Properties of second-order geometrical aberrations
NASA Astrophysics Data System (ADS)
Grammatin, A. P.
1994-08-01
This paper analyzes the properties of second-order aberrations that arise in centered optical systems that contain an aspherical surface whose sagittal equation contains a term proportional to the cube of the distance from a surface point to the optical axis. It is shown that the second-order spherical aberration decreases from the center of the field to its edge. No astigmatism appears in wide, oblique beams in the central part of the field. Coma increases linearly from zero at the center of the field to a value equal to the spherical aberration, and then remains constant over the field. A proof is given of the possibility of correcting the image curvature by using an aspherical surface of the type described above.
Li, Pei-Xin; Wang, Ming-Sheng; Zhang, Ming-Jian; Lin, Chen-Sheng; Cai, Li-Zhen; Guo, Sheng-Ping; Guo, Guo-Cong
2014-10-20
The first bulk electron-transfer photochromic compound with intrinsic second-order nonlinear optical (NLO) photoswitching properties has been synthesized. This system employs an electron-transfer photoactive asymmetric viologen ligand coordinated to a zinc(II) center. PMID:25195919
NASA Astrophysics Data System (ADS)
Liu, Yongjun; Liu, Ying; Zhang, Dongju; Hu, Haiquan; Liu, Chengbu
2001-08-01
On the basis of the ZINDO program, we have designed a program to calculate the second-order nonlinear polarizabilities βijk, β0 and βμ according to the sum-over-states (SOS) expression. A series of new 4-(dicyanomethylene)-2-methyl-6-( p-dithylamino-styryl)-4 H-pyran (DCM) derivatives were designed and their electron spectra and nonlinear optical properties were studied. It is proposed that these compounds possess two important excited states close to each other in energy, both contributing to hyperpolarizability in an additive fashion; 4-(dicyanomethylene)-2,6-bis-( p-donor-styryl)-4 H-pyran derivatives are more nonlinear than 4-(dicyanomethylene)-2,6-bis-( p-donor-phenyl)-azo-4 H-pyran derivatives. The high nonlinearities, good thermal stability and high transparency make them attractive candidates for second-order nonlinear applications such as electro-optic modulators and frequency doublers.
Ismagilov, Timur Z.
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
NASA Astrophysics Data System (ADS)
Zou, Wenli; Filatov, Michael; Cremer, Dieter
2012-08-01
Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties.
NASA Astrophysics Data System (ADS)
Fu, Chu-Yun Stacey
1995-01-01
Over the past decade, researchers have been actively involved in developing nonlinear optical polymers for device applications. One major obstacle with the current polymers is that the chromophores doped or covalently bonded to the backbones disorient following electric field poling and thus the nonlinear optical signal decreases with time. The optical stability must thus be optimized before useful devices made from these materials will be feasible. Although several synthetic approaches have been employed to optimize polymer structures and glass transition temperatures in order to maximize stability, the studies of the polymer physics of these high temperature stable polymers are still limited. It is critical to understand the polymer physics governing the relaxation behavior of these nonlinear optical polymers so that one can better predict the long-term thermal and temporal stability and changes in properties throughout the anticipated service life when utilizing them for device applications. The goal of this research is to investigate the structure/property relationships that influence the relaxation behavior of a class of thermally stable polymers called polyarylene ethers (synthesized by Dr. Duane B. Priddy, Jr., Mr. Greg D. Lyle, and Dr. James E. McGrath at Virginia Polytechnic Institute and State University). Specific issues such as the effects of polymer backbone structures, dopant/polymer interactions, chromophore functionalization, and chromophore concentration on the dopant orientational dynamics and intermolecular cooperativity in these polymer systems were studied. Attempts to correlate the molecular level parameters including the molecular weight and polydispersities to the observed physical properties were made. The effect of physical aging during poling on the chromophore orientational dynamics was also examined. Second harmonic generation, a second order nonlinear optical effect, and dielectric relaxation are the two techniques employed for these
Muhammad, Shabbir; Al-Sehemi, Abdullah G; Irfan, Ahmad; Chaudhry, Aijaz R
2016-07-01
Using the density functional theory methods, we effectively tune the second-order nonlinear optical (NLO) properties in some chalcone derivatives. Various unique push-pull configurations are used to efficiently enhance the intramolecular charge transfer process over the designed derivatives, which result in significantly larger amplitudes of the first hyperpolarizability as compared to their parent molecule. The ground state molecular geometries have been optimized using B3LYP/6-311G** level of theory. A variety of methods including B3LYP, CAM-B3LYP, PBE0, M06, BHandHLYP and MP2 are tested with 6-311G** basis set to calculate the first hyperpolarizability of parent system 1. The results of M06 are found closer to highly correlated MP2 method, which has been selected to calculate static and frequency dependent first hyperpolarizability amplitudes of all selected systems. At M06/6-311G** level of theory, the permanent electronic dipole moment (μtot), polarizability (α0) and static first hyperpolarizability (βtot) amplitudes for parent system 1 are found to be 5.139 Debye, 274a. u. and 24.22×10(-30)esu, respectively. These amplitudes have been significantly enhanced in designed derivatives 2 and 3. More importantly, the (βtot) amplitudes of systems 2 and 3 mount to 75.78×10(-30) and 128.51×10(-30)esu, respectively, which are about 3 times and 5 times larger than that of their parent system 1. Additionally, we have extended the structure-NLO property relationship to several newly synthesized chalcone derivatives. Interestingly, the amplitudes of dynamic frequency dependent hyperpolarizability μβω (SHG) are also significantly larger having values of 366.72×10(-48), 856.32×10(-48) and 1913.46×10(-48)esu for systems 1-3, respectively, at 1400nm of incident laser wavelength. The dispersion behavior over a wide range of change in wavelength has also been studied adopting a range of wavelength from 1907 to 544nm. Thus, the present work realizes the potential of
NASA Astrophysics Data System (ADS)
Espin, Johnny; Krasnov, Kirill
2015-06-01
It is known, though not commonly, that one can describe fermions using a second order in derivatives Lagrangian instead of the first order Dirac one. In this description the propagator is scalar, and the complexity is shifted to the vertex, which contains a derivative operator. In this paper we rewrite the Lagrangian of the fermionic sector of the Standard Model in such second order form. The new Lagrangian is extremely compact, and is obtained from the usual first order Lagrangian by integrating out all primed (or dotted) 2-component spinors. It thus contains just half of the 2-component spinors that appear in the usual Lagrangian, which suggests a new perspective on unification. We sketch a natural in this framework SU (2) × SU (4) ⊂ SO (9) unified theory.
NASA Astrophysics Data System (ADS)
Papon, G.; Marquestaut, N.; Petit, Y.; Royon, A.; Dussauze, M.; Rodriguez, V.; Cardinal, T.; Canioni, L.
2014-03-01
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 χeff(2) ˜ 0.6 pm V-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.
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.
Monago-Maraña, Olga; Durán-Merás, Isabel; Galeano-Díaz, Teresa; Muñoz de la Peña, Arsenio
2016-04-01
The influence of pH on the fluorescence of flavonoid compounds was investigated and the highest fluorescence emission was obtained in basic medium. Selected conditions to improve this signal were: pH 9.5, 0.14 M Britton Robinson buffer and methanol between 5% and 10%. The excitation-emission fluorescence matrices of a set of 36 samples of Spanish paprika were analyzed by means of parallel factor analysis (PARAFAC). Thus, the profiles of possible fluorescence components (PARAFAC loadings) were obtained. One of these profiles was identified by matching PARAFAC scores with LC analysis on the same samples. Two clusters of samples were obtained when score values were plotted against each other. Spectrofluorimetry coupled to second order multivariate calibration methods, as unfolded-partial least squares with residual bilinearization (U-PLS/RBL) and multidimensional-partial least-squares with residual bilinearization (N-PLS/RBL), was investigated to quantify quercetin and kaempferol in those samples. Good results were obtained for quercetin by this approach. PMID:26593589
NASA Technical Reports Server (NTRS)
Stiegman, A. E.; Graham, Eva; Khundkar, Lutfur R.; Perry, Joseph W.; Cheng, L.-T.; Perry, Kelly J.
1991-01-01
A series of donor-acceptor acetylene compounds was synthesized in which systematic changes in both the conjugation length and the donor-acceptor strength were made. The effect of these structural changes on the spectroscopic and electronic properties of the molecules and, ultimately, on the measured second-order molecular hyperpolarizabilities (beta) was investigated. It was found that increases in the donor-acceptor strength resulted in increases in the magnitude of beta. For this class of molecules, the increase is dominated by the energy of the intramolecular charge-transfer transition, while factors such as the ground to excited-state dipole moment change and the transition-moment integral are much less important. Increasing the conjugation length from one to two acetylene linkers did not result in an increase in the value of beta; however, beta increased sharply in going from two acetylenes to three. This increase is attributed to the superposition of several nearly isoenergetic excited states.
Feng, Xiaoxiao; Zhang, Junjie; Gao, Zeliang; Zhang, Shaojun; Sun, Youxuan; Tao, Xutang
2014-02-24
The complete set of second-order nonlinear optical (NLO) coefficients of Cs{sub 2}TeMo{sub 3}O{sub 12} single crystals were obtained using the Maker Fringe techniques. The NLO coefficients d{sub 32} and d{sub 33} were measured to be on the order of 6.8 and 6.5 pm/V, respectively. Irradiated by 1064 nm laser, the crystal is phase-matchable, and its effective nonlinear coefficient is 4.6 pm/V for type I phase matching at θ = 42.7°. The relationship between the second-order nonlinear properties and the crystal structure is also discussed. Considering its wide transmission range, phase matching, and large effective NLO coefficient, Cs{sub 2}TeMo{sub 3}O{sub 12} is a good candidate for IR NLO application.
NASA Astrophysics Data System (ADS)
Falkowski, M.; Kowalczyk, A.; Toliński, T.
2013-04-01
We present extended studies including the dc and ac magnetic susceptibility, magnetization, specific heat, electrical resistivity and magnetoresistivity measurements for the Dy5Si3 compound with the hexagonal Mn5Si3-type structure. The results indicate that this compound orders antiferromagnetically below TN=137 K. The magnetic properties of Dy5Si3 are mainly governed by the presence of the magnetic moments of Dy3+ ions. In the paramagnetic range, the magnetic susceptibility follows the Curie-Weiss law with μeff=10.57 μB/Dy, which is very close to the theoretical value of 10.6 μB. From the magnetometric, specific heat and transport data it has been found that below 50 K this compound reveals a non-collinear magnetic order, associated with a phase transition, probably of the first order type. On the basis of the thermodynamic approach, we report the magnetocaloric properties in the whole temperature range but concentrate mainly on the region around 50 K. The magnetocaloric effect was calculated in terms of the isothermal magnetic entropy change ΔSM as well as the adiabatic temperature change ΔTad using the specific heat data. In spite of the only moderate ΔSM values a significant relative cooling power has been observed.
Bondu, Flavie; Quertinmont, Jean; Rodriguez, Vincent; Pozzo, Jean-Luc; Plaquet, Aurélie; Champagne, Benoît; Castet, Frédéric
2015-12-14
The nonlinear optical (NLO) properties of a double photochrome molecular switch are reported for the first time by considering the four trans forms of a dithienylethene-indolinooxazolidine hybrid. The four forms are characterized by means of hyper-Rayleigh scattering (HRS) experiments and quantum chemical calculations. Experimental measurements provide evidence that the pH- and light-triggered transformations between the different forms of the hybrid are accompanied by large variations of the first hyperpolarizability, which makes this compound an effective multistate NLO switch. Quantum chemical calculations conducted at the time-dependent Hartree-Fock and time-dependent DFT levels agree with the experimental data and allow a complete rationalization of the NLO responses of the different forms. The HRS signal of the forms with an open indolinooxazolidine moiety are more than one order of magnitude larger than that measured for the other forms, whereas the open/closed status of the dithienylethene subunit barely influences the dynamic NLO properties. However, extrapolation of the NLO responses to the static limit leads to univocally distinguishable intrinsic responses for three of the various forms. This hybrid system thus acts as a highly efficient multistate NLO switch for eventual exploitation in optical memory systems with multiple storage and nondestructive readout capacity. PMID:26560091
Muhammad, Shabbir
2015-06-01
Using density functional theory (DFT) methods, the nonlinear optical (NLO) properties have been calculated with strong donor-π-conjugation-acceptor configurations. The static first hyperpolarizability (β0) and dynamic (frequency dependent) electric field induced second harmonic generation (EFISHG) first hyperpolarizability (μβ) are calculated for all designed systems. Our DFT calculations show dithienophenazine merged TTF (2) holds larger β0 amplitudes (β0=21.04×10(3)a.u.) as compared to its corresponding compounds of TTF merged-difurophenazine (1), dicyclopentaphenazine (3) and dipyrrolophenazine (4) derivatives having β0 amplitudes of 16.25×10(3), 12.69×10(3), and 18.38×10(3)a.u., respectively. Furthermore, substitution of dimalononitrile [C(CN)2]2 groups at acceptor end of these compounds results in new derivatives 1a-4a, respectively. Interestingly, a butterfly effect on first hyperpolarizability of all systems 1a-4a has been spotted, which not only results in their robustly larger β0 amplitudes but also changes the increasing order of β0 amplitudes from systems 3<1<4<2 to 1a<2a<3a<4a at both PBE0/6-31G* and CAM-B3LYP/6-31+G* levels of theory. For example, the increase in β0 amplitudes of systems 1a, 2a, 3a and 4a are 3, 3, 5, and 19 times as compared with their corresponding non dimalononitrile derivatives at PBE0/6-31G* level of theory, respectively. Remarkably, unlike the static first hyperpolarizability, the dynamic EFISHG hyperpolarizability (μβω) has the largest value for system 4a with its amplitudes of 1378.59×10(-46) and 1349.40×10(-46)esu, at PBE0/6-31G* and CAM-B3LYP/6-31+G* levels of theory, respectively. TD-DFT calculations have been performed to trace the origin of first hyperpolarizability. It has been found that the lower transition energy and higher oscillator strengths cause robustly large amplitudes especially in systems 3a and 4a, which consequently stems in strong donor-π-conjugation-acceptor configuration of these
Guo, Sheng-Ping; Chi, Yang; Liu, Bin-Wen; Guo, Guo-Cong
2016-06-21
A novel pentanary selenide (K3I)[InB12(InSe4)3] was obtained via a high-temperature solid-state method. It crystallizes in the hexagonal space group P6322 which features an InSe4 tetrahedron consolidated B12 icosahedron and 1-D chain constructed by InSe6 octahedron and B12Se12 cluster alternatively connected along the c-axis. Second-order nonlinear optical property measurement shows that it is second harmonic generation-active. Theory calculation indicates that it is an indirect semiconductor with the energy gap of 1.15 eV. PMID:27265446
Willow, Soohaeng Yoo; Salim, Michael A.; Kim, Kwang S.; Hirata, So
2015-01-01
A direct, simultaneous calculation of properties of a liquid using an ab initio electron-correlated theory has long been unthinkable. Here we present structural, dynamical, and response properties of liquid water calculated by ab initio molecular dynamics using the embedded-fragment spin-component-scaled second-order many-body perturbation method with the aug-cc-pVDZ basis set. This level of theory is chosen as it accurately and inexpensively reproduces the water dimer potential energy surface from the coupled-cluster singles, doubles, and noniterative triples with the aug-cc-pVQZ basis set, which is nearly exact. The calculated radial distribution function, self-diffusion coefficient, coordinate number, and dipole moment, as well as the infrared and Raman spectra are in excellent agreement with experimental results. The shapes and widths of the OH stretching bands in the infrared and Raman spectra and their isotropic-anisotropic Raman noncoincidence, which reflect the diverse local hydrogen-bond environment, are also reproduced computationally. The simulation also reveals intriguing dynamic features of the environment, which are difficult to probe experimentally, such as a surprisingly large fluctuation in the coordination number and the detailed mechanism by which the hydrogen donating water molecules move across the first and second shells, thereby causing this fluctuation. PMID:26400690
Willow, Soohaeng Yoo; Salim, Michael A; Kim, Kwang S; Hirata, So
2015-01-01
A direct, simultaneous calculation of properties of a liquid using an ab initio electron-correlated theory has long been unthinkable. Here we present structural, dynamical, and response properties of liquid water calculated by ab initio molecular dynamics using the embedded-fragment spin-component-scaled second-order many-body perturbation method with the aug-cc-pVDZ basis set. This level of theory is chosen as it accurately and inexpensively reproduces the water dimer potential energy surface from the coupled-cluster singles, doubles, and noniterative triples with the aug-cc-pVQZ basis set, which is nearly exact. The calculated radial distribution function, self-diffusion coefficient, coordinate number, and dipole moment, as well as the infrared and Raman spectra are in excellent agreement with experimental results. The shapes and widths of the OH stretching bands in the infrared and Raman spectra and their isotropic-anisotropic Raman noncoincidence, which reflect the diverse local hydrogen-bond environment, are also reproduced computationally. The simulation also reveals intriguing dynamic features of the environment, which are difficult to probe experimentally, such as a surprisingly large fluctuation in the coordination number and the detailed mechanism by which the hydrogen donating water molecules move across the first and second shells, thereby causing this fluctuation. PMID:26400690
NASA Astrophysics Data System (ADS)
Li, Xiao-Hong; Mei, Zheng; Zhang, Xian-Zhou
2014-01-01
The vibrational frequencies of acetophenone thiosemicarbazone in the ground state have been calculated using density functional method (B3LYP) with 6-31G(d), 6-31G(d,p) and 6-311++G(d,p) basis sets. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exist Nsbnd H…N and Nsbnd H…S hydrogen bonds in the title compound, which play a major role in stabilizing the molecule and are confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as second-order NLO material. In addition, the frontier molecular orbitals were analyzed and the crystal structure obtained by molecular mechanics belongs to the Pbca space group, with lattice parameters Z = 8, a = 16.0735 Å, b = 7.1719 Å, c = 7.8725 Å, ρ = 0.808 g/cm3.
Li, Xiao-Hong; Mei, Zheng; Zhang, Xian-Zhou
2014-01-24
The vibrational frequencies of acetophenone thiosemicarbazone in the ground state have been calculated using density functional method (B3LYP) with 6-31G(d), 6-31G(d,p) and 6-311++G(d,p) basis sets. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exist N-H…N and N-H…S hydrogen bonds in the title compound, which play a major role in stabilizing the molecule and are confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as second-order NLO material. In addition, the frontier molecular orbitals were analyzed and the crystal structure obtained by molecular mechanics belongs to the Pbca space group, with lattice parameters Z=8, a=16.0735 Å, b=7.1719 Å, c=7.8725 Å, ρ=0.808 g/cm(3). PMID:24084483
Second-Order Footsteps Illusions.
Kitaoka, Akiyoshi; Anstis, Stuart
2015-12-01
In the "footsteps illusion", light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures-even though luminance-based neural motion detectors are blind to such edges. PMID:27551366
Second-Order Footsteps Illusions
Anstis, Stuart
2015-01-01
In the “footsteps illusion”, light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures—even though luminance-based neural motion detectors are blind to such edges. PMID:27551366
Second-order coherence of supercontinuum light.
Genty, Goëry; Surakka, Minna; Turunen, Jari; Friberg, Ari T
2010-09-15
We analyze the coherence properties of supercontinuum generated in photonic crystal fibers by applying the second-order coherence theory of nonstationary light. Using an ensemble of simulated realizations, we construct two-frequency cross-spectral density and two-time mutual coherence functions. This allows us to introduce measures of temporal and spectral coherence. We show that, in the long-pulse regime, supercontinuum light can be decomposed into a sum of coherent and quasi-stationary contributions. Our approach and findings are also applicable in the short-pulse regime. PMID:20847777
Zhang, Ting; Ma, Nana; Yan, Likai; Wen, Shizheng; Ma, Tengying; Su, Zhongmin
2013-11-01
The second-order nonlinear optical (NLO) properties of hybrid complexes via coordination interaction between porphyrin and Keggin-type polyoxometalates (POMs) α-[MSiW11O39](3-) (M=Nb(V) or V(V)) are investigated by time-dependent density functional theory (TDDFT). The calculated results show that this kind of organic-inorganic hybrid complexes possesses remarkably large molecular second-order NLO polarizability, especially for the ZnP3P-C≡C-4-Py-[VSiW11O39](3-) (complex 4), which has a computed β0 value of 261,410 a.u. and might be an excellent second-order NLO material. The effects of substituted metal atom (M), metalloporphyrin, and π-conjugation on NLO response are analyzed, the substituted metal atom (M) with a large electronegativity, the metalloporphyrin, and the lengthening of π-conjugation are helpful in enhancing the optical nonlinearity of these systems, which reveal the general rules to design the complexes with large optical nonlinearities. Furthermore, the solvent effect largely affects the first-order hyperpolarizability of the complex, it implies that the second-order polarizabilities increased with the increase of the solvent in polarity. PMID:24149319
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Visualization of second order tensor fields and matrix data
NASA Technical Reports Server (NTRS)
Delmarcelle, Thierry; Hesselink, Lambertus
1992-01-01
We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.
Source of second order chromaticity in RHIC
Luo, Y.; Gu, X.; Fischer, W.; Trbojevic, D.
2011-01-01
In this note we will answer the following questions: (1) what is the source of second order chromaticities in RHIC? (2) what is the dependence of second order chromaticity on the on-momentum {beta}-beat? (3) what is the dependence of second order chromaticity on {beta}* at IP6 and IP8? To answer these questions, we use the perturbation theory to numerically calculate the contributions of each quadrupole and sextupole to the first, second, and third order chromaticities.
Binocular combination of second-order stimuli.
Zhou, Jiawei; Liu, Rong; Zhou, Yifeng; Hess, Robert F
2014-01-01
Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements. PMID:24404180
Binocular Combination of Second-Order Stimuli
Zhou, Jiawei; Liu, Rong; Zhou, Yifeng; Hess, Robert F.
2014-01-01
Phase information is a fundamental aspect of visual stimuli. However, the nature of the binocular combination of stimuli defined by modulations in contrast, so-called second-order stimuli, is presently not clear. To address this issue, we measured binocular combination for first- (luminance modulated) and second-order (contrast modulated) stimuli using a binocular phase combination paradigm in seven normal adults. We found that the binocular perceived phase of second-order gratings depends on the interocular signal ratio as has been previously shown for their first order counterparts; the interocular signal ratios when the two eyes were balanced was close to 1 in both first- and second-order phase combinations. However, second-order combination is more linear than previously found for first-order combination. Furthermore, binocular combination of second-order stimuli was similar regardless of whether the carriers in the two eyes were correlated, anti-correlated, or uncorrelated. This suggests that, in normal adults, the binocular phase combination of second-order stimuli occurs after the monocular extracting of the second-order modulations. The sensory balance associated with this second-order combination can be obtained from binocular phase combination measurements. PMID:24404180
NASA Astrophysics Data System (ADS)
Anitha, K.; Balachandran, V.
2015-07-01
Vibrational spectral analysis and quantum chemical computations based on density functional theory have been performed on the N-(2-cyanoethyl)-N-butylaniline. The geometry, structural properties, intermolecular hydrogen bond, and harmonic vibrational frequencies of the title molecule have been investigated with the help of DFT (B3LYP) and LC-DFT (CAM-B3LYP) method. Molecular electrostatic potential (MEP) have been performed. The various intramolecular interactions have been exposed by natural bond orbital analysis. The distribution of atomic charges and bending of natural hybrid orbitals also reflect the presence of intramolecular hydrogen bonding. Global reactivity and local reactivity descriptors of the title molecule have been calculated. The analysis of the electron density of HOMO and LUMO gives an idea of the delocalization and low value of energy gap indicated the electron transport in the molecule and thereby NLO activity. The effect of solvent on second-order NLO properties has been studied using polarized continuum model (PCM) in the tetrahydrofuran (THF) solution. The solvent leads to a slight enhancement of the NLO responses for the studied complexes relevant to their NLO responses in gas phase. The electronic absorption spectra were investigated by the TDDFT methods. The frequency-dependent first hyperpolarizabilities of the N-(2-cyanoethyl)-N-butylaniline were also evaluated. The 1H and 13C NMR chemical shifts have been calculated by gauge-indepedent atomic orbital (GIAO) method with B3LYP/6-311++G(d, p) approach.
The second-order gravitational red shift
NASA Technical Reports Server (NTRS)
Jaffe, J.
1973-01-01
The direct measurement of the nonlinear term of the gravitational field equations by using very stable clocks is discussed along with measuring the perhelion advance of a planet or satellite. These are considered measurements of the second-order gravitational red shift. The exact expression for the frequency shift of light in a gravitational field is derived. Other topics discussed include: The Doppler-cancelling technique; the second-order red shift in a spherically symmetric gravitational field; finite signal transit time; and the reality and interpretation of coordinates in the second-order red shift experiment.
Correction of second order chromaticity at Tevatron
Valishev, A.; Annala, G.; Lebedev, V.; Moore, R.S.; /Fermilab
2007-06-01
Correction of the second order betatron tune chromaticity is essential for operation at the working point near half integer resonance which is proposed as one of the ways to improve performance of the Tevatron. In this report the new chromaticity correction scheme with split sextupole families is described. Details of implementation and commissioning at the present working point are discussed.
Nine Practices of Second Order Schools
ERIC Educational Resources Information Center
Brown, Bill; Tucker, Patrick; Williams, Thomas L.
2012-01-01
Many schools are in some stage of implementing differentiated instruction, with some already in what Carol Tomlinson describes in "The Differentiated School" as "second order change," where the entire school practices differentiation. In high-performing schools, differentiation has proved to be an effective instructional strategy; in classroom…
Second-Order Conditioning in "Drosophila"
ERIC Educational Resources Information Center
Tabone, Christopher J.; de Belle, J. Steven
2011-01-01
Associative conditioning in "Drosophila melanogaster" has been well documented for several decades. However, most studies report only simple associations of conditioned stimuli (CS, e.g., odor) with unconditioned stimuli (US, e.g., electric shock) to measure learning or establish memory. Here we describe a straightforward second-order conditioning…
Solution of second order supersymmetrical intertwining relations in Minkowski plane
NASA Astrophysics Data System (ADS)
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Textural segmentation, second-order statistics, and textural elements.
Beck, J
1983-01-01
Beck (1972, 1973) hypothesized that textural segmentation occurs strongly on the basis of simple properties such as brightness, color, size, and the slopes of contours and lines of the elemental descriptors of a texture or textural elements. The experiment reported supports the hypothesis that specific stimulus features, rather than second-order statistics, account for textural segmentation. The results agree with Julesz (1981a,b) who has reported evidence disproving his original conjecture of the importance of second-order statistics. Julesz (1981a,b) now hypothesizes textural segmentation to be a function of local features which he called textons. Textons are features that give textural segmentation when textures have identical second-order statistics. The two hypotheses are to date in complete agreement on the stimulus features producing textural segmentation, and the experiment reported is consistent with both. PMID:6626590
Second-Order Invariants and Holography
NASA Astrophysics Data System (ADS)
Luongo, Orlando; Bonanno, Luca; Iannone, Gerardo
2012-12-01
Motivated by recent works on the role of the holographic principle in cosmology, we relate a class of second-order Ricci invariants to the IR cutoff characterizing the holographic dark energy density. The choice of second-order invariants provides an invariant way to account the problem of causality for the correct cosmological cutoff, since the presence of event horizons is not an a priori assumption. We find that these models work fairly well, by fitting the observational data, through a combined cosmological test with the use of SNeIa, BAO and CMB. This class of models is also able to overcome the fine-tuning and coincidence problems. Finally, to make a comparison with other recent models, we adopt the statistical tests AIC and BIC.
Calculating Second-Order Effects in MOSFET's
NASA Technical Reports Server (NTRS)
Benumof, Reuben; Zoutendyk, John A.; Coss, James R.
1990-01-01
Collection of mathematical models includes second-order effects in n-channel, enhancement-mode, metal-oxide-semiconductor field-effect transistors (MOSFET's). When dimensions of circuit elements relatively large, effects neglected safely. However, as very-large-scale integration of microelectronic circuits leads to MOSFET's shorter or narrower than 2 micrometer, effects become significant in design and operation. Such computer programs as widely-used "Simulation Program With Integrated Circuit Emphasis, Version 2" (SPICE 2) include many of these effects. In second-order models of n-channel, enhancement-mode MOSFET, first-order gate-depletion region diminished by triangular-cross-section deletions on end and augmented by circular-wedge-cross-section bulges on sides.
Visualizing second order tensor fields with hyperstreamlines
NASA Technical Reports Server (NTRS)
Delmarcelle, Thierry; Hesselink, Lambertus
1993-01-01
Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.
Spacetime encodings. III. Second order Killing tensors
Brink, Jeandrew
2010-01-15
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.
Second order Kerr-Newman time delay
NASA Astrophysics Data System (ADS)
He, G.; Lin, W.
2016-01-01
The explicit form for the post-Newtonian gravitational time delay of light signals propagating on the equatorial plane of a Kerr-Newman black hole is derived. Based on the null geodesic in Kerr-Newman spacetime, we adopt the iterative method to calculate the time delay. Our result reduces to the previous formulation for the Kerr black hole if we drop the contribution from the electrical charge. Our time-delay formula for the Reissner-Nordström geometry is different from the previous publication [Phys. Rev. D 69, 023002 (2004)], in which the largest second order contribution to the time delay is missing.
Analysis of second-order gratings
Hardy, A.; Welch, D.F.; Streifer, W. )
1989-10-01
The authors report the results of a second-order grating analysis. The gratings are used as distributed Bragg reflectors in surface-emitting lasers, which are currently being fabricated in several laboratories. The gratings provide reflection, output coupling, and power transmission to other gain segments for purposes of injection locking. The analysis determines these quantities for arbitrary-shaped grating teeth and includes the presence of a substrate reflector to reduce the radiated power in that direction. The reflector is shown to be effective, but only if it can be precisely positioned. Examples illustrating variations in dimensions, tooth shapes and heights, waveguide loss, and detuning are included.
Experimental Measurement of the Second-Order Coherence of Supercontinuum
NASA Astrophysics Data System (ADS)
Närhi, Mikko; Turunen, Jari; Friberg, Ari T.; Genty, Goëry
2016-06-01
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources.
Experimental Measurement of the Second-Order Coherence of Supercontinuum.
Närhi, Mikko; Turunen, Jari; Friberg, Ari T; Genty, Goëry
2016-06-17
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources. PMID:27367389
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
First- and second-order Poisson spots
NASA Astrophysics Data System (ADS)
Kelly, William R.; Shirley, Eric L.; Migdall, Alan L.; Polyakov, Sergey V.; Hendrix, Kurt
2009-08-01
Although Thomas Young is generally given credit for being the first to provide evidence against Newton's corpuscular theory of light, it was Augustin Fresnel who first stated the modern theory of diffraction. We review the history surrounding Fresnel's 1818 paper and the role of the Poisson spot in the associated controversy. We next discuss the boundary-diffraction-wave approach to calculating diffraction effects and show how it can reduce the complexity of calculating diffraction patterns. We briefly discuss a generalization of this approach that reduces the dimensionality of integrals needed to calculate the complete diffraction pattern of any order diffraction effect. We repeat earlier demonstrations of the conventional Poisson spot and discuss an experimental setup for demonstrating an analogous phenomenon that we call a "second-order Poisson spot." Several features of the diffraction pattern can be explained simply by considering the path lengths of singly and doubly bent paths and distinguishing between first- and second-order diffraction effects related to such paths, respectively.
Synchronization from Second Order Network Connectivity Statistics
Zhao, Liqiong; Beverlin, Bryce; Netoff, Theoden; Nykamp, Duane Q.
2011-01-01
We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates. PMID:21779239
Second order optical nonlinearity in silicon by symmetry breaking
NASA Astrophysics Data System (ADS)
Cazzanelli, Massimo; Schilling, Joerg
2016-03-01
Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ(2)) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ(2) in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on "competing" concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.
Espa, Davide; Pilia, Luca; Makedonas, Christodoulos; Marchiò, Luciano; Mercuri, M Laura; Serpe, Angela; Barsella, Alberto; Fort, Alain; Mitsopoulou, Christiana A; Deplano, Paola
2014-01-21
The mixed-ligand complexes [M(II)(Et2dazdt)(mnt)] (M = Ni, 1; Pd, 2; Pt, 3) [Et2dazdt = N,N'-diethyl-perhydrodiazepine-2,3-dithione; mnt = maleonitrile-2,3-dithiolate] have been prepared and fully characterized. X-ray diffractometric studies on 1-3 (the structure of 1 was already known) show that the crystals are isostructural (triclinic, P-1), and two independent molecular entities are present in the unit cell. These entities differ in the orientation of the ethyl substituents with respect to the epta-atomic ring. In the C2S2MS2C2 dithiolene core the four sulfur atoms define a square-planar coordination environment of the metal where the M-S bond distances involving the two ligands are similar, while the C-S bond distances in the C2S2 units exhibit a significant difference in Et2dazdt (dithione) and mnt (dithiolato) ligands. 1-3 show in the visible region one or two moderately strong absorption peaks, having ligand-to-ligand charge-transfer (CT) character with some contribution of the metal, and show negative solvatochromism and molecular quadratic optical nonlinearity, which was determined by the EFISH (electric-field-induced second-harmonic generation) technique. These complexes are redox active and show two reversible reduction waves and one irreversible oxidation wave. Theoretical calculations based on DFT and TD-DFT calculations on complexes 1-3 as well as on [Pt(Bz2pipdt)(mnt)] (4) and [Pt(Bz2pipdt)(dmit)] (5) highlight the factors which affect the optical properties of these second-order redox-active NLO chromophores. Actually, the torsion angle of the dithione system (δ2) inversely correlates either with the oscillator strengths of the main transition of the complexes or with their beta values. The high beta value of 5 can be attributed both to its lowest torsion angles and to the extent of the π system of its dithiolate ligand, dmit. PMID:24405208
A second order parameter for 3SAT
Sandholm, T.W.
1996-12-31
The 3-satisfiability problem (3SAT) has had a central role in the study of complexity. It was recently found that 3SAT instances transition sharply from satisfiable to nonsatisfiable as the ratio of clauses to variables increases. Because this phase transition is so sharp, the ratio - an order parameter - can be used to predict satisfiability. This paper describes a second order parameter for 3SAT. Like the classical order parameter, it can be computed in linear time, but it analyzes the structure of the problem instance more deeply. We present an analytical method for using this new order parameter in conjunction with the classical one to enhance satisfiability prediction accuracy. The assumptions of the method are verified by rigorous statistical testing. The method significantly increases the satisfiability prediction accuracy over using the classical order parameter alone. Hardness - i.e. how long it takes to determine satisfiability - results for one complete and one incomplete algorithm from the literature are also presented as a function of the two order parameters. The importance of new order parameters lies in the fact that they refine the locating of satisfiable vs. nonsatisfiable and hard vs. easy formulas in the space of all problem instances by adding a new dimension in the analysis.
Second-order parametrized-post-Newtonian Lagrangian
Benacquista, M.J. )
1992-02-15
A many-body Lagrangian to second post-Newtonian order using an extension of the parametrized-post-Newtonian (PPN) formalism is introduced and the properties of new parameters are explored. A parametrized gauge transformation is developed to permit comparison with theories of gravity in a variety of different coordinate systems. A procedure to impose Lorentz invariance on a general second-order post-Newtonian Lagrangian is developed. The Lagrangian is then constrained to possess Lorentz invariance and a Lorentz-invariant'' gauge is introduced. The constrained Lagrangian is found to be described by ten new second-order PPN parameters. When the Lagrangian is further constrained to describe theories of gravity for which test particles move along geodesics, one of the ten new parameters is given entirely in terms of first-order PPN parameters, leaving only nine PPN parameters to describe the second-order gravitational interaction. A metric'' gauge is introduced which allows the metric to be easily found from the Lagrangian and is shown to reduce to the gauge associated with the canonical formalism of Arnowitt, Deser, and Misner when the general-relativity values of the PPN parameters are used.
Analysis of implicit second-order upwind-biased stencils
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Warren, Gary P.
1993-01-01
Truncation error and stability properties of several implicit upwind schemes for the two-dimensional Euler equations are examined. The schemes use linear data reconstruction methods to achieve second-order flux integrations where the implicit Jacobian operators are first order. The stability properties of the schemes are examined by a Von Neumann analysis of the linearized, constant-coefficient Euler equations. The choice of the data reconstruction method used to evaluate the flux integral has a dramatic effect on the convergence properties of the implicit solution method. In particular, the typical one-dimensional data reconstruction methods used with structured grids exhibit poor convergence properties compared to the unstructured grid method considered. Of the schemes examined, the one with the superior convergence properties is well-suited for both unstructured and structured grids, which has important implications for the design of implicit methods.
Entanglement in a second-order quantum phase transition
Vidal, Julien; Palacios, Guillaume; Mosseri, Remy
2004-02-01
We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point {lambda}{sub c} in the thermodynamical limit. We also show that there exists a value {lambda}{sub 0}{>=}{lambda}{sub c} above which the ground state is not spin squeezed despite a nonvanishing concurrence.
Morrison, Erin S; Badyaev, Alexander V
2016-08-01
The network of the interactions among genes, proteins, and metabolites delineates a range of potential phenotypic diversifications in a lineage, and realized phenotypic changes are the result of differences in the dynamics of the expression of the elements and interactions in this deterministic network. Regulatory mechanisms, such as hormones, mediate the relationship between the structural and dynamic properties of networks by determining how and when the elements are expressed and form a functional unit or state. Changes in regulatory mechanisms lead to variable expression of functional states of a network within and among generations. Functional properties of network elements, and the magnitude and direction of evolutionary change they determine, depend on their location within a network. Here, we examine the relationship between network structure and the dynamic mechanisms that regulate flux through a metabolic network. We review the mechanisms that control metabolic flux in enzymatic reactions and examine structural properties of the network locations that are targets of flux control. We aim to establish a predictive framework to test the contributions of structural and dynamic properties of deterministic networks to evolutionary diversifications. PMID:27252203
Design of optimal second-order state estimators
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.
1991-01-01
The present consideration of the design of online computation-saving second-order state estimators for second-order vector-matrix differential systems proposes a class of such estimators which is proven to possess guaranteed convergence. A class of optimal second-order estimators is then obtained, and the conditions required for optimality are identified. The estimator proposed offers high performance in conjunction with online computation reductions sufficiently great to allow the estimation of the large number of state variables associated with control of large, flexible space structures represented by high-dimensional second-order systems.
The Morse Oscillator and Second-Order Perturbation Theory
NASA Astrophysics Data System (ADS)
Pettitt, B. A.
1998-09-01
This article shows how the energies of the Morse oscillator are obtained exactly from a second-order perturbation expansion in a harmonic oscillator basis. This exercise is recommended for its instructional value in intermediate quantum chemistry, in that the second-order term is entirely tractable, it arises within an important context (anharmonicity of vibrations), and it gives the right answer.
Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine: Preprint
Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A.
2014-07-01
The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at the MARIN offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST in the future. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method has been applied to the OC4-DeepCwind semisubmersible platform, supporting the NREL 5-MW baseline wind turbine. The loads and response of the system due to the second-order hydrodynamics are analysed and compared to first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads and induced response data are compared to the loads and motions induced by aerodynamic loading as solved by FAST.
Second-order state estimation experiments using acceleration measurements
NASA Technical Reports Server (NTRS)
Belvin, W. K.
1992-01-01
The estimation of dynamic states for feedback control of structural systems using second-order differential equations and acceleration measurements is described. The formulation of the observer model, and the design of the observer gains is discussed in detail. It is shown the second-order observer is highly stable because the stability constraints on the observer gains are model independent. The limitation of the proposed observer is the need for 'nearly' collocated actuators and accelerometers. Experimental results using a control-structure interaction testbed are presented that show the second-order observer provided more stability than a Kalman filter estimator without decreasing closed-loop performance.
Study of second order upwind differencing in a recirculating flow
NASA Technical Reports Server (NTRS)
Vanka, S. P.
1985-01-01
The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing.
A study of second-order supersonic flow theory
NASA Technical Reports Server (NTRS)
Van Dyke, Milton D
1952-01-01
Second-order solutions of supersonic-flow problems are sought by iteration, using the linearized solution as the first step. For plane and axially symmetric flows, particular solutions of the iteration equation are discovered which reduce the second-order problem to an equivalent linearized problem. Comparison of second-order solutions with exact and numerical results shows great improvement over linearized theory. For full three-dimensional flow, only a partial particular solution is found. The inclined cone is solved, and the possibility of treating more general problems is considered.
Method to render second order beam optics programs symplectic
Douglas, D.; Servranckx, R.V.
1984-10-01
We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs.
Drift kinetic equation exact through second order in gyroradius expansion
Simakov, Andrei N.; Catto, Peter J.
2005-01-01
The drift kinetic equation of Hazeltine [R. D. Hazeltine, Plasma Phys. 15, 77 (1973)] for a magnetized plasma of arbitrary collisionality is widely believed to be exact through the second order in the gyroradius expansion. It is demonstrated that this equation is only exact through the first order. The reason is that when evaluating the second-order gyrophase dependent distribution function, Hazeltine neglected contributions from the first-order gyrophase dependent distribution function, and then used this incomplete expression to derive the equation for the gyrophase independent distribution function. Consequently, the second-order distribution function and the stress tensor derived by this approach are incomplete. By relaxing slightly Hazeltine's orderings one is able to obtain a drift kinetic equation accurate through the second order in the gyroradius expansion. In addition, the gyroviscous stress tensor for plasmas of arbitrary collisionality is obtained.
Oscillation theorems for second order nonlinear forced differential equations.
Salhin, Ambarka A; Din, Ummul Khair Salma; Ahmad, Rokiah Rozita; Noorani, Mohd Salmi Md
2014-01-01
In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature. PMID:25077054
Fast second-order consensus via predictive mechanisms
NASA Astrophysics Data System (ADS)
Wu, Jie; Zhang, Li-Yi; Bai, Yu
2015-01-01
In this paper, we discuss second-order consensus problems for multi-agent systems with dynamic agents and fixed topologies. A new second-order consensus protocol incorporating the predictive mechanism is proposed and a convergence analysis related to the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network is provided. We establish a direct connection between the eigenvalues of the Laplacian matrix and parameters of the proposed second-order consensus model, and we compute a lower bound for the sum of parameters. It is proved under general conditions related to the second-order consensus protocol and the network topology that the asymptotic consensus is achieved and the convergence speed is increased via designing a state predictor. Finally, simulation results are provided to verify the effectiveness of the proposed protocol and the analytical claims.
Orthogonal canonical forms for second-order systems
NASA Technical Reports Server (NTRS)
Williams, Trevor; Laub, Alan
1989-01-01
The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.
Orthogonal canonical forms for second-order systems
NASA Technical Reports Server (NTRS)
Williams, Trevor; Laub, Alan J.
1992-01-01
It is shown that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations. However, it is also shown that such an orthogonal reduction is always possible for the modal damping commonly assumed for models of flexible structures. It is shown that modally damped models can be orthogonally reduced to a new triangular second-order Schur form.
Superconvergent discontinuous Galerkin methods for second-order elliptic problems
NASA Astrophysics Data System (ADS)
Cockburn, Bernardo; Guzman, Johnny; Wang, Haiying
2009-03-01
We identify discontinuous Galerkin methods for second-order elliptic problems in several space dimensions having superconvergence properties similar to those of the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods. These methods use polynomials of degree kge0 for both the potential as well as the flux. We show that the approximate flux converges in L^2 with the optimal order of k+1 , and that the approximate potential and its numerical trace superconverge, in L^2 -like norms, to suitably chosen projections of the potential, with order k+2 . We also apply element-by-element postprocessing of the approximate solution to obtain new approximations of the flux and the potential. The new approximate flux is proven to have normal components continuous across inter-element boundaries, to converge in L^2 with order k+1 , and to have a divergence converging in L^2 also with order k+1 . The new approximate potential is proven to converge with order k+2 in L^2 . Numerical experiments validating these theoretical results are presented.
A novel second-order flux splitting for ideal magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Borah, Kalpajyoti; Natarajan, Ganesh; Dass, Anoop K.
2016-05-01
A new flux splitting scheme based on wave-particle behaviour is developed for one-dimensional ideal magnetohydrodynamics. We exploit the idea that while ideal magnetohydrodynamics equations are non-convex with non-homogeneous fluxes as opposed to their hydrodynamic counterparts, they exhibit an overall wave-like structure. The proposed approach splits the flux vector into three distinct parts: the particle-like transport part and the wave-like pressure and magnetic parts, with the latter vanishing for pure hydrodynamics. The pressure part of the fluxes satisfy homogeneity property and the split flux Jacobians are constructed with a provision to regulate the numerical dissipation. The magnetic part of the fluxes however is non-homogeneous and is treated using a central scheme with artificial viscosity. This disparate treatment of the individual components of the total flux vector results in a scheme with a central-upwind character that can be implemented with low computational effort. Referred to as Magneto-acoustic Wave Particle Splitting (MWPS) scheme, it is extended to second-order accuracy by using slope limiters incorporated through the solution-dependent weighted least squares approach for gradient calculations. Several one-dimensional MHD problems are numerically solved to highlight the accuracy, positivity preservation and robustness of the MWPS scheme and comparative studies show that MWPS performs at least as well as the Advection Upstream Splitting Method (AUSM) and even outperforms it for some test cases.
[Second-order retrospective revaluation in human contingency learning].
Numata, Keitaro; Shimazaki, Tsuneo
2009-04-01
We demonstrated second-order retrospective revaluation with three cues (T1, T2, and C) and an outcome, in human contingency learning. Experimental task, PC-controlled video game in which participants were required to observe about the relations between firing missiles and the tank destruction, consisted of three training phases and two rating phases. Groups C+ and C- consisted of same first two training phases, CT+ (cues C and T with an outcome) and T1T2+ followed by C+, or C- training for Groups C+, C-, respectively. In rating phases, it is clearly demonstrated that the judgment of predictive value for the outcome of the T2 were higher by C+ training (second-order unovershadowing) and lowered by C- training (second-order backward blocking). The results for Groups RC+ and RC-, in which the orders of the first two training phase for Groups C+ and C- were interchanged, also showed second-order unovershadowing and second-order backward blocking. These results, the robustness of second-order retrospective revaluation against the order of the first training phases, can be explained by the extended comparator hypothesis and probabilistic contrast model. However, these results cannot be explained by traditional associative learning models. PMID:19489431
Second-Order Olfactory-Mediated Fear-Potentiated Startle
Paschall, Gayla Y.; Davis, Michael
2002-01-01
Recently, we reported that discrete (4-sec) olfactory cues paired with footshock serve as effective conditioned stimuli (CSs) for potentiating the acoustic startle response in rats using the fear-potentiated startle paradigm. Because odors are such salient cues for the rat, and because of the robust olfactory conditioning observed previously, the current studies investigated second-order fear conditioning using olfactory and visual cues. In Experiments 1 and 2, we used a small number of first-order and second-order training trials on separate days to investigate second-order fear-potentiated startle. Significant potentiated startle was observed in animals receiving Paired/Paired training in both studies, but surprisingly, control animals in the Unpaired/Paired group (Exp. 1) also showed significant potentiated startle to a light S2 at testing. These findings are addressed in the Discussion. Overall, the results of both experiments suggest that olfactory cues serve as efficient S1 and S2 stimuli in second-order fear-potentiated startle paradigms when only a small number of first and second-order training trials are presented. PMID:12464699
Second-order quasinormal mode of the Schwarzschild black hole
Nakano, Hiroyuki; Ioka, Kunihito
2007-10-15
We formulate and calculate the second-order quasinormal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational waves (GW) from a distorted BH, the so-called ringdowns, are well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with a high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second-order Zerilli equation by implementing the modified Leaver continued fraction method. The second-order QNM frequencies are found to be twice the first-order ones, and the GW amplitude is up to {approx}10% that of the first order for the binary BH mergers. Since the second-order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular, the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs, and (iii) to measure the distance to the BH.
Some restrictions on the existence of second order limit language
NASA Astrophysics Data System (ADS)
Ahmad, Muhammad Azrin; Sarmin, Nor Haniza; Yusof, Yuhani; Fong, Wan Heng
2015-10-01
The cut and paste phenomenon on DNA molecules with the presence of restriction enzyme and appropriate ligase has led to the formalism of mathematical modelling of splicing system. A type of splicing system named Yusof-Goode splicing system is used to present the transparent behaviour of the DNA splicing process. The limit language that is defined as the leftover molecules after the system reaches its equilibrium point has been extended to a second order limit language. The non-existence of the second order limit language biologically has lead to this study by using mathematical approach. In this paper, the factors that restrict the formation of the second order limit language are discussed and are presented as lemmas and theorem using Y-G approach. In addition, the discussion focuses on Yusof- Goode splicing system with at most two initial strings and two rules with one cutting site and palindromic crossing site and recognition sites.
Weak value amplification via second-order correlated technique
NASA Astrophysics Data System (ADS)
Ting, Cui; Jing-Zheng, Huang; Xiang, Liu; Gui-Hua, Zeng
2016-02-01
We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification (WVA) experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed. Project supported by the Union Research Centre of Advanced Spaceflight Technology (Grant No. USCAST2013-05), the National Natural Science Foundation of China (Grant Nos. 61170228, 61332019, and 61471239), and the High-Tech Research and Development Program of China (Grant No. 2013AA122901).
Second order perturbations during inflation beyond slow-roll
Huston, Ian; Malik, Karim A. E-mail: k.malik@qmul.ac.uk
2011-10-01
We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.
Deflection of light to second order in conformal Weyl gravity
NASA Astrophysics Data System (ADS)
Sultana, Joseph
2013-04-01
We reexamine the deflection of light in conformal Weyl gravity obtained in Sultana and Kazanas (2010), by extending the calculation based on the procedure by Rindler and Ishak, for the bending angle by a centrally concentrated spherically symmetric matter distribution, to second order in M/R, where M is the mass of the source and R is the impact parameter. It has recently been reported in Bhattacharya et al. (JCAP 09 (2010) 004; JCAP 02 (2011) 028), that when this calculation is done to second order, the term γr in the Mannheim-Kazanas metric, yields again the paradoxical contribution γR (where the bending angle is proportional to the impact parameter) obtained by standard formalisms appropriate to asymptotically flat spacetimes. We show that no such contribution is obtained for a second order calculation and the effects of the term γr in the metric are again insignificant as reported in our earlier work.
Second-order wave effects on TLP tendon tension responses
Xue, H.; Mercier, R.S.
1996-12-31
This paper presents a general procedure for analyzing the second-order wave effects on the tendon tension responses of a TLP. The approach solves both first- and second-order equation of motions for a TLP system in frequency domain. Viscous effects are included in the form of statistically linearized damping coefficients. An efficient algorithm has been devised for reducing the burden of second-order wave diffraction analysis, which selects the interacting frequency pairs according to springing frequency of interest to minimize the cost of computing quadratic transfer functions (QTFs) and allow accurate interpolation of QTFs. Moment statistics of the tension process are computed through an eigenvalue analysis. The developed method is applied to analyze the tendon tension responses of a TLP design in water depth of 3,000 ft.
Controlling flexible structures with second order actuator dynamics
NASA Technical Reports Server (NTRS)
Inman, Daniel J.; Umland, Jeffrey W.; Bellos, John
1989-01-01
The control of flexible structures for those systems with actuators that are modeled by second order dynamics is examined. Two modeling approaches are investigated. First a stability and performance analysis is performed using a low order finite dimensional model of the structure. Secondly, a continuum model of the flexible structure to be controlled, coupled with lumped parameter second order dynamic models of the actuators performing the control is used. This model is appropriate in the modeling of the control of a flexible panel by proof-mass actuators as well as other beam, plate and shell like structural numbers. The model is verified with experimental measurements.
The Poisson equation at second order in relativistic cosmology
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A. E-mail: Adam.Christopherson@nottingham.ac.uk
2013-08-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.
Static second-order polarizabilities of aminobenzophenones and nitrobenzophenones
NASA Technical Reports Server (NTRS)
Moore, Craig E.; Cardelino, Beatriz H.
1991-01-01
Static-field theoretical studies on molecular second-order polarizabilities (beta) of benzophenone derivatives were performed. Calculations were based on the use of shaped electric fields and semiempirical Hamiltonians. Either an electron-donating (amine) or an electron-withdrawing (nitro) substituent was incorporated into a phenyl ring of benzophenone; the phenyl rings of benzophenone were oriented either coplanar or perpendicular to the carbonyl. The change in charge transfer with respect to the electrophilic character of the carbonyl group was monitored to determine its effect on the molecular second-order polarizability. Calculations were performed for all constitutional isomers of the two benzophenone derivatives.
Kubo Formulas for Second-Order Hydrodynamic Coefficients
Moore, Guy D.; Sohrabi, Kiyoumars A.
2011-03-25
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity {eta} and on five additional ''second-order'' hydrodynamical coefficients {tau}{sub {Pi}}, {kappa}, {lambda}{sub 1}, {lambda}{sub 2}, and {lambda}{sub 3}. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient {lambda}{sub 3} can be evaluated directly by Euclidean means and does not in general vanish.
Second-order subsonic airfoil theory including edge effects
NASA Technical Reports Server (NTRS)
Van Dyke, Milton D
1956-01-01
Several recent advances in plane subsonic flow theory are combined into a unified second-order theory for airfoil sections of arbitrary shape. The solution is reached in three steps: the incompressible result is found by integration, it is converted into the corresponding subsonic compressible result by means of the second-order compressibility rule, and it is rendered uniformly valid near stagnation points by further rules. Solutions for a number of airfoils are given and are compared with the results of other theories and of experiment. A straight-forward computing scheme is outlined for calculating the surface velocities and pressures on any airfoil at any angle of attack
Elasto-plastic model with second order defect density tensor
NASA Astrophysics Data System (ADS)
Cleja-Ţigoiu, Sanda
2011-05-01
The paper deals with a second order finite elasto-plastic model, which involves the defect density tensor, as a measure of the extra material defects existing in the damaged microstructure. The material behaviour is described with respect to an anholonomic configuration, which is introduced through the second order plastic deformation, consisting in plastic distortion and plastic connection. The defect density tensor enters the expression of the plastic connection through its gradient and represents a measure of non-metricity. The constitutive and evolution equations are derived to be compatible with the free energy imbalance. The evolution equation for the defect density tensor is non-local and coupled with the plastic distortion.
A novel second order fast decoupled load flow method in polar coordinates
Nanda, J.; Kothari, D.P.; Srivastava, S.C. )
1988-01-01
This paper presents a novel and effective second order fast decoupled load flow model in polar co-ordinates employing a totally different approach than used in existing second order methods in polar co-ordinates. This work eliminates the need for storing and computing repeatedly the second order terms by prudently injecting the elements of the Hessian matrix into the Jacobian. This results in a memory requirement at par with the usual fast decoupled load flow method. Investigations reveal that for well-behaved systems, the new method and the fast decoupled load flow method have practically the same convergence properties, whereas for certain ill-conditioned systems, the new method shows distinctly better convergence properties.
A New Factorisation of a General Second Order Differential Equation
ERIC Educational Resources Information Center
Clegg, Janet
2006-01-01
A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…
Second-order variational equations for N-body simulations
NASA Astrophysics Data System (ADS)
Rein, Hanno; Tamayo, Daniel
2016-07-01
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.
Second-order accurate nonoscillatory schemes for scalar conservation laws
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1989-01-01
Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.
Remarks on the second-order Seiberg-Witten maps
Trampetic, Josip; Wohlgenannt, Michael
2007-12-15
In this brief report, we discuss the Seiberg-Witten maps up to the second order in the noncommutative parameter {theta}. They add to the recently published solutions in [A. Alboteanu, T. Ohl, and R. Rueckl, Phys. Rev. D 76, 105018 (2007).]. Expressions for the vector, fermion, and Higgs fields are given explicitly.
Second-order sliding mode control with experimental application.
Eker, Ilyas
2010-07-01
In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve the performance of control systems. A Proportional + Integral + Derivative (PID) sliding surface is used for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show the feasibility and effectiveness of the proposed second-order sliding mode control and factors involved in the design. The second-order plant parameters are experimentally determined using input-output measured data. The results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control (SMC) and PID control. It is demonstrated that the proposed 2-SMC system improves the performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability. PMID:20413118
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.
Children's Understanding of Second-Order Mental States
ERIC Educational Resources Information Center
Miller, Scott A.
2009-01-01
The most popular topic in theory-of-mind research has been first-order false belief: the realization that it is possible to hold false beliefs about events in the world. A more advanced development is second-order false belief: the realization that it is possible to hold a false belief about someone else's belief. This article reviews research…
Second-Order Conditioning of Human Causal Learning
ERIC Educational Resources Information Center
Jara, Elvia; Vila, Javier; Maldonado, Antonio
2006-01-01
This article provides the first demonstration of a reliable second-order conditioning (SOC) effect in human causal learning tasks. It demonstrates the human ability to infer relationships between a cause and an effect that were never paired together during training. Experiments 1a and 1b showed a clear and reliable SOC effect, while Experiments 2a…
Modeling Ability Differentiation in the Second-Order Factor Model
ERIC Educational Resources Information Center
Molenaar, Dylan; Dolan, Conor V.; van der Maas, Han L. J.
2011-01-01
In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…
Pecuniary Effects, Second-Order Conditions, and the LRAC Curve.
ERIC Educational Resources Information Center
Comolli, Paul M.
2000-01-01
Explores the importance of second-order conditions in the cost-minimization problem confronting the monopsonistic employer of factor inputs. Describes an alternative approach to the presence of pecuniary effects that does not depend on the assumption that firms are monopsonistic in factor markets. (CMK)
Solving Second-Order Differential Equations with Variable Coefficients
ERIC Educational Resources Information Center
Wilmer, A., III; Costa, G. B.
2008-01-01
A method is developed in which an analytical solution is obtained for certain classes of second-order differential equations with variable coefficients. By the use of transformations and by repeated iterated integration, a desired solution is obtained. This alternative method represents a different way to acquire a solution from classic power…
Forward and Backward Second-Order Pavlovian Conditioning in Honeybees
ERIC Educational Resources Information Center
Hussaini, Syed Abid; Komischke, Bernhard; Menzel, Randolf; Lachnit, Harald
2007-01-01
Second-order conditioning (SOC) is the association of a neutral stimulus with another stimulus that had previously been combined with an unconditioned stimulus (US). We used classical conditioning of the proboscis extension response (PER) in honeybees ("Apis mellifera") with odors (CS) and sugar (US). Previous SOC experiments in bees were…
PREDICTIONS OF HIGHWAY EMISSIONS BY A SECOND ORDER CLOSURE MODEL
The dispersion of sulfur hexafluoride tracer and sulfate from automobile emissions in the immediate vicinity of a highway were estimated for conditions similar to those existing during the General Motors sulfate dispersion experiment conducted at a GM test track. A second-order c...
Second-Order Conditioning during a Compound Extinction Treatment
ERIC Educational Resources Information Center
Pineno, Oskar; Zilski, Jessica M.; Schachtman, Todd R.
2007-01-01
Two conditioned taste aversion experiments with rats were conducted to establish if a target taste that had received a prior pairing with illness could be subject to second-order conditioning during extinction treatment in compound with a flavor that also received prior conditioning. In these experiments, the occurrence of second-order…
Generalized Second-Order Partial Derivatives of 1/r
ERIC Educational Resources Information Center
Hnizdo, V.
2011-01-01
The generalized second-order partial derivatives of 1/r, where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a…
Green's function of the second order differential operator with involution
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sarsenbi, Abdisalam A.
2016-08-01
In the present paper, the Green's function of the second order differential operator L defined by formula L u =α u″ (x ) -u″ (-x ) =λ u (x ) ,-1
On the second-order tangent bundle with horizontal lift connection
NASA Astrophysics Data System (ADS)
Gezer, Aydin; Magden, Abdullah; Karaca, Kubra
2016-04-01
Let M be an n-dimensional differentiable manifold equipped with a torsion-free linear connection ∇ and T2 M be its second-order tangent bundle. The present paper aims to study some curvature properties of T2 M with respect to the horizontal lift connection H∇.
Theoretical study of second-order hyperpolarizability for nitrogen radical cation
NASA Astrophysics Data System (ADS)
Tarazkar, Maryam; Romanov, Dmitri A.; Levis, Robert J.
2015-05-01
We report calculations of the static and dynamic hyperpolarizabilities of the nitrogen radical cation in doublet state. The electronic contributions were computed analytically using density functional theory and multi-configurational self-consistent field method with extended basis sets for non-resonant excitation. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient, {{γ }(2)}, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The second-order optical properties of nitrogen radical cation have been calculated as a function of bond length starting with the neutral molecular geometry (S0 minimum) and stretching the N-N triple bond, reaching the ionic D0 relaxed geometry all the way toward dissociation limit, to investigate the effect of internuclear bond distance on second-order hyperpolarizability.
Symmetries of second-order PDEs and conformal Killing vectors
NASA Astrophysics Data System (ADS)
Tsamparlis, Michael; Paliathanasis, Andronikos
2015-06-01
We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first derivatives we show that the Lie point symmetries are given by the conformal algebra of the metric modulo a constraint involving the linear part of the PDE. Important elements in this class are the Klein-Gordon equation and the Laplace equation. We apply the general results and determine the Lie point symmetries of these equations in various general classes of Riemannian spaces. Finally we study the type II hidden symmetries of the wave equation in a Riemannian space with a Lorenzian metric.
Robust eigensystem assignment for second-order estimators
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Maghami, Peiman G.
1990-01-01
An approach for the robust eigensystem assignment of flexible structures using full state or output feedback is developed. Using the second-order dynamic equations, the approach can assign the eigenvalues of the system via velocity and displacement feedbacks, or acceleration and velocity feedbacks. The eigenvalues and eigenvectors of the system are assigned, via the second-order eigenvalue problem for the structural system, in two steps. First, an orthonormal basis spanning the attainable closed-loop eigenvector space corresponding to each desired closed-loop eigenvalue is generated using the Singular Value or QR decompositions. Second, a sequential procedure is used to choose a set of closed-loop eigenvectors that are as close as possible to the column space of a well-conditioned target matrix. Among the possible choices of the target matrix, the closest unitary matrix to the open-loop eigenvector matrix appears to be a suitable choice. A numerical example is given to illustrate the proposed algorithm.
On the second order spatiochromatic structure of natural images.
Provenzi, Edoardo; Delon, Julie; Gousseau, Yann; Mazin, Baptiste
2016-03-01
We provide a theoretical analysis of some empirical facts about the second order spatiochromatic structure of natural images in color. In particular, we show that two simple assumptions on the covariance matrices of color images yield eigenvectors made by the Kronecker product of Fourier features times the triad given by luminance plus color opponent channels. The first of these assumptions is second order stationarity while the second one is commutativity between color correlation matrices. The validity of these assumptions and the predicted shape of the PCA components of color images are experimentally observed on two large image databases. As a by-product of this experimental study, we also provide novel data to support an exponential decay law of the spatiochromatic covariance between pairs of pixels as a function of their spatial distance. PMID:26024561
A Second-Order Achromat Design Based on FODO Cell
Sun, Yipeng; /SLAC
2011-08-19
Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first order dispersion and provide betatron focusing. Similarly a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to generate an isochronous section, quadrupoles are again needed to tune the first order transfer matrix element R{sub 56} equaling zero. Usually sextupoles are needed to correct second order dispersion in the bending plane, for both the dogleg optics and the chicane (with quad) optics. In this paper, an alternative optics design is introduced, which is based on a simple FODO cell and does not need sextupoles assistance to form a second-order achromat. It may provide a similar function of either a dogleg or a bypass, by using 2 or 4 of such combined supercells.
First- and second-order charged particle optics
Brown, K.L.; Servranckx, R.V.
1984-07-01
Since the invention of the alternating gradient principle there has been a rapid evolution of the mathematics and physics techniques applicable to charged particle optics. In this publication we derive a differential equation and a matrix algebra formalism valid to second-order to present the basic principles governing the design of charged particle beam transport systems. A notation first introduced by John Streib is used to convey the essential principles dictating the design of such beam transport systems. For example the momentum dispersion, the momentum resolution, and all second-order aberrations are expressed as simple integrals of the first-order trajectories (matrix elements) and of the magnetic field parameters (multipole components) characterizing the system. 16 references, 30 figures.
An application of integral inequality to second order nonlinear oscillation
NASA Astrophysics Data System (ADS)
Kwong, Man Kam; Wong, James S. W.
A simple result concerning integral inequalities enables us to give an alternative proof of Waltman's theorem: lim t → ∞ ∝ t0a( s) ds = ∞ implies oscillation of the second order nonlinear equation y″( t) + a( t) f( y( t)) = 0; to prove an analog of Wintner's theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations, assuming that lim t → ∞ ∝ t0a( s) ds exists; and to give an alternative proof and to extend a result of Butler. An often used condition on the coefficient a( t) is given a more familiar equivalent form and an oscillation criterion involving this condition is established.
Relativistic second-order dissipative hydrodynamics at finite chemical potential
NASA Astrophysics Data System (ADS)
Jaiswal, Amaresh; Friman, Bengt; Redlich, Krzysztof
2015-12-01
Starting from the Boltzmann equation in the relaxation time approximation and employing a Chapman-Enskog like expansion for the distribution function close to equilibrium, we derive second-order evolution equations for the shear stress tensor and the dissipative charge current for a system of massless quarks and gluons. The transport coefficients are obtained exactly using quantum statistics for the phase space distribution functions at non-zero chemical potential. We show that, within the relaxation time approximation, the second-order evolution equations for the shear stress tensor and the dissipative charge current can be decoupled. We find that, for large values of the ratio of chemical potential to temperature, the charge conductivity is small compared to the coefficient of shear viscosity. Moreover, we show that in the relaxation-time approximation, the limiting behaviour of the ratio of heat conductivity to shear viscosity is qualitatively similar to that obtained for a strongly coupled conformal plasma.
Analysis of the blazing effect in second-order gratings
Matsumoto, Masauki )
1992-10-01
The validity of the blazing effect for improving the output-coupling efficiency of second-order gratings for use in grating-coupled surface-emitting lasers is examined. The Floquet-Bloch expansion method is used for the analysis of finite-length gratings with asymmetric tooth shapes operated in resonance condition. It is shown that for saw-tooth gratings the blazing effect is almost lost around the second-order Bragg wavelength because the reflected guide mode generated in the distributed Bragg reflector radiates preferentially into the substrate. By using a parallelogram grating with equal tooth and groove lengths, however, a high efficiency of radiation into the air is attainable even at the Bragg wavelength while the reflectivity is reduced. 32 refs.
Second order upwind Lagrangian particle method for Euler equations
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
2016-06-01
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Second-order closure models for supersonic turbulent flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1991-01-01
Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.
Second order filter response with series coupled silica microresonators
NASA Technical Reports Server (NTRS)
Savchenkov, A.; Iitchenko, V. S.; Handley, T.; Maleki, L.
2002-01-01
We have demonstrated an approach for fabricating a photonic filter with second order response function. The filter consists of two germania-doped silica microtoroidal or microspherical resonators cascaded in series. We use UV irradiation to tune the mode of one microcavity to bring it close to the mode of the second microcavity. This approach produces a filter function with much sharper rolloff than can be obtained with the individual microresonators.
Extensions and applications of a second-order landsurface parameterization
NASA Technical Reports Server (NTRS)
Andreou, S. A.; Eagleson, P. S.
1983-01-01
Extensions and applications of a second order land surface parameterization, proposed by Andreou and Eagleson are developed. Procedures for evaluating the near surface storage depth used in one cell land surface parameterizations are suggested and tested by using the model. Sensitivity analysis to the key soil parameters is performed. A case study involving comparison with an "exact" numerical model and another simplified parameterization, under very dry climatic conditions and for two different soil types, is also incorporated.
Gravitational waves from global second order phase transitions
Jr, John T. Giblin; Price, Larry R.; Siemens, Xavier; Vlcek, Brian E-mail: larryp@caltech.edu E-mail: bvlcek@uwm.edu
2012-11-01
Global second-order phase transitions are expected to produce scale-invariant gravitational wave spectra. In this manuscript we explore the dynamics of a symmetry-breaking phase transition using lattice simulations. We explicitly calculate the stochastic gravitational wave background produced during the transition and subsequent self-ordering phase. We comment on this signal as it compares to the scale-invariant spectrum produced during inflation.
Second order parametric processes in nonlinear silica microspheres.
Xu, Yong; Han, Ming; Wang, Anbo; Liu, Zhiwen; Heflin, James R
2008-04-25
We analyze second order parametric processes in a silica microsphere coated with radially aligned nonlinear optical molecules. In a high-Q nonlinear microsphere, we discover that it is possible to achieve ultralow threshold parametric oscillation that obeys the rule of angular momentum conservation. Based on symmetry considerations, one can also implement parametric processes that naturally generate quantum entangled photon pairs. Practical issues regarding implementation of the nonlinear microsphere are also discussed. PMID:18518201
athena: Tree code for second-order correlation functions
NASA Astrophysics Data System (ADS)
Kilbinger, Martin; Bonnett, Christopher; Coupon, Jean
2014-02-01
athena is a 2d-tree code that estimates second-order correlation functions from input galaxy catalogues. These include shear-shear correlations (cosmic shear), position-shear (galaxy-galaxy lensing) and position-position (spatial angular correlation). Written in C, it includes a power-spectrum estimator implemented in Python; this script also calculates the aperture-mass dispersion. A test data set is available.
Non-Gaussianity from the second-order cosmological perturbation
NASA Astrophysics Data System (ADS)
Lyth, David H.; Rodríguez, Yeinzon
2005-06-01
Several conserved and/or gauge-invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-Gaussianity in the primordial curvature perturbation ζ, employing for the first time a unified notation and focusing on the normalization fNL of the bispectrum. When ζ first appears a few Hubble times after horizon exit, |fNL| is much less than 1 and is, therefore, negligible. Thereafter ζ (and hence fNL) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Nonadiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (“light noninflaton fields”). During single-component inflation fNL is constant, but multicomponent inflation might generate |fNL|˜1 or bigger. Preheating can affect fNL only in atypical scenarios where it involves light noninflaton fields. The simplest curvaton scenario typically gives fNL≪-1 or fNL=+5/4. The inhomogeneous reheating scenario can give a wide range of values for fNL. Unless there is a detection, observation can eventually provide a limit |fNL|≲1, at which level it will be crucial to calculate the precise observational limit using second-order theory.
Second-order reconstruction of the inflationary potential
NASA Technical Reports Server (NTRS)
Liddle, Andrew R.; Turner, Michael S.
1994-01-01
To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.
Free-Form Region Description with Second-Order Pooling.
Carreira, João; Caseiro, Rui; Batista, Jorge; Sminchisescu, Cristian
2015-06-01
Semantic segmentation and object detection are nowadays dominated by methods operating on regions obtained as a result of a bottom-up grouping process (segmentation) but use feature extractors developed for recognition on fixed-form (e.g. rectangular) patches, with full images as a special case. This is most likely suboptimal. In this paper we focus on feature extraction and description over free-form regions and study the relationship with their fixed-form counterparts. Our main contributions are novel pooling techniques that capture the second-order statistics of local descriptors inside such free-form regions. We introduce second-order generalizations of average and max-pooling that together with appropriate non-linearities, derived from the mathematical structure of their embedding space, lead to state-of-the-art recognition performance in semantic segmentation experiments without any type of local feature coding. In contrast, we show that codebook-based local feature coding is more important when feature extraction is constrained to operate over regions that include both foreground and large portions of the background, as typical in image classification settings, whereas for high-accuracy localization setups, second-order pooling over free-form regions produces results superior to those of the winning systems in the contemporary semantic segmentation challenges, with models that are much faster in both training and testing. PMID:26357341
Second-order (2 +1 ) -dimensional anisotropic hydrodynamics
NASA Astrophysics Data System (ADS)
Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
2014-11-01
We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.
Dressed four-wave mixing second-order Talbot effect
NASA Astrophysics Data System (ADS)
Chen, Haixia; Zhang, Xun; Zhu, Dayu; Yang, Chang; Jiang, Tao; Zheng, Huaibin; Zhang, Yanpeng
2014-10-01
We theoretically demonstrate second-order Talbot effect (SOTE) based on entangled photon pairs. The photon pairs are generated from the spontaneous parametric four-wave mixing (SPFWM) process in a cold atomic medium and can be taken as the imaging light in order to realize coincidence recording. A strong standing wave is used to create the electromagnetically induced grating in the entangled photon pairs channels. By changing the frequency detuning of the standing wave or the other optical fields participating in the process, we can manipulate the contrast of the second-order Talbot image. We use the second-order correlation function and the dressed-state picture to explain the SOTE occurring in the SPFWM process. Moreover, we demonstrate the scheme for SOTE based on the spatially correlated twin beams generated from the SPFWM process with injection. This scheme provides a convenient detection proposal for the SOTE at the cost of the image contrast. Compared to the previous self-imaging schemes, the present schemes have the characteristic of controllable image contrast and of nonlocal imaging, and thus, they might broaden their applications in imaging techniques and find applications in quantum lithography.
Carborane tuning on iridium complexes: redox-switchable second-order NLO responses.
Wang, Jiao; Wang, Wen-Yong; Fang, Xin-Yan; Qiu, Yong-Qing
2015-04-01
Much effort has been devoted to investigating the molecular geometries, electronic structures, redox properties and nonlinear optical (NLO) properties of Ir complexes involving o-, m- or p-carborane groups by density functional theory (DFT) methods. Switchable second-order NLO properties were induced by redox processes involving these complexes, and it was found that mainly the coordination bonds of Ir complexes changed during the oxidation process. Our calculations revealed that oxidation reactions have a significant influence on the second-order NLO response owing to the change in charge transfer pattern. The β tot values of oxidized species are at least ∼9 times larger for set I and ∼5 times larger for set II than those of the corresponding parent complexes. Introduction of carborane groups into ppy (phenylpyridine) ligands can enhance the second-order NLO response by 1.2- 1.6 times by a metal-to-ligand charge transfer (MLCT) transition between the Ir atom and carborane. The β tot of complex 2 [(ppy)2Ir(phen)](+) (phen = phenanthroline) is 3.3 times larger than that of complex 1 (ppy)2Ir(acce) (acce = acetylacetonate), which is caused by ligand-to-ligand charge transfer (LLCT) between ppy ligands and the ancillary ligand. Therefore, it can be concluded that the second-order NLO response can be effectively enhanced by oxidation reactions. PMID:25791353
Superquadric glyphs for symmetric second-order tensors.
Schultz, Thomas; Kindlmann, Gordon L
2010-01-01
Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics. PMID:20975202
Determination of robust stability margin for second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.; Kau, C.-T.; Juang, Jer-Nan
1992-01-01
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
P-stable boundary value methods for second order IVPs
NASA Astrophysics Data System (ADS)
Aceto, Lidia; Ghelardoni, Paolo; Magherini, Cecilia
2012-09-01
We introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. The aim is to obtain P-stable methods with arbitrary order of accuracy. This result allows to overcome the order barrier established by Lambert and Watson which limited to p = 2 the maximum order of a P-stable Linear Multistep Method. In addition, an extension of the methods in the Exponential Fitting framework is also considered.
Detection of a diffusive cloak via second-order statistics
NASA Astrophysics Data System (ADS)
Koirala, Milan; Yamilov, Alexey
2016-08-01
We propose a scheme to detect the diffusive cloak proposed by Schittny et al [Science 345, 427 (2014)]. We exploit the fact that diffusion of light is an approximation that disregards wave interference. The long-range contribution to intensity correlation is sensitive to locations of paths crossings and the interference inside the medium, allowing one to detect the size and position, including the depth, of the diffusive cloak. Our results also suggest that it is possible to separately manipulate the first- and the second-order statistics of wave propagation in turbid media.
Slowly rotating scalar field wormholes: The second order approximation
Kashargin, P. E.; Sushkov, S. V.
2008-09-15
We discuss rotating wormholes in general relativity with a scalar field with negative kinetic energy. To solve the problem, we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. We construct the rotating wormhole solution in the second-order approximation with respect to the small parameter. The analysis shows that the asymptotical mass of the rotating wormhole is greater than that of the nonrotating one, and the null energy condition violation in the rotating wormhole spacetime is weaker than that in the nonrotating one.
Detection of a diffusive cloak via second-order statistics.
Koirala, Milan; Yamilov, Alexey
2016-08-15
We propose a scheme to detect the diffusive cloak proposed by Schittny et al. [Science345, 427 (2014).SCIEAS0036-807510.1126/science.1254524]. We exploit the fact that diffusion of light is an approximation that disregards wave interference. The long-range contribution to intensity correlation is sensitive to the locations of path crossings and the interference inside the medium, allowing one to detect the size and position, including the depth, of the diffusive cloak. Our results also suggest that it is possible to separately manipulate the first- and the second-order statistics of wave propagation in turbid media. PMID:27519108
Second-order kinetic Kohn-Sham lattice model
NASA Astrophysics Data System (ADS)
Solórzano, S.; Mendoza, M.; Herrmann, H. J.
2016-06-01
In this work, we introduce a semi-implicit second-order correction scheme to the kinetic Kohn-Sham lattice model. This approach is validated by performing realistic exchange-correlation energy calculations of atoms and dimers of the first two rows of the Periodic Table, finding good agreement with the expected values. Additionally, we simulate the ethane molecule, where we recover the bond lengths and compare the results with standard methods. Finally, we discuss the current applicability of pseudopotentials within the lattice kinetic Kohn-Sham approach.
Supersonic second order analysis and optimization program user's manual
NASA Technical Reports Server (NTRS)
Clever, W. C.
1984-01-01
Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance theory was utilized to meet this objective. Numerical codes were developed for analysis and design of relatively general three dimensional geometries. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes. Case computational time of one minute on a CDC 176 are typical for practical aircraft arrangement.
A second-order impact model for forest fire regimes.
Maggi, Stefano; Rinaldi, Sergio
2006-09-01
We present a very simple "impact" model for the description of forest fires and show that it can mimic the known characteristics of wild fire regimes in savannas, boreal forests, and Mediterranean forests. Moreover, the distribution of burned biomasses in model generated fires resemble those of burned areas in numerous large forests around the world. The model has also the merits of being the first second-order model for forest fires and the first example of the use of impact models in the study of ecosystems. PMID:16723147
Stochastic systems with delay: Perturbation theory for second order statistics
NASA Astrophysics Data System (ADS)
Frank, T. D.
2016-03-01
Within the framework of delay Fokker-Planck equations, a perturbation theoretical method is developed to determine second-order statistical quantities such as autocorrelation functions for stochastic systems with delay. Two variants of the perturbation theoretical approach are presented. The first variant is based on a non-local Fokker-Planck operator. The second variant requires to solve a Fokker-Planck equation with source term. It is shown that the two variants yield consistent results. The perturbation theoretical approaches are applied to study negative autocorrelations that are induced by feedback delays and mediated by the strength of the fluctuating forces that act on the feedback systems.
A-posteriori error estimation for second order mechanical systems
NASA Astrophysics Data System (ADS)
Ruiner, Thomas; Fehr, Jörg; Haasdonk, Bernard; Eberhard, Peter
2012-06-01
One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies degrees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of mechanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advantage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demonstrated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.
Second-order modeling of arsenite transport in soils
NASA Astrophysics Data System (ADS)
Zhang, Hua; Magdi Selim, H.
2011-11-01
Rate limited processes including kinetic adsorption-desorption can greatly impact the fate and behavior of toxic arsenic compounds in heterogeneous soils. In this study, miscible displacement column experiments were carried out to investigate the extent of reactivity during transport of arsenite in soils. Arsenite breakthrough curves (BTCs) of Olivier and Windsor soils exhibited strong retardation with diffusive effluent fronts followed by slow release or tailing during leaching. Such behavior is indicative of the dominance of kinetic retention reactions for arsenite transport in the soil columns. Sharp decrease or increase in arsenite concentration in response to flow interruptions (stop-flow) further verified that non-equilibrium conditions are dominant. After some 40-60 pore volumes of continued leaching, 30-70% of the applied arsenite was retained by the soil in the columns. Furthermore, continued arsenite slow release for months was evident by the high levels of residual arsenite concentrations observed during leaching. In contrast, arsenite transport in a reference sand material exhibited no retention where complete mass recovery in the effluent solution was attained. A second-order model (SOM) which accounts for equilibrium, reversible, and irreversible retention mechanisms was utilized to describe arsenite transport results from the soil columns. Based on inverse and predictive modeling results, the SOM model successfully depicted arsenite BTCs from several soil columns. Based on inverse and predictive modeling results, a second-order model which accounts for kinetic reversible and irreversible reactions is recommended for describing arsenite transport in soils.
Natural Constraints to Species Diversification
Lewitus, Eric; Morlon, Hélène
2016-01-01
Identifying modes of species diversification is fundamental to our understanding of how biodiversity changes over evolutionary time. Diversification modes are captured in species phylogenies, but characterizing the landscape of diversification has been limited by the analytical tools available for directly comparing phylogenetic trees of groups of organisms. Here, we use a novel, non-parametric approach and 214 family-level phylogenies of vertebrates representing over 500 million years of evolution to identify major diversification modes, to characterize phylogenetic space, and to evaluate the bounds and central tendencies of species diversification. We identify five principal patterns of diversification to which all vertebrate families hold. These patterns, mapped onto multidimensional space, constitute a phylogenetic space with distinct properties. Firstly, phylogenetic space occupies only a portion of all possible tree space, showing family-level phylogenies to be constrained to a limited range of diversification patterns. Secondly, the geometry of phylogenetic space is delimited by quantifiable trade-offs in tree size and the heterogeneity and stem-to-tip distribution of branching events. These trade-offs are indicative of the instability of certain diversification patterns and effectively bound speciation rates (for successful clades) within upper and lower limits. Finally, both the constrained range and geometry of phylogenetic space are established by the differential effects of macroevolutionary processes on patterns of diversification. Given these properties, we show that the average path through phylogenetic space over evolutionary time traverses several diversification stages, each of which is defined by a different principal pattern of diversification and directed by a different macroevolutionary process. The identification of universal patterns and natural constraints to diversification provides a foundation for understanding the deep-time evolution of
Natural Constraints to Species Diversification.
Lewitus, Eric; Morlon, Hélène
2016-08-01
Identifying modes of species diversification is fundamental to our understanding of how biodiversity changes over evolutionary time. Diversification modes are captured in species phylogenies, but characterizing the landscape of diversification has been limited by the analytical tools available for directly comparing phylogenetic trees of groups of organisms. Here, we use a novel, non-parametric approach and 214 family-level phylogenies of vertebrates representing over 500 million years of evolution to identify major diversification modes, to characterize phylogenetic space, and to evaluate the bounds and central tendencies of species diversification. We identify five principal patterns of diversification to which all vertebrate families hold. These patterns, mapped onto multidimensional space, constitute a phylogenetic space with distinct properties. Firstly, phylogenetic space occupies only a portion of all possible tree space, showing family-level phylogenies to be constrained to a limited range of diversification patterns. Secondly, the geometry of phylogenetic space is delimited by quantifiable trade-offs in tree size and the heterogeneity and stem-to-tip distribution of branching events. These trade-offs are indicative of the instability of certain diversification patterns and effectively bound speciation rates (for successful clades) within upper and lower limits. Finally, both the constrained range and geometry of phylogenetic space are established by the differential effects of macroevolutionary processes on patterns of diversification. Given these properties, we show that the average path through phylogenetic space over evolutionary time traverses several diversification stages, each of which is defined by a different principal pattern of diversification and directed by a different macroevolutionary process. The identification of universal patterns and natural constraints to diversification provides a foundation for understanding the deep-time evolution of
Phillips, Steven; Wilson, William H.
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other “structurally related” cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
Phillips, Steven; Wilson, William H
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other "structurally related" cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
Magnetic Compensation for Second-Order Doppler Shift in LITS
NASA Technical Reports Server (NTRS)
Burt, Eric; Tjoelker, Robert
2008-01-01
The uncertainty in the frequency of a linear-ion-trap frequency standard (LITS) can be reduced substantially by use of a very small magnetic inhomogeneity tailored to compensate for the residual second-order Doppler shift. An effect associated with the relativistic time dilatation, one cause of the second-order Doppler shift, is ion motion that is attributable to the trapping radio-frequency (RF)electromagnetic field used to trap ions. The second-order Doppler shift is reduced by using a multi-pole trap; however it is still the largest source of systematic frequency shift in the latest generation of LITSs, which are among the most stable clocks in the world. The present compensation scheme reduces the frequency instability of the affected LITS to about a tenth of its previous value. The basic principles of prior generation LITSs were discussed in several prior NASA Tech Briefs articles. Below are recapitulated only those items of basic information necessary to place the present development in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of the ground state hyperfine transition of 199Hg+ ions. The comparison involves a combination of optical and microwave excitation and interrogation of the ions in a linear ion trap in the presence of a nominally uniform magnetic field. In the current version of the LITS, there are two connected traps (see figure): (1) a quadrupole trap wherein the optical excitation and measurement take place and (2) a 12-pole trap (denoted the resonance trap), wherein the microwave interrogation takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. Shuttling ions into the resonance trap allows sensitive microwave interrogation to take place well away from loading interference. The axial magnetic field for the resonance trap is generated by an electric current in a finely wound wire coil surrounded by
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1990-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Second-Order Fermi Acceleration and Emission in Blazar Jets
NASA Astrophysics Data System (ADS)
Asano, Katsuaki; Takahara, Fumio; Toma, Kenji; Kusunose, Masaaki; Kakuwa, Jun
The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations, adopt it for 1ES 1101-232, and Mrk 421. The Fermi-II model with radial evolution of the electron injection rate and/or diffusion coefficient can reproduce the spectra from the radio to the gamma-ray regime. For Mrk 421, an external radio photon field with a luminosity of 4.9 begin{math} {times} 10 (38) erg s (-1) is required to agree with the observed GeV flux. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.
New implicitly solvable potential produced by second order shape invariance
Cannata, F.; Ioffe, M.V.; Kolevatova, E.V.; Nishnianidze, D.N.
2015-05-15
The procedure proposed recently by Bougie et al. (2010) to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order SUSY QM with supercharges of second order in momentum. A new shape invariant potential is constructed by this method. It is singular at the origin, it grows at infinity, and its spectrum depends on the choice of connection conditions in the singular point. The corresponding Schrödinger equation is solved explicitly: the wave functions are constructed analytically, and the energy spectrum is defined implicitly via the transcendental equation which involves Confluent Hypergeometric functions. - Highlights: • New potential with 2nd order irreducible shape invariance was constructed. • The connection conditions at the singularity of potential were obtained. • The explicit expressions for all wave functions were derived. • The implicit equation for the energy spectrum was obtained.
A new approach for second-order perturbation theory.
Tomlinson, David G; Asadchev, Andrey; Gordon, Mark S
2016-05-30
A new second-order perturbation theory (MP2) approach is presented for closed shell energy evaluations. The new algorithm has a significantly lower memory footprint, a lower FLOP (floating point operations) count, and a lower time to solution compared to previously implemented parallel MP2 methods in the GAMESS software package. Additionally, this algorithm features an adaptive approach for the disk/distributed memory storage of the MP2 amplitudes. The algorithm works well on a single workstation, small cluster, and large Cray cluster, and it allows one to perform large calculations with thousands of basis functions in a matter of hours on a single workstation. The same algorithm has been adapted for graphical processing unit (GPU) architecture. The performance of the new GPU algorithm is also discussed. © 2016 Wiley Periodicals, Inc. PMID:26940648
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1989-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Compact Two-State-Variable Second-Order Memristor Model.
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2016-06-01
A key requirement for using memristors in functional circuits is a predictive physical model to capture the resistive switching behavior, which shall be compact enough to be implemented using a circuit simulator. Although a number of memristor models have been developed, most of these models (i.e., first-order memristor models) have utilized only a one-state-variable. However, such simplification is not adequate for accurate modeling because multiple mechanisms are involved in resistive switching. Here, a two-state-variable based second-order memristor model is presented, which considers the axial drift of the charged vacancies in an applied electric field and the radial vacancy motion caused by the thermophoresis and diffusion. In particular, this model emulates the details of the intrinsic short-term dynamics, such as decay and temporal heat summation, and therefore, it accurately predicts the resistive switching characteristics for both DC and AC input signals. PMID:27152649
K-inflationary power spectra at second order
Martin, Jérôme; Vennin, Vincent; Ringeval, Christophe E-mail: christophe.ringeval@uclouvain.be
2013-06-01
Within the class of inflationary models, k-inflation represents the most general single field framework that can be associated with an effective quadratic action for the curvature perturbations and a varying speed of sound. The incoming flow of high-precision cosmological data, such as those from the Planck satellite and small scale Cosmic Microwave Background (CMB) experiments, calls for greater accuracy in the inflationary predictions. In this work, we calculate for the first time the next-to-next-to-leading order scalar and tensor primordial power spectra in k-inflation needed in order to obtain robust constraints on the inflationary theory. The method used is the uniform approximation together with a second order expansion in the Hubble and sound flow functions. Our result is checked in various limits in which it reduces to already known situations.
Second-Order Nonlinear Optical Imaging of Chiral Crystals
Kissick, David J.; Wanapun, Debbie; Simpson, Garth J.
2012-01-01
Second-order nonlinear optical imaging of chiral crystals (SONICC) is an emerging technique for crystal imaging and characterization. We provide a brief overview of the origin of second harmonic generation signals in SONICC and discuss recent studies using SONICC for biological applications. Given that they provide near-complete suppression of any background, SONICC images can be used to determine the presence or absence of protein crystals through both manual inspection and automated analysis. Because SONICC creates high-resolution images, nucleation and growth kinetics can also be observed. SONICC can detect metastable, homochiral crystalline forms of amino acids crystallizing from racemic solutions, which confirms Ostwald’s rule of stages for crystal growth. SONICC’s selectivity, based on order, and sensitivity, based on background suppression, make it a promising technique for numerous fields concerned with chiral crystal formation. PMID:21469954
Gravitational Microlensing by Ellis Wormhole: Second Order Effects
NASA Astrophysics Data System (ADS)
Lukmanova, Regina; Kulbakova, Aliya; Izmailov, Ramil; Potapov, Alexander A.
2016-07-01
Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.
Invariant classification of second-order conformally flat superintegrable systems
NASA Astrophysics Data System (ADS)
Capel, J. J.; Kress, J. M.
2014-12-01
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools from algebraic geometry and classical invariant theory. The results obtained show, through Stäckel equivalence, that the list of known nondegenerate superintegrable systems over three-dimensional conformally flat spaces is complete. In particular, a seven-dimensional manifold is determined such that each point corresponds to a conformal class of superintegrable systems. This manifold is foliated by the nonlinear action of the conformal group in three dimensions. Two systems lie in the same conformal class if and only if they lie in the same leaf of the foliation. This foliation is explicitly described using algebraic varieties formed from representations of the conformal group. The proof of these results rely heavily on Gröbner basis calculations using the computer algebra software packages Maple and Singular.
Second-order UV contamination in astronomical spectra
NASA Astrophysics Data System (ADS)
Gutierrez-Moreno, A.; Heathcote, S.; Moreno, H.; Hamuy, M.
1994-11-01
Observations of the planetary nebula Me 2-1 are used to discuss some effects of contamination produced by the second-order ultraviolet spectrum in the first-order red, longer than approximately 6200 A. It is found that this contamination is present with some instrumental setups, and that the contaminating lines are displaced in wavelength with respect to the predictions from diffraction theory by an amount which varies slightly for different setups. From the theoretical and empirical analysis of these displacements, it is concluded that the shift in wavelength is due to the presence of chromatic difference in magnification in spectrograph cameras including any transmission element, as in the case in the semi-solid Schmidt-Cassegrain cameras used in our observations.
Relativistic quantum transport coefficients for second-order viscous hydrodynamics
NASA Astrophysics Data System (ADS)
Florkowski, Wojciech; Jaiswal, Amaresh; Maksymiuk, Ewa; Ryblewski, Radoslaw; Strickland, Michael
2015-05-01
We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the nonequilibrium part. Focusing on the case of transversally homogeneous and boost-invariant longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of the massive 0+1 d relativistic Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained by employing the Chapman-Enskog method lead to better agreement with the exact solution of the relativistic Boltzmann equation.
Pump power dependence of second order correlation in nondegenerate SPDC
NASA Astrophysics Data System (ADS)
Kim, Charles; Kanner, Gary
2009-08-01
We observed the second order correlation peak for nondegenerate spontaneous parametric down conversion (SPDC) of a pulsed pump at 532 nm into 810 nm and 1550 nm entangled beams. We used a Si avalanche photodiode (APD) to detect the 810 nm photons, and an InGaAs APD to detect those at 1550 nm. We defined both a visibility and signal-to-noise ratio (SNR) based on the data, which were obtained at various pump powers. In contrast to classical imaging systems, for which SNR increases monotonically with transmitted power, the SNR for the correlation peak in our setup exhibited a gradual decay as the pump power increased. We derived an empirical relation for the SNR, which was inversely proportional to the square root of pump power.
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action
NASA Astrophysics Data System (ADS)
Bettoni, Dario; Liberati, Stefano
2013-10-01
The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and properties are worth analyzing along the experience accumulated in the latter context. Here, we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for scalar-tensor theories a là Brans-Dicke. We identify the most general transformation preserving second-order field equations and discuss the issue of viable frames for this kind of theory, in particular, the possibility to cast the action in the so-called Einstein frame. Interestingly, we find that only for a subset of the Horndeski Lagrangian such a frame exists. Finally, we investigate the transformation properties of such frames under field redefinitions and frame transformations and their reciprocal relationship.
WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS.
Mu, Lin; Wang, Junping; Wei, Guowei; Ye, Xiu; Zhao, Shan
2013-10-01
Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L 2 and L ∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order [Formula: see text] to [Formula: see text] for the solution itself in L ∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order [Formula: see text] to [Formula: see text] in the L ∞ norm for C (1) or Lipschitz continuous interfaces associated with a C (1) or H (2) continuous solution. PMID:24072935
Second order closure modeling of turbulent buoyant wall plumes
NASA Technical Reports Server (NTRS)
Zhu, Gang; Lai, Ming-Chia; Shih, Tsan-Hsing
1992-01-01
Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.
Ninth order block hybrid collocation method for second order ordinary differential equations
NASA Astrophysics Data System (ADS)
Yap, Lee Ken; Ismail, Fudziah
2016-02-01
A ninth order block hybrid collocation method is proposed for solving general second order ordinary differential equations directly. The derivation involves interpolation and collocation of basic polynomial that generates the main and additional methods. These methods are applied simultaneously to provide approximate solutions at five main points and three off-step points. The stability properties of the block method are discussed. Some illustrative examples are given to demonstrate the efficiency of the method.
Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra
2016-01-01
In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result. PMID:27218008
Second order gyrokinetic theory for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-01
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell-Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
A planar second-order DC SQUID gradiometer.
Carelli, P; Chiaventi, L; Leoni, R; Pullano, M; Schirripa Spagnolo, G
1991-01-01
In this work we describe a DC SQUID gradiometer, sensitive to the second spatial derivative of the magnetic field. The sensitive area of the gradiometer is the inductive body of the DC SQUID itself. The isoflux line distribution generated by a dipolar source, obtained by performing magnetic measurements with an array of such detectors, is relatively complicated, but its localisation capability is similar to that one usually achieves with axial detector arrays. Planar gradiometers also show a better resolution for near sources and a stronger rejection of far disturbances. The final device is expected to have an inductance of a few hundreds of pH in order to obtain performances typical of a low noise DC SQUID. The pick-up coils will be the combination of four square holes of 500 microns side with a 1.05 cm baseline. Due to the magnetic field concentration (in the final device it can be a factor 10) the gradiometer will have a sensitivity of 10(-11) T m-2 Hz-1/2 and a field sensitivity of about 2 fT Hz-1/2. Some preliminary results, obtained on detectors with an intermediate area between the prototype and final device, are reported here. The process used to fabricate this second-order gradiometer is based on Nb-NbO chi-PbAuIn Josephson tunnel junctions. Some possible improvements will also be described. PMID:1807874
Second-order perturbation theory: Problems on large scales
NASA Astrophysics Data System (ADS)
Pound, Adam
2015-11-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.
Modal cost analysis for linear matrix-second-order systems
NASA Technical Reports Server (NTRS)
Skelton, R. E.; Hughes, P. C.
1980-01-01
Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency, and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using modal cost analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.
Second order anisotropy contribution in perpendicular magnetic tunnel junctions
Timopheev, A. A.; Sousa, R.; Chshiev, M.; Nguyen, H. T.; Dieny, B.
2016-01-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form −K2cos4θ must be added to the conventional uniaxial –K1cos2θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated −K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from “easy-axis” to “easy-cone” regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface. PMID:27246631
Modeling Second-Order Chemical Reactions using Cellular Automata
NASA Astrophysics Data System (ADS)
Hunter, N. E.; Barton, C. C.; Seybold, P. G.; Rizki, M. M.
2012-12-01
Cellular automata (CA) are discrete, agent-based, dynamic, iterated, mathematical computational models used to describe complex physical, biological, and chemical systems. Unlike the more computationally demanding molecular dynamics and Monte Carlo approaches, which use "force fields" to model molecular interactions, CA models employ a set of local rules. The traditional approach for modeling chemical reactions is to solve a set of simultaneous differential rate equations to give deterministic outcomes. CA models yield statistical outcomes for a finite number of ingredients. The deterministic solutions appear as limiting cases for conditions such as a large number of ingredients or a finite number of ingredients and many trials. Here we present a 2-dimensional, probabilistic CA model of a second-order gas phase reaction A + B → C, using a MATLAB basis. Beginning with a random distribution of ingredients A and B, formation of C emerges as the system evolves. The reaction rate can be varied based on the probability of favorable collisions of the reagents A and B. The model permits visualization of the conversion of reagents to products, and allows one to plot concentration vs. time for A, B and C. We test hypothetical reaction conditions such as: limiting reagents, the effects of reaction probabilities, and reagent concentrations on the reaction kinetics. The deterministic solutions of the reactions emerge as statistical averages in the limit of the large number of cells in the array. Modeling results for dynamic processes in the atmosphere will be presented.
Second order anisotropy contribution in perpendicular magnetic tunnel junctions.
Timopheev, A A; Sousa, R; Chshiev, M; Nguyen, H T; Dieny, B
2016-01-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form -K2cos(4)θ must be added to the conventional uniaxial -K1cos(2)θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated -K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from "easy-axis" to "easy-cone" regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface. PMID:27246631
Cavity-Enhanced Second-Order Nonlinear Photonic Logic Circuits
NASA Astrophysics Data System (ADS)
Trivedi, Rahul; Khankhoje, Uday K.; Majumdar, Arka
2016-05-01
A large obstacle for realizing photonic logic is the weak optical nonlinearity of available materials, which results in large power consumption. In this paper, we present the theoretical design of all-optical logic with second-order (χ(2 )) nonlinear bimodal cavities and their networks. Using semiclassical models derived from the Wigner quasiprobability distribution function, we analyze the power consumption and signal-to-noise ratio (SNR) of networks implementing an optical and gate and an optical latch. A comparison between the second- and third-order (χ(3 )) optical logic reveals that, while the χ(3 ) design outperforms the χ(2 ) design in terms of the SNR for the same input power, employing the χ(3 ) nonlinearity necessitates the use of cavities with ultrahigh-quality factors (Q ˜106) to achieve a gate power consumption comparable to that of the χ(2 ) design at significantly smaller quality factors (Q ˜104). Using realistic estimates of the χ(2 ) and χ(3 ) nonlinear susceptibilities of available materials, we show that, at achievable quality factors (Q ˜104), the χ(2 ) design is an order of magnitude more energy efficient than the corresponding χ(3 ) design.
Second order sliding mode control for a quadrotor UAV.
Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang
2014-07-01
A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. PMID:24751475
The motion of ellipsoids in a second order fluid
NASA Astrophysics Data System (ADS)
Kim, S.
1985-09-01
The rigid body motion of an ellipsoid in a second order fluid (SOF) under the action of specified (time independent) external forces and torques have been obtained to first order in the Weissenberg number by inverting the resistance relations for the force an torque under specified rigid body motions. The reciprocal theorem of Lorentz was used to bypass the calculation of the O(W) velocity field. The results agree with known analytic solutions for SOF with the secondary to primary normal stress ratio of -1/2. The solution procedure was also tested by computing the torque on a translating prolate spheroid with aspect ratios ranging from slender bodies to near-spheres. One result is that for a SOF with zero secondary normal stress (Weissenberg fluid), previous asymptotic results for near-spheres were found to be accurate even at fairly large aspect ratios. New results of nondegenerate ellipsoids suggest that the orientation (as monitored by Euler angles) and trajectory of sedimenting, nonaxisymmetric particles such as ellipsoids provide useful information on the rheology of the suspending fluid.
Second order anisotropy contribution in perpendicular magnetic tunnel junctions
NASA Astrophysics Data System (ADS)
Timopheev, A. A.; Sousa, R.; Chshiev, M.; Nguyen, H. T.; Dieny, B.
2016-06-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form ‑K2cos4θ must be added to the conventional uniaxial –K1cos2θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated ‑K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from “easy-axis” to “easy-cone” regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface.
Photonic second-order duty-cycle modulator
NASA Astrophysics Data System (ADS)
Costanzo-Caso, Pablo A.; Reeves, Erin; Jin, Yiye; Granieri, Sergio; Siahmakoun, Azad
2011-09-01
The delta sigma modulator (DSM) is a device which transforms the amplitude information of an analog input signal to the duty cycle and frequency of a binary output. This device, typically employed in oversampled analog-to-digital converters, is based on a feedback loop which includes at least one integrator and one quantizer in the forward path. In this paper, a novel photonic second-order DSM is proposed and experimentally demonstrated. The system is composed of two inverted leaky integrator and one electro-optic quantizer. The maximum input frequency is around 2 MHz, limited by the fiber length of the accumulator and feedback loops, and the quantizer rise/fall times. The system is characterized at different input frequencies and waveforms (sinusoidal and saw tooth) to analyze the modulator performance and linearity. The binary output is acquired, processed and demodulated using a personal computer, in order to reconstruct the input analog signal. The reported fiber-optic DSM is very promising for future integration increasing the operation frequency up to GHz range.
Correction of the Chromaticity up to Second Order for MEIC
H. K. Sayed, S.A. Bogacz, P. Chevtsov
2010-03-01
The proposed electron collider lattice exhibits low β- functions at the Interaction Point (IP) (βx*100mm - βy* 20 mm) and rather large equilibrium momentum spread of the collider ring (δp/p = 0.00158). Both features make the chromatic corrections of paramount importance. Here the chromatic effects of the final focus quadruples are cor- rected both locally and globally. Local correction features symmetric sextupole families around the IP, the betatron phase advances from the IP to the sextupoles are chosen to eliminate the second order chromatic aberration. Global interleaved families of sextupoles are placed in the figure-8 arc sections, and non-interleaved families at straight sec- tion making use of the freely propagated dispersion wave from the arcs. This strategy minimizes the required sex- tupole strength and eventually leads to larger dynamic aper- ture of the collider. The resulting spherical aberrations induced by the sextupoles are mitigated by design; the straight and arc sections optics features an inverse identity transformation between sextupoles in each pair.
Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D.; Head-Gordon, Martin
2004-08-02
A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Moller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite spin second order energy (SOS-MP2) yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the 5th order computational steps associated with MP2 theory, even without exploiting any spatial locality. A 4th order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.
Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation
Petersson, N A; Sjogreen, B
2012-03-26
second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a
Second order multidimensional sign-preserving remapping for ALE methods
Hill, Ryan N; Szmelter, J.
2010-12-15
A second-order conservative sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods is developed utilising concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The algorithm is inherently multidimensional, and so does not introduce splitting errors. The remapping is implemented in a two-dimensional, finite element ALE solver employing staggered quadrilateral meshes. The MPDATA remapping uses a finite volume discretization developed for volume coordinates. It is applied for the remapping of density and internal energy arranged as cell centered, and velocity as nodal, dependent variables. In the paper, the advection of scalar fields is examined first for test cases with prescribed mesh movement. A direct comparison of MPDATA with the performance of the van Leer MUSCL scheme indicates advantages of a multidimensional approach. Furthermore, distinctly different performance between basic MPDATA and the infinite gauge option is illustrated using benchmarks involving transport of a sign changing velocity field. Further development extends the application of MPDATA remapping to the full ALE solver with a staggered mesh arrangement for density, internal energy and momentum using volume coordinates. At present, two options of the algorithm - basic and infinite gauge - are implemented. To ensure a meaningful assessment, an identical Lagrangian solver and computational mesh update routines are used with either MPDATA or van Leer MUSCL remapping. The evaluation places particular focus on the abilities of both schemes to accurately model multidimensional problems. Theoretical considerations are supported with numerical examples. In addition to the prescribed mesh movement cases for advection of scalars, the demonstrations include two-dimensional Eulerian and ALE flow simulations on quadrilateral meshes with both fixed and variable timestep control. The key comparisons include the standard test cases of Sod and Noh
Montoncello, F.; Giovannini, L.; Nizzoli, F.; Vavassori, P.; Grimsditch, M.; Materials Science Division; Univ. di Ferrara; CNISM; CNR-INFM; CIC nanoGUNE Res. Ctr.
2008-06-01
We study the magnetization reversal in elliptical nanodots with the external field applied exactly along the minor (hard) axis. By varying the magnitude of the applied field, several first and second order transitions take place and the system proceeds through magnetic configurations characterized by different symmetry properties. The dynamical matrix method is used to calculate the spin excitations as function of the applied field. This model system allows us to investigate the relationship between the singularities of the magnetization, the presence of soft spin excitations, and the symmetry properties of the static and dynamic magnetization fields. Rules that govern the transitions are formulated.
Second-order dispersion interactions in π-conjugated polymers
NASA Astrophysics Data System (ADS)
Barford, William; Paiboonvorachat, Nattapong; Yaron, David
2011-06-01
We calculate the ground state and excited state second-order dispersion interactions between parallel π-conjugated polymers. The unperturbed eigenstates and energies are calculated from the Pariser-Parr-Pople model using CI-singles theory. Based on large-scale calculations using the molecular structure of trans-polyacetylene as a model system and by exploiting dimensional analysis, we find that: (1) For inter-chain separations, R, greater than a few lattice spacings, the ground-state dispersion interaction, Δ E_{GS}, satisfies, Δ E_{GS} ˜ L^2/R^6 for L ≪ R and Δ E_{GS} ˜ L/R^5 for R ≪ L, where L is the chain length. The former is the London fluctuating dipole-dipole interaction while the latter is a fluctuating line dipole-line dipole interaction. (2) The excited state screening interaction exhibits a crossover from fluctuating monopole-line dipole interactions to either fluctuating dipole-dipole or fluctuating line dipole-line dipole interactions when R exceeds a threshold Rc, where Rc is related to the root-mean-square separation of the electron-hole excitation. Specifically, the excited state screening interaction, ΔEn, satisfies, ΔEn ˜ L/R6 for Rc < L ≪ R and ΔEn ˜ L0/R5 for Rc < R ≪ L. For R < Rc < L, ΔEn ˜ R-ν, where ν ≃ 3. We also investigate the relative screening of the primary excited states in conjugated polymers, namely the n = 1, 2, and 3 excitons. We find that a larger value of n corresponds to a larger value of ΔEn. For example, for poly(para-phenylene), ΔEn = 1 ≃ 0.1 eV, ΔEn = 2 ≃ 0.6 eV, and ΔEn = 3 ≃ 1.2 eV (where n = 1 is the 11B1 state, n = 2 is the m1A state, and n = 3 is the n1B1 state). Finally, we find that the strong dependence of ΔEn on inter-chain separation implies a strong dependency of ΔEn on density fluctuations. In particular, a 10% density fluctuation implies a fluctuation of 13 meV, 66 meV, and 120 meV for the 11B1, m1A state, and n1B1 states of poly(para-phenylene), respectively. Our results
Second-order bosonic Kadanoff-Baym equations for plasmon-accompanied optical absorption
NASA Astrophysics Data System (ADS)
Schüler, Michael; Pavlyukh, Yaroslav
2016-03-01
The availability of ultra-short and strong light sources opens the door for a variety of new experiments such as transient absorption, where optical properties of systems can be studied in extreme nonequilibrium situations. The nonequilibrium Green's function formalism is an efficient approach to investigate these processes theoretically. Here we apply the method to the light-matter interaction of the magnesium 2p core level accompanied by electron-plasmon interaction due to collective excitations in the conduction band. The plasmons are described as massive bosonic quasi-particle excitations, leading to a second-order equations of motion, requiring a new approach for their propagation.
Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta
Giovannini, Massimo
2011-01-15
The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also superchaotic. Testable inequalities are derived in the limit of large-angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.
Spacecraft Attitude Estimation Using the Second-Order Extended H Infinity Filter
NASA Astrophysics Data System (ADS)
Reis Silva, William; Koiti Kuga, Helio; Zanardi, Maria Cecilia
In this work, will be described the attitude determination and the gyros drift estimation using the Second-Order Extended H Infinity Filter for nonlinear systems. Such filter uses the Taylor series to approximate the non-linearity of the known dynamics and assumes that the noise sources have approximately known statistical properties. The application uses simulated measurement data for orbit and attitude through the propagator PROPAT. The attitude dynamical model is described by nonlinear equations involving the Euler angles. The attitude sensors available are two DSS (Digital Sun Sensors), two IRES (Infra-Red Earth Sensor), and one triad of mechanical gyros. These sensors configurations are similar to those found in real satellite CBERS-2 (China Brazil Earth Resources Satellite). According to the theory, in comparison with the Kalman filtering, the H Infinity filtering has some advantages in state estimation. In the H Infinity filter, the nature is assumed to be perverse and actively seeks to degrade our state estimate as much as possible, whereas the Kalman filtering, the nature is assumed to be indifferent. Thus, Extended H Infinity Filter is simply a robust version of the extended Kalman filter because to add tolerance to unmodeled noise and dynamics. Using the Second-Order Extend H Infinity Filter, the aim is to highlight and magnify the properties of the H Infinity Filter in terms of its favourable characteristics, since this is a refinement of the Extended H∞ Filter and certainly the Second-Order Extend H Infinity Filter provides better results. The results in this work show that one can reach accuracies in attitude determination within the prescribed requirements, besides providing estimates of the gyro drifts which can be further used to enhance the gyro error model. It is known that gyros present several sources of error of which the drift is the most troublesome,because over time the accumulation of errorshinder the accuracy in the estimation process
New - and Photoswitchable Chromophores for Second-Order Nonlinear Optics
NASA Astrophysics Data System (ADS)
Sanguinet, L.; Ahmed, S.; Pozzo, J. L.; Rodriguez, V.; Adamietz, F.
New acidochromic and photochromic compounds with nonlinear optical properties have been designed and synthesized. The hyperpolarizabilities of the zwitterionic colored forms have been quantified with polarized hyper-Rayleigh scattering experiments. The static value of oxazolidino-indoline 2 is found to be as high as Disperse Red One. This opens the way to novel multi-addressable NLO-systems.
Zhao, J.M.; Tan, J.Y.; Liu, L.H.
2013-01-01
A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.
A second order residual based predictor-corrector approach for time dependent pollutant transport
NASA Astrophysics Data System (ADS)
Pavan, S.; Hervouet, J.-M.; Ricchiuto, M.; Ata, R.
2016-08-01
We present a second order residual distribution scheme for scalar transport problems in shallow water flows. The scheme, suitable for the unsteady cases, is obtained adapting to the shallow water context the explicit Runge-Kutta schemes for scalar equations [1]. The resulting scheme is decoupled from the hydrodynamics yet the continuity equation has to be considered in order to respect some important numerical properties at discrete level. Beyond the classical characteristics of the residual formulation presented in [1,2], we introduce the possibility to iterate the corrector step in order to improve the accuracy of the scheme. Another novelty is that the scheme is based on a precise monotonicity condition which guarantees the respect of the maximum principle. We thus end up with a scheme which is mass conservative, second order accurate and monotone. These properties are checked in the numerical tests, where the proposed approach is also compared to some finite volume schemes on unstructured grids. The results obtained show the interest in adopting the predictor-corrector scheme for pollutant transport applications, where conservation of the mass, monotonicity and accuracy are the most relevant concerns.
Effects of Deception on Children's Understanding of Second-Order False Belief
ERIC Educational Resources Information Center
Miller, Scott A.
2013-01-01
This research examined two questions: effects of deception on children's understanding of second-order false belief, and possible effects of number of siblings on second-order performance. Kindergarten children responded to 3 second-order problems that varied in the presence and the nature of deception. Performance was better on the problems…
Adolescent, but not adult, rats exhibit ethanol-mediated appetitive second-order conditioning
Pautassi, Ricardo Marcos; Myers, Mallory; Spear, Linda Patia; Molina, Juan Carlos; Spear, Norman E.
2008-01-01
Background Adolescent rats are less sensitive to the sedative effects of ethanol than older animals. They also seem to perceive the reinforcing properties of ethanol. However, unlike neonates or infants, ethanol-mediated appetitive behavior has yet to be clearly shown in adolescents. Appetitive ethanol reinforcement was assessed in adolescent (postnatal day 33, P33) and adult rats (P71) through second-order conditioning (SOC). Methods On P32 or P70 animals were intragastrically administered ethanol (0.5 or 2.0 g/kg) paired with intraoral pulses of sucrose (CS1, first-order conditioning phase). CS1 delivery took place either 5-20 (Early pairing) or 30-45 (Late pairing) min following ethanol. CS1 exposure and ethanol administration were separated by 240 min in unpaired controls. On P33 or P71, animals were presented the CS1 (second-order conditioning phase) while in a distinctive chamber (CS2). Then, they were tested for CS2 preference. Results Early and late paired adolescents, but not adults, had greater preference for the CS2 than controls, a result indicative of ontogenetic variation in ethanol-mediated reinforcement. During the CS1 - CS2 associative phase, paired adolescents given 2.0 g/kg ethanol wall-climbed more than controls. Blood and brain ethanol levels associated with the 0.5 and 2.0 g/kg doses at the onset of each conditioning phase did not differ substantially across age, with mean BECs of 38 and 112 mg %. Conclusions These data indicate age-related differences between adolescent and adult rats in terms of sensitivity to ethanol’s motivational effects. Adolescents exhibit high sensitivity for ethanol’s appetitive effects. These animals also showed EtOH-mediated behavioral activation during the second-order conditioning phase. The SOC preparation provides a valuable conditioning model for assessing ethanol’s motivational effects across ontogeny. PMID:18782343
Gao, L.H.; Wang, K.Z.; Huang, C.H.
1995-06-01
A series of novel azo dyes composed of a lanthanide complex anion and an azo cation, in which strongly electron-donating (dihexadecylamino)phenyl and electron-accepting pyridinium groups are separated by an azo group, was designed as second-order nonlinear optical Langmuir-Blodgett (LB) film materials. The compounds are of good film-forming properties. The values of second-order molecular hyperpolarizability {beta} were determined to be (1.20-3.03) x 10{sup {minus}27} esu, comparable to the largest value known for azo LB materials. The compounds studied may be attactive in the application in future optical devices. 13 refs., 5 figs., 1 tab.
ERIC Educational Resources Information Center
Fuchs, Susanne; Perrier, Pascal; Hartinger, Mariam
2011-01-01
Purpose: Linear second-order models have often been used to investigate properties of speech production. However, these models are inaccurate approximations of the speech apparatus. This study aims at assessing how reliably stiffness can be estimated from kinematics with these models. Method: Articulatory movements were collected for 9 speakers of…
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.
NASA Astrophysics Data System (ADS)
Dobes, Jiri; Deconinck, Herman
2008-06-01
matrix [M. Mezine, M. Ricchiuto, R. Abgrall, H. Deconinck, Monotone and stable residual distribution schemes on prismatic space-time elements for unsteady conservation laws, 33rd Computational Fluid Dynamics Course, Von Karman Institute for Fluid Dynamics, 2003; R. Abgrall, M. Mezine, Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems, J. Comput. Phys. 188 (2003) 16-55]. For the time integration, a three point backward scheme is selected for its accuracy and robustness and the shock capturing operator is modified appropriately, to handle moving shocks. We present a numerical solution of several challenging test cases involving the solution of the Euler equations from the subsonic to the hypersonic regime. All the tests shows very good accuracy, robustness and convergence properties.
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method. PMID:19840985
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
A generalized LSTM-like training algorithm for second-order recurrent neural networks
Monner, Derek; Reggia, James A.
2011-01-01
The Long Short Term Memory (LSTM) is a second-order recurrent neural network architecture that excels at storing sequential short-term memories and retrieving them many time-steps later. LSTM’s original training algorithm provides the important properties of spatial and temporal locality, which are missing from other training approaches, at the cost of limiting it’s applicability to a small set of network architectures. Here we introduce the Generalized Long Short-Term Memory (LSTM-g) training algorithm, which provides LSTM-like locality while being applicable without modification to a much wider range of second-order network architectures. With LSTM-g, all units have an identical set of operating instructions for both activation and learning, subject only to the configuration of their local environment in the network; this is in contrast to the original LSTM training algorithm, where each type of unit has its own activation and training instructions. When applied to LSTM architectures with peephole connections, LSTM-g takes advantage of an additional source of back-propagated error which can enable better performance than the original algorithm. Enabled by the broad architectural applicability of LSTM-g, we demonstrate that training recurrent networks engineered for specific tasks can produce better results than single-layer networks. We conclude that LSTM-g has the potential to both improve the performance and broaden the applicability of spatially and temporally local gradient-based training algorithms for recurrent neural networks. PMID:21803542
The Face Inversion Effect: Roles of First- and Second-Order Configural Information.
Civile, Ciro; McLaren, Rossy; McLaren, Ian P L
2016-01-01
The face inversion effect (FIE) is a reduction in recognition performance for inverted faces compared with upright faces. Several studies have proposed that a type of configural information, called second-order relational information, becomes more important with increasing expertise and gives rise to the FIE. However, recently it has been demonstrated that it is possible to obtain an FIE with facial features presented in isolation, showing that configural information is not necessary for this effect to occur. In this article we test whether there is a role for configural information in producing the FIE and whether second- or first-order relational information is particularly important. In Experiment 1, we investigated the role of configural information and local feature orientation by using a new type of "Thatcherizing" transformation on our set of faces, aiming to disrupt second-order and local feature orientation information but keeping all first-order properties unaltered. The results showed a significant reduction in the FIE for these "new" Thatcherized faces, but it did not entirely disappear. Experiment 2 confirmed the FIE for new Thatcherized faces, and Experiment 3 establishes that both local feature orientation and first-order relational information have a role in determining the FIE. PMID:27029104
Beyond the GW approximation: a second-order screened exchange correction
NASA Astrophysics Data System (ADS)
Rinke, Patrick; Caruso, Fabio; Ren, Xinguo; Scheffler, Matthias; Marom, Noa
2013-03-01
Despite the success of the GW method in describing the photoemission spectra of solids, molecules and clusters, challenges remain. For aromatic molecules for example absolute as well as relative positions of ionisation energies and affinities are not well reproduced in perturbative G0W0 schemes with different starting points as well as in self-consistent GW, sometimes even giving the wrong orbital order. Motivated by renormalized second-order perturbation theory for the ground-state energy, we propose a second-order screened exchange correction (SOSEX) to the GW self-energy. This correction follows the spirit of the SOSEX correction to the random-phase approximation for the electron correlation energy and reduces the self-correlation error. The performance of the GW +SOSEX scheme has been benchmarked for a set of molecular systems, including the G2 set, commonly used acceptor molecules, benzene and the azabenzene molecules. We find that the SOSEX correction improves the description of the spectral properties including the orbital order with respect to the different GW schemes, highlighting the importance of reducing the self-correlation error.
Second order formalism for spin (1/2) fermions and Compton scattering
Delgado-Acosta, E. G.; Napsuciale, Mauro; Rodriguez, Simon
2011-04-01
We develop a second order formalism for massive spin 1/2 fermions based on the projection over Poincare invariant subspaces in the ((1/2),0)+(0,(1/2)) representation of the homogeneous Lorentz group. Using the U(1){sub em} gauge principle we obtain a second order description for the electromagnetic interactions of a spin 1/2 fermion with two free parameters, the gyromagnetic factor g and a parameter {xi} related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case g=2, {xi}=0, and for states with well-defined parity, we recover Dirac results. In general, we find the correct classical limit and a finite value r{sub c}{sup 2} for the forward differential cross section, independent of the photon energy and of the value of the parameters g and {xi}. The differential cross section vanishes at high energies for all g, {xi} except in the forward direction. The total cross section at high energies vanishes only for g=2, {xi}=0. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.
Li, Yuan-Na; Wu, Hai-Long; Qing, Xiang-Dong; Nie, Chong-Chong; Li, Shu-Fang; Yu, Yong-Jie; Zhang, Shu-Rong; Yu, Ru-Qin
2011-07-15
A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L(-1) sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL(-1), respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices. PMID:21645706
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
NASA Astrophysics Data System (ADS)
Cockburn, Bernardo; Dong, Bo; Guzman, Johnny
2008-12-01
We identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree kge0 for both the potential as well as the flux, the order of convergence in L^2 of both unknowns is k+1 . Moreover, both the approximate potential as well as its numerical trace superconverge in L^2 -like norms, to suitably chosen projections of the potential, with order k+2 . This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order k+2 in L^2 . The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.
Second-order optical effects in several pyrazolo-quinoline derivatives
NASA Astrophysics Data System (ADS)
Makowska-Janusik, M.; Gondek, E.; Kityk, I. V.; Wisła, J.; Sanetra, J.; Danel, A.
2004-11-01
Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 μm varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities.
Unbalanced and Minimal Point Equivalent Estimation Second-Order Split-Plot Designs
NASA Technical Reports Server (NTRS)
Parker, Peter A.; Kowalski, Scott M.; Vining, G. Geoffrey
2007-01-01
Restricting the randomization of hard-to-change factors in industrial experiments is often performed by employing a split-plot design structure. From an economic perspective, these designs minimize the experimental cost by reducing the number of resets of the hard-to- change factors. In this paper, unbalanced designs are considered for cases where the subplots are relatively expensive and the experimental apparatus accommodates an unequal number of runs per whole-plot. We provide construction methods for unbalanced second-order split- plot designs that possess the equivalence estimation optimality property, providing best linear unbiased estimates of the parameters; independent of the variance components. Unbalanced versions of the central composite and Box-Behnken designs are developed. For cases where the subplot cost approaches the whole-plot cost, minimal point designs are proposed and illustrated with a split-plot Notz design.
Asynchronous consensus of multiple second-order agents with partial state information
NASA Astrophysics Data System (ADS)
Gao, Yanping; Zuo, Min; Jiang, Tongqiang; Du, Junping; Ma, Jingwei
2013-05-01
This article studies the asynchronous consensus problem of multiple second-order agents in a sampled-data setting, where asynchrony means that the sampling period of each agent is independent of the others. It is assumed that each agent can only obtain the information of its positions relative to its neighbours at sampling instants. First, a discrete-time protocol is provided based on velocity estimation, and a sufficient and necessary condition for consensus under this protocol is established in virtue of properties of periodic systems. Second, a continuous-time protocol is presented by the theory of dynamic output feedback control, and a sufficient condition for consensus under this protocol is obtained by applying an input delay approach. Simulations are performed to illustrate the effectiveness of the theoretical results.
Relative form boundedness and compactness for a second-order differential operator
NASA Astrophysics Data System (ADS)
Brown, Richard C.; Hinton, D. B. Don B.
2004-10-01
If A and L are self-adjoint operators on a Hilbert space such that A is nonnegative and L≥[var epsilon]I for some [var epsilon]>0 we study conditions under which A is form bounded or form compact with respect to L and contrast these concepts with the stronger properties that A be relatively operator bounded or compact with respect to L. In particular several definitions of form compactness are shown to be equivalent. The principal application of the theory is to self-adjoint second order operators. In this case conditions that A be form bounded or form compact with respect to L are shown in some cases to be necessary and sufficient. Examples include the energy operator of the hydrogen atom.
Fisher information of special functions and second-order differential equations
NASA Astrophysics Data System (ADS)
Yáñez, R. J.; Sánchez-Moreno, P.; Zarzo, A.; Dehesa, J. S.
2008-08-01
We investigate a basic question of analytic information theory, namely, the evaluation of the Fisher information and the relative Fisher information with respect to a non-negative function, for the probability distributions obtained by squaring the special functions of mathematical physics which are solutions of second-order differential equations. We obtain explicit expressions for these information-theoretic properties via the expectation values of the coefficients of the differential equation. We illustrate our approach for various nonrelativistic D-dimensional wavefunctions and some special functions of physicomathematical interest. Emphasis is made in the Nikiforov-Uvarov hypergeometric-type functions, which include and generalize the Hermite functions and the Gauss and Kummer hypergeometric functions, among others.
A second-order learning algorithm for multilayer networks based on block Hessian matrix.
Wang, Yi Jen; Lin, Chin Teng
1998-12-01
This article proposes a new second-order learning algorithm for training the multilayer perceptron (MLP) networks. The proposed algorithm is a revised Newton's method. A forward-backward propagation scheme is first proposed for network computation of the Hessian matrix, H, of the output error function of the MLP. A block Hessian matrix, H(b), is then defined to approximate and simplify H. Several lemmas and theorems are proved to uncover the important properties of H and H(b), and verify the good approximation of H(b) to H; H(b) preserves the major properties of H. The theoretic analysis leads to the development of an efficient way for computing the inverse of H(b) recursively. In the proposed second-order learning algorithm, the least squares estimation technique is adopted to further lessen the local minimum problems. The proposed algorithm overcomes not only the drawbacks of the standard backpropagation algorithm (i.e. slow asymptotic convergence rate, bad controllability of convergence accuracy, local minimum problems, and high sensitivity to learning constant), but also the shortcomings of normal Newton's method used on the MLP, such as the lack of network implementation of H, ill representability of the diagonal terms of H, the heavy computation load of the inverse of H, and the requirement of a good initial estimate of the solution (weights). Several example problems are used to demonstrate the efficiency of the proposed learning algorithm. Extensive performance (convergence rate and accuracy) comparisons of the proposed algorithm with other learning schemes (including the standard backpropagation algorithm) are also made. PMID:12662732
Barbot, Antoine; Landy, Michael S.; Carrasco, Marisa
2012-01-01
The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention—the more automatic, stimulus-driven component of spatial attention—helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention—the more voluntary, conceptually-driven component of spatial attention—affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions. PMID:22895879
Linear matrix inequalities for analysis and control of linear vector second-order systems
Adegas, Fabiano D.; Stoustrup, Jakob
2014-10-06
Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form.
NASA Astrophysics Data System (ADS)
Juhui, Chen; Yanjia, Tang; Dan, Li; Pengfei, Xu; Huilin, Lu
2013-07-01
Flow behavior of gas and particles is predicted by the large eddy simulation of gas-second order moment of solid model (LES-SOM model) in the simulation of flow behavior in CFB. This study shows that the simulated solid volume fractions along height using a two-dimensional model are in agreement with experiments. The velocity, volume fraction and second-order moments of particles are computed. The second-order moments of clusters are calculated. The solid volume fraction, velocity and second order moments are compared at the three different model constants.
Dai, William W. Scannapieco, Anthony J.
2015-01-15
A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials.
Second order effects of structural and material damage on ultrasonic waves
NASA Astrophysics Data System (ADS)
O'Neill, Brian E.
Damage mechanics is a relatively new and powerful approach to the analysis of material degradation and failure. The idea is to build a continuum model of a solid containing a distribution of microcracks. Such a model, relying on the thermodynamics and statistical mechanics of microcracks, very naturally ties into other continuum models of solids, including acoustic and elastic models. In this dissertation, the impact of material and structural damage is investigated, with an emphasis on the relation between this effect and specific second order ultrasonic effects. The investigation has two main streams. The first, more experimental stream involves damage in the bulk. In this case, we chose to look at fatigue damage in the Ni-based alloy, waspaloy, which is used particularly for high strength, high temperature applications in the aerospace industry, as well as exhibiting very intriguing physical and thermodynamic properties. The approach was to monitor the changes in two second order parameters, the so-called nonlinearity, or beta parameter, and the acousto-elastic parameter. Results of these experiments seem to indicate that the latter is a better indicator of fatigue and damage, at least in this material. The second, more theoretical stream concerns damage along an individual weak interface. In this case, a nonlinear "thin layer" model was developed for propagation of ultrasonic waves through a weak bonded interface, as well as a time-domain approach to a general solution to this problem for a multiply layered system. This was combined with a simple damage model, and used to demonstrate how poorly bonded interfaces may be interpreted as locally damaged materials. It was also demonstrated how the nonlinearity of intensive ultrasound passing through or reflecting off an interface bond may be used, along with an appropriate damage model, to estimate the ultimate strength of this bond.
Second-order theory of the rotation of an artificial satellite
NASA Astrophysics Data System (ADS)
Bois, Eric
The attitude evolution of the motion of a satellite subjected to specified torques is investigated analytically, extending the theory of Bois (1986) to second order. The formulation and reduction of the second-order differential equations are outlined, and the derivation of the solutions is given in detail. Numerical results for the ESA Hipparcos astrometric satellite are presented in graphs and briefly characterized.
The Second Order Approximation to Sample Influence Curve in Canonical Correlation Analysis.
ERIC Educational Resources Information Center
Fung, Wing K.; Gu, Hong
1998-01-01
A second order approximation to the sample influence curve (SIC) has been derived in the literature. This paper presents a more accurate second order approximation, which is exact for the SIC of the squared multiple correction coefficient. An example is presented. (SLD)
ERIC Educational Resources Information Center
Coull, Greig J.; Leekam, Susan R.; Bennett, Mark
2006-01-01
This study investigated how 4- to 7-year-old children's second-order belief attribution might be facilitated by either reducing information processing or varying the sequence of task questions. In Experiment 1, compared with Perner and Wimmer's (1985) original second-order false-belief task, a new task with reduced information-processing demands…
The similarity rules for second-order subsonic and supersonic flow
NASA Technical Reports Server (NTRS)
Van Dyke, Milton D
1958-01-01
The similarity rules for linearized compressible flow theory (Gothert's rule and its supersonic counterpart) are extended to second order. It is shown that any second-order subsonic flow can be related to "nearly incompressible" flow past the same body, which can be calculated by the Janzen-Rayleigh method.
Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations
ERIC Educational Resources Information Center
Robin, W.
2007-01-01
The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
On group classification of normal systems of linear second-order ordinary differential equations
NASA Astrophysics Data System (ADS)
Meleshko, S. V.; Moyo, S.
2015-05-01
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results and subsequent theorem arising from this particular study are discussed here. This paper considers the study of irreducible systems of second-order ordinary differential equations.
Post processing with first- and second-order hidden Markov models
NASA Astrophysics Data System (ADS)
Taghva, Kazem; Poudel, Srijana; Malreddy, Spandana
2013-01-01
In this paper, we present the implementation and evaluation of first order and second order Hidden Markov Models to identify and correct OCR errors in the post processing of books. Our experiments show that the first order model approximately corrects 10% of the errors with 100% precision, while the second order model corrects a higher percentage of errors with much lower precision.
Teacher's Corner: Testing Measurement Invariance of Second-Order Factor Models
ERIC Educational Resources Information Center
Chen, Fang Fang; Sousa, Karen H.; West, Stephen G.
2005-01-01
We illustrate testing measurement invariance in a second-order factor model using a quality of life dataset (n = 924). Measurement invariance was tested across 2 groups at a set of hierarchically structured levels: (a) configural invariance, (b) first-order factor loadings, (c) second-order factor loadings, (d) intercepts of measured variables,…
Tomita, Kenji; Inoue, Kaiki Taro
2008-05-15
We study second order gravitational effects of local inhomogeneities on the cosmic microwave background radiation in flat universes with matter and a cosmological constant {lambda}. We find that the general relativistic correction to the Newtonian approximation is negligible at second order provided that the size of the inhomogeneous region is sufficiently smaller than the horizon scale. For a spherically symmetric top-hat type quasilinear perturbation, the first order temperature fluctuation corresponding to the linear integrated Sachs-Wolfe effect is enhanced (suppressed) by the second order one for a compensated void (lump). As a function of redshift of the local inhomogeneity, the second order temperature fluctuations due to evolution of the gravitational potential have a peak before the matter-{lambda} equality epoch for a fixed comoving size and a density contrast. The second order gravitational effects from local quasilinear inhomogeneities at a redshift z{approx}1 may significantly affect the cosmic microwave background.
Second-order optical non-linearity of proton exchanged lithium tantalate waveguides
NASA Astrophysics Data System (ADS)
Korkishko, Y. N.; Fedorov, V. A.; Alkaev, A. N.; Laurell, F.
2001-10-01
A detailed correlation between the fabrication conditions, crystallographic phase state of HxLi1-xTaO3 waveguides and second-order optical non-linearity has been investigated by using reflected SHG measurements from the polished waveguide end face. The non-linearity, strongly reduced after the initial proton exchange, is found to be restored and even increased after annealing. However, this apparent increase in the non-linearity is accompanied by a strong degradation of the quality of the SHG reflected beam in the region of the initial as-exchanged waveguide due to beam scattering. The high temperature proton exchange technique has been shown to produce high-quality α-phase waveguides with essentially undegraded non-linear optical properties. There is no phase transition when the α-phase waveguides are fabricated by direct exchange. This phase presents the same crystalline structure as that of LiTaO3 and maintains the excellent non-linear properties of the bulk material. The results obtained are important for the design, fabrication and optimization of guided-wave non-linear optical devices in LiTaO3.
NASA Astrophysics Data System (ADS)
Grima, Ramon
2015-10-01
It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.
In unison: First- and second-order information combine for integration of shape information.
Tan, Ken W S; Dickinson, J Edwin; Badcock, David R
2016-09-01
The modulation of orientation around radial frequency (RF) patterns and RF textures is globally processed in both cases. This psychophysical study investigates whether the combination-a textured RF path obtained by applying an RF texture to an RF contour-is processed like a texture or a contour when making judgements about shape. Unlike RF textures, the impression of a closed flow was not required for global integration of textured RF paths, suggesting that these paths were processed as second-order, or contrast-defined contours. Luminance-defined (LD) RF paths were shown to globally integrate but with thresholds approximately half of those for the proposed second-order textured paths. The next experiment investigated whether this benefit was due to LD stimuli possessing double the amount of information (first- and second-order information). A mixed three-part contour composed of two different second-order texture components and an LD component was then employed to determine how the different cues combined. The mixed path thresholds matched predictions derived from a linear combination of first- and second-order cues. The conclusion is that the shape of isolated contours is processed using both first- and second-order information equally and that the contribution of texture is to carry additional second-order signal. PMID:27618513
Bose-Einstein or HBT Correlation Signals of a Second Order QCD Phase Transition
Csoergo, T.; Hegyi, S.; Novak, T.; Zajc, W. A.
2006-04-11
For particles emerging from a second order QCD phase transition, we show that a recently introduced shape parameter of the Bose-Einstein correlation function, the Levy index of stability equals to the correlation exponent -- one of the critical exponents that characterize the behaviour of the matter in the vicinity of the second order phase transition point. Hence the shape of the Bose-Einstein / HBT correlation functions, when measured as a function of bombarding energy and centrality in various heavy ion reactions, can be utilized to locate experimentally the second order phase transition and the critical end point of the first order phase transition line in QCD.
Orientation-selective adaptation to first- and second-order patterns in human visual cortex
Larsson, Jonas; Landy, Michael S.; Heeger, David J.
2006-01-01
Second-order textures – patterns that cannot be detected by mechanisms sensitive only to luminance changes – are ubiquitous in visual scenes, but the neuronal mechanisms mediating perception of such stimuli are not well understood. We used an adaptation protocol to measure neural activity in the human brain selective for the orientation of second-order textures. FMRI responses were measured in three subjects to presentations of first- and second-order probe gratings after adapting to a high-contrast first- or second-order grating that was either parallel or orthogonal to the probe gratings. First-order (LM) stimuli were generated by modulating the stimulus luminance. Second-order stimuli were generated by modulating the contrast (CM) or orientation (OM) of a first-order carrier. We used four combinations of adapter and probe stimuli: LM:LM, CM:CM, OM:OM, and LM:OM. The fourth condition tested for cross-modal adaptation with first-order adapter and second-order probe stimuli. Attention was diverted from the stimulus by a demanding task at fixation. Both first- and second-order stimuli elicited orientation-selective adaptation in multiple cortical visual areas, including V1, V2, V3, V3A/B, a newly identified visual area anterior to dorsal V3 which we have termed LO1, hV4, and VO1. For first-order stimuli (condition LM:LM), the adaptation was no larger in extrastriate areas than in V1, implying that the orientation-selective first-order (luminance) adaptation originated in V1. For second-order stimuli (conditions CM:CM and OM:OM), the magnitude of adaptation, relative to the absolute response magnitude, was significantly larger in VO1 (and for condition CM:CM, also in V3A/B and LO1) than in V1, suggesting that second-order stimulus orientation was extracted by additional processing after V1. There was little difference in the amplitude of adaptation between the second-order conditions. No consistent effect of adaptation was found in the cross-modal condition LM
First and second order approximations to stage numbers in multicomponent enrichment cascades
Scopatz, A.
2013-07-01
This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the free and open source PyNE library. (authors)
First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
Bonnans, J. Frederic; Silva, Francisco J.
2012-06-15
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
An Example of Following Second-Order Kinetics by Simple Laboratory Means
ERIC Educational Resources Information Center
Schreiber, Gisela
1976-01-01
Describes a procedure for studying the kinetics of the second-order hydrolysis of ethylene bromohydrine in alkaline medium by incorporating a substance that changes color as one of the reacting components is depleted. (MLH)
Completeness of first and second order ODE flows and of Euler-Lagrange equations
NASA Astrophysics Data System (ADS)
Minguzzi, Ettore
2015-11-01
Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to Lagrangian mechanics and gravitational waves are given.
Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.
A second order accurate embedded boundary method for the wave equation with Dirichlet data
Kreiss, H O; Petersson, N A
2004-03-02
The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.
NASA Technical Reports Server (NTRS)
Schmidt, K. H.
1970-01-01
IBM 1620 computer prepares tables to enable fast calculation of the first- and second-order rate constants from two half-lives and the corresponding initial concentrations, obtained from either one or two decay curves.
NASA Astrophysics Data System (ADS)
Huang, Juntao; Hu, Zexi; Yong, Wen-An
2016-04-01
In this paper, we present a kind of second-order curved boundary treatments for the lattice Boltzmann method solving two-dimensional convection-diffusion equations with general nonlinear Robin boundary conditions. The key idea is to derive approximate boundary values or normal derivatives on computational boundaries, with second-order accuracy, by using the prescribed boundary condition. Once the approximate information is known, the second-order bounce-back schemes can be perfectly adopted. Our boundary treatments are validated with a number of numerical examples. The results show the utility of our boundary treatments and very well support our theoretical predications on the second-order accuracy thereof. The idea is quite universal. It can be directly generalized to 3-dimensional problems, multiple-relaxation-time models, and the Navier-Stokes equations.
Comparison of Second-Order Loads on a Tension-Leg Platform for Wind Turbines: Preprint
Gueydon, S.; Wuillaume, P.; Jonkman, J.; Robertson, A.; Platt, A.
2015-03-01
The first objective of this work is to compare the two floating offshore wind turbine simulation packages {DIFFRAC+aNySIM} and {WAMIT+FAST}. The focus is on second-order wave loads, and so first- and second-order wave loads are applied to a structure sequentially for a detailed comparison and a more precise analysis of the effects of the second-order loads. aNySIM does not have the capability to model flexible bodies, and so the simulations performed in this tool are done assuming a rigid body. FAST also assumes that the platform is rigid, but can account for the flexibility of the tower. The second objective is to study the effects of the second-order loads on the response of a TLP floating wind turbine. The flexibility of the tower must be considered for this investigation, and therefore only FAST is used.
Multiple Positive Solutions in the Second Order Autonomous Nonlinear Boundary Value Problems
NASA Astrophysics Data System (ADS)
Atslega, Svetlana; Sadyrbaev, Felix
2009-09-01
We construct the second order autonomous equations with arbitrarily large number of positive solutions satisfying homogeneous Dirichlet boundary conditions. Phase plane approach and bifurcation of solutions are the main tools.
Second-order contributions to relativistic time delay in the parametrized post-Newtonian formalism
Richter, G.W.; Matzner, R.A.
1983-12-15
Using a parametrized expansion of the solar metric to second order in the Newtonian potential, we calculate the relativistic delay in the round-trip travel time of a radar signal reflected from a nearby planet. We find that one second-order contribution to the delay is on the order of ten nanoseconds, which is comparable to the uncertainties in present-day experiments involving the Viking spacecraft.
Parallel coding of first- and second-order stimulus attributes by midbrain electrosensory neurons.
McGillivray, Patrick; Vonderschen, Katrin; Fortune, Eric S; Chacron, Maurice J
2012-04-18
Natural stimuli often have time-varying first-order (i.e., mean) and second-order (i.e., variance) attributes that each carry critical information for perception and can vary independently over orders of magnitude. Experiments have shown that sensory systems continuously adapt their responses based on changes in each of these attributes. This adaptation creates ambiguity in the neural code as multiple stimuli may elicit the same neural response. While parallel processing of first- and second-order attributes by separate neural pathways is sufficient to remove this ambiguity, the existence of such pathways and the neural circuits that mediate their emergence have not been uncovered to date. We recorded the responses of midbrain electrosensory neurons in the weakly electric fish Apteronotus leptorhynchus to stimuli with first- and second-order attributes that varied independently in time. We found three distinct groups of midbrain neurons: the first group responded to both first- and second-order attributes, the second group responded selectively to first-order attributes, and the last group responded selectively to second-order attributes. In contrast, all afferent hindbrain neurons responded to both first- and second-order attributes. Using computational analyses, we show how inputs from a heterogeneous population of ON- and OFF-type afferent neurons are combined to give rise to response selectivity to either first- or second-order stimulus attributes in midbrain neurons. Our study thus uncovers, for the first time, generic and widely applicable mechanisms by which parallel processing of first- and second-order stimulus attributes emerges in the brain. PMID:22514313
Tripathy, Arun Kumar
2014-01-01
Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterization technique is used to establish duality results under generalized second order ρ-univexity assumption. PMID:27379308
Comments on the present state of second-order closure models for incompressible flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1992-01-01
Second-order closure models account for history and nonlocal effects of the mean velocity gradients on the Reynolds stress tensor. Turbulent flows involving body forces or curvature, Reynolds stress relaxational effects, and counter-gradient transport are usually better described. The topics are presented in viewgraph form and include: (1) the Reynolds stress transport equation; (2) issues in second-order closure modeling; and (3) near wall models.
Second-order many-body perturbation study of ice Ih.
He, Xiao; Sode, Olaseni; Xantheas, Sotiris S; Hirata, So
2012-11-28
Ice Ih is arguably the most important molecular crystal in nature, yet our understanding of its structural and dynamical properties is still far from complete. We present embedded-fragment calculations of the structures and vibrational spectra of the three-dimensional, proton-disordered phase of ice Ih performed at the level of second-order many-body perturbation theory with a basis-set superposition error correction. Our calculations address previous controversies such as the one related to the O-H bond length as well as the existence of two types of hydrogen bonds with strengths differing by a factor of two. For the latter, our calculations suggest that the observed spectral features arise from the directionality or the anisotropy of collective hydrogen-bond stretching vibrations rather than the previously suggested vastly different force constants. We also report a capability to efficiently compute infrared and Raman intensities of a periodic solid. Our approach reproduces the infrared and Raman spectra, the variation of inelastic neutron scattering spectra with deuterium concentration, and the anomaly of heat capacities at low temperatures for ice Ih. PMID:23206017
A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence
NASA Astrophysics Data System (ADS)
Grebenev, Vladimir N.; Oberlack, Martin
2009-02-01
We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals - 1.
Tomic, Slavisa; Beko, Marko; Dinis, Rui
2014-01-01
In this paper, we propose a new approach based on convex optimization to address the received signal strength (RSS)-based cooperative localization problem in wireless sensor networks (WSNs). By using iterative procedures and measurements between two adjacent nodes in the network exclusively, each target node determines its own position locally. The localization problem is formulated using the maximum likelihood (ML) criterion, since ML-based solutions have the property of being asymptotically efficient. To overcome the non-convexity of the ML optimization problem, we employ the appropriate convex relaxation technique leading to second-order cone programming (SOCP). Additionally, a simple heuristic approach for improving the convergence of the proposed scheme for the case when the transmit power is known is introduced. Furthermore, we provide details about the computational complexity and energy consumption of the considered approaches. Our simulation results show that the proposed approach outperforms the existing ones in terms of the estimation accuracy for more than 1.5 m. Moreover, the new approach requires a lower number of iterations to converge, and consequently, it is likely to preserve energy in all presented scenarios, in comparison to the state-of-the-art approaches. PMID:25275350
Numerical minimization of a second-order functional for image segmentation
NASA Astrophysics Data System (ADS)
Zanetti, Massimo; Ruggiero, Valeria; Miranda, Michele, Jr.
2016-07-01
In this paper we address the numerical minimization of a variational approximation of the Blake-Zisserman functional given by Ambrosio, Faina and March. Our approach exploits a compact matricial formulation of the objective functional and its decomposition into quadratic sparse convex sub-problems. This structure is well suited for using a block-coordinate descent method that cyclically determines a descent direction with respect to a block of variables by few iterations of a preconditioned conjugate gradient algorithm. We prove that the computed search directions are gradient related and, with convenient step-sizes, we obtain that any limit point of the generated sequence is a stationary point of the objective functional. An extensive experimentation on different datasets including real and synthetic images and digital surface models, enables us to conclude that: (1) the numerical method has satisfying performance in terms of accuracy and computational time; (2) a minimizer of the proposed discrete functional preserves the expected good geometrical properties of the Blake-Zisserman functional, i.e., it is able to detect first and second order edge-boundaries in images and (3) the method allows the segmentation of large images.
ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order
NASA Astrophysics Data System (ADS)
Verstraelen, T.; Ayers, P. W.; Van Speybroeck, V.; Waroquier, M.
2013-02-01
A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)], 10.1021/ja00275a013 in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.
Analyzing a stochastic time series obeying a second-order differential equation
NASA Astrophysics Data System (ADS)
Lehle, B.; Peinke, J.
2015-06-01
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2 N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.
Analyzing a stochastic time series obeying a second-order differential equation.
Lehle, B; Peinke, J
2015-06-01
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series. PMID:26172667
Beyond Wenzel and Cassie-Baxter: second-order effects on the wetting of rough surfaces.
Hejazi, Vahid; Moghadam, Afsaneh Dorri; Rohatgi, Pradeep; Nosonovsky, Michael
2014-08-12
The Wenzel and Cassie-Baxter models are almost exclusively used to explain the contact angle dependence of the structure of rough and patterned solid surfaces. However, these two classical models do not always accurately predict the wetting properties of surfaces since they fail to capture the effect of many interactions occurring during wetting, including, for example, the effect of the disjoining pressure and of crystal microstructure, grains, and defects. We call such effects the second-order effects and present here a model showing how the disjoining pressure isotherm can affect wettability due to the formation of thin liquid films. We measure water contact angles on pairs of metallic surfaces with nominally the same Wenzel roughness obtained by abrasion and by chemical etching. These two methods of surface roughening result in different rough surface structure, thus leading to different values of the contact angle, which cannot be captured by the Wenzel- and Cassie-type models. The chemical and physical changes that occur on the stainless steel and aluminum alloy surfaces as a result of intergranular corrosion, along with selective intermetallic dissolution, lead to a surface roughness generated on the nano- and microscales. PMID:25051526
Second-order nonlinear optical characteristics of nanoscale self-assembled multilayer organic films
NASA Astrophysics Data System (ADS)
Neyman, Patrick J.
(30 pm/V). Thermal and temporal stability are important properties of electro-optic device implementation, and are demonstrated for CHISAM films. CHISAM films have remained stable at room temperature for more than 420 days, and suffered no loss of chi(2) when held at 80°C for 36 hours, followed by 150°C for 24 hours. Studies are also presented that demonstrate the ability to produce ISAM chi (2) films that are nearly one micron thick, and exhibit no evidence of a thickness limitation to the polar order. Analytical considerations for second-order NLO characterization of thick films are addressed in detail. The effect of absorption of the second harmonic wavelength and resonant enhancement of chi(2) are investigated, and it is demonstrated that accurate determination of chi(2) may be made for thick films and for films that absorb the second harmonic. The temporal and thermal stability of a variety of ISAM and CHISAM NLO films are examined in detail. In some cases, a decrease in the NLO response is observed at elevated temperature that is completely restored upon cooling. Studies are presented that suggest this effect is a result of thermally induced trans-to- cis isomerization of azo linkages in the NLO chromophores.
NASA Technical Reports Server (NTRS)
Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James
1992-01-01
Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.
NASA Astrophysics Data System (ADS)
Togni, Riccardo; Cimarelli, Andrea; Lozano-Durán, Adrián; De Angelis, Elisabetta
2016-04-01
One of the most peculiar aspects of turbulence in wall bounded-flows is the ability of the turbulent fluctuations to regenerate themselves through self-sustained processes. The dynamics of these self-sustaining mechanisms has been extensively investigated in the past via two complementary approaches. From one side, the possibility to identify very robust kinematic features within the flow feeds the hope of the scientific community to obtain a complete and consistent dynamical description of the physics of the turbulent regeneration cycles in terms of the so-called coherent structures. From the other side, the multi-scale and inhomogeneous features of the self-sustaining mechanisms of turbulence have been addressed by means of global statistical quantities based on two-point averages such as second-order structure functions. The present work attempts to link these two approaches, by identifying how turbulent cycle mechanisms and turbulent structures reflect on the global statistical properties of second-order structure function. To this aim we use Direct Numerical Simulation data of thermally driven turbulence in the Rayleigh-Bénard convection and we analyse for the first time the behaviour of the second-order structure function of temperature in the complete four-dimensional space of spatio-temporal scales and wall-distances. The observed behaviour is then interpreted in terms of the dynamics of coherent thermal structures and of their commonly accepted model of life-cycle.
Piponnier, Jean-Claude; Forget, Robert; Gagnon, Isabelle; McKerral, Michelle; Giguère, Jean-François; Faubert, Jocelyn
2016-01-15
Mild traumatic brain injury (mTBI) has subtle effects on several brain functions that can be difficult to assess and follow up. We investigated the impact of mTBI on the perception of sine-wave gratings defined by first- and second-order characteristics. Fifteen adults diagnosed with mTBI were assessed at 15 days, 3 months, and 12 months postinjury. Fifteen matched controls followed the same testing schedule. Reaction times (RTs) for flicker detection and motion direction discrimination were measured. Stimulus contrast of first- and second-order patterns was equated to control for visibility, and correct-response RT means, standard deviations (SDs), medians, and interquartile ranges (IQRs) were calculated. The level of symptoms was also evaluated to compare it to RT data. In general in mTBI, RTs were longer, and SDs as well as IQRs larger, than those of controls. In addition, mTBI participants' RTs to first-order stimuli were shorter than those to second-order stimuli, and SDs as well as IQRs larger for first- than for second-order stimuli in the motion condition. All these observations were made over the three sessions. The level of symptoms observed in mTBI was higher than that of control participants, and this difference did also persist up to 1 year after the brain injury, despite an improvement. The combination of RT measures with particular stimulus properties is a highly sensitive method for measuring mTBI-induced visuomotor anomalies and provides a fine probe of the underlying mechanisms when the brain is exposed to mild trauma. PMID:25950948
Oxazines: A New Class of Second-Order Nonlinear Optical Switches.
Beaujean, Pierre; Bondu, Flavie; Plaquet, Aurélie; Garcia-Amorós, Jaume; Cusido, Janet; Raymo, Françisco M; Castet, Frédéric; Rodriguez, Vincent; Champagne, Benoît
2016-04-20
A combined experimental-theoretical investigation has revealed that oxazine-based compounds are multiaddressable, multistate, and multifunctional molecular switches exhibiting contrasts of both linear and second-order nonlinear optical properties. The switching properties are particularly large when the substituent is a donor group. In this study, the cleavage of the C-O bond at the junction of the indole and oxazine cycles (of the closed a forms) is acido-triggered, leading to an open form (b(+)) characterized by larger first hyperpolarizabilities (βHRS) and smaller excitation energies than in the closed form. These results are confirmed and interpreted utilizing ab initio calculations that have been carried out on a broad set of compounds to unravel the role of the substituent. With respect to acceptor groups, oxazines bearing donor groups are characterized not only by larger βHRS and βHRS contrast ratios but also by smaller excitation energies, larger opening-induced charge transfer, and reduction of the bond length alternation, as well as smaller Gibbs energies of the opening reaction. Compared to protonated open forms (b(+)), calculations on the zwitterionic open forms (b) have pointed out similarities in the long-wavelength UV/vis absorption spectra, whereas their βHRS values might differ strongly as a function of the substituent. Indeed, the open forms present two NLOphores, the indoleninium-substituent entity and the nitrophenol (present in the protonated open form, b(+)) or nitrophenolate (present in the zwitterionic open form, b) moiety. Then, nitrophenolate displays a larger first hyperpolarizability than nitrophenol and the β tensor of the two entities might reinforce or cancel each other. PMID:26996994