissociation from the hippocampus, is discussed. PMID:27208598
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.
Higher order theories and their relationship with noncommutativity
NASA Astrophysics Data System (ADS)
Sánchez-Santos, Oscar; Vergara, José David
2014-06-01
We present a relationship between noncommutativity and higher order time derivative theories using a perturbation method. We make a generalization of the Chern-Simons quantum mechanics for higher order time derivatives. This model presents noncommutativity in a natural way when we project to low-energy physical states without the necessity of taking the strong field limit. We quantize the theory using a Bopp's shift of the noncommutative variables and we obtain a spectrum without negative energies, under the perturbation limits. In addition, we extent the model to high order time derivatives and noncommutativity with variable dependent parameter.
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.
Optimized higher-order automatic differentiation for the Faddeeva function
NASA Astrophysics Data System (ADS)
Charpentier, Isabelle
2016-08-01
Considerable research efforts have been directed at implementing the Faddeeva function w(z) and its derivatives with respect to z, but these did not consider the key computing issue of a possible dependence of z on some variable t. The general case is to differentiate the compound function w(z(t)) = w ∘ z(t) with respect to t by applying the chain rule for a first order derivative, or Faà di Bruno's formula for higher-order ones. Higher-order automatic differentiation (HOAD) is an efficient and accurate technique for derivative calculation along scientific computing codes. Although codes are available for w(z) , a special symbolic HOAD is required to compute accurate higher-order derivatives for w ∘ z(t) in an efficient manner. A thorough evaluation is carried out considering a nontrivial case study in optics to support this assertion.
Should evolutionary geneticists worry about higher-order epistasis?
Weinreich, Daniel M; Lan, Yinghong; Wylie, C Scott; Heckendorn, Robert B
2013-12-01
Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.
Superposition of Solitons with Arbitrary Parameters for Higher-order Equations
NASA Astrophysics Data System (ADS)
Ankiewicz, A.; Chowdury, A.
2016-07-01
The way in which solitons propagate and collide is an important theme in various areas of physics. We present a systematic study of the superposition of solitons in systems governed by higher-order equations related to the nonlinear Schrödinger family. We allow for arbitrary amplitudes and relative velocities and include an infinite number of equations in our analysis of collisions and superposed solitons. The formulae we obtain can be useful in determining the influence of subtle effects like higher-order dispersion in optical fibres and small delays in the material responses to imposed impulses.
Higher-order motion sensitivity in fly visual circuits
Lee, Yu-Jen; Nordström, Karin
2012-01-01
In higher-order motion stimuli, the direction of object motion does not follow the direction of luminance change. Such stimuli could be generated by the wing movements of a flying butterfly and further complicated by its motion in and out of shadows. Human subjects readily perceive the direction of higher-order motion, although this stands in stark contrast to prevailing motion vision models. Flies and humans compute motion in similar ways, and because flies behaviorally track bars containing higher-order motion cues, they become an attractive model system for investigating the neurophysiology underlying higher-order motion sensitivity. We here use intracellular electrophysiology of motion-vision–sensitive neurons in the hoverfly lobula plate to quantify responses to stimuli containing higher-order motion. We show that motion sensitivity can be broken down into two separate streams, directionally coding for elementary motion and figure motion, respectively, and that responses to Fourier and theta motion can be predicted from these. The sensitivity is affected both by the stimulus’ time course and by the neuron’s underlying receptive field. Responses to preferred-direction theta motion are sexually dimorphic and particularly robust along the visual midline. PMID:22586123
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.
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.
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 mode laser beam scintillations in oceanic medium
NASA Astrophysics Data System (ADS)
Baykal, Yahya
2016-01-01
In a horizontal oceanic optical wireless communication link, the scintillation index (the measure for the intensity fluctuations) of the received intensity caused by the oceanic turbulence is formulated and evaluated when the source is a higher order mode laser. Variations in the scintillation index vs. the underwater turbulence parameters, size of the higher order mode laser source, link length, and the wavelength are examined. Underwater turbulence parameters are the ratio that determines the relative strength of temperature and salinity in driving the index fluctuations, the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, and the Kolmogorov microscale length.
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.
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
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 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.
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.
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 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…
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…
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.
Higher-Order Thinking: A "Basic" Skill for Everyone.
ERIC Educational Resources Information Center
Chancellor, Dinah
1991-01-01
Described are activities involving higher order thinking skills developed for gifted students that can be used for all students. Discussed is a framework for designing activities using Bloom's Taxonomy of the Cognitive Domain and William's Student Behaviors. Sample activities are included. (KR)
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,…
Multiple-Try Feedback and Higher-Order Learning Outcomes
ERIC Educational Resources Information Center
Clariana, Roy B.; Koul, Ravinder
2005-01-01
Although feedback is an important component of computer-based instruction (CBI), the effects of feedback on higher-order learning outcomes are not well understood. Several meta-analyses provide two rules of thumb: any feedback is better than no feedback and feedback with more information is better than feedback with less information. …
Recent Advances in Higher-order Multimodal Biomedical Imaging Agents
Rieffel, James; Chitgupi, Upendra
2015-01-01
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 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, 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, we review recent progress in higher-order multimodal imaging agents, which span a range of material and structural classes, that have demonstrated utility in three (or more) imaging modalities. PMID:26185099
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.…
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 structure of Saccharomyces cerevisiae chromatin
Lowary, P.T.; Widom, J. )
1989-11-01
We have developed a method for partially purifying chromatin from Saccharomyces cerevisiae (baker's yeast) to a level suitable for studies of its higher-order folding. This has required the use of yeast strains that are free of the ubiquitous yeast killer virus. Results from dynamic light scattering, electron microscopy, and x-ray diffraction show that the yeast chromatin undergoes a cation-dependent folding into 30-nm filaments that resemble those characteristic of higher-cell chromatin; moreover, the packing of nucleosomes within the yeast 30-nm filaments is similar to that of higher cells. These results imply that yeast has a protein or protein domain that serves the role of the histone H 1 found in higher cells; physical and genetic studies of the yeast activity could help elucidate the structure and function of H 1. Images of the yeast 30-nm filaments can be used to test crossed-linker models for 30-nm filament structure.
Higher order correlation beams in atmosphere under strong turbulence conditions.
Avetisyan, H; Monken, C H
2016-02-01
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.
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.
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.
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.
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 notemore » 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.« less
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.
Stabilization with target oriented control for higher order difference equations
NASA Astrophysics Data System (ADS)
Braverman, Elena; Franco, Daniel
2015-06-01
For a physical or biological model whose dynamics is described by a higher order difference equation un+1 = f (un ,un-1 , … ,u n - k + 1), we propose a version of a target oriented control un+1 = cT + (1 - c) f (un ,un-1 , … ,u n - k + 1), with T ≥ 0, c ∈ [ 0 , 1). In ecological systems, the method incorporates harvesting and recruitment and for a wide class of f, allows to stabilize (locally or globally) a fixed point of f. If a point which is not a fixed point of f has to be stabilized, the target oriented control is an appropriate method for achieving this goal. As a particular case, we consider pest control applied to pest populations with delayed density-dependence. This corresponds to a proportional feedback method, which includes harvesting only, for higher order equations.
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.
Spatial complexity of solutions of higher order partial differential equations
NASA Astrophysics Data System (ADS)
Kukavica, Igor
2004-03-01
We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .
Third order nonlinear optical response exhibited by mono- and few-layers of WS2
Torres-Torres, Carlos; Perea-López, Néstor; Elías, Ana Laura; Gutiérrez, Humberto R.; Cullen, David A.; Berkdemir, Ayse; López-Urías, Florentino; Terrones, Humberto; Terrones, Mauricio
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.
Third order nonlinear optical response exhibited by mono- and few-layers of WS2
NASA Astrophysics Data System (ADS)
Torres-Torres, Carlos; Perea-López, Néstor; Elías, Ana Laura; Gutiérrez, Humberto R.; Cullen, David A.; Berkdemir, Ayse; López-Urías, Florentino; Terrones, Humberto; Terrones, Mauricio
2016-06-01
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. We envision applications for developing all-optical bidimensional nonlinear optical devices.
SU(2) Higher-order effective quark interactions from polarization
NASA Astrophysics Data System (ADS)
Braghin, Fábio L.
2016-10-01
Higher order quark effective interactions are found for SU(2) flavor by departing from a non-local quark-quark interaction. By integrating out a component of the quark field, the determinant is expanded in chirally symmetric and symmetry breaking effective interactions up to the fifth order in the quark bilinears. The resulting coupling constants are resolved in the leading order of the longwavelength limit and exact numerical ratios between several of these coupling constants are obtained in the large quark mass limit. In this level, chiral invariant interactions only show up in even powers of the quark bilinears, i.e. O(ψ bar ψ) 2 n (n = 1 , 2 , 3 , . .), whereas (explicit) chiral symmetry breaking terms emerge as O(ψ bar ψ) n being always proportional to some power of the Lagrangian quark mass.
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.
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Vibrational higher-order resonances in an overdamped bistable system with biharmonic excitation
NASA Astrophysics Data System (ADS)
Chizhevsky, V. N.
2014-10-01
Experimental evidence of vibrational higher-order resonances in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies is reported. The phenomenon shows up in a parameter space (the dc current, the amplitude of the high-frequency signal) as well-defined structures with multiple local maxima at higher harmonics of the low-frequency signal. Such structures appear due to a strong suppression of higher harmonics for certain values of the high-frequency amplitude and the dc current. Complexity of the structures and the total number of the local maxima depend on the harmonic order k . The behavior of nonlinear distortion factor is also studied. The experimental results are in a good agreement with the numerical results which were obtained in the model of the bistable overdamped oscillator with biharmonic excitation.
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.
Axicons for mode conversion in high peak power, higher-order mode, fiber amplifiers.
Nicholson, J W; DeSantolo, A; Westbrook, P S; Windeler, R S; Kremp, T; Headley, C; DiGiovanni, D J
2015-12-28
Higher-order mode fiber amplifiers have demonstrated effective areas as large as 6000 μm2, allowing for high pulse energy and peak power amplification. Long-period gratings are used to convert the fundamental mode to the higher-order mode at the entrance to the amplifier, and reconvert back to the fundamental at the exit, to achieve a diffraction limited beam. However, long period gratings are susceptible to nonlinearity at high peak power. In this work, we propose and demonstrate axicons for linear bulk-optic mode conversion at the output of higher order mode amplifiers. We achieve an M2 of less than 1.25 for 80% mode conversion efficiency. Experiments with pulsed amplifiers confirm that the mode conversion is free from nonlinearity. Furthermore, chirp pulse amplifier experiments confirm that HOM amplifiers plus axicon mode convertors provide energy scalability in femtosecond pulses, compared to smaller effective area, fundamental mode fiber amplifiers. We also propose and demonstrate a route towards fiber integration of the axicon mode convertor by fabricating axicons directly on the tip of the fiber amplifier end-cap.
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 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.
Integrable higher order deformations of Heisenberg supermagnetic model
Guo Jiafeng; Yan Zhaowen; Wang Shikun; Wu Ke; Zhao Weizhong
2009-11-15
The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S{sup 2}=3S-2I for S is an element of USPL(2/1)/S(U(2)xU(1)) and (ii) S{sup 2}=S for S is an element of USPL(2/1)/S(L(1/1)xU(1)). In terms of the gauge transformation, their corresponding gauge equivalent counterparts are derived.
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. PMID:25210664
Higher-order factors of the Big Five.
Digman, J M
1997-12-01
Estimated factor correlations from 14 studies supporting the 5 factor, Big Five model of personality trait organization--5 studies based on children and adolescents, 9 on adults--were factor analyzed. Two higher-order factors were clearly evident in all studies. One was principally related to the Big Five trait dimensions Agreeableness, Conscientiousness, and Emotional Stability; the other, the dimensions Extraversion and Intellect. Two models, one for children and adolescents, the other for adults, were tested by confirmatory factor analysis with generally excellent results. Many personality theorists appear to have considered one or both of these 2 metatraits, provisionally labeled alpha and beta.
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.
Expected precision for neutron multiplicity assay using higher order moments
Ensslin, N.; Gavron, A.; Harker, W.C.
1997-11-01
This paper reports on the development of a new Figure of Merit code that can calculate the expected precision in neutron multiplicity assay using higher order moments. The code is used to provide a first look at the quadruple coincidence count rate and its expected precision. The results are good enough to warrant further study of potential applications of quadruple (quad) coincidences for large multiplying plutonium items. Also, the new code makes it possible to estimate the multiplicity assay precision if only randomly-triggered moments are used. This approach is described briefly, along with the current status of the investigation.
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.
Introduction to Higher Order Spatial Statistics in Cosmology
NASA Astrophysics Data System (ADS)
Szapudi, I.
Higher order spatial statistics characterize non-Gaussian aspects of random fields, which are ubiquitous in cosmology: from the cosmic microwave background (CMB) to the large-scale structure (LSS) of the universe. These random fields are rich in their properties; they can be continuous or discrete; can have one through three, or even more dimensions; their degree of non- Gaussianity ranges from tiny to significant. Yet, there are several techniques and ideas, which are applicable to virtually all cosmological random fields, be it Lyman-a forests, LSS, or CMB.
NASA Astrophysics Data System (ADS)
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.
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.
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.
Aero-optical jitter estimation using higher-order wavefronts
NASA Astrophysics Data System (ADS)
Whiteley, Matthew R.; Goorskey, David J.; Drye, Richard
2013-07-01
Wavefront measurements from wind tunnel or flight testing of an optical system are affected by jitter sources due to the measurement platform, system vibrations, or aero-mechanical buffeting. Depending on the nature of the testing, the wavefront jitter will be a composite of several effects, one of which is the aero-optical jitter; i.e., the wavefront tilt due to random air density fluctuations. To isolate the aero-optical jitter component from recent testing, we have developed an estimation technique that uses only higher-order wavefront measurements to determine the jitter. By analogy with work done previously with free-stream turbulence, we have developed a minimum mean-square error estimator using higher-order wavefront modes to compute the current-frame tilt components through a linear operation. The estimator is determined from computational fluid dynamics evaluation of aero-optical disturbances, but does not depend on the strength of such disturbances. Applying this technique to turret flight test data, we found aero-optical jitter to be 7.7±0.8 μrad and to scale with (ρ/ρSL)M2 (˜1 μrad in the actual test cases examined). The half-power point of the aero-optical jitter variance was found to be ˜2u∞/Dt and to roll off in temporal frequency with a power law between f and f.
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
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.
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
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.
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.
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
Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.
Khan, Hasib; Jafari, Hossein; 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 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.
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. PMID:20361813
The assembly bias of dark matter haloes to higher orders
NASA Astrophysics Data System (ADS)
Angulo, R. E.; Baugh, C. M.; Lacey, C. G.
2008-06-01
We use an extremely large volume (2.4h-3Gpc3), high-resolution N-body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. As a result of the large simulation volume and the use of a novel `cross-moment' counts-in-cells technique which suppresses discreteness noise, we are able to measure the clustering of haloes corresponding to rarer peaks than was possible in previous studies; the rarest haloes for which we measure the variance are 100 times more clustered than the dark matter. We are able to extract, for the first time, halo bias parameters from linear up to fourth order. For all orders measured, we find that the bias parameters are a strong function of mass for haloes more massive than the characteristic mass M*. Currently, no theoretical model is able to reproduce this mass dependence closely. We find that the bias parameters also depend on the internal structure of the halo up to fourth order. For haloes more massive than M*, we find that the more concentrated haloes are more weakly clustered than the less concentrated ones. We see no dependence of clustering on concentration for haloes with masses M < M* this is contrary to the trend reported in the literature when segregating haloes by their formation time. Our results are insensitive to whether haloes are labelled by the total mass returned by the friends-of-friends group finder or by the mass of the most massive substructure. This implies that our conclusions are not an artefact of the particular choice of group finding algorithm. Our results will provide important input to theoretical models of galaxy clustering.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Fogg, Stephen L.
2006-05-01
Nonlinear `parametric' sonar is distinguished by highly predictable in-water formations of identifiable von Helmholtz spectral energies produced directly as a result of two or more preselected primaries simultaneously contained in a transmit waveform. In the nearly half-century of scientific endeavors within the field of parametric sonar, the methodical investigation into formulation techniques and practical applications using higher-order combination tones has been noticeably lagging the attention received by their more commonly recognized kin of second-order sum and difference frequencies. Generalized mathematical and graphical viewing techniques are presented for elucidating the abundance of cross-band complexities and facilitating preliminary design efforts specifically employing any of these higher-order parametric frequency components on operational systems. Recent sonar experiments implementing pulsed parametric transmit waveforms intended to fully exploit their intrinsic broadband nonlinear energy have demonstrated the potential for improved underwater target detection and classification in acoustically harsh environments. However, research efforts could benefit from more efficient and universal tools for predetermining all of the desired in-water spectral-temporal characteristics. New developments utilizing this methodology have led to unique approaches for designing stepped CW, LFM and hyperbolic FM detection waveforms incorporating enhanced signal processing qualities and constructing coding schemes for reliable underwater acoustic digital communications.
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.
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 behavior classes: contingencies, beliefs, and verbal behavior.
Catania, A C
1995-09-01
The concepts of reinforcement and of higher-order classes of behavior are reviewed and applied to analyses of self-reinforcement, self-efficacy, the causal status of private events, and the role of verbal behavior in human action. The analyses support the case that Bandura's criticisms of behavior analytic thought rest upon several misunderstandings, the most important of which are the distinctions between theories and phenomena and a neglect of the process of ontogenic selection. Bandura's persistence in promoting these misunderstandings is puzzling, because over a period of at least two decades he has repeated without substantial correction arguments that were refuted at the time he first made them. Bandura's views on these concepts can be interpreted as a contemporary variety of creationism in behavioral science. PMID:8576398
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.
Intermediary LEO propagation including higher order zonal harmonics
NASA Astrophysics Data System (ADS)
Hautesserres, Denis; Lara, Martin
2016-10-01
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.
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 modes of phase conjugate resonators.
Hardy, A; Hochhauser, S
1982-07-01
A numerical analysis based on the Prony algorithm was carried out to find the higher-order modes of phase conjugate optical resonators with hard-edged apertures. The mode patterns are nearly Hermite-Gaussians even for unstable resonator configurations. This indicates that there is not a phase conjugate analog of conventional unstable resonators. The eigenvalues and the extent to which the phase fronts match the surface of the conventional mirror were also calculated for a variety of resonator parameters. When there is one limiting aperture in the resonator and all others (including the phase conjugating mirror) can be considered as unbound, the eigenvalues and phase matching parameter are scalable by the ratio g/N, where N is the Fres-nel number of the aperture and g = 1 - L/R as in conventional resonator theory. PMID:20396031
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.
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.
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.
Detailed Modeling of Higher Order Hierarchical Kepler Star Systems
NASA Astrophysics Data System (ADS)
Gore, Joanna; Orosz, Jerome A.
2016-06-01
Most stars have stellar companions (i.e. they exist in double, triple, or higher order configurations). Binary star systems are those which contain two stars. These systems are valued scientifically because they allow for the measurement of fundamental stellar properties such as masses and radii. These properties in turn allow for detailed studies of stellar evolution. The Kepler space telescope has discovered roughly 2900 eclipsing binary stars in its field of view. Various studies have shown that roughly 20% of the Kepler eclipsing binaries contain companions are are most likely triple star systems. We present a preliminary survey of the orbital properties of the tertiary bodies in a sample of thirty triple systems. In addition, a small number of the triple systems show eclipse events due to the third star. We present the results of detailed modeling of two of these systems, and discuss how in some cases these triple systems allow for extremely precise measurements of the fundamental stellar parameters.
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.
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.
Phantom Friedmann cosmologies and higher-order characteristics of expansion
Dabrowski, Mariusz P. . E-mail: mpdabfz@sus.univ.szczecin.pl; Stachowiak, Tomasz . E-mail: toms@oa.uj.edu.pl
2006-04-15
We discuss a more general class of phantom (p < -{rho}) cosmologies with various forms of both phantom (w < -1), and standard (w > -1) matter. We show that many types of evolution which include both Big-Bang and Big-Rip singularities are admitted and give explicit examples. Among some interesting models, there exist non-singular oscillating (or 'bounce') cosmologies, which appear due to a competition between positive and negative pressure of variety of matter content. From the point of view of the current observations the most interesting cosmologies are the ones which start with a Big-Bang and terminate at a Big-Rip. A related consequence of having a possibility of two types of singularities is that there exists an unstable static universe approached by the two asymptotic models-one of them reaches Big-Bang, and another reaches Big-Rip. We also give explicit relations between density parameters {omega} and the dynamical characteristics for these generalized phantom models, including higher-order observational characteristics such as jerk and 'kerk.' Finally, we discuss the observational quantities such as luminosity distance, angular diameter, and source counts, both in series expansion and explicitly, for phantom models. Our series expansion formulas for the luminosity distance and the apparent magnitude go as far as to the fourth-order in redshift z term, which includes explicitly not only the jerk, but also the 'kerk' (or 'snap') which may serve as an indicator of the curvature of the universe.
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.
From Second to Higher Order Tensors in Diffusion-MRI
NASA Astrophysics Data System (ADS)
Ghosh, Aurobrata; Deriche, Rachid
Diffusion MRI, which is sensitive to the Brownian motion of molecules, has become today an excellent medical tool for probing the tissue micro-structure of cerebral white matter in vivo and non-invasively. It makes it possible to reconstruct fiber pathways and segment major fiber bundles that reflect the structures in the brain which are not visible to other non-invasive imaging modalities. Since this is possible without operating on the subject, but by integrating partial information from Diffusion Weighted Images into a reconstructed ‘complete’ image of diffusion, Diffusion MRI opens a whole new domain of image processing. Here we shall explore the role that tensors play in the mathematical model. We shall primarily deal with Cartesian tensors and begin with 2nd order tensors, since these are at the core of Diffusion Tensor Imaging. We shall then explore higher and even ordered symmetric tensors, that can take into account more complex micro-geometries of biological tissues such as axonal crossings in the white matter.
A consolidation algorithm for genomes fractionated after higher order polyploidization
2012-01-01
Background It has recently been shown that fractionation, the random loss of excess gene copies after a whole genome duplication event, is a major cause of gene order disruption. When estimating evolutionary distances between genomes based on chromosomal rearrangement, fractionation inevitably leads to significant overestimation of classic rearrangement distances. This bias can be largely avoided when genomes are preprocessed by "consolidation", a procedure that identifies and accounts for regions of fractionation. Results In this paper, we present a new consolidation algorithm that extends and improves previous work in several directions. We extend the notion of the fractionation region to use information provided by regions where this process is still ongoing. The new algorithm can optionally work with this new definition of fractionation region and is able to process not only tetraploids but also genomes that have undergone hexaploidization and polyploidization events of higher order. Finally, this algorithm reduces the asymptotic time complexity of consolidation from quadratic to linear dependence on the genome size. The new algorithm is applied both to plant genomes and to simulated data to study the effect of fractionation in ancient hexaploids. PMID:23282012
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
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
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
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.
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 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 adaptive finite-element methods for orbital-free density functional theory
Motamarri, Phani; Iyer, Mrinal; Knap, Jaroslaw; Gavini, Vikram
2012-08-15
In the present work, we study various numerical aspects of higher-order finite-element discretizations of the non-linear saddle-point formulation of orbital-free density-functional theory. We first investigate the robustness of viable solution schemes by analyzing the solvability conditions of the discrete problem. We find that a staggered solution procedure where the potential fields are computed consistently for every trial electron-density is a robust solution procedure for higher-order finite-element discretizations. We next study the convergence properties of higher-order finite-element discretizations of orbital-free density functional theory by considering benchmark problems that include calculations involving both pseudopotential as well as Coulomb singular potential fields. Our numerical studies suggest close to optimal rates of convergence on all benchmark problems for various orders of finite-element approximations considered in the present study. We finally investigate the computational efficiency afforded by various higher-order finite-element discretizations, which constitutes the main aspect of the present work, by measuring the CPU time for the solution of discrete equations on benchmark problems that include large Aluminum clusters. In these studies, we use mesh coarse-graining rates that are derived from error estimates and an a priori knowledge of the asymptotic solution of the far-field electronic fields. Our studies reveal a significant 100-1000 fold computational savings afforded by the use of higher-order finite-element discretization, alongside providing the desired chemical accuracy. We consider this study as a step towards developing a robust and computationally efficient discretization of electronic structure calculations using the finite-element basis.
Studies on third-order nonlinear optical properties of chalcone derivatives in polymer host
NASA Astrophysics Data System (ADS)
Shettigar, Seetharam; Umesh, G.; Chandrasekharan, K.; Sarojini, B. K.; Narayana, B.
2008-04-01
In this paper we present the experimental study of the third-order nonlinear optical properties of two chalcone derivatives, viz., 1-(4-methoxyphenyl)-3-(4-butyloxyphenyl)-prop-2-en-1-one and 1-(4-methoxyphenyl)-3-(4-propyloxyphenyl)-prop-2-en-1-one in PMMA host, with the prospective of reaching a compromise between good processability and high nonlinear optical properties. The nonlinear optical properties have been investigated by Z-scan technique using 7 ns laser pulses at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, magnitude of third-order susceptibility and the coupling factor have been determined. The values obtained are of the order of 10 -14 cm 2/W, 1 cm/GW, 10 -13 esu and 0.2, respectively. The molecular second hyperpolarizability for the chalcone derivatives in polymer is of the order of 10 -31 esu. Different guest/host concentrations have also been studied. The results suggest that the nonlinear properties of the chalcones have been improved when they are used as dopants in polymer matrix. The nonlinear parameters obtained are comparable with the reported values of II-VI compound semiconductors. Hence, these chalcons are a promising class of nonlinear optical dopant materials for optical device applications.
ERIC Educational Resources Information Center
Shukla, Divya; Dungsungnoen, Aj Pattaradanai
2016-01-01
Higher order thinking skills (HOTS) has portrayed immense industry demand and the major goal of educational institution in imparting education is to inculcate higher order thinking skills. This compiles and mandate the institutions and instructor to develop the higher order thinking skills among students in order to prepare them for effective…
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.
Transcriptional Derepression Uncovers Cryptic Higher-Order Genetic Interactions
Taylor, Matthew B.; Ehrenreich, Ian M.
2015-01-01
Disruption of certain genes can reveal cryptic genetic variants that do not typically show phenotypic effects. Because this phenomenon, which is referred to as ‘phenotypic capacitance’, is a potential source of trait variation and disease risk, it is important to understand how it arises at the genetic and molecular levels. Here, we use a cryptic colony morphology trait that segregates in a yeast cross to explore the mechanisms underlying phenotypic capacitance. We find that the colony trait is expressed when a mutation in IRA2, a negative regulator of the Ras pathway, co-occurs with specific combinations of cryptic variants in six genes. Four of these genes encode transcription factors that act downstream of the Ras pathway, indicating that the phenotype involves genetically complex changes in the transcriptional regulation of Ras targets. We provide evidence that the IRA2 mutation reveals the phenotypic effects of the cryptic variants by disrupting the transcriptional silencing of one or more genes that contribute to the trait. Supporting this role for the IRA2 mutation, deletion of SFL1, a repressor that acts downstream of the Ras pathway, also reveals the phenotype, largely due to the same cryptic variants that were detected in the IRA2 mutant cross. Our results illustrate how higher-order genetic interactions among mutations and cryptic variants can result in phenotypic capacitance in specific genetic backgrounds, and suggests these interactions might reflect genetically complex changes in gene expression that are usually suppressed by negative regulation. PMID:26484664
Image Segmentation Using Higher-Order Correlation Clustering.
Kim, Sungwoong; Yoo, Chang D; Nowozin, Sebastian; Kohli, Pushmeet
2014-09-01
In this paper, a hypergraph-based image segmentation framework is formulated in a supervised manner for many high-level computer vision tasks. To consider short- and long-range dependency among various regions of an image and also to incorporate wider selection of features, a higher-order correlation clustering (HO-CC) is incorporated in the framework. Correlation clustering (CC), which is a graph-partitioning algorithm, was recently shown to be effective in a number of applications such as natural language processing, document clustering, and image segmentation. It derives its partitioning result from a pairwise graph by optimizing a global objective function such that it simultaneously maximizes both intra-cluster similarity and inter-cluster dissimilarity. In the HO-CC, the pairwise graph which is used in the CC is generalized to a hypergraph which can alleviate local boundary ambiguities that can occur in the CC. Fast inference is possible by linear programming relaxation, and effective parameter learning by structured support vector machine is also possible by incorporating a decomposable structured loss function. Experimental results on various data sets show that the proposed HO-CC outperforms other state-of-the-art image segmentation algorithms. The HO-CC framework is therefore an efficient and flexible image segmentation framework. PMID:26352230
Higher order finite element analysis of thick composite laminates
NASA Technical Reports Server (NTRS)
Goering, J.; Kim, H. J.
1992-01-01
A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.
Dynamical stability of Minkowski space in higher order gravity
NASA Astrophysics Data System (ADS)
Tretyakov, Petr V.
2015-06-01
We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space is proposed. This method was applied for some modified gravity theories, such as f(R) gravity, f(R)+αR□R gravity and scalar-tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of f(R) gravity Minkowski solution is asymptotically stable in ghost-free (f‧ > 0) and tachyon-free (f″ > 0) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of higher order gravity with αR□R correction conditions of Minkowski stability with respect to isotropic perturbations are significantly different: f‧(0) < 0, f″(0) < 0 and 3f‧(0) + f″(0)2/α > 0. And in the case of scalar-tensor gravity with non-minimal kinetic coupling Minkowski solution is asymptotically stable in expanding Universe with respect to isotropic perturbations of metric. Moreover, the developed method may be used for finding additional restrictions on parameters of different modified gravity theories.
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
Higher-order scene statistics of breast images
NASA Astrophysics Data System (ADS)
Abbey, Craig K.; Sohl-Dickstein, Jascha N.; Olshausen, Bruno A.; Eckstein, Miguel P.; Boone, John M.
2009-02-01
Researchers studying human and computer vision have found description and construction of these systems greatly aided by analysis of the statistical properties of naturally occurring scenes. More specifically, it has been found that receptive fields with directional selectivity and bandwidth properties similar to mammalian visual systems are more closely matched to the statistics of natural scenes. It is argued that this allows for sparse representation of the independent components of natural images [Olshausen and Field, Nature, 1996]. These theories have important implications for medical image perception. For example, will a system that is designed to represent the independent components of natural scenes, where objects occlude one another and illumination is typically reflected, be appropriate for X-ray imaging, where features superimpose on one another and illumination is transmissive? In this research we begin to examine these issues by evaluating higher-order statistical properties of breast images from X-ray projection mammography (PM) and dedicated breast computed tomography (bCT). We evaluate kurtosis in responses of octave bandwidth Gabor filters applied to PM and to coronal slices of bCT scans. We find that kurtosis in PM rises and quickly saturates for filter center frequencies with an average value above 0.95. By contrast, kurtosis in bCT peaks near 0.20 cyc/mm with kurtosis of approximately 2. Our findings suggest that the human visual system may be tuned to represent breast tissue more effectively in bCT over a specific range of spatial frequencies.
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.
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 Synaptic Interactions Coordinate Dynamics in Recurrent Networks.
Chambers, Brendan; MacLean, Jason N
2016-08-01
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
Shock waves with higher order effects in an electron depleted dusty Plasma
NASA Astrophysics Data System (ADS)
Ghai, Yashika; Singh Saini, Nareshpal; Singh, Manpreet
2016-07-01
Shock waves are characterized as a sudden change in properties of the medium that propagate faster than the speed of sound. A plasma system in which dissipation is dominant over dispersion of the medium, the balance between dissipation and nonlinearity leads to the formation of shock structures. A number of observations and in-situ measurements have confirmed the presence of excess superthermal populations in astrophysical and space plasmas. In fact, two temperature superthermal ion populations have been observed by Geotail spacecraft in earth's magnetotail. Moreover, charging of dust by accumulation of electrons in plasma leads to electron depleted plasma. In present investigation, shocks in an electron depleted dusty plasma with two temperature superthermal ions have been studied by using Burger's equation. Further, to incorporate higher order nonlinear effects, we have derived modified Burger's equation and studied its shock solution. The effects of various physical parameters such as superthermality of ions, kinematic viscosity and dust concentration have been observed on properties of shock structures. The results of present investigation may be useful in understanding the nonlinear structures formed in earth's atmosphere where dust and two temperature superthermal ions are observed.
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.
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 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.
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.
Solutions to higher-order anisotropic parabolic equations in unbounded domains
Kozhevnikova, L M; Leont'ev, A A
2014-01-31
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,∞)×Ω, where Ω⊂R{sup n}, n≥3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t→∞ 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.
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.
An efficient technique for higher order fractional differential equation.
Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2016-01-01
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems. PMID:27047707
Higher order chromatin structures in maize and Arabidopsis.
Paul, A L; Ferl, R J
1998-01-01
We are investigating the nature of plant genome domain organization by using DNase I- and topoisomerase II-mediated cleavage to produce domains reflecting higher order chromatin structures. Limited digestion of nuclei with DNase I results in the conversion of the >800 kb genomic DNA to an accumulation of fragments that represents a collection of individual domains of the genome created by preferential cleavage at super-hypersensitive regions. The median size of these fragments is approximately 45 kb in maize and approximately 25 kb in Arabidopsis. Hybridization analyses with specific gene probes revealed that individual genes occupy discrete domains within the distribution created by DNase I. The maize alcohol dehydrogenase Adh1 gene occupies a domain of 90 kb, and the maize general regulatory factor GRF1 gene occupies a domain of 100 kb in length. Arabidopsis Adh was found within two distinct domains of 8.3 and 6.1 kb, whereas an Arabidopsis GRF gene occupies a single domain of 27 kb. The domains created by topoisomerase II-mediated cleavage are identical in size to those created by DNase I. These results imply that the genome is not packaged by means of a random gathering of the genome into domains of indiscriminate length but rather that the genome is gathered into specific domains and that a gene consistently occupies a discrete physical section of the genome. Our proposed model is that these large organizational domains represent the fundamental structural loop domains created by attachment of chromatin to the nuclear matrix at loop basements. These loop domains may be distinct from the domains created by the matrix attachment regions that typically flank smaller, often functionally distinct sections of the genome. PMID:9707534
Higher order variability properties of accreting black holes
NASA Astrophysics Data System (ADS)
Maccarone, Thomas J.; Coppi, Paolo S.
2002-11-01
To better constrain the emission mechanism underlying the hard state of galactic black hole candidates, we use high-time resolution RXTE light curves for Cyg X-1 and GX 339-4 to compute two higher order variability statistics for these objects, the skewness and the Fourier bispectrum. Similar analyses, in particular using the skewness measure, have been attempted previously, but the photon collection area of RXTE allows us to present results of much greater statistical significance. The results for the two objects are qualitatively similar, reinforcing the idea that the same basic mechanisms are at work in both. We find a significantly positive skewness for variability time-scales less than ~1 s, and a negative skewness for time-scales from 1 to 5 s. Such a skewness pattern cannot be reproduced by the simplest shot variability models where individual shots have a fixed profile and intensity and are uncorrelated in time. Further evidence against simple-shot models comes from the significant detection of a non-zero bicoherence for Fourier periods ~0.1-10 s, implying that significant coupling does exist between variations on these time-scales. We discuss how current popular models for variability in black hole systems can be modified to match these observations. Using simulated light curves, we suggest that the most likely way to reproduce this observed behaviour is to have the variability come in groups of many shots, with the number of shots per unit time fitting an envelope function that has a rapid rise and a slow decay, while the individual shots have a slow rise and a rapid decay. Invoking a finite-energy reservoir that is depleted by each shot is a natural way of producing the required shot correlations.
Limb apraxias: higher-order disorders of sensorimotor integration.
Leiguarda, R C; Marsden, C D
2000-05-01
Limb apraxia comprises a wide spectrum of higher-order motor disorders that result from acquired brain disease affecting the performance of skilled, learned movements. At present, limb apraxia is primarily classified by the nature of the errors made by the patient and the pathways through which these errors are elicited, based on a two-system model for the organization of action: a conceptual system and a production system. Dysfunction of the former would cause ideational (or conceptual) apraxia, whereas impairment of the latter would induce ideomotor and limb-kinetic apraxia. Currently, it is possible to approach several types of limb apraxia within the framework of our knowledge of the modular organization of the brain. Multiple parallel parietofrontal circuits, devoted to specific sensorimotor transformations, have been described in monkeys: visual and somatosensory transformations for reaching; transformation of information about the location of body parts necessary for the control of movements; somatosensory transformation for posture; visual transformation for grasping; and internal representation of actions. Evidence from anatomical and functional brain imaging studies suggests that the organization of the cortical motor system in humans is based on the same principles. Imitation of postures and movements also seems to be subserved by dedicated neural systems, according to the content of the gesture (meaningful versus meaningless) to be imitated. Damage to these systems would produce different types of ideomotor and limb-kinetic praxic deficits depending on the context in which the movement is performed and the cognitive demands of the action. On the other hand, ideational (or conceptual) apraxia would reflect an inability to select and use objects due to the disruption of normal integration between systems subserving the functional knowledge of actions and those involved in object knowledge.
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.
The effect of problem perturbations on nonlinear dynamical systems and their reduced order models
Serban, R; Homescu, C; Petzold, L
2005-03-03
Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'
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.
Second order nonlinear optical properties of In-doped lithium niobate
NASA Astrophysics Data System (ADS)
Xue, D.; Betzler, K.; Hesse, H.
2001-01-01
Second order nonlinear optical properties of In-doped lithium niobate crystals have been quantitatively studied from the chemical bond viewpoint. The results show that the second order nonlinear optical response of In-doped lithium niobate crystals at 1079 nm decreases remarkably with increasing In concentration in the crystal. This approximately linear composition-property correlation in In-doped lithium niobate crystals is quantitatively expressed in the current work. Furthermore, the different influences of Mg, Zn, and In dopants, respectively, on the nonlinear susceptibility of lithium niobate single crystals are also compared in the present work.
Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass.
Choi, Jiyeon; Bellec, Matthieu; Royon, Arnaud; Bourhis, Kevin; Papon, Gautier; Cardinal, Thierry; Canioni, Lionel; Richardson, Martin
2012-03-15
We demonstrate that direct femtosecond laser writing in silver-containing zinc and gallium phosphate glass enables generation of three-dimensional (3D) optical second-order nonlinear microstructures having an χ(2) value about 2.5 times that of quartz. The proposed physical model involves photo-reduction, photo-dissociation, and migration of silver species within the glass matrix. 3D laser-written second-order nonlinear structures could become a new class of nonlinear optical components. PMID:22446213
NASA Astrophysics Data System (ADS)
Pramodini, S.; Poornesh, P.
2014-11-01
We report thermally induced third-order nonlinearity and optical limiting behaviour of Indigo Carmine dye. z-Scan technique was used to determine the sign and magnitude of absorptive and refractive nonlinearities. Continuous wave (CW) He-Ne laser operating at 633 nm was used as source of excitation. In open aperture z-scan experiments, samples exhibited reverse saturable absorption (RSA) process. For closed aperture z-scan experiments, samples revealed self-defocusing property. The presence of donor and acceptor groups in the structure increases the conjugation length and in turn increases the optical nonlinearity. Induced self-diffraction rings pattern was recorded for the samples and it is attributed to refractive index change and thermal lensing. Also, optical limiting and clamping studies were carried out for various input power. Optical clamping of about ~1 mW was observed. This endorses that the dye under investigation is a positive candidate for opto-electronic and photonic applications.
NASA Astrophysics Data System (ADS)
Demiray, Hilmi
2014-12-01
The basic equations describing the nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions, in the long-wave limit, are re-examined through the use of the modified PLK method. Introducing the concept of strained coordinates and expanding the field variables into a power series of the smallness parameter ɛ, a set of evolution equations is obtained for various order terms in the perturbation expansion. The evolution equation for the lowest order term in the perturbation expansion is characterized by the conventional modified Korteweg-deVries (mKdV) equation, whereas the evolution equations for the higher order terms in the expansion are described by the degenerate(linearized) mKdV equation. By studying the localized traveling wave solution to the evolution equations, the strained coordinate for this order is determined so as to remove possible secularities that might occur in the solution. It is observed that the coefficient of the strained coordinate for this order corresponds to the correction term in the wave speed. The numerical results reveal that the contribution of second order term to the wave amplitude is about 20 %, which cannot be ignored.
Construction of higher order accurate vortex and particle methods
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.
1986-01-01
The standard point vortex method has recently been shown to be of high order of accuracy for problems on the whole plane, when using a uniform initial subdivision for assigning the vorticity to the points. If obstacles are present in the flow, this high order deteriorates to first or second order. New vortex methods are introduced which are of arbitrary accuracy (under regularity assumptions) regardless of the presence of bodies and the uniformity of the initial subdivision.
NASA Astrophysics Data System (ADS)
Aeineh, N.; Tavassoly, M. K.
2015-08-01
In this paper, we investigate the higher-order nonclassical properties of a particular class of generalized coherent states namely the deformed photon-added nonlinear coherent states (DPACS) A†m |α, f, m>. To achieve this purpose we pay attention to higher-orders of squeezing (both Hillery- and Hong-Mandel-types), sub-Poissonian statistics and anti-bunching of the mentioned states with a well-known nonlinearity function. It is shown that for enough large values of field intensity (|α|2) for a fixed N (the order of squeezing) by increasing m (the order of excitation) the degree of squeezing evaluated by Hillery and Hong-Mandel approaches increases, while for a chosen fixed value of m, by increasing N for Hillery (Hong-Mandel) type of squeezing the strength of squeezing decreases (increases). Similarly, the degree of higher-order sub-Poissonian statistics (with fixed K) becomes lower when m increases, while (with fixed m) it gets greater values when the order of sub-Poissonian K increases. At last, higher-order anti-bunching of the DPACS is evaluated, by which we established that its (always) negative values increase with increasing m, α and l (the order of anti-bunching) individually, i.e. the degree of anti-bunching increases.
Silva, Carlos A B; Rodrigues, Clóves G; Ramos, J Galvão; Luzzi, Roberto
2015-06-01
Construction, in the framework of a nonequilibrium statistical ensemble formalism, of a higher-order generalized hydrodynamics, also referred to as mesoscopic hydrothermodynamics, that is, covering phenomena involving motion of fluids displaying variations short in space and fast in time-unrestricted values of Knudsen numbers, is presented. In that way, an approach is provided enabling the coupling and simultaneous treatment of the kinetics and hydrodynamic levels of descriptions. It is based on a complete thermostatistical approach in terms of the densities of matter and energy and their fluxes of all orders covering systems arbitrarily driven away from equilibrium. The set of coupled nonlinear integrodifferential hydrodynamic equations is derived. They are the evolution equations of the Gradlike moments of all orders, derived from a generalized kinetic equation built in the framework of the nonequilibrium statistical ensemble formalism. For illustration, the case of a system of particles embedded in a fluid acting as a thermal bath is fully described. The resulting enormous set of coupled evolution equations is of unmanageable proportions, thus requiring in practice to introduce an appropriate description using the smallest possible number of variables. We have obtained a hierarchy of Maxwell times, associated to the set of all the higher-order fluxes, which have a particular relevance in the process of providing criteria for establishing the contraction of description. PMID:26172796
Silva, Carlos A B; Rodrigues, Clóves G; Ramos, J Galvão; Luzzi, Roberto
2015-06-01
Construction, in the framework of a nonequilibrium statistical ensemble formalism, of a higher-order generalized hydrodynamics, also referred to as mesoscopic hydrothermodynamics, that is, covering phenomena involving motion of fluids displaying variations short in space and fast in time-unrestricted values of Knudsen numbers, is presented. In that way, an approach is provided enabling the coupling and simultaneous treatment of the kinetics and hydrodynamic levels of descriptions. It is based on a complete thermostatistical approach in terms of the densities of matter and energy and their fluxes of all orders covering systems arbitrarily driven away from equilibrium. The set of coupled nonlinear integrodifferential hydrodynamic equations is derived. They are the evolution equations of the Gradlike moments of all orders, derived from a generalized kinetic equation built in the framework of the nonequilibrium statistical ensemble formalism. For illustration, the case of a system of particles embedded in a fluid acting as a thermal bath is fully described. The resulting enormous set of coupled evolution equations is of unmanageable proportions, thus requiring in practice to introduce an appropriate description using the smallest possible number of variables. We have obtained a hierarchy of Maxwell times, associated to the set of all the higher-order fluxes, which have a particular relevance in the process of providing criteria for establishing the contraction of description.
Dynamics and phenomenology of higher order gravity cosmological models
NASA Astrophysics Data System (ADS)
Moldenhauer, Jacob Andrew
2010-10-01
I present here some new results about a systematic approach to higher-order gravity (HOG) cosmological models. The HOG models are derived from curvature invariants that are more general than the Einstein-Hilbert action. Some of the models exhibit late-time cosmic acceleration without the need for dark energy and fit some current observations. The open question is that there are an infinite number of invariants that one could select, and many of the published papers have stressed the need to find a systematic approach that will allow one to study methodically the various possibilities. We explore a new connection that we made between theorems from the theory of invariants in general relativity and these cosmological models. In summary, the theorems demonstrate that curvature invariants are not all independent from each other and that for a given Ricci Segre type and Petrov type (symmetry classification) of the space-time, there exists a complete minimal set of independent invariants (a basis) in terms of which all the other invariants can be expressed. As an immediate consequence of the proposed approach, the number of invariants to consider is dramatically reduced from infinity to four invariants in the worst case and to only two invariants in the cases of interest, including all Friedmann-Lemaitre-Robertson-Walker metrics. We derive models that pass stability and physical acceptability conditions. We derive dynamical equations and phase portrait analyses that show the promise of the systematic approach. We consider observational constraints from magnitude-redshift Supernovae Type Ia data, distance to the last scattering surface of the Cosmic Microwave Background radiation, and Baryon Acoustic Oscillations. We put observational constraints on general HOG models. We constrain different forms of the Gauss-Bonnet, f(G), modified gravity models with these observations. We show some of these models pass solar system tests. We seek to find models that pass physical and
Upgrading the Marketing Curriculum: The Integration of Higher-Order Skills. A Perspective.
ERIC Educational Resources Information Center
Schoettinger, Nancy L.
1985-01-01
Discusses the support for higher-order skills in the secondary school and vocational curricula, the need for higher-order skills in the marketing curriculum, methods of teaching higher-order skills, and implications for teacher education. (CT)
Substituent Dependence of Third-Order Optical Nonlinearity in Chalcone Derivatives
NASA Astrophysics Data System (ADS)
Kiran, Anthony John; Satheesh Rai, Nooji; Chandrasekharan, Keloth; Kalluraya, Balakrishna; Rotermund, Fabian
2008-08-01
The third-order nonlinear optical properties of derivatives of dibenzylideneacetone were investigated using the single beam z-scan technique at 532 nm. A strong dependence of third-order optical nonlinearity on electron donor and acceptor type of substituents was observed. An enhancement in χ(3)-value of one order of magnitude was achieved upon the substitution of strong electron donors compared to that of the molecule substituted with an electron acceptor. The magnitude of nonlinear refractive index of these chalcones is as high as of 10-11 esu. Their nonlinear optical coefficients are larger than those of widely used thiophene oligomers and trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide (DABA-PEI) organic compounds.
Observation and sliding mode observer for nonlinear fractional-order system with unknown input.
Djeghali, Nadia; Djennoune, Said; Bettayeb, Maamar; Ghanes, Malek; Barbot, Jean-Pierre
2016-07-01
The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach.
A proposed ringing analysis model for higher order tether response
Natvig, B.J.
1994-12-31
The problem of high-frequency transient responses of Tension Leg Platforms, TLPs, under certain severe sea situations has been known for some time. Until recently, it was not known that this type of loading and response mechanism could produce tether loads of critical importance to the structural integrity of such structures. Presently, there is considerable ongoing discussion as to what causes tether ringing. NPD (1992) assembled a document where the views of the Norwegian Shelf operators and one Norwegian engineering company were summarized. At present there seems to be consensus that ringing, at least to a large extent, is caused by nonlinearities in the free surface variable wetting region of the TLP. Ringing is not predicted by linearized frequency domain analysis methods. There are a number of variable wetting contributions. Some of these are fairly obvious while others are less straight forward. A number of the contributions, of purely theoretical or engineering nature, identified to date are discussed in this paper. Based on this an intuitive method for ringing analysis is presented.
Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene.
Wu, Sanfeng; Mao, Li; Jones, Aaron M; Yao, Wang; Zhang, Chuanwei; Xu, Xiaodong
2012-04-11
Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, and optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here, we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable second order nonlinear susceptibility χ((2)) once an in-plane electric field is applied. χ((2)) can be electrically tuned from 0 to ~10(5) pm/V, 3 orders of magnitude larger than the widely used nonlinear crystal AgGaSe(2). We show that the unusually large χ((2)) arise from two different quantum enhanced two-photon processes thanks to the unique electronic spectrum of BLG. The tunable electronic bandgap of BLG adds additional tunability on the resonance of χ((2)), which corresponds to a tunable wavelength ranging from ~2.6 to ~3.1 μm for the up-converted photon. Combined with the high electron mobility and optical transparency of the atomically thin BLG, our scheme suggests a new regime of nonlinear photonics based on BLG. PMID:22369519
Higher-order exchange interactions leading to metamagnetism in FeRh
NASA Astrophysics Data System (ADS)
Barker, Joseph; Chantrell, Roy W.
2015-09-01
The origin of the metamagnetic antiferromagnetic-ferromagnetic phase transition of FeRh is a subject of debate. Competing explanations invoke magnetovolume effects or a purely thermodynamic transition within the spin system. It is experimentally difficult to observe the changes in the magnetic system and the lattice simultaneously, leading to conflicting evidence over which mechanism causes the phase transition. A noncollinear electronic structure study by Mryasov [Phase Transitions 78, 197 (2005), 10.1080/01411590412331316591] showed that nonlinear behavior of the Rh moment leads to higher-order exchange terms in FeRh. Using atomistic spin dynamics, we show that the phase transition can occur due to the competition between bilinear and the higher-order four spin exchange terms in an effective spin Hamiltonian. The phase transition we see is of first order and shows thermal hysteresis in agreement with experimental observations. Simulating subpicosecond laser heating, we show an agreement with pump-probe experiments with a ferromagnetic response on a picosecond time scale.
Adaptation to Changes in Higher-Order Stimulus Statistics in the Salamander Retina
Tkačik, Gašper; Ghosh, Anandamohan; Schneidman, Elad; Segev, Ronen
2014-01-01
Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution. PMID:24465742
Adaptation to changes in higher-order stimulus statistics in the salamander retina.
Tkačik, Gašper; Ghosh, Anandamohan; Schneidman, Elad; Segev, Ronen
2014-01-01
Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.
Higher-order diagrammatic vibrational coupled-cluster theory.
Faucheaux, Jacob A; Hirata, So
2015-10-01
Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(N(m+⌊n/2⌋)), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm(-1) for transitions involving (m - 3) modes and of a few cm(-1) for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated.
Higher-order diagrammatic vibrational coupled-cluster theory
NASA Astrophysics Data System (ADS)
Faucheaux, Jacob A.; Hirata, So
2015-10-01
Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(Nm+⌊n/2⌋), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm-1 for transitions involving (m - 3) modes and of a few cm-1 for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated.
Higher-order diagrammatic vibrational coupled-cluster theory.
Faucheaux, Jacob A; Hirata, So
2015-10-01
Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(N(m+⌊n/2⌋)), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm(-1) for transitions involving (m - 3) modes and of a few cm(-1) for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated. PMID:26450290
Investigation of higher order correlations in swirling pipe flows
NASA Astrophysics Data System (ADS)
Acrivlellis, M.; Jungbluth, H.; Cantrak, S.
1982-04-01
Statistical quantities of swirling pipe flows generated by radial guide vanes were studied by a triple hot-wire probe and digital data reduction at two cross-sections of the pipe, one directly behind the swirl generator and the other some distance downstream from the vanes. The influence of swirl intensity on the axial pipe flow was investigated with the measured second and third order correlations as well as the third and fourth order central moments. The probability-density distribution shows the significance of the turbulence transfer mechanism in the complicated process of swirling flows.
Third-Order Nonlinear Optical Properties and Optical Switching of Palladium (I) Complex
NASA Astrophysics Data System (ADS)
Manjunatha, K. B.; Dileep, R.; Vikas, M. Shelar; Umesh, G.; Satyanarayan, M. N.; Bhat, B. Ramachandra
2011-10-01
We report the third-order nonlinear optical, optical power limiting and optical switching study of palladium-N-(2-pyridyl)-N'- (5-amino salicylidene) hydrazine triphenylphosphine, using Z-scan technique and pump-probe technique. The measured nonlinear refractive index is n2 = -6.022×10-9 esu. The complex exhibits the reverse saturable absorption (RSA), the nonlinear absorption coefficient of β = 10.748×10-9 m/W. The good optical power limiting and optical switching behavior were observed in this complex. These suggest that this complex is a potential molecule for photonic applications.
NASA Astrophysics Data System (ADS)
Umezawa, Hirohito; Jackson, Matthew; Lebel, Olivier; Nunzi, Jean-Michel; Sabat, Ribal Georges
2016-10-01
The second-order nonlinear optical coefficients of thin films of mexylaminotriazine-functionalized azobenzene molecular glass derivatives were measured using second harmonic generation. The thin films were poled using a custom corona poling set-up and the second harmonic light from a pulsed 1064-nm laser was detected. Four out of the six tested compounds showed optical nonlinearity and a maximum coefficient of 75 pm/V was obtained. The time dependence of the nonlinear coefficients was studied under ambient light and under dark; the second harmonic generation intensity stayed constant for thiazole-containing derivatives while a significant decay was measured for the other compounds.
X-ray third-order nonlinear dynamical diffraction in a crystal
Balyan, M. K.
2015-12-15
The dynamic diffraction of an X-ray wave in a crystal with a third-order nonlinear response to external field strength has been theoretically investigated. General equations for the wave propagation in crystal and nonlinear Takagi equations for both ideal and deformed crystals are derived. Integrals of motion are determined for the nonlinear problem of dynamic diffraction. The results of the numerical calculations of reflectivity in the symmetric Laue geometry for an incident plane wave and the intensity distributions on the output crystal surface for a point source are reported as an example.
Third-order nonlinear optical characterization of side-chain copolymers
NASA Astrophysics Data System (ADS)
Norwood, Robert A.; Sounik, James R.; Popolo, J.; Holcomb, Douglas P.
1991-12-01
Third order nonlinear optical properties of side-chain methacrylate copolymers incorporating 4-amino-4'-nitrostilbene, 4-oxy-4'nitrostilbene, and functionalized silicon phthalocyanine chromophores are measured by picosecond degenerate four wave mixing at 598 nm. The nonresonant stilbene system exhibits a pulse limited ultrafast response, while the resonant phthalocyanine system has a large excited state nonlinearity. Comparison of silicon phthalocyanine copolymers with solubilized guest/host systems dispersed in polymethylmethacrylate illustrate the importance of aggregation and phthalocyanine ring interaction in determining the linear optical properties and the magnitude and speed of the nonlinear optical response.
Higher Order Thinking Skills for Students with Special Needs.
ERIC Educational Resources Information Center
Savage, Louise; Lombardi, Thomas P.
1993-01-01
This article describes methods for teaching higher level thinking skills to children. A four-step teaching plan utilizing Beyer's Taxonomy of thinking skills provides a sequential technique for teaching these skills as do increased verbal interaction, skillful questioning, and use of knowledge organizers. The I PLAN strategy can aid decision…
The Structure of Higher Education: Order in the Academy
ERIC Educational Resources Information Center
Smith, Clair A.
2009-01-01
Higher education in the U.S. is provided by an interesting mix of public, private non-profit, and for-profit institutions. The for-profit educational firm serves the residual claimant owners and has the greatest incentive for efficient operation. The public and private non-profit schools have less efficient incentives, but benefit from charitable…
High-order rogue waves in vector nonlinear Schrödinger equations.
Ling, Liming; Guo, Boling; Zhao, Li-Chen
2014-04-01
We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber. PMID:24827185
Higher-Order Semi-Implicit Projection Methods
Minion, M L
2001-09-06
A semi-implicit form of the method of spectral deferred corrections is applied to the solution of the incompressible Navier-Stokes equations. A methodology for constructing semi-implicit projection methods with arbitrarily high order of temporal accuracy in both the velocity and pressure is presented. Three variations of projection methods are discussed which differ in the manner in which the auxiliary velocity and the pressure are calculated. The presentation will make clear that project methods in general need not be viewed as fractional step methods as is often the practice. Two simple numerical examples re used to demonstrate fourth-order accuracy in time for an implementation of each variation of projection method.
Machine learning using a higher order correlation network
Lee, Y.C.; Doolen, G.; Chen, H.H.; Sun, G.Z.; Maxwell, T.; Lee, H.Y.
1986-01-01
A high-order correlation tensor formalism for neural networks is described. The model can simulate auto associative, heteroassociative, as well as multiassociative memory. For the autoassociative model, simulation results show a drastic increase in the memory capacity and speed over that of the standard Hopfield-like correlation matrix methods. The possibility of using multiassociative memory for a learning universal inference network is also discussed. 9 refs., 5 figs.
The period functionsʼ higher order derivatives
NASA Astrophysics Data System (ADS)
Sabatini, M.
We prove a formula for the n-th derivative of the period function T in a period annulus of a planar differential system. For n=1, we obtain Freire, Gasull and Guillamon formula for the period's first derivative (Chicone and Dumortier, 1993) [17]. We apply such a result to Hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order ODE's to be convex.
Wavelet steerability and the higher-order Riesz transform.
Unser, Michael; Van De Ville, Dimitri
2010-03-01
Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions ( d >or= 2). To that end, we introduce a self-reversible, Nth-order extension of the Riesz transform. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of [Formula: see text] into another "steerable" wavelet frame, while preserving the frame bounds. The concept provides a functional counterpart to Simoncelli's steerable pyramid whose construction was primarily based on filterbank design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filterbank algorithm. We illustrate the method with the design of a novel family of multidimensional Riesz-Laplace wavelets that essentially behave like the N th-order partial derivatives of an isotropic Gaussian kernel. PMID:20031498
Higher-order virial coefficients of water models.
Benjamin, Kenneth M; Singh, Jayant K; Schultz, Andrew J; Kofke, David A
2007-10-01
We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water are observed to greatly exceed the magnitude of corresponding coefficients for the simple Lennard-Jones model. We examine the coefficients in the context of the equation of state and the Joule-Thomson coefficient. Comparisons of these properties are made both to established molecular simulation data for each respective model and to real water. For all models, the virial series up to B5 describes the equation of state along the saturated vapor line better than the series that includes B6. At supercritical temperatures, however, the sixth-order series often describes pressure-volume-temperature behavior better than the fifth-order series. For example, the sixth-order virial equation of state for SPC/E water predicts the 673 K isotherm within 8% of published molecular simulation values up to a density of 9 mol/L (roughly half the critical density of SPC/E water).
Probing higher-order primordial non-Gaussianity with galaxy surveys
NASA Astrophysics Data System (ADS)
Yamauchi, Daisuke; Takahashi, Keitaro
2016-06-01
With a radio continuum galaxy survey by the Square Kilometre Array (SKA), a photometric galaxy survey by Euclid, and their combination, we forecast future constraints on primordial non-Gaussianity. We focus on the potential impact of local-type higher-order nonlinear parameters on the parameter estimation and particularly the confirmation of the inflationary consistency inequality. Nonstandard inflationary models, such as multifield models, introduce the scale-dependent stochastic clustering of galaxies on large scales, which is a unique probe of mechanism for generating primordial density fluctuations. Our Fisher matrix analysis indicates that a deep and wide survey provided by SKA is more advantageous to constrain τNL, while Euclid has a strong constraining power for fNL due to the redshift information, suggesting that the joint analysis between them is quite essential to break the degeneracy between the nonlinear parameters. The combination of the full SKA and Euclid will achieve the precision level needed to confirm the consistency inequality even for fNL≈1.5 and τNL≈17 , though it is still hard for a single survey to confirm it when fNL≲2.7 .
NASA Astrophysics Data System (ADS)
Zhang, Wei; Su, Housheng; Wang, Hongwei; Han, Zhengzhi
2012-12-01
This paper aims to design full-order and reduced-order observers for one-sided Lipschitz nonlinear systems. The system under consideration is an extension of its known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. For such system, we first develop a novel Riccati equation approach to design a full-order observer, for which rigorous mathematical analysis is performed. Consequently, we show that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. A design method for the reduced-order observer that is dependent on the solution of the Riccati equation is then presented. The proposed conditions are easily and numerically tractable via standard numerical software. Furthermore, it is theoretically proven that the obtained conditions are less conservative than some existing ones in recent literature. The effectiveness of the proposed observers is illustrated via a simulative example.
Precision Measurements of Higher-Order Angular Galaxy. Correlations Using 10 Million SDSS Galaxies
NASA Astrophysics Data System (ADS)
Ross, Ashley J.; Brunner, R. J.; Myers, A. D.
2006-06-01
We present estimates of the galaxy, N-point, area-averaged angular correlation functions, ωN(θ),; for N = 2,...,7 from the third data release (DR3) of the Sloan Digital Sky Survey. Our sample was constructed from galaxies with r magnitude between 18 and 21, and is currently the largest study of galaxy higher-order correlations. The calculated angular correlation functions are used to measure the projected, sN, and real space, SN, hierarchical amplitudes. Our measurements of the real space amplitudes are remarkably precise over the physical scales 0.2-10 h-1 Mpc, and are consistent with Gaussian primordial density fluctuations. Our measurements also suggest that higher-order galaxy bias is non-negligible. By defining b1 = 1, we find that c2 = -0.26 ± 0.10 and c3 = 1.0 ± 0.9. This is the first reported measurement of a marginally significant third-order bias, and it hints at the importance of even higher-order bias terms. We find early-type galaxies exhibit significantly different clustering than late-types at both small and large scales. At large scales (r > 1 h-1 Mpc), we find the SN for late-type galaxies are lower than for early-types, implying a difference between the higher-order bias of the respective samples. We find b1,early = 1.38 ± 0.10, c2,early = 0.29 ± 0.12, b1,late = 0.81 ± 0.03, and c2,late = -0.68 ± 0.09. This supports recent measurements of the higher-order correlations of infrared-selected galaxies, which found a positive c2, presumably due to the dominance of early-type galaxies in the 2MASS sample (Frith et al. 2005). We have extended our analysis to photometrically-selected quasars in the SDSS DR3, and are planning to leverage future SDSS data releases to make even tighter constraints on primordial non-Gaussianity and non-linear bias components. We acknowledge support from NASA grants NAG5-12578 and NAG5-12580, Microsoft Research, and the NSF PACI Project.
Higher-order symplectic Born-Oppenheimer molecular dynamics
Niklasson, Anders; Bock, Nicolas; Challacombe, Matt; Odell, Anders; Delin, Anna; Johansson, Borje
2009-01-01
The extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics (TR-BOMD) enables the use of geometric integrators in the propagation of both the nuclear and the electronic degrees of freedom on the Born-Oppenheimer potential energy surface. Different symplectic integrators up to the 6th order have been adapted and optimized to TR-BOMD in the framework of ab initio self-consistent-field theory. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular for the case of very high accuracy requirements.
D'silva, E.D.; Podagatlapalli, G. Krishna; Venugopal Rao, S.; Dharmaprakash, S.M.
2012-11-15
Graphical abstract: Photograph and schematic representation of Z-scan experimental setup used to investigate third order nonlinear properties of the chalcone materials. Highlights: ► Br and NO{sub 2} substituted chalcone derivatives were exposed to picosecond laser pulses. ► Third-order nonlinear optical (NLO) properties were investigated. ► Compounds show promising third-order and optical limiting properties. ► These materials found suitable for electrical and optical applications. -- Abstract: In this paper we present results from the experimental study of third-order nonlinear optical (NLO) properties of three molecules of Br and NO{sub 2} substituted chalcone derivatives namely (2E)-1-(4-bromophenyl)-3-[4(methylsulfanyl)phenyl]prop-2-en-1-one (4Br4MSP), (2E)-1-(3-bromophenyl)-3-[4-(methylsulfanyl) phenyl]prop-2-en-1-one (3Br4MSP) and (2E)-3[4(methylsulfanyl) phenyl]-1-(4-nitrophenyl)prop-2-en-1-one (4N4MSP). The NLO properties have been investigated by Z-scan technique using 2 ps laser pulses at 800 nm. The nonlinear refractive indices, nonlinear absorption coefficient, and the magnitude of third-order susceptibility have been determined. The values obtained are of the order of 10{sup −7} cm{sup 2}/GW, 10{sup −3} cm/GW and 10{sup −14} esu respectively. The molecular second hyperpolarizability for the chalcone derivatives is of the order of 10{sup −32} esu. The coupling factor, excited state cross section, ground state cross section etc. were determined. The optical limiting (OL) property was studied. The results suggest that the nonlinear properties investigated for present chalcones are comparable with some of the reported chalcone derivatives and can be desirable for NLO applications.
NASA Astrophysics Data System (ADS)
Yang, Zuhao; Cao, Chenpeng; Shi, Jiulin; Luo, Ningning; Zhang, Yubao; He, Xingdao; Chen, Zhongping
2016-11-01
We report on the generation of higher-order stimulated Raman scattering (SRS) in a saturated aqueous solution of MgSO4, pumped by a 532 nm frequency-doubled Nd:YAG laser operating with multiple longitudinal modes. The first- (∼561.4 nm), second- (∼594 nm), and third-order (∼630 nm) Stokes components of SRS were observed, and were attributed to the symmetric vibrations of the [SO4] tetrahedral structural groups. Two possible physical mechanisms for generating higher-order SRS were analyzed. The results point to an efficient method for generating new laser wavelengths from a liquid blended media system through a higher-order nonlinear SRS process.
Third-order nonlinear optical properties of methylammonium lead halide perovskite films
Johnson, Justin C.; Li, Zhen; Ndione, Paul F.; Zhu, Kai
2016-01-01
We report third-order nonlinear coefficient values and decay time kinetics vs. halide composition (CH3NH3PbBr3 and CH3NH3PbBr2I), temperature, and excitation wavelength. The maximum values of the third-order nonlinear susceptibility X(3) (-1.6 x 10-6 esu) are similar to or larger than many common third-order materials. The source of the nonlinearity is shown to be primarily excitonic in the tribromide film by virtue of its strong enhancement near the exciton resonance. Nonresonant excitation reduces the nonlinearity significantly, as does increasing the temperature. Substitution of one I for one Br also reduces the nonlinearity by at least one order of magnitude, presumably due to the lack of strong exciton resonance in the substituted form. The thin films are stable, highly homogenous (lacking significant light scattering), and simple and inexpensive to fabricate, making them potentially useful in a variety of optoelectronic applications in which wavelength selectivity is important.
Higher-order gravitational lensing reconstruction using Feynman diagrams
Jenkins, Elizabeth E.; Manohar, Aneesh V.; Yadav, Amit P.S.; Waalewijn, Wouter J. E-mail: amanohar@ucsd.edu E-mail: ayadav@physics.ucsd.edu
2014-09-01
We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O (φ{sup 4}) in the lensing potential φ. We consider both the diagonal noise TT TT, EB EB, etc. and, for the first time, the off-diagonal noise TT TE, TB EB, etc. The previously noted large O (φ{sup 4}) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the φ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one B component of the CMB, such as EE EB.
Polarization and visibility of higher-order rainbows.
Können, Gunther P
2015-02-01
The degree of polarization of rainbows of order k with k≥3 is bounded in the interval [75%, 78%], where 75% is the limit for k→∞. A polarization filter can improve the signal-to-background ratio of the third and fourth rainbows by a factor of 2, which may lift their visibilities in natural circumstances above the threshold of human visual perception. Under optimal circumstances, the latter may be true for the recently photographed green fingerprint of the fifth rainbow, even without the aid of a polarization filter. The prospects for observing the sixth rainbow are unclear. There exists a possibility that the signal of the natural seventh rainbow (appearing at 64° from the Sun) may be separated from its background if photographed under perfect conditions through a polarization filter. PMID:25967836
Nonlinear Acoustic Response of an Aircraft Fuselage Sidewall Structure by a Reduced-Order Analysis
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.; Groen, David S.
2006-01-01
A reduced-order nonlinear analysis of a structurally complex aircraft fuselage sidewall panel is undertaken to explore issues associated with application of such analyses to practical structures. Of primary interest is the trade-off between computational efficiency and accuracy. An approach to modal basis selection is offered based upon the modal participation in the linear regime. The nonlinear static response to a uniform pressure loading and nonlinear random response to a uniformly distributed acoustic loading are computed. Comparisons of the static response with a nonlinear static solution in physical degrees-of-freedom demonstrate the efficacy of the approach taken for modal basis selection. Changes in the modal participation as a function of static and random loading levels suggest a means for improvement in the basis selection.
Higher order vortex gyrotropic modes in circular ferromagnetic nanodots.
Ding, Junjia; Kakazei, Gleb N; Liu, Xinming; Guslienko, Konstantin Y; Adeyeye, Adekunle O
2014-01-01
Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50-100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators. PMID:24762659
Higher order vortex gyrotropic modes in circular ferromagnetic nanodots
Ding, Junjia; Kakazei, Gleb N.; Liu, Xinming; Guslienko, Konstantin Y.; Adeyeye, Adekunle O.
2014-01-01
Magnetic vortex that consists of an in-plane curling magnetization configuration and a needle-like core region with out-of-plane magnetization is known to be the ground state of geometrically confined submicron soft magnetic elements. Here magnetodynamics of relatively thick (50–100 nm) circular Ni80Fe20 dots were probed by broadband ferromagnetic resonance in the absence of external magnetic field. Spin excitation modes related to the thickness dependent vortex core gyrotropic dynamics were detected experimentally in the gigahertz frequency range. Both analytical theory and micromagnetic simulations revealed that these exchange dominated modes are flexure oscillations of the vortex core string with n = 0,1,2 nodes along the dot thickness. The intensity of the mode with n = 1 depends significantly on both dot thickness and diameter and in some cases is higher than the one of the uniform mode with n = 0. This opens promising perspectives in the area of spin transfer torque oscillators. PMID:24762659
Higher-order differential phase shift keyed modulation
NASA Astrophysics Data System (ADS)
Vanalphen, Deborah K.; Lindsey, William C.
1994-02-01
Advanced modulation/demodulation techniques which are robust in the presence of phase and frequency uncertainties continue to be of interest to communication engineers. We are particularly interested in techniques which accommodate slow channel phase and frequency variations with minimal performance degradation and which alleviate the need for phase and frequency tracking loops in the receiver. We investigate the performance sensitivity to frequency offsets of a modulation technique known as binary Double Differential Phase Shift Keying (DDPSK) and compare it to that of classical binary Differential Phase Shift Keying (DPSK). We also generalize our analytical results to include n(sup -th) order, M-ary DPSK. The DDPSK (n = 2) technique was first introduced in the Russian literature circa 1972 and was studied more thoroughly in the late 1970's by Pent and Okunev. Here, we present an expression for the symbol error probability that is easy to derive and to evaluate numerically. We also present graphical results that establish when, as a function of signal energy-to-noise ratio and normalized frequency offset, binary DDPSK is preferable to binary DPSK with respect to performance in additive white Gaussian noise. Finally, we provide insight into the optimum receiver from a detection theory viewpoint.
Discrete-time reduced order neural observers for uncertain nonlinear systems.
Alanis, Alma Y; Sanchez, Edgar N; Ricalde, Luis J
2010-02-01
This paper focusses on a novel discrete-time reduced order neural observer for nonlinear systems, which model is assumed to be unknown. This neural observer is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF)-based algorithm, using a parallel configuration. This work includes the stability proof of the estimation error on the basis of the Lyapunov approach; to illustrate the applicability, simulation results for a nonlinear oscillator are included. PMID:20180251
Fu, Haijin; Hu, Pengcheng; Tan, Jiubin; Fan, Zhigang
2015-07-10
A simple method was proposed by using a tunable attenuator fitted in the reference or measurement arm of a heterodyne laser interferometer to adjust the values of mixing laser beams while the spectrum of the measurement signal is monitored using a signal analyzer. The effectiveness of the proposed method in reducing the first-order optical nonlinearity was verified through experiments. Results indicated that the peak value of the first-order optical nonlinearity could be reduced from 5.15 to 0.24 nm. It was therefore concluded that the proposed method was applicable to ultraprecision laser interferometry. PMID:26193410
NASA Technical Reports Server (NTRS)
Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.
2002-01-01
The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.
Third-order nonlinear optical properties of sulfur-rich compounds
Breitzer, J.G.; Dlott, D.D.; Iwaki, L.K.; Kirkpatrick, S.M.; Rauchfuss, T.B.
1999-09-02
The molecular third-order optical nonlinearity {gamma}{sub R} (second hyperpolarizability or nonlinear refractive index) was measured for a series of sulfur-rich molecules: sulfur (S{sub 8}), carbon-sulfur compounds, and metal thiolate clusters. Z-scan techniques (pulse width 27 ps, wavelength 527 nm) were used to measure these properties in solution by comparing the solution to the pure solvent. The authors approach is an efficient way to evaluate a number of different compounds and to quickly direct synthetic strategies for improved nonlinear and linear optical properties. The optical nonlinearities were evaluated in terms of figures of merit {vert{underscore}bar}W{vert{underscore}bar}/I{sub 0} and [T]{sup {minus}1}, where {vert{underscore}bar}W{vert{underscore}bar}/I{sub 0} is the ratio of nonlinear refraction to linear absorption and [T]{sup {minus}1} is the ratio of nonlinear refraction to nonlinear absorption. Among the carbon-sulfur compounds, C{sub 6}S{sub 8}O{sub 2} had the largest figures of merit: {vert{underscore}bar}W{vert{underscore}bar}/I{sub 0} = 4.3 x 10{sup {minus}13} m{sup 2} W{sup {minus}1} and [T]{sup {minus}1} > 5. The metal thiolate cluster with the largest second hyperpolarizability was [Zn{sub 10}S{sub 4}(SPh){sub 16}]{sup 4{minus}} ({gamma}{sub R} = {minus}7.8 x 10{sup {minus}56} C m{sup 4} V{sup {minus}3}, {minus}6.3 x 10{sup {minus}31} esu). This cluster exhibited no measurable linear or nonlinear absorption, so the figures of merit were effectively infinite. Previous work on the second hyperpolarizability of sulfur-rich compounds examined species that were hampered by substantial linear absorption coefficients. The present work shows that high figures of merit can be achieved without significant linear or nonlinear absorption.
Schizophrenia is a disorder of higher order hierarchical processing.
Krishnan, Ranga R; Keefe, Richard; Kraus, Michael
2009-06-01
Schizophrenia is a mental disorder in which the patient manifests with auditory hallucinations, paranoid or bizarre delusions, and disorganized speech and thinking. It is associated with significant social dysfunction. There are many hypotheses regarding schizophrenia. Most of these focus on schizophrenia as a manifestation of abnormalities from genetic [Mulle JG. Genomic structural variation and schizophrenia. Curr Psychiatry Rep 2008;10(2):171-7], viral [Fruntes V, Limosin F. Schizophrenia and viral infection during neurodevelopment: a pathogenesis model? Med Sci Monit 2008;14(6):RA71-7], neurochemical [e.g. dopamine (Lewis DA, Akil M. Cortical dopamine in schizophrenia: strategies for postmortem studies. J Psychiatr Res 1997;31(2):175-95) or interactions between neurotransmitters (Duncan GE, Sheitman BB, Lieberman JA. An integrated view of pathophysiological models of schizophrenia. Brain Res Brain Res Rev 1999;29(2):250-64)] or brain structural [Kotrla KJ, Weinberger DR. Brain imaging in schizophrenia. Annu Rev Med 1995;46:113-22] origins. Most of these hypotheses do not account for how or why these presumed causes lead to the manifestations of schizophrenia. We argue that brain structure and function is compatible with a hierarchical processing structure that forms the basis for perception and thought in healthy humans. We propose that perturbations of the types listed above lead to disruption of higher levels of perception and hierarchical temporal processing by the brain and that this constitutes the core deficit in schizophrenia. We present evidence that this model explains many of the features of schizophrenia and we make a series of predictions about schizophrenia.
MJO structure associated with the higher-order CEOF modes
NASA Astrophysics Data System (ADS)
Liu, Ping
2014-10-01
the total 432 CEOF modes retain all variance of the baseline MJO, while those higher than 10 contain less information and more noise and can be discarded. Furthermore, this study indicated that the longitudinal STD of the reconstructed anomalies detects the MJO phases and magnitudes in the western Pacific with more physical meaning and in better agreement with the Hovmöller diagrams than the RMM-like amplitude. The results provide an integral figure of the MJO structure from the CEOF analysis and a more robust RMM framework for monitoring the MJO's evolution in real time and for validating its numerical forecast and simulations.
Higher-order multipole amplitudes in charmonium radiative transitions
NASA Astrophysics Data System (ADS)
Artuso, M.; Blusk, S.; Khalil, S.; Mountain, R.; Randrianarivony, K.; Skwarnicki, T.; Stone, S.; Wang, J. C.; Zhang, L. M.; Bonvicini, G.; Cinabro, D.; Lincoln, A.; Smith, M. J.; Zhou, P.; Zhu, J.; Naik, P.; Rademacker, J.; Asner, D. M.; Edwards, K. W.; Reed, J.; Robichaud, A. N.; Tatishvili, G.; White, E. J.; Briere, R. A.; Vogel, H.; Onyisi, P. U. E.; Rosner, J. L.; Alexander, J. P.; Cassel, D. G.; Ehrlich, R.; Fields, L.; Galik, R. S.; Gibbons, L.; Gray, S. W.; Hartill, D. L.; Heltsley, B. K.; Hunt, J. M.; Kreinick, D. L.; Kuznetsov, V. E.; Ledoux, J.; Mahlke-Krüger, H.; Patterson, J. R.; Peterson, D.; Riley, D.; Ryd, A.; Sadoff, A. J.; Shi, X.; Stroiney, S.; Sun, W. M.; Yelton, J.; Rubin, P.; Lowrey, N.; Mehrabyan, S.; Selen, M.; Wiss, J.; Kornicer, M.; Mitchell, R. E.; Shepherd, M. R.; Tarbert, C. M.; Besson, D.; Pedlar, T. K.; Xavier, J.; Cronin-Hennessy, D.; Gao, K. Y.; Hietala, J.; Poling, R.; Zweber, P.; Dobbs, S.; Metreveli, Z.; Seth, K. K.; Tan, B. J. Y.; Tomaradze, A.; Brisbane, S.; Libby, J.; Martin, L.; Powell, A.; Spradlin, P.; Thomas, C.; Wilkinson, G.; Mendez, H.; Ge, J. Y.; Miller, D. H.; Shipsey, I. P. J.; Xin, B.; Adams, G. S.; Hu, D.; Moziak, B.; Napolitano, J.; Ecklund, K. M.; Insler, J.; Muramatsu, H.; Park, C. S.; Thorndike, E. H.; Yang, F.
2009-12-01
Using 24×106 ψ'≡ψ(2S) decays in CLEO-c, we have searched for higher multipole admixtures in electric-dipole-dominated radiative transitions in charmonia. We find good agreement between our data and theoretical predictions for magnetic quadrupole (M2) amplitudes in the transitions ψ'→γχc1,c2 and χc1,c2→γJ/ψ, in striking contrast to some previous measurements. Let b2J and a2J denote the normalized M2 amplitudes in the respective aforementioned decays, where the superscript J refers to the angular momentum of the χcJ. By performing unbinned maximum likelihood fits to full five-parameter angular distributions, we found the following values of M2 admixtures for Jχ=1: a2J=1=(-6.26±0.63±0.24)×10-2 and b2J=1=(2.76±0.73±0.23)×10-2, which agree well with theoretical expectations for a vanishing anomalous magnetic moment of the charm quark. For Jχ=2, if we fix the electric octupole (E3) amplitudes to zero as theory predicts for transitions between charmonium S states and P states, we find a2J=2=(-9.3±1.6±0.3)×10-2 and b2J=2=(1.0±1.3±0.3)×10-2. If we allow for E3 amplitudes we find, with a four-parameter fit, a2J=2=(-7.9±1.9±0.3)×10-2, b2J=2=(0.2±1.4±0.4)×10-2, a3J=2=(1.7±1.4±0.3)×10-2, and b3J=2=(-0.8±1.2±0.2)×10-2. We determine the ratios a2J=1/a2J=2=0.67-0.13+0.19 and a2J=1/b2J=1=-2.27-0.99+0.57, where the theoretical predictions are independent of the charmed quark magnetic moment and are a2J=1/a2J=2=0.676±0.071 and a2J=1/b2J=1=-2.27±0.16.
Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting
Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart
2015-02-14
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less
Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting
Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart
2015-02-14
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.
The Meaning of Higher-Order Factors in Reflective-Measurement Models
ERIC Educational Resources Information Center
Eid, Michael; Koch, Tobias
2014-01-01
Higher-order factor analysis is a widely used approach for analyzing the structure of a multidimensional test. Whenever first-order factors are correlated researchers are tempted to apply a higher-order factor model. But is this reasonable? What do the higher-order factors measure? What is their meaning? Willoughby, Holochwost, Blanton, and Blair…
NASA Astrophysics Data System (ADS)
Sugita, Atsushi; Hirabayashi, Takuma; Nihashi, Shunsuke; Ono, Atsushi; Kawata, Yoshimasa
2015-08-01
The second harmonic generations (SHG) from Au nanorods coated with the nonlinear optical (NLO) polymers will be presented. The thin films of the NLO polymers with the different transition frequencies were prepared. The SHG conversion efficiencies were highly enhanced by coating the NLO polymers on the nanorods. The conversion efficiencies were higher, as the transition wavelengths of the NLO polymers were closer either to the pump light wavelength or its second harmonic wavelength. About five-fold enhancement in the conversion efficiency was recorded from the nanorods of which absorption peak was almost exactly resonant to the second harmonic wavelength, comparing with that from the pristine PMMA coated nanorods.
Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite
NASA Astrophysics Data System (ADS)
Tripathi, S. K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta
2015-09-01
Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ~10-5 cm2/W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications.
High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation
Bihari, B L; Brown, P N
2005-03-29
The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.
Rana, Anup; Lee, Sangsu; Kim, Dongho; Panda, Pradeepta K
2015-05-01
A novel electron deficient β-octakis(methylthio)porphycene, along with its Zn(ii) and Ni(ii) derivatives, was synthesized for the first time. The macrocyclic structure exhibits core ruffling with a largely red shifted absorption band (∼750 nm) and also a large enhancement in the third order nonlinear optical response.
Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions
NASA Technical Reports Server (NTRS)
Bjorklund, G. C.
1975-01-01
Third-order nonlinear processes in isotropic media have been successfully used for tripling the efficiency of high-power laser radiation for the production of tunable and fixed-frequency coherent vacuum UV radiation and for up-conversion of IR radiation. The effects of focusing on two processes of this type are studied theoretically and experimentally.
Nonlinear H ∞ control of a Quadrotor (UAV), using high order sliding mode disturbance estimator
NASA Astrophysics Data System (ADS)
Kerma, Mokhtar; Mokhtari, Abdellah; Abdelaziz, Benallegue; Orlov, Yuri
2012-12-01
A nonlinear H ∞ output feedback controller is proposed and coupled to a high-order sliding mode estimator to regulate an UAV in the presence of the unmatched perturbations. The plant to be controlled is a Quadrotor helicopter described by nonlinear dynamics with plant uncertainties due to the variations of inertia moments and payload operation. A robust state estimation is considered under model uncertainties as well as external/measurement disturbances. Performance issues of the controller are illustrated in a simulation study made for an UAV prototype.
Computation of Nonlinear Backscattering Using a High-Order Numerical Method
NASA Technical Reports Server (NTRS)
Fibich, G.; Ilan, B.; Tsynkov, S.
2001-01-01
The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.
Creating second-order nonlinearity in pure synthetic silica optical fibers by thermal poling.
An, Honglin; Fleming, Simon
2007-04-01
A twin-hole optical fiber with pure synthetic silicate glass between the two electrode holes was thermally poled. The induced second-order nonlinearity (SON) was located at the core-cladding interface sections that were nearly parallel to the poling electric field. The polarization dependence of the induced SON suggests that nonlinearity was due to the presence of a space-charge field, which was probably formed by electron migration among the defects located at the core-cladding interface. The magnitude of the induced SON was measured to be approximately 0.06 pm /V.
Thermal poling induced second-order nonlinearity in femtosecond- laser-modified fused silica
An Honglin; Fleming, Simon; McMillen, Benjamin W.; Chen, Kevin P.; Snoke, David
2008-08-11
Thermal poling was utilized to induce second-order nonlinearity in regions of fused silica modified by 771 nm femtosecond laser pulses. With second-harmonic microscopy, it was found that the nonlinearity in the laser-modified region was much lower than that in nonmodified regions. This is attributed to a more rigid glass network after irradiation by the femtosecond laser pulses and/or lack of mobile alkali ions. Measurement of the distribution of chemical elements in the femtosecond-laser-modified region in a soda lime glass revealed a lower level of sodium ions.
Second-order theory for nonlinear composites and application to isotropic constituents
NASA Astrophysics Data System (ADS)
Idiart, Martín I.; Danas, Kostas; Ponte Castañeda, Pedro
2006-10-01
New prescriptions are proposed for the 'reference' fields in the context of the 'second-order' nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737-757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, 'second-order' estimates of the Hashin-Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered. To cite this article: M.I. Idiart et al., C. R. Mecanique 334 (2006).
NASA Astrophysics Data System (ADS)
Castro, Hemerson P. S.; Wender, Heberton; Alencar, Márcio A. R. C.; Teixeira, Sergio R.; Dupont, Jairton; Hickmann, Jandir M.
2013-11-01
The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.
Castro, Hemerson P. S.; Alencar, Márcio A. R. C.; Hickmann, Jandir M.; Wender, Heberton; Teixeira, Sergio R.; Dupont, Jairton
2013-11-14
The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.
Efficient Modal Basis Selection Criteria for Reduced-Order Nonlinear Simulation
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2008-01-01
A modal basis selection technique for a reduced-order nonlinear numerical simulation with application to two-dimensional structures is presented as a two-step procedure. A system identification analysis is first performed using proper orthogonal decomposition. Using these results, a set of load-invariant bases consisting of the normal modes is next selected. Two criteria for making the basis selection are offered; one using the modal assurance criterion and the other using the modal expansion theorem. The quality of the subsequent reduced-order analyses are examined through comparison with computationally intensive finite element nonlinear simulations in physical degrees-of-freedom. A clamped flat isotropic plate under a random acoustic loading is considered to demonstrate the procedure. It is found that the subject procedure enables formation of an accurate and computationally efficient reduced-order system applicable to a broad range of loading conditions.
Alternative Modal Basis Selection Procedures For Reduced-Order Nonlinear Random Response Simulation
NASA Technical Reports Server (NTRS)
Przekop, Adam; Guo, Xinyun; Rizi, Stephen A.
2012-01-01
Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of a computationally taxing full-order analysis in physical degrees of freedom are taken as the benchmark for comparison with the results from the three reduced-order analyses. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.
Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2005-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.
Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2006-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.
Culzoni, María J; Damiani, Patricia C; García-Reiriz, Alejandro; Goicoechea, Héctor C; Olivieri, Alejandro C
2007-07-01
Three different experimental systems have been studied regarding the determination of analytes in complex samples, using non-linear second-order instrumental data, which are intrinsically able to provide the second-order advantage. This permits the quantitation of calibrated analytes in the presence of unexpected sample components, although a suitable algorithm is required. The recently described combination of artificial neural networks with post-training residual bilinearization has been applied to the three data sets, with successful results concerning prediction accuracy and precision, as well as profile recovery for the potential interferents in test samples. The studies involve: (1) the determination of two pharmaceuticals in the presence of an unexpected excipient by absorbance-pH matrix measurements, (2) the quantitation of iron(II) by its catalytic effect on the kinetics of the bromate oxidation of a colorant in the presence of a second interfering organic dye, and (3) the analysis of the antibiotic amoxicillin by fluorescence excitation-emission matrices in the presence of a fluorescent anti-inflammatory. The prediction results were compared and shown to be significantly better than those yielded by the unfolded partial least-squares/residual bilinearization model, due to the non-linear nature of the studied data.
Enhancement of Second-Order Nonlinear-Optical Signals by Optical Stimulation
NASA Astrophysics Data System (ADS)
Goodman, A. J.; Tisdale, W. A.
2015-05-01
Second-order nonlinear optical interactions such as sum- and difference-frequency generation are widely used for bioimaging and as selective probes of interfacial environments. However, inefficient nonlinear optical conversion often leads to poor signal-to-noise ratio and long signal acquisition times. Here, we demonstrate the dramatic enhancement of weak second-order nonlinear optical signals via stimulated sum- and difference-frequency generation. We present a conceptual framework to quantitatively describe the interaction and show that the process is highly sensitive to the relative optical phase of the stimulating field. To emphasize the utility of the technique, we demonstrate stimulated enhancement of second harmonic generation (SHG) from bovine collagen-I fibrils. Using a stimulating pulse fluence of only 3 nJ /cm2 , we obtain an SHG enhancement >104 relative to the spontaneous signal. The stimulation enhancement is greatest in situations where spontaneous signals are the weakest—such as low laser power, small sample volume, and weak nonlinear susceptibility—emphasizing the potential for this technique to improve signal-to-noise ratios in biological imaging and interfacial spectroscopy.
An efficient flexible-order model for 3D nonlinear water waves
Engsig-Karup, A.P. Bingham, H.B.; Lindberg, O.
2009-04-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.
Dhanalakshmi, B.; Ponnusamy, S.; Muthamizhchelvan, C.; Subhashini, V.
2015-10-15
Highlights: • EDA4NPH crystal possesses negative nonlinear refractive index. • The crystal exhibits high third-order NLO susceptibility. • Wide transparency of the crystal makes it suitable for NLO applications. • Dielectric studies substantiate the suitability for electro-optic applications. • The crystal possesses suitable mechanical strength for device fabrication. - Abstract: Bulk crystals of the charge-transfer complex, ethylenediamine-4-nitrophenolate monohydrate, were grown by slow solvent evaporation method from aqueous solution at room temperature. The X-ray diffraction measurements showed that the crystal belongs to centrosymmetric space group C2/c of monoclinic system. The functional groups in the complex were identified using FTIR, FTRaman and FTNMR analyses. The Z-scan measurements revealed the negative nonlinear refractive index of the crystal. The nonlinear absorption coefficient and third order nonlinear optical susceptibility calculated from the measurements were −3.5823 × 10{sup −3} cm/W and 2.3762 × 10{sup −6} esu respectively. The crystal was shown to be highly transparent above 366 nm by UV–vis spectroscopy and a yellow fluorescence was observed from PL spectrum. The TG–DTA and DSC analyses showed that the crystal is thermally stable up to 117.4 °C. The crystals were characterized by dielectric, etching and microhardness studies.
Multi-Order Investigation of the Nonlinear Susceptibility Tensors of Individual Nanoparticles
Schmidt, Cédric; Riporto, Jérémy; Uldry, Aline; Rogov, Andrii; Mugnier, Yannick; Dantec, Ronan Le; Wolf, Jean-Pierre; Bonacina, Luigi
2016-01-01
We use Hyper Rayleigh Scattering and polarization resolved multiphoton microscopy to investigate simultaneously the second and third-order nonlinear response of Potassium Niobate and Bismuth Ferrite harmonic nanoparticles. We first derive the second-to-third harmonic intensity ratio for colloidal ensembles and estimate the average third-order efficiency of these two materials. Successively, we explore the orientation dependent tensorial response of individual nanoparticles fixed on a substrate. The multi-order polarization resolved emission curves are globally fitted with an analytical model to retrieve individual elements of susceptibility tensors. PMID:27140074
Multi-Order Investigation of the Nonlinear Susceptibility Tensors of Individual Nanoparticles
NASA Astrophysics Data System (ADS)
Schmidt, Cédric; Riporto, Jérémy; Uldry, Aline; Rogov, Andrii; Mugnier, Yannick; Dantec, Ronan Le; Wolf, Jean-Pierre; Bonacina, Luigi
2016-05-01
We use Hyper Rayleigh Scattering and polarization resolved multiphoton microscopy to investigate simultaneously the second and third-order nonlinear response of Potassium Niobate and Bismuth Ferrite harmonic nanoparticles. We first derive the second-to-third harmonic intensity ratio for colloidal ensembles and estimate the average third-order efficiency of these two materials. Successively, we explore the orientation dependent tensorial response of individual nanoparticles fixed on a substrate. The multi-order polarization resolved emission curves are globally fitted with an analytical model to retrieve individual elements of susceptibility tensors.
Time-Ordering Effects in the Generation of Entangled Photons Using Nonlinear Optical Processes
NASA Astrophysics Data System (ADS)
Quesada, Nicolás; Sipe, J. E.
2015-03-01
We study the effects of time ordering in photon generation processes such as spontaneous parametric down-conversion (SPDC) and four wave mixing (SFWM). The results presented here are used to construct an intuitive picture that allows us to predict when time-ordering effects significantly modify the joint spectral amplitude (JSA) of the photons generated in SPDC and SFWM. These effects become important only when the photons being generated lie with the pump beam that travels through the nonlinear material for a significant amount of time. Thus sources of spectrally separable photons are ideal candidates for the observation of modifications of the JSA due to time ordering.
Nonlinear filtering and limiting in high order methods for ideal and non-ideal MHD
NASA Technical Reports Server (NTRS)
Yee,H. C.; Sjogreen, B.
2004-01-01
The various filtering mechanisms and base scheme options of the newly developed adaptive numerical dissipation control in spatially high order filter schemes for the ideal and non-ideal magnetohydrodynamics (MHD) equations are investigated. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The type of spatial base scheme to be used in conjunction with our filter idea is very general. For example, spectral, compact and non-compact spatially central finite difference schemes are possible candidates. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and to leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is also very general. The objective of this paper is to investigate the performance of using compact and non-compact central base schemes in conjunction with three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD. This extended abstract shows the performance of three nonlinear filters in conjunction with a sixth-order non-compact spatial central base scheme. In the final paper, the high order compact spatial central base scheme will be illustrated and compared with the non-compact base scheme. The reason for the investigation of the high order compact spatial central base scheme over the non-compact base scheme is to evaluate if additional accuracy can be gained in regions of
NASA Astrophysics Data System (ADS)
Okumura, K.; Tanimura, Y.
1997-03-01
After the pioneering work by Tanimura and Mukamel [J. Chem. Phys. 99, 9496 (1993)], the fifth-order off-resonant experiment or the two dimensional Raman spectroscopy has been actively performed around the world. In the original theory the nonlinear dependence of the polarizability on nuclear coordinates is the origin of the fifth- and higher-order signals. These high order off-resonant signals, however, may arise from anharmonicity of adiabatic potentials instead of the nonlinear polarizability. Profiles of the signals should reflect relative importance of the two effects ---the anharmonicity and the nonlinearity. Using the novel Feynman rule on the unified time path, which has been developed extensively by the authors, we succeeded in taking the effects of anharmonicities into the previous theory to obtain reasonably compact analytical expressions for the signals. Comparison of our results for the fifth-order with the experimental data on CS2 suggests some signs of anharmonicity in CS_2. The analytical expression is also obtained for the general (2n+1)th-order if the polarizability is linear. The expression is proportional g_n+1 where gn is the coefficient of the anharmonic potential V(q)= g_3q^3 + g_4q^4 +\\cdots . Here q is the nuclear coordinate. This fact opens a way to detect the (n+1)th-order anharmonicity directly from the (2n+1)th-order experiment. Click here for the abstracts of the full papers (http://fuji.ims.ac.jp/okumura/abst.htm)
Third-order nonlinear and linear time-dependent dynamical diffraction of X-rays in crystals.
Balyan, Minas K
2016-07-01
For the first time the third-order nonlinear time-dependent Takagi's equations of X-rays in crystals are obtained and investigated. The third-order nonlinear and linear time-dependent dynamical diffraction of X-rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third-order nonlinear time-dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.
Perceptual information for the age level of faces as a higher order invariant of growth.
Pittenger, J B; Shaw, R E; Mark, L S
1979-08-01
Previous work supports the hypothesis that cardioidal strain, a nonlinear topological transformation, offers a plausible mathematical model for the perceived global changes in human craniofacial morphology due to growth. Experiment 1 examined the generality of the effect of this growth transformation on relative age judgments by applying it to profiles of a dog, bird, and monkey. Experiment 2 investigated the abstractness of this transformation by looking at its effect on perceived age level of a Volkswagen "Beetle." In both experiments, cardioidal strain resulted in changes in the perceived age of the nonhuman profiles that were similar to those produced on human faces in earlier work. A second transformation, affine shear, failed to produce as significant an effect on perceived age as cardioidal strain when applied to the same structures. Because cardioidal strain produces changes in structures that do not share an isomorphism of rigid (Euclidian) local features or rigid feature configurations, this transformation seems both sufficiently general and abstract to specify what J.J. Gibson has called a "higher-order invariant of perceptual information. PMID:528953
Higher and sub-harmonic Lamb wave mode generation due to debond-induced contact nonlinearity
NASA Astrophysics Data System (ADS)
Guha, Anurup; Bijudas, C. R.
2016-04-01
Non-cumulative higher and sub-harmonic Lamb wave mode generation as a result of partial-debond of piezoelectric wafer transducers (PWT) bonded onto an Aluminium plate, is numerically investigated and experimentally validated. The influence of excitation frequency on the extent of nonlinearity due to clapping mechanism of the partially-debonded PWTs is discussed. A set of specific frequency range is arrived at based on the Eigen-value and Harmonic analyses of PWTs used in the model. It is found that, at these frequencies, which are integral multiple of the first width-direction mode of a PWT, significantly higher amplitudes of higher-harmonics are observed. It is also seen that at specific debond-positions and lengths, sharp sub-harmonics in addition to higher-harmonics are present. Signal processing is carried out using Fast Fourier transform, which is normalized for comparisons.
Validation of a RANS transition model using a high-order weighted compact nonlinear scheme
NASA Astrophysics Data System (ADS)
Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang
2013-04-01
A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.
Du, Yigang; Fan, Rui; Li, Yong; Chen, Siping; Jensen, Jørgen Arendt
2016-07-01
An ultrasound imaging framework modeled with the first order nonlinear pressure-velocity relations (NPVR) and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA) with a RMS error of 3% at the focal point for a 2D field, and Field II with RMS errors of 0.8% and 1.5% at the electronic and the elevation focuses for 3D fields, respectively. The accuracy for the NPVR based nonlinear propagation is investigated by comparing with the Abersim simulation for pulsed fields and with the nonlinear ASA for monochromatic fields. The RMS errors of the nonlinear pulses calculated by the NPVR and Abersim are respectively 2.4%, 7.4%, 17.6% and 36.6% corresponding to initial pressure amplitudes of 50kPa, 200kPa, 500kPa and 1MPa at the transducer. By increasing the sampling frequency for the strong nonlinearity, the RMS error for 1MPa initial pressure amplitude is reduced from 36.6% to 27.3%. PMID:27107165
The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses
Guo, Haitao; Chen, Hongyan; Hou, Chaoqi; Lin, Aoxiang; Zhu, Yonggang; Lu, Shoudi; Gu, Shaoxuan; Lu, Min; Peng, Bo
2011-05-15
Research highlights: {yields} It is firstly demonstrated that the nonlinear refractive index n{sub 2} is dependent on the covalency of bonds in chalcogenide glass. {yields} Homopolar metallic bonds in chalcogenide glass have positive contribution to large nonlinear refractive index n{sub 2} also. {yields} The 80GeS{sub 2}.20Sb{sub 2}S{sub 3} glass would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths. -- Abstract: The third-order optical nonlinearities of 80GeS{sub 2}.(20 - x)Ga{sub 2}S{sub 3}.xY{sub 2}S{sub 3} (x = 0, 5, 10, 15, 20 and Y = Sb or In) chalcogenide glasses were investigated utilizing the Z-scan method at the wavelength of 800 nm and their linear optical properties and structure were also studied. By analyzing the compositional dependences and possible influencing factors including the linear refractive index, the concentration of lone electron pairs, the optical bandgap and the amount of weak covalent/homopolar bonds, it indicates that the electronic contribution in weak heteropolar covalent and homopolar metallic bonds is responsible for large nonlinear refractive index n{sub 2} in the chalcogenide glasses. These chalcogenide glasses have characteristics of environmentally friendship, wide transparency in the visible region, high nonlinear refractive index n{sub 2} and low nonlinear absorption coefficient {beta}, and would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths.
Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems.
Zhao, Xudong; Shi, Peng; Zheng, Xiaolong; Zhang, Jianhua
2016-09-01
This brief is concerned with the problem of intelligent tracking control for a class of high-order nonlinear systems with completely unknown nonlinearities. An intelligent adaptive control algorithm is presented by combining the adaptive backstepping technique with the neural networks' approximation ability. It is shown that the practical output tracking performance of the system is achieved using the proposed state-feedback controller under two mild assumptions. In particular, by introducing a parameter in the derivations, the tracking error between the time-varying target signal and the output can be reduced via tuning the controller design parameters. Moreover, in order to solve the problem of overparameterization, which is a common issue in adaptive control design, a controller with one adaptive law is also designed. Finally, simulation results are given to show the effectiveness of the theoretical approaches and the potential of the proposed new design techniques.
A method for high order linear system reduction and nonlinear system simplification
NASA Technical Reports Server (NTRS)
Desrochers, A. A.; Al-Jaar, R. Y.
1985-01-01
Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).
Stable surface relief grating with second-order nonlinearity on urethane urea copolymer film
NASA Astrophysics Data System (ADS)
Che, Yanlong; Sugihara, Okihiro; Fujimura, Hisashi; Okamoto, Naomichi; Egami, Chikara; Kawata, Yoshimasa; Tsuchimori, Masaaki; Watanabe, Osamu
2003-01-01
Surface relief gratings (SRGs) on azobenzene-contained urethane-urea copolymer film with second-order nonlinearity are fabricated by laser-interferometric method. The surface relief structures are obtained upon exposure an interference pattern of a CW Ar + laser and a single-pulse UV laser. The SRG is thermally stable even at Tg of the copolymer. The mechanism of the stability is investigated by comparing the pulse UV laser inscribed SRG. It is suggested that laser ablation of the copolymer surface by the high-power laser irradiation is taken into account. Second-order nonlinearity is induced by corona-poling process after grating formation. Diffraction of second-harmonic generation (SHG) is observed by inserting a fundamental beam, which is in agreement with vector diagram.
A reduced-order nonlinear sliding mode observer for vehicle slip angle and tyre forces
NASA Astrophysics Data System (ADS)
Chen, Yuhang; Ji, Yunfeng; Guo, Konghui
2014-12-01
In this paper, a reduced-order sliding mode observer (RO-SMO) is developed for vehicle state estimation. Several improvements are achieved in this paper. First, the reference model accuracy is improved by considering vehicle load transfers and using a precise nonlinear tyre model 'UniTire'. Second, without the reference model accuracy degraded, the computing burden of the state observer is decreased by a reduced-order approach. Third, nonlinear system damping is integrated into the SMO to speed convergence and reduce chattering. The proposed RO-SMO is evaluated through simulation and experiments based on an in-wheel motor electric vehicle. The results show that the proposed observer accurately predicts the vehicle states.
Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models
Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.
2011-01-01
We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.
NASA Astrophysics Data System (ADS)
Bhattacharjee, Satyaki; Matouš, Karel
2016-05-01
A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and the macroscopic loading parameters are linked to the reduced space using a Neural Network. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. To construct the manifold, we perform a number of large three-dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy.
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
NASA Astrophysics Data System (ADS)
Gao, Fangzheng; Wu, Yuqiang; Yuan, Fushun
2016-07-01
This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov- Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.
Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Zhou, Gang
2007-05-01
In this paper we consider generalized nonlinear Schrödinger equations with external potentials. We find the expressions for the fourth and the sixth order Fermi golden rules (FGRs), conjectured in Gang and Sigal [Rev. Math. Phys. 17, 1143-1207 (2005); Geom. Funct. Anal. 16, No. 7, 1377-1390 (2006)]. The FGR is a key condition in a study of the asymptotic dynamics of trapped solitons.
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
NASA Astrophysics Data System (ADS)
Fisher, Travis C.; Carpenter, Mark H.
2013-11-01
Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps.
Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems
NASA Astrophysics Data System (ADS)
Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei
2016-07-01
This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps. PMID:27410804
Phase-dependent ultrafast third-order optical nonlinearities in metallophthalocyanine thin films
NASA Astrophysics Data System (ADS)
Kumar, Samir; Anil Kumar, K. V.; Dharmaprakash, S. M.; Das, Ritwick
2016-09-01
We present a comprehensive study on the impact of phase transformations of metallophthalocyanine thin films on their third-order nonlinear optical (NLO) properties. The metallophthalocyanine thin films are prepared by thermally evaporating the commercially available Copper(II)2,9,16,23-Tetra-tert-butyl-29H,31H-phthalocyanine (CuPc) and Zinc(II) 2,9,16,23-Tetra-tert-butyl-29H,31H-phthalocyanine (ZnPc) powder on glass substrate. Thermal annealing causes a phase transformation which has a distinct signature in powder X-ray diffraction and UV-Vis-NIR spectroscopy. The NLO characteristics which include nonlinear refractive index n2, as well as nonlinear absorption coefficient (βeff), were measured by using a single beam Z-scan technique. An ultrashort pulsed fiber laser emitting femtosecond pulses (Δτ ≈ 250 fs) at 1064 nm central wavelength is used as a source for the Z-scan experiment. The βeff values in as prepared thin films were ascertained to be smaller as compared to the annealed one due to the smaller value of saturation intensity (Is) which, in turn, is a consequence of ground-state bleaching in the thermally unstable amorphous state of the molecule. Interestingly, the nonlinear refractive indices bear opposite sign for CuPc and ZnPc. The variations in the third-order nonlinearity in CuPc and ZnPc are discussed in terms of molecular packing and geometries of metallophthalocyanine molecules.
Compensation of nonlinear phase shifts with third-order dispersion in short-pulse fiber amplifiers.
Zhou, Shian; Kuznetsova, Lyuba; Chong, Andy; Wise, Frank
2005-06-27
We show that nonlinear phase shifts and third-order dispersion can compensate each other in short-pulse fiber amplifiers. This compen-sation can be exploited in any implementation of chirped-pulse amplification, with stretching and compression accomplished with diffraction gratings, single-mode fiber, microstructure fiber, fiber Bragg gratings, etc. In particular, we consider chirped-pulse fiber amplifiers at wavelengths for which the fiber dispersion is normal. The nonlinear phase shift accumulated in the amplifier can be compensated by the third-order dispersion of the combination of a fiber stretcher and grating compressor. A numerical model is used to predict the compensation, and experimental results that exhibit the main features of the calculations are presented. In the presence of third-order dispersion, an optimal nonlinear phase shift reduces the pulse duration, and enhances the peak power and pulse contrast compared to the pulse produced in linear propagation. Contrary to common belief, fiber stretchers can perform as well or better than grating stretchers in fiber amplifiers, while offering the major practical advantages of a waveguide medium.
NASA Astrophysics Data System (ADS)
Hoshino, Tasuku
This paper deals with an approximate linearization control of 2-DOF underactuated-by-1 nonlinear systems, proposing a novel linearization coordinate which reduces the approximation error over the state space around the operating point. The coordinate is analytically constructed in a systematic way by solving two first order linear partial differential equations and the solution is given in an infinite series of configuration variables. The resulting linearization feedback is highly nonlinear and the basin of attraction of the stabilized system using proposed coordinate is large, comparing with those of a conventional first order or other lower order linearization coordinates. The approximate linearization control based on the proposed coordinate is applied to the stabilization of a rotational inverted pendulum; the advantage is verified in simulations and experiments. Some perspectives on availability of the linearization coordinate are discussed and they are computed also for a mobile inverted pendulum, Acrobot, and for Pendubot as examples.
Higher Order Thinking Skills among Secondary School Students in Science Learning
ERIC Educational Resources Information Center
Saido, Gulistan Mohammed; Siraj, Saedah; Bin Nordin, Abu Bakar; Al Amedy, Omed Saadallah
2015-01-01
A central goal of science education is to help students to develop their higher order thinking skills to enable them to face the challenges of daily life. Enhancing students' higher order thinking skills is the main goal of the Kurdish Science Curriculum in the Iraqi-Kurdistan region. This study aimed at assessing 7th grade students' higher order…
A Study of Higher Order Need Strength and Job Satisfaction in Secondary Public School Teachers.
ERIC Educational Resources Information Center
Pastor, Margaret C.; Erlandson, David A.
1982-01-01
Teacher motivation was explored through surveys determining the relationship between higher order needs (such as autonomy, variety) or lower order needs (such as high pay) and job satisfaction. Conclusions are that needs of the teachers studied are predominantly higher order and that job satisfaction is significantly related to teacher needs. (MJL)
Influence of baryons on the spatial distribution of matter: higher order correlation functions
NASA Astrophysics Data System (ADS)
Zhu, Xiao-Jun; Pan, Jun
2012-12-01
Physical processes involving baryons could leave a non-negligible imprint on the distribution of cosmic matter. A series of simulated data sets at high resolution with identical initial conditions are employed for count-in-cell analysis, including one N-body pure dark matter run, one with only adiabatic gas and one with dissipative processes. Variances and higher order cumulants Sn of dark matter and gas are estimated. It is found that physical processes with baryons mainly affect distributions of dark matter at scales less than 1 h-1 Mpc. In comparison with the pure dark matter run, adiabatic processes alone strengthen the variance of dark matter by ~ 10% at a scale of 0.1 h-1 Mpc, while the Sn parameters of dark matter only mildly deviate by a few percent. The dissipative gas run does not differ much from the adiabatic run in terms of variance for dark matter, but renders significantly different Sn parameters describing the dark matter, bringing about a more than 10% enhancement to S3 at 0.1 h-1 Mpc and z = 0 and being even larger at a higher redshift. Distribution patterns of gas in two hydrodynamical simulations are quite different. Variance of gas at z = 0 decreases by ~ 30% in the adiabatic simulation but by ~ 60% in the nonadiabatic simulation at 0.1 h-1 Mpc. The attenuation is weaker at larger scales but is still obvious at ~ 10 h-1 Mpc. Sn parameters of gas are biased upward at scales < ~ 4 h-1 Mpc, and dissipative processes show an ~ 84% promotion at z = 0 to S3 at 0.1 h-1 Mpc in contrast with the ~ 7% change in the adiabatic run. The segregation in clustering between gas and dark matter could have dramatic implications on modeling distributions of galaxies and relevant cosmological applications demanding fine details of matter distribution in a strongly nonlinear regime.
NASA Astrophysics Data System (ADS)
Afra, Sardar; Gildin, Eduardo
2016-09-01
Parameter estimation through robust parameterization techniques has been addressed in many works associated with history matching and inverse problems. Reservoir models are in general complex, nonlinear, and large-scale with respect to the large number of states and unknown parameters. Thus, having a practical approach to replace the original set of highly correlated unknown parameters with non-correlated set of lower dimensionality, that captures the most significant features comparing to the original set, is of high importance. Furthermore, de-correlating system's parameters while keeping the geological description intact is critical to control the ill-posedness nature of such problems. We introduce the advantages of a new low dimensional parameterization approach for reservoir characterization applications utilizing multilinear algebra based techniques like higher order singular value decomposition (HOSVD). In tensor based approaches like HOSVD, 2D permeability images are treated as they are, i.e., the data structure is kept as it is, whereas in conventional dimensionality reduction algorithms like SVD data has to be vectorized. Hence, compared to classical methods, higher redundancy reduction with less information loss can be achieved through decreasing present redundancies in all dimensions. In other words, HOSVD approximation results in a better compact data representation with respect to least square sense and geological consistency in comparison with classical algorithms. We examined the performance of the proposed parameterization technique against SVD approach on the SPE10 benchmark reservoir model as well as synthetic channelized permeability maps to demonstrate the capability of the proposed method. Moreover, to acquire statistical consistency, we repeat all experiments for a set of 1000 unknown geological samples and provide comparison using RMSE analysis. Results prove that, for a fixed compression ratio, the performance of the proposed approach
A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media
NASA Astrophysics Data System (ADS)
Baruch, G.; Fibich, G.; Tsynkov, S.
2009-06-01
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics: Singular behavior of solutions when the scattering in the medium is assumed predominantly forward (paraxial regime), and the presence of discontinuities in the optical properties of the medium. Specifically, we consider a slab of nonlinear material which may be grated in the direction of propagation and which is immersed in a linear medium as a whole. The key components of the methodology are a semi-compact high-order finite-difference scheme that maintains accuracy across the discontinuities and enables sub-wavelength resolution on large domains at a tolerable cost, a nonlocal two-way artificial boundary condition (ABC) that simultaneously facilitates the reflectionless propagation of the outgoing waves and forward propagation of the given incoming waves, and a nonlinear solver based on Newton's method. The proposed methodology combines and substantially extends the capabilities of our previous techniques built for 1D and for multi-D. It facilitates a direct numerical study of nonparaxial propagation and goes well beyond the approaches in the literature based on the "augmented" paraxial models. In particular, it provides the first ever evidence that the singularity of the solution indeed disappears in the scalar NLH model that includes the nonparaxial effects. It also enables simulation of the wavelength-width spatial solitons, as well as of the counter-propagating solitons.
On the effective behavior of nonlinear inelastic composites: II. A second-order procedure
NASA Astrophysics Data System (ADS)
Lahellec, Noël; Suquet, Pierre
2007-09-01
A new method for determining the overall behavior of composite materials comprising nonlinear viscoelastic and elasto-viscoplastic constituents is presented. Part I of this work showed that upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In part I of this paper the nonlinearity was handled using a variational (or secant) technique. In this second part of the study, a proper modification of the second-order procedure of Ponte Castañeda is proposed and leads to replacing, at each time-step, the actual nonlinear viscoelastic composite by a linear viscoelastic one. The linearized problem is even further simplified by using an "effective internal variable" in each individual phase. The resulting predictions are in good agreement with exact results and improve on the predictions of the secant model proposed in part I of this paper.
NASA Technical Reports Server (NTRS)
Zhu, Lin-Fa; Kim, Soo; Chattopadhyay, Aditi; Goldberg, Robert K.
2004-01-01
A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
NASA Technical Reports Server (NTRS)
Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)
2001-01-01
We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.
Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong
2015-01-23
In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.
Third order optical nonlinearity and optical limiting studies of propane hydrazides
NASA Astrophysics Data System (ADS)
Naseema, K.; Manjunatha, K. B.; Sujith, K. V.; Umesh, G.; Kalluraya, Balakrishna; Rao, Vijayalakshmi
2012-09-01
Four hydrazones, 2-(4-isobutylphenyl)-N'-[phenylmethylene] propanehydrazide (P1), 2-(4-isobutylphenyl)-N'-[(4- tolyl)methylene] propane hydrazide (P2), 2-(4-isobutylphenyl)-N'-[1-(4- chlorophenyl)ethylidene] propanehydrazide (P3) and 2-(4-isobutylphenyl)-N'-[1-(4-Nitrrophenyl)ethylidene] propane hydrazide (P4) were synthesized and their third order nonlinear optical properties have been investigated using a single beam Z-scan technique with nanosecond laser pulses at 532 nm. The measurement on the compound-P1 is not reported as there is no detectable nonlinear response. Open aperture data of the other three compounds indicate two photon absorption at this wavelength. The nonlinear refractive index n2, nonlinear absorption coefficient β, magnitude of effective third order susceptibility χ(3), the second order hyperpolarizability γh and the coupling factor ρ have been estimated. The values obtained are comparable with the values obtained for 4-methoxy chalcone derivatives and dibenzylideneacetone derivatives. The experimentally determined values of β, n2, Re χ(3) and Im χ(3), γh and ρ of the compound-P4 are 1.42 cm/GW, -0.619 × 10-11 esu, -0.663 × 10-13 esu, 0.22 × 10-13 esu, 0.34 × 10-32 esu and 0.33 respectively. Further the compound-P4 exhibited the best optical power limiting behavior at 532 nm among the compounds studied. Our studies suggest that compounds P2, P3 and P4 are potential candidates for the optical device applications such as optical limiters and optical switches.
Wang, X Y; Wang, J B; Qiu, B B; Hu, L F
2015-12-01
Based on the proposed higher order gradient quasi-continuum model, the numerical investigations of the basic mechanical properties and deformation behaviors of human red blood cell (RBC) membrane under large deformation at room temperature (i.e., 300 K) are carried out in the present paper. The results show that RBC membrane is a nonlinear hyperelastic material. The mechanical properties of RBC membrane is dominated by isotropic nature at the stage of initial deformation, however, its anisotropic material properties emerge clearly with the loading increasing. The out-of-plane wrinkling of RBC membrane upon shear loading can be reproduced numerically. With the use of the so-called higher order Cauchy-Born rule as the kinematic description, the bending stiffness of RBC membrane can be considered conveniently.
Higher-Order Harmonic Generation from Fullerene by Means of the Plasma Harmonic Method
Ganeev, R. A.; Bom, L. B. Elouga; Abdul-Hadi, J.; Ozaki, T.; Wong, M. C. H.; Brichta, J. P.; Bhardwaj, V. R.
2009-01-09
We demonstrate, for the first time, high-order harmonic generation from C{sub 60} by an intense femtosecond Ti:sapphire laser. Laser-produced plasmas from C{sub 60}-rich epoxy and C{sub 60} films were used as the nonlinear media. Harmonics up to the 19th order were observed. The harmonic yield from fullerene-rich plasma is about 25 times larger compared with those produced from a bulk carbon target. Structural studies of plasma debris confirm the presence and integrity of fullerenes within the plasma plume, indicating fullerenes as the source of high-order harmonics.
Exact Traveling Wave Solutions of a Higher-Dimensional Nonlinear Evolution Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy; Wazzan, Luwai
The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh-coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
New Exact Traveling Wave Solutions of Some Nonlinear Higher-Dimensional Physical Models
NASA Astrophysics Data System (ADS)
Kim, Hyunsoo; Sakthivel, Rathinasamy
2012-08-01
In this paper, some new traveling wave solutions of the (4 + 1)-dimensional Fokas equation, (3 + 1)-dimensional Jumbo-Miwa equation and (2 + 1)-dimensional Boiti-Leon-Pempinelli equation are obtained through the ({GG)-expansion technique. The key idea of this technique is to take full advantage of a Riccati equation involving two parameters and use its solutions in obtaining the traveling wave solutions. The results reveal that this technique is very effective and powerful for solving higher-dimensional nonlinear problems arising in mathematical physics.
The nonlinear wave equation for higher harmonics in free-electron lasers
NASA Technical Reports Server (NTRS)
Colson, W. B.
1981-01-01
The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.
NASA Technical Reports Server (NTRS)
Walker, K. P.; Freed, A. D.
1991-01-01
New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.
On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjogreen, B.
2004-01-01
The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.
NASA Astrophysics Data System (ADS)
Fedotov, I. A.; Polyanin, A. D.
2011-09-01
Broad classes of nonlinear equations of mathematical physics are described that admit order reduction by applying the von Mises transformation (with the unknown function used as a new independent variable and with a suitable partial derivative used as a new dependent variable) and by applying the Crocco transformation (with the first and second partial derivatives used as new independent and dependent variables, respectively). Associated Bäcklund transformations are constructed that connect evolution equations of general form (their special cases include Burgers, Korteweg-de Vries, and Harry Dym type equations and many other nonlinear equations of mathematical physics). Transformations are indicated that reduce the order of hydrodynamic-type equations of higher orders. The generalized Calogero equation and a number of other new integrable nonlinear equations, reducible to linear equations, are considered.
NASA Astrophysics Data System (ADS)
Siji Narendran, N. K.; Soman, Rahul; Arunkumar, Chellaiah; Chandrasekharan, K.
2015-02-01
We report here the experimental investigation on third-order nonlinear optical parameters of 5,10,15,20-tetrakis(2,3,5,6-tetrafluoro-N,N-dimethyl-4-anilinyl)porphyrin and its various metal complexes, using Z-scan technique at 532 nm. The third-order nonlinear optical susceptibilities (χ(3)) were of the order 10-12 esu and are compared through degenerate four wave mixing (DFWM). The operating mechanism is reverse saturable absorption (RSA) as the effective excited-state absorption cross-section was found higher than ground state absorption cross-section as well as the magnitude of nonlinear absorption coefficient was found decreasing with on-axis input intensity. The compounds found to exhibit good optical limiting at 532 nm, 7 ns excitation steering applications in laser safety.
NASA Astrophysics Data System (ADS)
Thangaraj, M.; Vinitha, G.; Sabari Girisun, T. C.; Anandan, P.; Ravi, G.
2015-10-01
Optical nonlinearity of metal complexes of p-nitrophenolate (M=Li, Na and K) in ethanol is studied by using a continuous wave (cw) diode pumped Nd:YAG laser (532 nm, 50 mW). The predominant mechanism of observed nonlinearity is thermal in origin. The nonlinear refractive index and the nonlinear absorption coefficient of the samples were found to be in the order of 10-8 cm2/W and 10-3 cm/W respectively. Magnitude of third-order optical parameters varies according to the choice of alkali metal chosen for metal complex formation of p-nitrophenolate. The third-order nonlinear susceptibility was found to be in the order of 10-6 esu. The observed saturable absorption and the self-defocusing effect were used to demonstrate the optical limiting action at 532 nm by using the same cw laser beam.
Solving nonlinear system of third-order boundary value problems using block method
NASA Astrophysics Data System (ADS)
See, Phang Pei; Majid, Zanariah Abdul; Suleiman, Mohamed; Ismail, Fudziah Bt; Othman, Khairil Iskandar
2015-05-01
In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using variable step size strategy. The method will be implemented with the multiple shooting technique via the three-step iterative method to generate the missing initial value. Most of the existence method will reduce the third-order boundary value problems to a system of first order equations where the systems of six equations need to be solved. The method we proposed in this paper will solve the third-order boundary value problems directly. Two numerical examples are given to illustrate the efficiency of the proposed method.
NASA Astrophysics Data System (ADS)
Nakagawa, Ryo; Suzuki, Takanao; Shimizu, Hiroshi; Kyoya, Haruki; Nako, Katsuhiro; Hashimoto, Ken-ya
2016-07-01
In this paper, we discuss the generation mechanisms of third-order nonlinearity in surface acoustic wave (SAW) devices on the basis of simulation results, which are obtained by a proposed method for this discussion. First, eight nonlinear terms are introduced to the piezoelectric constitutive equations, and nonlinear stress and electric flux fields are estimated using linear strain and electric fields calculated by a linear analysis, i.e., the coupling of mode simulation. Then, their contributions are embedded as voltage and current sources, respectively, in an equivalent circuit model, and nonlinear signals appearing at external ports are estimated. It is shown that eight coefficients of the nonlinear terms can be determined from a series of experiments carried out at various driving and resulting frequencies. This is because the effect of each nonlinear term on the nonlinear signal outputs changes markedly with the conditions. When the coefficients are determined properly, the simulations agree well with some measurement results under various conditions.
Ultrafast control of third-order optical nonlinearities in fishnet metamaterials
NASA Astrophysics Data System (ADS)
Shorokhov, Alexander S.; Okhlopkov, Kirill I.; Reinhold, Jörg; Helgert, Christian; Shcherbakov, Maxim R.; Pertsch, Thomas; Fedyanin, Andrey A.
2016-06-01
Nonlinear photonic nanostructures that allow efficient all-optical switching are considered to be a prospective platform for novel building blocks in photonics. We performed time-resolved measurements of the photoinduced transient third-order nonlinear optical response of a fishnet metamaterial. The mutual influence of two non-collinear pulses exciting the magnetic resonance of the metamaterial was probed by detecting the third-harmonic radiation as a function of the time delay between pulses. Subpicosecond-scale dynamics of the metamaterial’s χ(3) was observed; the all-optical χ(3) modulation depth was found to be approximately 70% at a pump fluence of only 20 μJ/cm2.
Ultrafast control of third-order optical nonlinearities in fishnet metamaterials
Shorokhov, Alexander S.; Okhlopkov, Kirill I.; Reinhold, Jörg; Helgert, Christian; Shcherbakov, Maxim R.; Pertsch, Thomas; Fedyanin, Andrey A.
2016-01-01
Nonlinear photonic nanostructures that allow efficient all-optical switching are considered to be a prospective platform for novel building blocks in photonics. We performed time-resolved measurements of the photoinduced transient third-order nonlinear optical response of a fishnet metamaterial. The mutual influence of two non-collinear pulses exciting the magnetic resonance of the metamaterial was probed by detecting the third-harmonic radiation as a function of the time delay between pulses. Subpicosecond-scale dynamics of the metamaterial’s χ(3) was observed; the all-optical χ(3) modulation depth was found to be approximately 70% at a pump fluence of only 20 μJ/cm2. PMID:27335268
High-order optical processes in intense laser field: Towards nonperturbative nonlinear optics
NASA Astrophysics Data System (ADS)
Strelkov, V. V.
2016-05-01
We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schrödinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields, we derive and analytically solve propagation equations describing high-order (HO) wave mixing, HO parametric amplification, and HO stimulated scattering. These processes provide a way of efficient coherent xuv generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the superexponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.
Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2011-09-01
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.
High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering
NASA Technical Reports Server (NTRS)
Fibich, Gadi; Tsynkov, Semyon
2000-01-01
When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.
Topics of Higher Order Electroweak Processes and Nonleptonic Weak Processes in Standard Model.
NASA Astrophysics Data System (ADS)
Chong-Huah, Lo.
This thesis is devoted to the calculation of higher order electroweak processes and nonleptonic weak interaction processes in the framework of the standard model. Primarily to standardize the notation, the thesis begins with a brief discussion of the Feynman rules and the dimensional regularization in a general renormalizable gauge for a spontaneously broken gauge theory. A typical process where higher order corrections are significant is the s(--->)d(gamma) transition. Amplitude including QCD radiative corrections for this process is calculated using a free quark model, which is then used to compute hyperon weak radiative decays. Explicit evaluation of the transition amplitude of the (SIGMA)(--->)P(gamma) mode is given. The quark fields are expanded in terms of MIT bag modes, so as to be consistent with quark confinement. We rederive the traditional baryon-pole model result and discover some evidence for a (V + A) weak hadronic current. The thesis also contains a phenomenological Lagrangian model for charmed meson decays. The model consists of a SU(,L)(3) x SU(,R)(3) nonlinear chiral Lagrangian with gauge fields. The charmed meson triplet (D('0), D('-), F('-)) is incorporated into the Lagrangian following the general framework proposed by Coleman, Wess and Zumino. The model can describe many body decay processes as well as two body decay processes. It also gives a unified description of pseudo-scalar, vector and axial vector meson decay modes of the charmed mesons. The model gives a one-parameter prediction of all two body and three body decay data. We predict the life time ratio (tau)(D)/(tau)(D('0)) = 3.75 and branching ratio of D('0) decay modes, namely B(,r)(D('0)( --->)K('0)(pi)('0))/B(,r)(D('0)(--->)K('-)(pi)('+)) = 1.04. These are in good agreement with experimental results. Several results of the flavor symmetry model, e.g. the sum rule for the D meson decay amplitudes, are rederived in the model. Dalitz plots of three body decay processes are also
Higher order feed-forward control of reticle writing error fingerprints
NASA Astrophysics Data System (ADS)
van Haren, Richard; Cekli, Hakki Ergun; Beltman, Jan; Pastol, Anne; Sundermann, Frank; Gatefait, Maxime
2015-10-01
The understanding and control of the intra-field overlay budget becomes crucial particularly after the introduction of multi-patterning applications. The intra-field overlay budget is built-up out of many contributors, each with its own characteristic. Some of them are (semi-)static like the reticle writing error (RWE) fingerprint, the scanner lens fingerprint, or the intra-field processing signature. Others are more dynamic. Examples are reticle heating and lens heating due to the absorption of a small portion of the exposure light. Ideally, all overlay contributors that are understood and known could be taken out of the feed-back control loop and send as feed-forward corrections to the scanner. As a consequence, only non-correctable overlay residuals are measured on the wafer. In the current work, we have studied the possibility to characterize the reticle writing error fingerprint by an off-line position measurement tool and use this information to send feed-forward corrections to the ASML TWINSCANTM exposure tool. The current work is an extension of the work we published earlier. To this end, we have selected a reticle pair out of 50 production reticles that are used to manufacture a 28-nm technology device. These two reticles are special in the sense that the delta fingerprint contains a significant higher order RWE signature. While previously only the linear parameters were sent as feed-forward corrections to the ASML TWINSCANTM exposure tool, this time we additionally demonstrate the capability to correct for the non-linear terms as well. Since the concept heavily relies on the quality of the off-line mask registration measurements, a state-of-the-art reticle registration tool was chosen. Special care was taken to eliminate any effects of the tool induced shifts that may affect the quality of the measurements. The on-wafer overlay verification measurements were performed on an ASML YieldStar metrology tool as well as on a different vendor tool. In conclusion
NASA Astrophysics Data System (ADS)
Nithyanandan, K.; Raja, R. Vasantha Jayakantha; Porsezian, K.; Kalithasan, B.
2012-08-01
We investigate the cross-phase-modulation-induced modulational instability (MI) of two co-propagating optical beams in the system of relaxing Kerr nonlinearity with the effect of higher-order dispersion (HOD) and walk-off effect. We identify and discuss the salient features of relaxation of nonlinear responses and HOD using suitable theoretical model. First, we analyzed the impact of HOD and walk-off on the MI spectrum and found both analytically and numerically that the MI exhibits alternate characteristics like the evolution of different spectral bands in addition to the conventional MI bands. The walk-off effects in the virtue of HOD not only consist of the conventional group velocity mismatch (GVM) but also the difference in third-order dispersion (TOD) of the two beams, and thereby significantly modify the dynamical behavior of the MI. We also consider the combined effect of relaxation of nonlinear response and the HOD effects, and we observe that any finite value of delay leads to the evolution of two unstable modes and thereby extends the range of unstable frequency; HOD on the other hand along with the walk-off effect brings other characteristic spectral bands. A detailed discussion about the various combinations of parameters and the relative competence of one over the other on the MI spectrum is presented. Thus the evolution of MI from cross-phase modulation in the system of relaxing Kerr nonlinearity is emphasized in detail and the influence of HOD and the walk-off effect are highlighted.
Effects on noise properties of GPS time series caused by higher-order ionospheric corrections
NASA Astrophysics Data System (ADS)
Jiang, Weiping; Deng, Liansheng; Li, Zhao; Zhou, Xiaohui; Liu, Hongfei
2014-04-01
Higher-order ionospheric (HOI) effects are one of the principal technique-specific error sources in precise global positioning system (GPS) analysis. These effects also influence the non-linear characteristics of GPS coordinate time series. In this paper, we investigate these effects on coordinate time series in terms of seasonal variations and noise amplitudes. Both power spectral techniques and maximum likelihood estimators (MLE) are used to evaluate these effects quantitatively and qualitatively. Our results show an overall improvement for the analysis of global sites if HOI effects are considered. We note that the noise spectral index that is used for the determination of the optimal noise models in our analysis ranged between -1 and 0 both with and without HOI corrections, implying that the coloured noise cannot be removed by these corrections. However, the corrections were found to have improved noise properties for global sites. After the corrections were applied, the noise amplitudes at most sites decreased, among which the white noise amplitudes decreased remarkably. The white noise amplitudes of up to 81.8% of the selected sites decreased in the up component, and the flicker noise of 67.5% of the sites decreased in the north component. Stacked periodogram results show that, no matter whether the HOI effects are considered or not, a common fundamental period of 1.04 cycles per year (cpy), together with the expected annual and semi-annual signals, can explain all peaks of the north and up components well. For the east component, however, reasonable results can be obtained only based on HOI corrections. HOI corrections are useful for better detecting the periodic signals in GPS coordinate time series. Moreover, the corrections contributed partly to the seasonal variations of the selected sites, especially for the up component. Statistically, HOI corrections reduced more than 50% and more than 65% of the annual and semi-annual amplitudes respectively at the
Purohit, Gunjan Rawat, Priyanka; Chauhan, Prashant; Mahmoud, Saleh T.
2015-05-15
This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled laser beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate.
Questions for Assessing Higher-Order Cognitive Skills: It's Not Just Bloom's
ERIC Educational Resources Information Center
Lemons, Paula P.; Lemons, J. Derrick
2013-01-01
We present an exploratory study of biologists' ideas about higher-order cognition questions. We documented the conversations of biologists who were writing and reviewing a set of higher-order cognition questions. Using a qualitative approach, we identified the themes of these conversations. Biologists in our study used Bloom's Taxonomy to…
ERIC Educational Resources Information Center
Schraw, Gregory, Ed.; Robinson, Daniel H., Ed.
2011-01-01
This volume examines the assessment of higher order thinking skills from the perspectives of applied cognitive psychology and measurement theory. The volume considers a variety of higher order thinking skills, including problem solving, critical thinking, argumentation, decision making, creativity, metacognition, and self-regulation. Fourteen…
From "Hello" to Higher-Order Thinking: The Effect of Coaching and Feedback on Online Chats
ERIC Educational Resources Information Center
Stein, David S.; Wanstreet, Constance E.; Slagle, Paula; Trinko, Lynn A.; Lutz, Michelle
2013-01-01
This exploratory study examined the effect of a coaching and feedback intervention in teaching presence and social presence on higher-order thinking in an online community of inquiry. Coaching occurred before each chat, and feedback was provided immediately afterwards. The findings suggest that over time, the frequency of higher-order thinking…
Teaching Higher Order Thinking in the Introductory MIS Course: A Model-Directed Approach
ERIC Educational Resources Information Center
Wang, Shouhong; Wang, Hai
2011-01-01
One vision of education evolution is to change the modes of thinking of students. Critical thinking, design thinking, and system thinking are higher order thinking paradigms that are specifically pertinent to business education. A model-directed approach to teaching and learning higher order thinking is proposed. An example of application of the…
Authentic Instruction for 21st Century Learning: Higher Order Thinking in an Inclusive School
ERIC Educational Resources Information Center
Preus, Betty
2012-01-01
The author studied a public junior high school identified as successfully implementing authentic instruction. Such instruction emphasizes higher order thinking, deep knowledge, substantive conversation, and value beyond school. To determine in what ways higher order thinking was fostered both for students with and without disabilities, the author…
Improving Computer-Assisted Instruction in Teaching Higher-Order Skills
ERIC Educational Resources Information Center
Sinclair, Kelsey J.; Renshaw, Carl E.; Taylor, Holly A.
2004-01-01
Computer-assisted instruction (CAI) has been shown to enhance rote memory skills and improve higher order critical thinking skills. The challenge now is to identify what aspects of CAI improve which specific higher-order skills. This study focuses on the effectiveness of using CAI to teach logarithmic graphing and dimensional analysis. Two groups…
An Analysis of Higher-Order Thinking on Algebra I End-of-Course Tests
ERIC Educational Resources Information Center
Thompson, Tony
2011-01-01
This research provides insight into one US state's effort to incorporate higher-order thinking on its Algebra I End-of-Course tests. To facilitate the inclusion of higher-order thinking, the state used "Dimensions of Thinking" (Marzano et al., 1988) and "Bloom's Taxonomy" (Bloom et al., 1956). An analysis of Algebra I test items found that the…
Reinstating higher order properties of a study list by retrieving a list item.
Humphreys, Michael S; Murray, Krista L; Koh, Joyce Yanfang
2014-05-01
In two experiments, we looked at the role of higher order list properties in episodic recall. A probabilistic paired-associate paradigm was used in which each cue was repeatedly paired with two different targets. This paradigm permitted us to cue for a target that had been studied with that cue in the last list, or to cue for either of the two targets that had been repeatedly paired with that cue, although neither the cue nor either of its two targets had been studied in the last list. In Experiment 1, the higher order property was whether all of the targets in a given list were animal names or vegetable names. In Experiment 2, the higher order property was whether all of the pairs in a list were associatively related or unrelated. The assumption was that if participants were using these higher order properties when they retrieved a target that had been studied in the last list, they would also use these properties when recalling in response to a cue that had been studied in other lists but not in the most recent list. The results supported the use of both kinds of higher order properties in episodic access. They also showed that these higher order properties were reinstated by retrieving a target, and were then used in the next memory access operation. The questions of why the retrieval of a target would reinstate a higher order list property and how these very different higher order list properties aid in episodic access were also discussed.
ERIC Educational Resources Information Center
Fischer, Christopher; Bol, Linda; Pribesh, Shana
2011-01-01
This study investigated the extent to which higher-order thinking skills are promoted in social studies classes in high schools that are implementing smaller learning communities (SLCs). Data collection in this mixed-methods study included classroom observations and in-depth interviews. Findings indicated that higher-order thinking was rarely…
Assessing Higher-Order Cognitive Constructs by Using an Information-Processing Framework
ERIC Educational Resources Information Center
Dickison, Philip; Luo, Xiao; Kim, Doyoung; Woo, Ada; Muntean, William; Bergstrom, Betty
2016-01-01
Designing a theory-based assessment with sound psychometric qualities to measure a higher-order cognitive construct is a highly desired yet challenging task for many practitioners. This paper proposes a framework for designing a theory-based assessment to measure a higher-order cognitive construct. This framework results in a modularized yet…
Ability, Breadth, and Parsimony in Computational Models of Higher-Order Cognition
ERIC Educational Resources Information Center
Cassimatis, Nicholas L.; Bello, Paul; Langley, Pat
2008-01-01
Computational models will play an important role in our understanding of human higher-order cognition. How can a model's contribution to this goal be evaluated? This article argues that three important aspects of a model of higher-order cognition to evaluate are (a) its ability to reason, solve problems, converse, and learn as well as people do;…
Linearisation of asymmetrical Doherty amplifier by the even-order non-linear signals
NASA Astrophysics Data System (ADS)
Maleš-Ilić, Nataša; Atanasković, Aleksandar; Blau, Kurt; Hein, Matthias
2016-08-01
This paper considers the linearisation of an asymmetrical two-way Doherty amplifier by the method that uses the second harmonics and fourth-order non-linear signals for linearisation. These even-order signals for linearisation are extracted at the output of the peaking amplifier, adjusted in amplitude and phase and injected at the input and output of the carrier amplifier transistor in the Doherty configuration. The effect of linearisation has been experimentally confirmed on a fabricated asymmetrical Doherty amplifier with the additional circuit for linearisation. The suppression of the third-order intermodulation products has been carried out for two-tone test, 64QAM and WCDMA digitally modulated signals in a range of signal power.
The massive O(N) non-linear sigma model at high orders
NASA Astrophysics Data System (ADS)
Bijnens, Johan; Carloni, Lisa
2011-02-01
We extend our earlier work on the massive O(N) non-linear sigma model to other observables. We derive expressions at leading order in the large N expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson-meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general N we derive the expressions for the n-th-loop-order leading logarithms (M/Flog (/M))n, up to five loops for the decay constant and vacuum expectation value (VEV) and up to four loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large N results do not give a good approximation for the case N=3. We use our results to study the convergence of the perturbative series and compare with elastic unitarity.
NASA Astrophysics Data System (ADS)
Jayabalan, J.; Singh, Manoranjan P.; Banerjee, Arup; Rustagi, K. C.
2008-01-01
In this paper, we present results of calculations of linear and second-order nonlinear polarizabilities of sector-shaped metallic nanoparticles (hemisphere is a special case) using free electron theory. The dependences of the ground state electron density distribution and polarizabilities on various shape parameters of sector are analyzed. The ground state electron densities near the corners and edges of sector-shaped nanoparticle are very low and do not contribute to the linear and second-order polarizabilities. The second-order polarizability is found to depend strongly on the angle of the sector and is shown to be proportional to the product of an appropriately defined asymmetric volume of the particle and the third power of the electron cloud length.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
In Part I of this work, an improved "second-order" homogenization theory was developed. This new theory makes use of generalized secant moduli that are intermediate between the standard secant and tangent moduli of the nonlinear phases, and that depend not only on the averages, or first-moments of the fields in the phases, but also on the second-moments of the field fluctuations, or phase covariance tensors. In this article, the theory, which is known to be exact to second-order in the heterogeneity contrast, is applied to the special cases of rigidly reinforced and porous materials. These are cases corresponding to infinite contrast where fairly explicit analytical expressions of the Hashin-Shtrikman and self-consistent-type may be generated for nonlinear composites. The results show that the new theory improves on the earlier theory (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) in at least two ways. First, the new theory satisfies rigorous bounds, even near the percolation limit, where field fluctuations become important, and the earlier second-order theory had been found to fail. Second, the new theory predicts fully compressible behavior for porous materials with an incompressible matrix phase, where the earlier theory had also been found to fail. In addition, the new estimates are found to be in better agreement with numerical simulations available from the literature.
Nonsingular decoupled terminal sliding-mode control for a class of fourth-order nonlinear systems
NASA Astrophysics Data System (ADS)
Bayramoglu, Husnu; Komurcugil, Hasan
2013-09-01
This paper presents a nonsingular decoupled terminal sliding mode control (NDTSMC) method for a class of fourth-order nonlinear systems. First, the nonlinear fourth-order system is decoupled into two second-order subsystems which are referred to as the primary and secondary subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients which are computed by linear functions derived from the input-output mapping of the one-dimensional fuzzy rule base. Then, the control target of the secondary subsystem was embedded to the primary subsystem by the help of an intermediate signal. Thereafter, a nonsingular terminal sliding mode control (NTSMC) method was utilized to make both subsystems converge to their equilibrium points in finite time. The simulation results on the inverted pendulum system are given to show the effectiveness of the proposed method. It is seen that the proposed method exhibits a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods.
NASA Astrophysics Data System (ADS)
Sabesan, Ramkumar; Jeong, Tae Moon; Carvalho, Luis; Cox, Ian G.; Williams, David R.; Yoon, Geunyoung
2007-04-01
Higher-order aberration correction in abnormal eyes can result in significant vision improvement, especially in eyes with abnormal corneas. Customized optics such as phase plates and customized contact lenses are one of the most practical, nonsurgical ways to correct these ocular higher-order aberrations. We demonstrate the feasibility of correcting higher-order aberrations and improving visual performance with customized soft contact lenses in keratoconic eyes while compensating for the static decentration and rotation of the lens. A reduction of higher-order aberrations by a factor of 3 on average was obtained in these eyes. The higher-order aberration correction resulted in an average improvement of 2.1 lines in visual acuity over the conventional correction of defocus and astigmatism alone.
Das, K.P.; Majumdar, S.R.; Paul, S.N. ||
1995-05-01
An integrated form of the governing equations in terms of pseudopotential higher-order nonlinear and dispersive effects is obtained by applying the reductive perturbation method for ion-acoustic solitary waves in a collisionless unmagnetized multicomponent plasma having warm ions and two-component nonisothermal electrons. The present method is advantageous because instead of solving an inhomogeneous second-order differential equation at each order, as in the standard procedure, we solve a first-order inhomogeneous equation at each order except at the lowest. The expressions of both Mach number and width of the solitary wave are obtained as a function of the amplitude of the wave for third-order nonlinear and dispersive effects. The variations of potential, width, and Mach number against soliton amplitude are shown graphically, taking into consideration the nonisothermality of two-component electrons in the plasma.
Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity
NASA Astrophysics Data System (ADS)
Gerace, Dario; Savona, Vincenzo
2014-03-01
It is shown that noncentrosymmetric materials with bulk second-order nonlinear susceptibility can be used to generate strongly antibunched radiation at an arbitrary wavelength, solely determined by the resonant behavior of suitably engineered coupled microcavities. The proposed scheme exploits the unconventional photon blockade of a coherent driving field at the input of a coupled cavity system, where one of the two cavities is engineered to resonate at both fundamental and second harmonic frequencies, respectively. Remarkably, the unconventional blockade mechanism occurs with reasonably low quality factors at both harmonics, and does not require a sharp doubly resonant condition for the second cavity, thus proving its feasibility with current semiconductor technology.
POD/MAC-Based Modal Basis Selection for a Reduced Order Nonlinear Response Analysis
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2007-01-01
A feasibility study was conducted to explore the applicability of a POD/MAC basis selection technique to a nonlinear structural response analysis. For the case studied the application of the POD/MAC technique resulted in a substantial improvement of the reduced order simulation when compared to a classic approach utilizing only low frequency modes present in the excitation bandwidth. Further studies are aimed to expand application of the presented technique to more complex structures including non-planar and two-dimensional configurations. For non-planar structures the separation of different displacement components may not be necessary or desirable.
Second-order nonlinear optical susceptibilities of AIIBVI and AIIIBV semiconductors
NASA Astrophysics Data System (ADS)
Kumar, V.; Sinha, Anita; Singh, B. P.; Chandra, S.
2016-10-01
The second-order nonlinear optical (NLO) susceptibilities χ123(2) of AIIBVI and AIIIBV groups of semiconductors with zincblende (ZB) structure have been studied. Two relations have been proposed for the calculation of χ123(2) (0) at zero frequency. One is based on bond charge model of Levine and the other is based on plasma oscillations theory of solids. Calculated values of χ123(2) (0) for all compounds are in fair agreement with the available experimental and reported values.
Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces
NASA Astrophysics Data System (ADS)
Mabdaoui, M.; Moussa, H.; Rhoudaf, M.
2016-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem [Equation not available: see fulltext.]where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× {R}→ {R}^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R , satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).
Second and third order nonlinear optical properties of conjugated molecules and polymers
NASA Technical Reports Server (NTRS)
Perry, Joseph W.; Stiegman, Albert E.; Marder, Seth R.; Coulter, Daniel R.; Beratan, David N.; Brinza, David E.
1988-01-01
Second- and third-order nonlinear optical properties of some newly synthesized organic molecules and polymers are reported. Powder second-harmonic-generation efficiencies of up to 200 times urea have been realized for asymmetric donor-acceptor acetylenes. Third harmonic generation chi(3)s have been determined for a series of small conjugated molecules in solution. THG chi(3)s have also been determined for a series of soluble conjugated copolymers prepared using ring-opening metathesis polymerization. The results are discussed in terms of relevant molecular and/or macroscopic structural features of these conjugated organic materials.
The third-order nonlinear optical properties of unsymmetrical trimethine cyanine dyes
NASA Astrophysics Data System (ADS)
He, Xuemei; Yang, Junyi; Fang, Yu; Zhou, Feng; Song, Yinglin
2015-10-01
In this paper, we investigate the nonlinear optical properties of unsymmetrical trimethine cyanine dyes(ethyl-4-(3-(3-ethylbenzo[d]xazole-2(3H)-ylidene)prop-1-en-1-yl)quinolin-1-iumiodidebenzo[d]xa zole group) by conducting Z-scan technique at 532 nm and time-resolved pump probe with phase object (POPP). Pronounced reverse saturable absorption (RSA) and positive refraction are observed. Moreover, the relevant third-order NLO photo-physical parameters of unsymmetrical trimethine cyanine dyes determined unambiguously.
Regarding on the prototype solutions for the nonlinear fractional-order biological population model
NASA Astrophysics Data System (ADS)
Baskonus, Haci Mehmet; Bulut, Hasan
2016-06-01
In this study, we have submitted to literature a method newly extended which is called as Improved Bernoulli sub-equation function method based on the Bernoulli Sub-ODE method. The proposed analytical scheme has been expressed with steps. We have obtained some new analytical solutions to the nonlinear fractional-order biological population model by using this technique. Two and three dimensional surfaces of analytical solutions have been drawn by wolfram Mathematica 9. Finally, a conclusion has been submitted by mentioning important acquisitions founded in this study.
Third-order nonlinear optical properties of undoped polyaniline solutions and films probed at 532 nm
Maciel, Glauco S.; Bezerra, Arandi G.; Rakov, Nikifor; de Araujo, Cid B.; Gomes, Anderson S. L.; de Azevedo, Walter M.
2001-08-01
The third-order nonlinear optical properties of polyaniline (PANI) solutions and films were investigated at 532 nm by use of Z-scan, power limiting, and optical Kerr gate techniques. The polymers studied were the undoped partially oxidized (emeraldine base) and fully reduced (leucoemeraldine base) forms of PANI. Our results demonstrate that the leucoemeraldine base is more suitable for use in devices such as all-optical switches and optical power limiters operating at 532 nm. The worse performance of the emeraldine base is due to the presence of defects inside the bandgap of the polymer. {copyright} 2001 Optical Society of America
Development of higher-order modal methods for transient thermal and structural analysis
NASA Technical Reports Server (NTRS)
Camarda, Charles J.; Haftka, Raphael T.
1989-01-01
A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements.
Higher-order Schrödinger and Hartree–Fock equations
Carles, Rémi; Lucha, Wolfgang; Moulay, Emmanuel
2015-12-15
The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then, the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.
ERIC Educational Resources Information Center
Scandura, Joseph M.; And Others
A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of construction problems…
Novel Object Exploration as a Potential Assay for Higher Order Repetitive Behaviors in Mice.
Steinbach, Jessica M; Garza, Elizabeth T; Ryan, Bryce C
2016-01-01
Restricted, repetitive behaviors (RRBs) are a core feature of autism spectrum disorder (ASD) and disrupt the lives of affected individuals. RRBs are commonly split into lower-order and higher-order components, with lower order RRBs consisting of motor stereotypies and higher order RRBs consisting of perseverative and sequencing behaviors. Higher order RRBs are challenging to model in mice. Current assays for RRBs in mice focus primarily on the lower order components, making basic biomedical research into potential treatments or interventions for higher-order RRBs difficult. Here we describe a new assay, novel object exploration. This assay uses a basic open-field arena with four novel objects placed around the perimeter. The test mouse is allowed to freely explore the arena and the order in which the mouse investigates the novel objects is recorded. From these data, patterned sequences of exploration can be identified, as can the most preferred object for each mouse. The representative data shared here and past results using the novel object exploration assay illustrate that inbred mouse strains do demonstrate different behavior in this assay and that strains with elevated lower order RRBs also show elevated patterned behavior. As such, the novel object exploration assay appears to possess good face validity for higher order RRBs in humans and may be a valuable assay for future studies investigating novel therapeutics for ASD. PMID:27583676
Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
NASA Astrophysics Data System (ADS)
Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin
2014-09-01
The uniform asymptotic approximation method provides a powerful, systematically improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M Theory, loop quantum cosmology and Hořava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to high orders for the cases where the modified dispersion relation (linear or nonlinear) has only one turning point (or zero). We obtain the general expressions for the power spectra and spectral indices of both scalar and tensor perturbations up to the third order, at which the error bounds are ≲0.15%. As an application of these formulas, we calculate the power spectra and spectral indices in the slow-roll inflation with a nonlinear power-law dispersion relation. To check the consistency of our formulas, we further restrict ourselves to the relativistic case, and calculate the corresponding power spectra, spectral indices and runnings to the second order. Then, we compare our results with the ones obtained by the Green function method and show explicitly that the results obtained by these two different methods are consistent within the allowed errors.
POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model
NASA Astrophysics Data System (ADS)
Ştefănescu, R.; Navon, I. M.
2013-03-01
In the present paper we consider a 2-D shallow-water equations (SWE) model on a β-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yields a number of nonlinear systems of algebraic equations. We then use a proper orthogonal decomposition (POD) to reduce the dimension of the SWE model. Due to the model nonlinearities, the computational complexity of the reduced model still depends on the number of variables of the full shallow - water equations model. By employing the discrete empirical interpolation method (DEIM) we reduce the computational complexity of the reduced order model due to its depending on the nonlinear full dimension model and regain the full model reduction expected from the POD model. To emphasize the CPU gain in performance due to use of POD/DEIM, we also propose testing an explicit Euler finite difference scheme (EE) as an alternative to the ADI implicit scheme for solving the swallow water equations model. We then proceed to assess the efficiency of POD/DEIM as a function of number of spatial discretization points, time steps, and POD basis functions. As was expected, our numerical experiments showed that the CPU time performances of POD/DEIM schemes are proportional to the number of mesh points. Once the number of spatial discretization points exceeded 10000 and for 90 DEIM interpolation points, the CPU time decreased by a factor of 10 in case of POD/DEIM implicit SWE scheme and by a factor of 15 for the POD/DEIM explicit SWE scheme in comparison with the corresponding POD SWE schemes. Moreover, our numerical tests revealed that if the number of points selected by DEIM algorithm reached 50, the approximation errors due to POD/DEIM and POD reduced systems have the same orders of magnitude, thus supporting the theoretical results existing in the literature.
NASA Astrophysics Data System (ADS)
Domin, Daniel S.
1999-01-01
The science laboratory instructional environment is ideal for fostering the development of problem-solving, manipulative, and higher-order thinking skills: the skills needed by today's learner to compete in an ever increasing technology-based society. This paper reports the results of a content analysis of ten general chemistry laboratory manuals. Three experiments from each manual were examined for evidence of higher-order cognitive activities. Analysis was based upon the six major cognitive categories of Bloom's Taxonomy of Educational Objectives: knowledge, comprehension, application, analysis, synthesis, and evaluation. The results of this study show that the overwhelming majority of general chemistry laboratory manuals provide tasks that require the use of only the lower-order cognitive skills: knowledge, comprehension, and application. Two of the laboratory manuals were disparate in having activities that utilized higher-order cognition. I describe the instructional strategies used within these manuals to foster higher-order cognitive development.
Higher-order mass defect analysis for mass spectra of complex organic mixtures.
Roach, Patrick J; Laskin, Julia; Laskin, Alexander
2011-06-15
Higher-order mass defect analysis is introduced as a unique formula assignment and visualization method for the analysis of complex mass spectra. This approach is an extension of the concepts of Kendrick mass transformation widely used for identification of homologous compounds differing only by a number of base units (e.g., CH(2), H(2), O, CH(2)O, etc.) in complex mixtures. We present an iterative renormalization routine for defining higher-order homologous series and multidimensional clustering of mass spectral features. This approach greatly simplifies visualization of complex mass spectra and increases the number of chemical formulas that can be confidently assigned for given mass accuracy. The potential for using higher-order mass defects for data reduction and visualization is shown. Higher-order mass defect analysis is described and demonstrated through third-order analysis of a deisotoped high-resolution mass spectrum of crude oil containing nearly 13,000 peaks. PMID:21526851
Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM
NASA Technical Reports Server (NTRS)
Navon, I. M.; Bloom, S. C.; Takacs, L.
1984-01-01
Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.
Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions
NASA Technical Reports Server (NTRS)
Prezekop, Adam
2008-01-01
Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification leading to formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure gradients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency and span of the oscillating pressure gradient.
Nonlinear diffusion in two-dimensional ordered porous media based on a free volume theory
NASA Astrophysics Data System (ADS)
Godec, A.; Gaberscek, M.; Jamnik, J.; Merzel, F.
2009-12-01
A continuum nonlinear diffusion model is developed to describe molecular transport in ordered porous media. An existing generic van der Waals equation of state based free volume theory of binary diffusion coefficients is modified and introduced into the two-dimensional diffusion equation. The resulting diffusion equation is solved numerically with the alternating-direction fully implicit method under Neumann boundary conditions. Two types of pore structure symmetries are considered, hexagonal and cubic. The former is modeled as parallel channels while in case of the latter equal-sized channels are placed perpendicularly thus creating an interconnected network. First, general features of transport in both systems are explored, followed by the analysis of the impact of molecular properties on diffusion inside and out of the porous matrix. The influence of pore size on the diffusion-controlled release kinetics is assessed and the findings used to comment recent experimental studies of drug release profiles from ordered mesoporous silicates.
NASA Astrophysics Data System (ADS)
Badri, Pouya; Amini, Amir; Sojoodi, Mahdi
2016-12-01
This paper deals with designing a robust fixed-order non-fragile dynamic output feedback controller for active suspension system of a quarter-car, by means of convex optimization and linear matrix inequalities (LMIs). Our purpose is to design a low-order controller that keeps the desired design specifications besides the simplicity of the implementation. The proposed controller is capable of asymptotically stabilizing the closed-loop system and developing H∞ control, despite model uncertainties and nonlinear dynamics of the quarter-car as well as the norm bounded perturbations of controller parameters. Furthermore, controller parameters are prevented from taking very large and undesirable amounts through appropriate LMI constraints. Finally, a numerical example is presented to show the effectiveness of the proposed method by comparing it with similar works.
NASA Astrophysics Data System (ADS)
Bijlani, Bhavin J.
2011-07-01
This thesis explored the theory, design, fabrication and characterization of AlGaAs Bragg reflection waveguides (BRW) towards the goal of a platform for monolithic integration of active and optically nonlinear devices. Through integration of a diode laser and nonlinear phase-matched cavity, the possibility of on-chip nonlinear frequency generation was explored. Such integrated devices would be highly useful as a robust, alignment free, small footprint and electrically injected alternative to bulk optic systems. A theoretical framework for modal analysis of arbitrary 1-D photonic crystal defect waveguides is developed. This method relies on the transverse resonance condition. It is then demonstrated in the context of several types of Bragg reflection waveguides. The framework is then extended to phase-match second-order nonlinearities and incorporating quantum-wells for diode lasers. Experiments within a slab and ridge waveguide demonstrated phase-matched Type-I second harmonic generation at fundamental wavelength of 1587 and 1600 nm, respectively; a first for this type of waveguide. For the slab waveguide, conversion efficiency was 0.1 %/W. In the more strongly confined ridge waveguides, efficiency increased to 8.6 %/W owing to the increased intensity. The normalized conversion efficiency was estimated to be at 600 %/Wcm2. Diode lasers emitting at 980 nm in the BRW mode were also fabricated. Verification of the Bragg mode was performed through imaging the near- field of the mode. Propagation loss of this type of mode was measured directly for the first time at ≈ 14 cm-1. The lasers were found to be very insensitive with characteristic temperature at 215 K. Two designs incorporating both laser and phase-matched nonlinearity within the same cavity were fabricated, for degenerate and non-degenerate down-conversion. Though the lasers were sub-optimal, a parametric fluorescence signal was readily detected. Fluorescence power as high as 4 nW for the degenerate design
Application of Higher-Order Cumulant in Fault Diagnosis of Rolling Bearing
NASA Astrophysics Data System (ADS)
Shen, Yongjun; Yang, Shaopu; Wang, Junfeng
2013-07-01
In this paper a new method of pattern recognition based on higher-order cumulant and envelope analysis is presented. The core of this new method is to construct analytical signals from the given signals and obtain the envelope signals firstly, then compute and compare the higher-order cumulants of the envelope signals. The higher-order cumulants could be used as a characteristic quantity to distinguish these given signals. As an example, this method is applied in fault diagnosis for 197726 rolling bearing of freight locomotive. The comparisons of the second-order, third-order and fourth-order cumulants of the envelope signals from different vibration signals of rolling bearing show this new method could discriminate the normal and two fault signals distinctly.
Nonlocal Symmetry Reductions, CTE Method and Exact Solutions for Higher-Order KdV Equation
NASA Astrophysics Data System (ADS)
Ren, Bo; Liu, Xi-Zhong; Liu, Ping
2015-02-01
The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems. The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion (CTE) method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.
Pulse transmission receiver with higher-order time derivative pulse correlator
Dress, Jr., William B.; Smith, Stephen F.
2003-09-16
Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission receiver includes: a higher-order time derivative pulse correlator; a demodulation decoder coupled to the higher-order time derivative pulse correlator; a clock coupled to the demodulation decoder; and a pseudorandom polynomial generator coupled to both the higher-order time derivative pulse correlator and the clock. 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.
Luo, Ruiyao; Li, Lei; Cui, Wenda; Yang, Zining; Wang, Hongyan; Xu, Xiaojun
2016-06-13
In this paper, we have set up a diode laser pumped rubidium amplifier for higher-order Laguerre-Gauss (LG) modes. We experimentally realized amplification of higher-order LG modes including helical and sinusoidal LG_{03}, LG_{13}, LG_{23}, and LG_{33} modes with their high purity held. This novel scheme of generating high-purity higher-order LG beams at high laser power is preferred to the second-generation gravitational wave interferometers. To the best of our knowledge, it is the first time this scheme is formulated. PMID:27410352
On the capabilities of higher-order neurons: a radial basis function approach.
Schmitt, Michael
2005-03-01
Higher-order neurons with k monomials in n variables are shown to have Vapnik-Chervonenkis (VC) dimension at least nk + 1. This result supersedes the previously known lower bound obtained via k-term monotone disjunctive normal form (DNF) formulas. Moreover, it implies that the VC dimension of higher-order neurons with k monomials is strictly larger than the VC dimension of k-term monotone DNF. The result is achieved by introducing an exponential approach that employs gaussian radial basis function neural networks for obtaining classifications of points in terms of higher-order neurons.
NASA Astrophysics Data System (ADS)
Francés, Jorge; Bleda, Sergio; Bej, Subhajit; Tervo, Jani; Navarro-Fuster, Víctor; Fenoll, Sandra; Martínez-Gaurdiola, Francisco J.; Neipp, Cristian
2016-04-01
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
Soliton solutions of the KdV equation with higher-order corrections
NASA Astrophysics Data System (ADS)
Wazwaz, Abdul-Majid
2010-10-01
In this work, the Korteweg-de Vries (KdV) equation with higher-order corrections is examined. We studied the KdV equation with first-order correction and that with second-order correction that include the terms of the fifth-order Lax, Sawada-Kotera and Caudrey-Dodd-Gibbon equations. The simplified form of the bilinear method was used to show the integrability of the first-order models and therefore to obtain multiple soliton solutions for each one. The obstacles to integrability of some of the models with second-order corrections are examined as well.
NASA Astrophysics Data System (ADS)
Sun, Yuan Gong; Wong, James S. W.
2007-10-01
We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities: where , p(t) is positive and differentiable, [alpha]1>...>[alpha]m>1>[alpha]m+1>...>[alpha]n. No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n=1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993) 813-817], Wong [J.S.W. Wong, Oscillation criteria for a forced second linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240], Sun, Ou and Wong [Y.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a linear second order differential equation, Comput. Math. Appl. 48 (2004) 1693-1699] for the linear equation, Nazr [A.H. Nazr, Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for the superlinear equation, and Sun and Wong [Y.G. Sun, J.S.W. Wong, Note on forced oscillation of nth-order sublinear differential equations, JE Math. Anal. Appl. 298 (2004) 114-119] for the sublinear equation.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castañeda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work.
Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills
NASA Astrophysics Data System (ADS)
Hall, John; Low, Andrew
2014-06-01
We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.
Evidence of higher-order effects in thermally driven rapid granular flows
NASA Astrophysics Data System (ADS)
Hrenya, C. M.; Galvin, J. E.; Wildman, R. D.
Molecular dynamic (MD) simulations are used to probe the ability of Navier heat flux, stress tensor and dissipation rate - associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect)
Higher-order corrections to dust ion-acoustic soliton in a quantum dusty plasma
Chatterjee, Prasanta; Das, Brindaban; Mondal, Ganesh; Muniandy, S. V.; Wong, C. S.
2010-10-15
Dust ion-acoustic soliton is studied in an electron-dust-ion plasma by employing a two-fluid quantum hydrodynamic model. Ions and electrons are assumed to follow quantum mechanical behaviors in dust background. The Korteweg-de Vries (KdV) equation and higher order contribution to KdV equations are derived using reductive perturbation technique. The higher order contribution is obtained as a higher order inhomogeneous differential equation. The nonsecular solution of the higher order contribution is obtained by using the renormalization method and the particular solution of the inhomogeneous equation is determined using a truncated series solution method. The effects of dust concentration, quantum parameter for ions and electrons, and soliton velocity on the amplitude and width of the dressed soliton are discussed.
Simple loss scaling laws for quadrupoles and higher-order multipoles used in antihydrogen traps
Fajans, J.; Bertsche, W.; Burke, K.; Deutsch, A.; Chapman, S. F.; Gomberoff, K.; Wurtele, J. S.; Werf, D. P. van der
2006-10-18
Simple scaling laws strongly suggest that for antihydrogen relevant parameters, quadrupole magnetic fields will transport particles into, or near to, the trap walls. Consequently quadrupoles are a poor choice for antihydrogen trapping. Higher order multipoles lead to much less transport.
Zembrzycki, Andreas; Stocker, Adam M; Leingärtner, Axel; Sahara, Setsuko; Chou, Shen-Ju; Kalatsky, Valery; May, Scott R; Stryker, Michael P; O'Leary, Dennis DM
2015-01-01
In mammals, the neocortical layout consists of few modality-specific primary sensory areas and a multitude of higher order ones. Abnormal layout of cortical areas may disrupt sensory function and behavior. Developmental genetic mechanisms specify primary areas, but mechanisms influencing higher order area properties are unknown. By exploiting gain-of and loss-of function mouse models of the transcription factor Emx2, we have generated bi-directional changes in primary visual cortex size in vivo and have used it as a model to show a novel and prominent function for genetic mechanisms regulating primary visual area size and also proportionally dictating the sizes of surrounding higher order visual areas. This finding redefines the role for intrinsic genetic mechanisms to concomitantly specify and scale primary and related higher order sensory areas in a linear fashion. DOI: http://dx.doi.org/10.7554/eLife.11416.001 PMID:26705332
Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere.
Zhou, Guoquan
2011-02-28
The propagation of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a higher-order cosh-Gaussian in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere are also examined in detail.
Regularity properties of fiber derivatives associated with higher-order mechanical systems
NASA Astrophysics Data System (ADS)
Colombo, Leonardo; Prieto-Martínez, Pedro Daniel
2016-08-01
The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in T∗T(k-1)Q, we find necessary and sufficient conditions for such a function to describe the dynamics of a kth-order autonomous dynamical system, thus being a kth-order Hamiltonian function. Then, we give a suitable definition of (hyper)regularity for these higher-order Hamiltonian functions in terms of their fiber derivative. In addition, we also study an alternative characterization of the dynamics in Lagrangian submanifolds in terms of the solutions of the higher-order Euler-Lagrange equations.
Bolognini, Gabriele; Bononi, Alberto
2009-04-27
We present a theoretical study of the performance of distributed Raman amplifiers with higher order pumping schemes, focusing in particular on double Rayleigh scattering (DRS) noise. Results show an unexpected significant DRS noise reduction for pumping order higher than third, allowing for an overall performance improvement of carefully designed distributed amplifiers, ensuring a large optical signal-to-noise ratio improvement together with reduced DRS-induced penalties.
Higher order mode of a microstripline fed cylindrical dielectric resonator antenna
NASA Astrophysics Data System (ADS)
Kumar, A. V. Praveen
2016-03-01
A microstrip transmission line can be used to excite the broadside radiating mode of a cylindrical dielectric resonator antenna (CDRA). The same is found to excite considerably well a higher order mode (HOM) as well. However unlike the broadside mode, the higher order mode gives distorted radiation pattern which makes this mode less useful for practical applications. The cause of distortion in the HOM radiation and the dependence of HOM coupling on the microstrip feed line are explored using HFSS simulations.
Fast algorithm for scaling analysis with higher-order detrending moving average method
NASA Astrophysics Data System (ADS)
Tsujimoto, Yutaka; Miki, Yuki; Shimatani, Satoshi; Kiyono, Ken
2016-05-01
Among scaling analysis methods based on the root-mean-square deviation from the estimated trend, it has been demonstrated that centered detrending moving average (DMA) analysis with a simple moving average has good performance when characterizing long-range correlation or fractal scaling behavior. Furthermore, higher-order DMA has also been proposed; it is shown to have better detrending capabilities, removing higher-order polynomial trends than original DMA. However, a straightforward implementation of higher-order DMA requires a very high computational cost, which would prevent practical use of this method. To solve this issue, in this study, we introduce a fast algorithm for higher-order DMA, which consists of two techniques: (1) parallel translation of moving averaging windows by a fixed interval; (2) recurrence formulas for the calculation of summations. Our algorithm can significantly reduce computational cost. Monte Carlo experiments show that the computational time of our algorithm is approximately proportional to the data length, although that of the conventional algorithm is proportional to the square of the data length. The efficiency of our algorithm is also shown by a systematic study of the performance of higher-order DMA, such as the range of detectable scaling exponents and detrending capability for removing polynomial trends. In addition, through the analysis of heart-rate variability time series, we discuss possible applications of higher-order DMA.
Study of higher order non-classical properties of squeezed Kerr state
NASA Astrophysics Data System (ADS)
Mishra, Devendra Kumar
2010-09-01
Recently, Prakash and Mishra [J. Phys. B: at. Mol. Opt. Phys., 39, 2291(2006); 40, 2531(2007)] have studied higher order sub-Poissonian photon statistic conditions for non-classicality in the form of general inequalities for expectation values of products of arbitrary powers of photon number and of photon-number fluctuation. It is, therefore, vital to study the generation of these higher order sub-Poissonian photon statistics (phase-insensitive behavior) in a physically realizable medium and their relations to higher order squeezing (phase-sensitive behavior). In the present paper, we study higher order non-classical properties, such as Hong and Mandel squeezing, amplitude-squared squeezing and higher order sub-Poissonian photon statistics, of squeezed Kerr state which is generated by squeezing the output of a Kerr medium whose input is coherent light. Such states can be realized if laser light is sent through an optical fiber and then into a degenerate parametric amplifier. It is established that the squeezed Kerr state can exhibit higher order non-classical properties.
Questions for assessing higher-order cognitive skills: it's not just Bloom's.
Lemons, Paula P; Lemons, J Derrick
2013-01-01
We present an exploratory study of biologists' ideas about higher-order cognition questions. We documented the conversations of biologists who were writing and reviewing a set of higher-order cognition questions. Using a qualitative approach, we identified the themes of these conversations. Biologists in our study used Bloom's Taxonomy to logically analyze questions. However, biologists were also concerned with question difficulty, the length of time required for students to address questions, and students' experience with questions. Finally, some biologists demonstrated an assumption that questions should have one correct answer, not multiple reasonable solutions; this assumption undermined their comfort with some higher-order cognition questions. We generated a framework for further research that provides an interpretation of participants' ideas about higher-order questions and a model of the relationships among these ideas. Two hypotheses emerge from this framework. First, we propose that biologists look for ways to measure difficulty when writing higher-order questions. Second, we propose that biologists' assumptions about the role of questions in student learning strongly influence the types of higher-order questions they write.
Effect of carbazole as a donor moiety on the second-order nonlinearity of organic molecules
NASA Astrophysics Data System (ADS)
Meshulam, Guilia; Berkovic, Garry; Kotler, Zvi; Ben-Asuly, Amos; Mazor, Royi; Shapiro, Lev; Khodorkovsky, Vladimir
1999-10-01
The second order nonlinearity of conjugated organic molecules involving, 1,3 indandione derivatives as an acceptor moiety has been studied. Varying the donor from dialkylamino to the chemically similar substituent, N- carbazolyl resulted in a drastic reduction of electric field induced second harmonic (beta) values. For some molecules, even a small negative value of (beta) was received. Quantum chemical calculations indicate that the decrease occurs as a result of two overlapping transitions, which contribute to (beta) with opposite signs. The charge transfer band gives a positive (beta) zzz along the molecular long axis, while a transition essentially within the carbazole moiety provides a negative (beta zzz contribution to (beta EFISH. Thus, these molecules must be described with a 2D model as opposed to the 'classical' model of 1D nonlinear optical chromophores. The prediction of the 2D model was verified experimentally by using a combination of two methods, EFISH and Hyper-Rayleigh Scattering, which probe different combination of the (beta) tensor elements.
"What Do I Do Here?": Higher Order Learning Effects of Enhancing Task Instructions
ERIC Educational Resources Information Center
Chamberlain, Susanna; Zuvela, Danni
2014-01-01
This paper reports the findings of a one-year research project focused on a series of structured interventions aimed at enhancing task instruction to develop students' understanding of higher assessment practices, and encouraging higher order learning. It describes the nature and iterations of the interventions, made into a large-enrolment online…
ERIC Educational Resources Information Center
Gamino, Jacquelyn F.; Chapman, Sandra B.; Cook, Lori G.
2009-01-01
Little is known about strategic learning ability in preteens and adolescents with traumatic brain injury (TBI). Strategic learning is the ability to combine and synthesize details to form abstracted gist-based meanings, a higher-order cognitive skill associated with frontal lobe functions and higher classroom performance. Summarization tasks were…
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Iwashige, Kengo; Ikeda, Takashi
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
Development of a Process To Assess Higher Order Thinking Skills for College Graduates.
ERIC Educational Resources Information Center
Rock, Donald A.
Issues in the development of assessments of higher order thinking skills for college graduates are discussed in the order in which they were presented when this series of papers was commissioned. With regard to Issue 1, it is generally agreed that the development of these skills is a desirable goal, but there is little consensus on how they should…
Higher Order, Critical Thinking Skills in National Police Academy Course Development
ERIC Educational Resources Information Center
Barker, Beth A.
2011-01-01
Law enforcement requires the officer to invoke reason and critical thinking skills in order to solve intricate problems in real time, on the job. This study examined the course development of a large national organization (State Police Academies) to ascertain what strategies are being used in their courses to promote training for higher order,…
ERIC Educational Resources Information Center
Toledo, Santiago; Dubas, Justin M.
2016-01-01
An emphasis on higher-order thinking within the curriculum has been a subject of interest in the chemical and STEM literature due to its ability to promote meaningful, transferable learning in students. The systematic use of learning taxonomies could be a practical way to scaffold student learning in order to achieve this goal. This work proposes…
ERIC Educational Resources Information Center
Scandura, Joseph M.; And Others
The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…
Hamiltonian structure of the higher-order corrections to the Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
Menyuk, C. R.; Chen, H.-H.
1985-10-01
Higher-order corrections to the Korteweg-de Vries equation are examined by Hamiltonian methods. Starting from the underlying Hamiltonian systems (e.g., the two-fluid equations in the case of ion-acoustic waves), one finds that the corrected equations have the same Poisson bracket as the Korteweg-de Vries equation at every order. One also finds that the underlying equations become nonlocal at sufficiently high order.
Spectral Line Profile Analysis Using Higher Diffraction Order in Vacuum Ultraviolet Region
Machida, M.; Daltrini, A. M.; Severo, J. H. F.; Nascimento, I. C.; Sanada, E. K.; Elizondo, J. I.; Kuznetsov, Y. K.; Galvao, R. M. O.
2008-04-07
Using a one meter VUV spectrometer and a MCP coupled to a CCD detector on TCABR tokamak, ion temperatures from impurity species have been measured and much better spectral resolution was obtained using higher order diffraction lines. Due to very small Doppler effect in the VUV region compared to large instrumental broadening, ion temperatures obtained from first order diffraction present large errors. The use of second, third and fourth order diffraction emissions increases the line broadening and results in lower error temperature measurements.
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
2014-03-21
We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with χ{sub eff}{sup (2)} ∼ 0.6 pm V{sup −1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
Nonlinear Reduced-Order Simulation Using Stress-Free and Pre-Stressed Modal Bases
NASA Technical Reports Server (NTRS)
Przekop, Adam; Stover, Michael A.; Rizzi, Stephen A.
2009-01-01
A study is undertaken to determine the advantages and disadvantages associated with application of stress-free and pre-stressed modal bases in a reduced-order finite-element-based nonlinear simulation. A planar beam is chosen as an application example and its response due to combined thermal and random pressure loadings is examined. Combinations of two random pressure levels and two thermal conditions are investigated. The latter consists of an ambient temperature condition and an elevated temperature condition in the post-buckled regime. It is found that stress-free normal modes establish a broadly applicable modal basis yielding accurate results for all the loading regimes considered. In contrast, the range of applicability for a thermally pre-stressed modal basis is found to be limited. The behavior is explained by scrutinizing the coupling found in the linear stiffness and the effect this coupling has on the structural response characteristics under the range of loading conditions considered.
Synchronisation of high-order MIMO nonlinear systems using distributed neuro-adaptive control
NASA Astrophysics Data System (ADS)
Ghiti Sarand, Hassan; Karimi, Bahram
2016-07-01
This paper addresses synchronisation problem of high-order multi-input/multi-output (MIMO) multi-agent systems. Each agent has unknown nonlinear dynamics and is subject to uncertain external disturbances. The agents must follow a reference trajectory. An adaptive distributed controller based on relative information of neighbours of each agent is designed to solve the problem for any undirected connected communication topology. A radial basis function neural network is used to represent the controller's unknown structure. Lyapunov stability analysis is employed to guarantee stability of the overall system. By the theoretical analysis, the closed-loop control system is shown to be uniformly ultimately bounded. Finally, simulations are provided to show effectiveness of the proposed control method against uncertainty and disturbances.
Determination of Second-Order Nonlinear Optical Susceptibility of GaN Films on Sapphire
NASA Astrophysics Data System (ADS)
Fujita, Takashi; Hasegawa, Tatsuo; Haraguchi, Masanobu; Okamoto, Toshihiro; Fukui, Masuo; Nakamura, Syuji
2000-05-01
The second-order nonlinear susceptibilities of GaN films on sapphire were determined by the Maker fringe technique. In deriving the second-harmonic intensity, the bound wave propagating from the GaN-air interface to the GaN-sapphire interface and that propagating in the opposite direction were taken into account. We obtained |χ(2)zxx|=14.7±0.2 pm/V, |χ(2)xzx|=14.4±0.2 pm/V and |χ(2)zzz|=29.7±0.7 pm/V for the GaN film with a thickness of 2.55 μm using fundamental light with a wavelength of 1.064 μm.
Second-order estimates for nonlinear isotropic composites with spherical pores and rigid particles
NASA Astrophysics Data System (ADS)
Idiart, Martín; Ponte Castañeda, Pedro
2005-02-01
The 'second-order' nonlinear homogenization method (Ponte Castañeda, J. Mech. Phys. Solids 50 (2002) 737-757) is used to generate estimates of the Hashin-Shtrikman-type for the effective behavior of viscoplastic materials with isotropically distributed spherical pores or rigid particles. In the limiting case of an ideally plastic matrix with a dilute concentration of pores, the resulting estimates were found to exhibit a linear dependence on the porosity when the material is subjected to axisymmetric shear, but this dependence becomes singular for simple shear. In the process of this work, an alternative prescription for certain reference tensors used in the method is proposed, and shown to lead to more consistent estimates for the effective behavior than the earlier prescription. To cite this article: M. Idiart, P. Ponte Castañeda, C. R. Mecanique 333 (2005).
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-01
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
NASA Astrophysics Data System (ADS)
Saravanan, M.; Senthil, A.; Rajasekar, S. Abraham
2016-09-01
Good optical quality, potential second order nonlinear optical crystal L-asparaginium picrate (LASP) was grown by the slow cooling method. The solubility and metastable zone width of LASP specimen was studied. The LASP crystal belongs to monoclinic crystal system with noncentrosymmetric space group P21. UV-Visible-NIR transmittance spectrum determines the optical band gap of LASP. Excellence of the grown crystal is ascertained by the etching studies. Laser Damage Threshold and Photoluminescence studies designate that the grown crystal contains less imperfection. The mechanical behaviour of LASP sample was investigated at different temperatures. The piezoelectric nature, Photoconductive nature and the relative Second Harmonic Generation (for various particle sizes) of the material were also studied. Birefringence and ocular (optical) homogeneity of the crystal were assessed using modified channel spectrum method.
Clayton, C
1982-07-01
"The structure of human geographical systems is often of a hierarchical nature. Population migration systems can usefully be conceptualized as a series of hierarchically related levels of migration fields: the fields at one level nesting within the fields at the next higher level. Such migration fields and the relationships between different levels can be extracted from large population migration origin-destination matrices with the aid of higher order factor analysis." A case study of the western United States illustrating the application of higher order factor analysis to large interaction matrices is presented.
NASA Technical Reports Server (NTRS)
Heyman, J. S.; Allison, S. G.; Salama, K.
1985-01-01
The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.
Marquette, Ian
2010-07-15
We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladder operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.
A single dose of oxytocin nasal spray improves higher-order social cognition in schizophrenia.
Guastella, Adam J; Ward, Philip B; Hickie, Ian B; Shahrestani, Sara; Hodge, Marie Antoinette Redoblado; Scott, Elizabeth M; Langdon, Robyn
2015-11-01
Schizophrenia is associated with significant impairments in both higher and lower order social cognitive performance and these impairments contribute to poor social functioning. People with schizophrenia report poor social functioning to be one of their greatest unmet treatment needs. Recent studies have suggested the potential of oxytocin as such a treatment, but mixed results render it uncertain what aspects of social cognition are improved by oxytocin and, subsequently, how oxytocin might best be applied as a therapeutic. The aim of this study was to determine whether a single dose of oxytocin improved higher-order and lower-order social cognition performance for patients with schizophrenia across a well-established battery of social cognition tests. Twenty-one male patients received both a single dose of oxytocin nasal spray (24IU) and a placebo, two weeks apart in a randomized within-subjects placebo controlled design. Following each administration, participants completed the social cognition tasks, as well as a test of general neurocognition. Results revealed that oxytocin particularly enhanced performance on higher order social cognition tasks, with no effects on general neurocognition. Results for individual tasks showed most improvement on tests measuring appreciation of indirect hints and recognition of social faux pas. These results suggest that oxytocin, if combined to enhance social cognition learning, may be beneficial when targeted at higher order social cognition domains. This study also suggests that these higher order tasks, which assess social cognitive processing in a social communication context, may provide useful markers of response to oxytocin in schizophrenia.
An efficient higher-order PML in WLP-FDTD method for time reversed wave simulation
NASA Astrophysics Data System (ADS)
Wei, Xiao-Kun; Shao, Wei; Ou, Haiyan; Wang, Bing-Zhong
2016-09-01
Derived from a stretched coordinate formulation, a higher-order complex frequency shifted (CFS) perfectly matched layer (PML) is proposed for the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs). The higher-order PML is implemented with an auxiliary differential equation (ADE) approach. In order to further improve absorbing performance, the parameter values of stretching functions in the higher-order PML are optimized by the multi-objective genetic algorithm (MOGA). The optimal solutions can be chosen from the Pareto front for trading-off between two independent objectives. It is shown in a numerical test that the higher-order PML is efficient in terms of attenuating propagating waves and reducing late time reflections. Moreover, the higher-order PML can be placed very close to the wall when analyzing the channel characteristics of time reversal (TR) waves in a multipath indoor environment. Numerical examples of TR wave propagation demonstrate the availability of the proposed method.
NASA Astrophysics Data System (ADS)
Jayakrishnan, K.; Joseph, Antony; Bhattathiripad, Jayakrishnan; Ramesan, M. T.; Chandrasekharan, K.; Siji Narendran, N. K.
2016-04-01
We report our results on the identification of large order enhancement in nonlinear optical coefficients of polymerized indole and its comparative study with reference to its monomer counterpart. Indole monomer shows virtually little third order effects whereas its polymerized version exhibits phenomenal increase in its third order nonlinear optical parameters such as nonlinear refractive index and nonlinear absorption. Open aperture Z-scan trace of polyindole done with Q-switched Nd:YAG laser source (532 nm, 7 ns), shows β value as high as 89 cm/GW at a beam energy of 0.83 GW/cm2. Closed aperture Z-scan done at identical energies reveals nonlinear refractive index of the order of -3.55 × 10-17 m2/W. Band gap measurement of polyindole was done with UV-Vis absorption spectra and compared with that of Indole. FTIR spectra of the monomer and polymerized versions were recorded and relevant bond formations were confirmed from the characteristic peaks. Photo luminescent spectra were investigated to know the emission features of both molecules. Beam energy (I0) versus nonlinear absorption coefficient (β) plot indicates reverse saturable type of absorption behaviour in polyindole molecules. Degenerate Four Wave Mixing (DFWM) plot of polyindole reveals quite a cubic dependence between probe and phase conjugate signal and the resulting χ(3) is comparable with Z-scan results. Optical limiting efficiency of polyindole is comparable with certain derivatives of porphyrins, phthalocyanines and graphene oxides.
NASA Astrophysics Data System (ADS)
Chen, Jingwei; Wang, Xinqiang; Ren, Quan; Patil, P. S.; Li, Tingbin; Yang, Hongliang; Zhang, Jingnan; Li, Guochao; Zhu, Luyi
2011-11-01
A novel chalcone derivative, (2 E)-1-(2,4-di- chloro-5-fluorophenyl)-3-[4-dimethylamino)phenyl]prop-2-en-1-one, abbreviated as NNDC, was prepared and characterized by elemental analyses, infrared (IR) and proton nuclear magnetic resonance (1H NMR) spectrum, and thermal analyses. The NNDC-doped poly(methyl methacrylate) (PMMA) thin films with five different doping concentrations by weight were prepared by using a spin-coating method. Their linear optical properties were investigated by using a prism coupling measuring system. The third-order nonlinear optical properties of NNDC in 1,2-dichloroethane (NNDC/1,2-dichloroethane) solution and NNDC-doped PMMA (NNDC/PMMA) films were investigated by using the laser Z-scan technique with 20 ps pulses at 532 nm. A self-focusing effect was observed from the Z-scan curves for solution and thin films and the nonlinear refractive index of the film increases with the increase of the doping concentration. In addition, nonlinear absorption was negligible for all samples. The magnitude of third-order nonlinear refraction index n 2 and the third-order nonlinear susceptibility χ (3) for thin films were 10-15 m2/W and 10-9 esu, respectively, which are about three orders larger than that of NNDC/1,2-dichloroethane solution. Some necessary analyses were presented. The results show that this material is a promising candidate for application in the nonlinear optical devices at 532 nm.
Quasi suppression of higher-order diffractions with inclined rectangular apertures gratings
Liu, Yuwei; Zhu, Xiaoli; Gao, Yulin; Zhang, Wenhai; Fan, Quanping; Wei, Lai; Yang, Zuhua; Zhang, Qiangqiang; Qian, Feng; Chen, Yong; He, Weihua; Wu, Yinzhong; Yan, Zhuoyang; Hua, Yilei; Zhao, Yidong; Cui, Mingqi; Qiu, Rong; Zhou, Weimin; Gu, Yuqiu; Zhang, Baohan; Xie, Changqing; Cao, Leifeng
2015-01-01
Advances in the fundamentals and applications of diffraction gratings have received much attention. However, conventional diffraction gratings often suffer from higher-order diffraction contamination. Here, we introduce a simple and compact single optical element, named inclined rectangular aperture gratings (IRAG), for quasi suppression of higher-order diffractions. We show, both in the visible light and soft x-ray regions, that IRAG can significantly suppress higher-order diffractions with moderate diffraction efficiency. Especially, as no support strut is needed to maintain the free-standing patterns, the IRAG is highly advantageous to the extreme-ultraviolet and soft x-ray regions. The diffraction efficiency of the IRAG and the influences of fabrication constraints are also discussed. The unique quasi-single order diffraction properties of IRAG may open the door to a wide range of photonic applications. PMID:26563588
Design and Application of Strategies/Tactics in Higher Order Logics
NASA Technical Reports Server (NTRS)
Archer, Myla (Editor); diVito, Ben (Editor); Munoz, Cesar (Editor)
2003-01-01
This Proceedings includes both a paper from the implementors of PVS providing guidance for PVS strategy writers and a tutorial on PVS strategy writing distilled from the experience of three PVS users who have written extensive sets of PVS user strategies. Following these are three full papers from the higher-order logic theorem proving community that discuss PVS strategies to enhance arithmetic and other interactive reasoning in PVS; implementing first-order tactics in higher-order provers; and a proposed technique for specifying small step semantics that can be used in multiple higher order logic theorem provers, with illustrations from both Coq and PVS. The Proceedings concludes with three position papers for a panel session that discuss three settings in which development of PVS strategies is worth while.
Higher-order cumulants and spectral kurtosis for early detection of subterranean termites
NASA Astrophysics Data System (ADS)
de la Rosa, Juan José González; Moreno Muñoz, Antonio
2008-02-01
This paper deals with termite detection in non-favorable SNR scenarios via signal processing using higher-order statistics. The results could be extrapolated to all impulse-like insect emissions; the situation involves non-destructive termite detection. Fourth-order cumulants in time and frequency domains enhance the detection and complete the characterization of termite emissions, non-Gaussian in essence. Sliding higher-order cumulants offer distinctive time instances, as a complement to the sliding variance, which only reveal power excesses in the signal; even for low-amplitude impulses. The spectral kurtosis reveals non-Gaussian characteristics (the peakedness of the probability density function) associated to these non-stationary measurements, specially in the near ultrasound frequency band. Contrasted estimators have been used to compute the higher-order statistics. The inedited findings are shown via graphical examples.
Quasi suppression of higher-order diffractions with inclined rectangular apertures gratings.
Liu, Yuwei; Zhu, Xiaoli; Gao, Yulin; Zhang, Wenhai; Fan, Quanping; Wei, Lai; Yang, Zuhua; Zhang, Qiangqiang; Qian, Feng; Chen, Yong; He, Weihua; Wu, Yinzhong; Yan, Zhuoyang; Hua, Yilei; Zhao, Yidong; Cui, Mingqi; Qiu, Rong; Zhou, Weimin; Gu, Yuqiu; Zhang, Baohan; Xie, Changqing; Cao, Leifeng
2015-01-01
Advances in the fundamentals and applications of diffraction gratings have received much attention. However, conventional diffraction gratings often suffer from higher-order diffraction contamination. Here, we introduce a simple and compact single optical element, named inclined rectangular aperture gratings (IRAG), for quasi suppression of higher-order diffractions. We show, both in the visible light and soft x-ray regions, that IRAG can significantly suppress higher-order diffractions with moderate diffraction efficiency. Especially, as no support strut is needed to maintain the free-standing patterns, the IRAG is highly advantageous to the extreme-ultraviolet and soft x-ray regions. The diffraction efficiency of the IRAG and the influences of fabrication constraints are also discussed. The unique quasi-single order diffraction properties of IRAG may open the door to a wide range of photonic applications.
Quasi suppression of higher-order diffractions with inclined rectangular apertures gratings.
Liu, Yuwei; Zhu, Xiaoli; Gao, Yulin; Zhang, Wenhai; Fan, Quanping; Wei, Lai; Yang, Zuhua; Zhang, Qiangqiang; Qian, Feng; Chen, Yong; He, Weihua; Wu, Yinzhong; Yan, Zhuoyang; Hua, Yilei; Zhao, Yidong; Cui, Mingqi; Qiu, Rong; Zhou, Weimin; Gu, Yuqiu; Zhang, Baohan; Xie, Changqing; Cao, Leifeng
2015-01-01
Advances in the fundamentals and applications of diffraction gratings have received much attention. However, conventional diffraction gratings often suffer from higher-order diffraction contamination. Here, we introduce a simple and compact single optical element, named inclined rectangular aperture gratings (IRAG), for quasi suppression of higher-order diffractions. We show, both in the visible light and soft x-ray regions, that IRAG can significantly suppress higher-order diffractions with moderate diffraction efficiency. Especially, as no support strut is needed to maintain the free-standing patterns, the IRAG is highly advantageous to the extreme-ultraviolet and soft x-ray regions. The diffraction efficiency of the IRAG and the influences of fabrication constraints are also discussed. The unique quasi-single order diffraction properties of IRAG may open the door to a wide range of photonic applications. PMID:26563588
Bounding higher-order ionosphere errors for the dual-frequency GPS user
NASA Astrophysics Data System (ADS)
Datta-Barua, S.; Walter, T.; Blanch, J.; Enge, P.
2008-10-01
Civil signals at L2 and L5 frequencies herald a new phase of Global Positioning System (GPS) performance. Dual-frequency users typically assume a first-order approximation of the ionosphere index of refraction, combining the GPS observables to eliminate most of the ranging delay, on the order of meters, introduced into the pseudoranges. This paper estimates the higher-order group and phase errors that occur from assuming the ordinary first-order dual-frequency ionosphere model using data from the Federal Aviation Administration's Wide Area Augmentation System (WAAS) network on a solar maximum quiet day and an extremely stormy day postsolar maximum. We find that during active periods, when ionospheric storms may introduce slant range delays at L1 as high as 100 m, the higher-order group errors in the L1-L2 or L1-L5 dual-frequency combination can be tens of centimeters. The group and phase errors are no longer equal and opposite, so these errors accumulate in carrier smoothing of the dual-frequency code observable. We show the errors in the carrier-smoothed code are due to higher-order group errors and, to a lesser extent, to higher-order phase rate errors. For many applications, this residual error is sufficiently small as to be neglected. However, such errors can impact geodetic applications as well as the error budgets of GPS Augmentation Systems providing Category III precision approach.
Transient even and odd order nonlinearity of a YBCO transmission line
NASA Astrophysics Data System (ADS)
Huizen, Richard; Remillard, Stephen
Second (IMD2) and third (IMD3) order intermodulation distortions were found to exhibit dependencies on temperature and magnetic field. A carrier wave at the 890 MHz resonant frequency of the type-II YBa2Cu3O7-δ superconducting resonator circuit, with TC = 89K, was introduced into the circuit via an electric coupling antenna. Two off-resonance probe signals were injected into the circuit via a separate magnetic coupling element. The combination of these three signals locally excited synchronous second and third order IMD. A static magnetic field was applied perpendicularly to the film which induced magnetic flux vortices in the sample. Upon removal of the static magnetic field, IMD2 and IMD3 exhibited distinct transient decay modes correlating to temperature. Between 85.0K and 87.5K, IMD3 decayed exponentially. Above 87.5K, IMD3 exhibited bounded exponential growth, while within a narrow temperature range around 87.5K, removal of a static magnetic field strongly suppressed IMD3. IMD2 exhibited exponential decay at all temperatures. Even and odd order microwave nonlinearities were thus shown to result from different, magnetically coupled, physical mechanisms. Funding for this project was provided by Award Number DMR-1206149 from the National Science Foundation.
A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields.
Fix, Alexander; Gruber, Aritanan; Boros, Endre; Zabih, Ramin
2015-07-01
Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1], [2], both theoretically and experimentally. While [1], [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n non-submodular terms, while [1], [2] produces O(nk). We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. We show experimentally that our method produces smaller weight of non-submodular edges, and that this metric is directly related to the effectiveness of QPBO [3]. Running on the same field of experts dataset used in [1], [2] we optimally label significantly more variables (96 versus 80 percent) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higher-order MRF's used in stereo [4] and segmentation [5] are also locally complete and would thus benefit from our work.
NASA Astrophysics Data System (ADS)
Tanaka, Satoshi; Garmon, Savannah; Kanki, Kazuki; Petrosky, Tomio
2016-08-01
We have theoretically investigated the time-symmetry-breaking phase-transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue problem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy dependence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry-breaking phase transition: As a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.
Gavrishchaka, V.V.; Ganguli, G.I.; Bakshi, P.M.; Koepke, M.E.
1998-01-01
The formalism necessary to study the collective properties of a plasma system with inhomogeneous flows is nonlocal and generally in the form of an integrodifferential equation. Usually the eigenvalue condition is reduced to a second-order differential equation for simplicity. While the gross physical behavior of the system can be obtained from the second-order differential equation level of description, higher-order corrections are necessary for greater accuracy. The limit in which the scale-size of the velocity inhomogeneity is large compared to the ion gyroradius is considered and a transverse flow profile sharply localized in space ({open_quotes}top-hat{close_quotes} profile) is assumed. In this limit, a simple analytical method for the solution of the general eigenvalue condition to all orders is developed. A comparison of the properties of the solutions obtained from the second-order differential equation level of description with those obtained from higher orders is presented. Both the resonant (dissipative) and the nonresonant (reactive) effects of velocity shear are considered. It is found that while the overall features are well represented by the second-order level of description, the higher-order corrections moderate the destabilizing effects due to velocity shear, which can be quite significant in some cases. {copyright} {ital 1998 American Institute of Physics.}
NASA Technical Reports Server (NTRS)
Crivellini, A.; Golubev, V.; Mankbadi, R.; Scott, J. R.; Hixon, R.; Povinelli, L.; Kiraly, L. James (Technical Monitor)
2002-01-01
The nonlinear response of symmetric and loaded airfoils to an impinging vortical gust is investigated in the parametric space of gust dimension, intensity, and frequency. The study, which was designed to investigate the validity limits for a linear analysis, is implemented by applying a nonlinear high-order prefactored compact code and comparing results with linear solutions from the GUST3D frequency-domain solver. Both the unsteady aerodynamic and acoustic gust responses are examined.