Crystal structures and second-order NLO properties of borogermanates
Zhang, Jian-Han; Kong, Fang; Xu, Xiang; Mao, Jiang-Gao
2012-11-15
Borogermanates are a class of very important compounds in materials chemistry. In this paper, the syntheses, structures, and properties of metal borogermanates are reviewed. Organically templated borogermanates with zeolite-like open-frameworks show potential applications as microporous materials. Many compounds in alkali or alkaline-earth borogermanate systems are structurally acentric or polar, some of which exhibit excellent Second Harmonic Generation (SHG) coefficients, wide transparency regions, and high optical-damage thresholds as well as excellent thermal stability. Most of the lanthanide borogermanates are structurally centrosymmetric and not SHG active; however, they are able to emit strong luminescence in visible or near-IR region. In the B-rich compounds, BO{sub 3} and BO{sub 4} groups can be polymerized into a variety of discrete polynuclear anionic cluster units or extended architectures via B-O-B bridges; whereas in the Ge-rich compounds, GeO{sub 4} and GeO{sub 6} polyhedra can also be polymerized. The combinations of borate and germinate afforded rich structural and topological types. - Graphical abstract: Borogermanates are a class of very important compounds in materials chemistry. Both BO{sub x} (x=3, 4) and GeO{sub y} (y=4, 6) polyhedra can be polymerized into a variety of discrete polynuclear anionic cluster units or extended architectures. The combinations of borate and germanate groups in the same oxide framework not only give rise to a rich structural chemistry, but also afford many polar compounds with good SHG properties. Highlights: Black-Right-Pointing-Pointer Borogermanates are a class of new materials. Black-Right-Pointing-Pointer They feature to be the combination of B and Ge atoms into the same oxide framework. Black-Right-Pointing-Pointer They can form a large number of novel 2D and 3D framework structures. Black-Right-Pointing-Pointer Some of them are acentric or polar with moderate strong SHG responses.
Restoration and enhancement of textural properties in SAR images using second-order statistics
NASA Astrophysics Data System (ADS)
Nezry, Edmond; Kohl, Hans-Guenther; De Groof, Hugo
1994-12-01
Local second order properties, describing spatial relations between pixels are introduced into the single-point speckle adaptive filtering processes, in order to account for the effects of speckle spatial correlation and to enhance scene textural properties in the restored image. To this end, texture measures originating, first from local grey level co-occurrence matrices (GLCM), and second from the local autocorrelation functions (ACF) are used. Results obtained on 3-look processed ERS-1 FDC and PRI spaceborne images illustrate the performance allowed by the introduction of these texture measures in the structure retaining speckle adaptive filters. The observable texture in remote sensing images is related to the physical spatial resolution of the sensor. For this reason, other spatial speckle decorrelation methods, more simple and easier to implement, for example post-filtering and linear image resampling, are also presented in this paper. In the particular case of spaceborne SAR imagery, all these methods lead to visually similar results. They produce filtered (radar reflectivity) images visually comparable to optical images.
NASA Astrophysics Data System (ADS)
Yuan, Jian-Hui; Chen, Ni; Zhang, Yan; Mo, Hua; Zhang, Zhi-Hai
2016-03-01
Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells are studied theoretically. Both the second-harmonic generation susceptibility and nonlinear optical rectification depend dramatically on the direction and the strength of the electric field. Numerical results show that both the second-harmonic generation susceptibility and nonlinear optical rectification are always weakened as the electric field increases where the direction of the electric field is along the growth direction of the quantum wells, which is in contrast to the conventional case. However, the second-harmonic generation susceptibility is weakened, but the nonlinear optical rectification is strengthened as the electric field increases where the direction of the electric field is against the growth direction of the quantum wells. Also it is the blue (or red) shift of the resonance that is induced by increasing of the electric field when the direction of the electric field is along (or against) the growth direction of the quantum wells. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.
Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.
2005-01-15
We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at {lambda}=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples.
NASA Astrophysics Data System (ADS)
Schroeder, Craig; Stomakhin, Alexey; Howes, Russell; Teran, Joseph M.
2014-05-01
We present a numerical method for the solution of the Navier-Stokes equations in three dimensions that handles interfacial discontinuities due to singular forces and discontinuous fluid properties such as viscosity and density. We show that this also allows for the enforcement of normal stress and velocity boundary conditions on irregular domains. The method improves on results in [1] (which solved the Stokes equations in two dimensions) by providing treatment of fluid inertia as well as a new discretization of jump and boundary conditions that accurately resolves null modes in both two and three dimensions. We discretize the equations using an embedded approach on a uniform MAC grid to yield discretely divergence-free velocities that are second order accurate. We maintain our interface using the level set method or, when more appropriate, the particle level set method. We show how to implement Dirichlet (known velocity), Neumann (known normal stress), and slip velocity boundary conditions as special cases of our interface representation. The method leads to a discrete, symmetric KKT system for velocities, pressures, and Lagrange multipliers. We also present a novel simplification to the standard combination of the second order semi-Lagrangian and BDF schemes for discretizing the inertial terms. Numerical results indicate second order spatial accuracy for the velocities (L∞ and L2) and first order for the pressure (in L∞, second order in L2). Our temporal discretization is also second order accurate.
Parron, Carole; Fagot, Joël
2008-05-01
A two-alternative forced-choice discrimination task was used to assess whether baboons (N=7) spontaneously process qualitative (i.e., first-order) or quantitative (i.e., second-order) variations in the configural arrangement of facial features. Experiment 1 used as test stimuli second-order pictorial faces of humans or baboons in which the mouth and the eyes were rotated upside down relative to the normal face. Baboons readily discriminated two different normal faces but did not discriminate a normal face from its second-order modified version. Experiment 2 used human or baboon faces for which the first-order configural properties had been distorted by reversing the location of the eyes and mouth within the face. Discrimination was prompt with these stimuli. Experiment 3 replicated some of the conditions and the results of experiment 1, thus ruling out possible effects of learning. It is concluded that baboons are more adept at spontaneously processing first- than second-order configural facial properties, similar to what is known in the human developmental literature.
Wang, Wen-Yong; Du, Xiao-Feng; Ma, Na-Na; Sun, Shi-Ling; Qiu, Yong-Qing
2013-04-01
As a kind of novel organometallic complexes, the cyclopentadienylcobalt (CpCo) linear [4]phenylene complexes (4 = number of benzene rings) display efficient switchable nonlinear optical (NLO) response when CpCo reversibly migrates along the linear [4]phenylene triggered by heating or lighting. In this paper, the second-order NLO properties for CpCo linear [4]phenylene complexes were calculated by using the density functional theory (DFT) methods with four functionals. All of the functionals yield the same order of β tot values: 1<2<4<3. 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 vacuo. The electronic absorption spectra were investigated by the TDDFT methods. The TDDFT calculations indicate that the maximum absorption peaks of complexes 2-4 in the near-infrared spectrum area show the bathochromic shift together with a decreasing intensity compared to complex 1. We have also found that the cobalt (Co) atom acts as a donor in all the organometallic complexes and the d → π* and π → π* charge transfer (CT) transitions contribute to the enhancement of second-order NLO response. Furthermore, two experimentally existing complexes 1 and 3 are found to have a large difference in β tot values. It is our expectation that this difference may stimulate the search for a new type of switchable NLO material based on CpCo linear [4]phenylene complexes.
Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît
2013-09-21
In this paper it is shown that modest calculations combining first principles evaluations of the molecular properties with electrostatic interaction schemes to account for the crystal environment effects are reliable for predicting and interpreting the experimentally measured electric linear and second-order nonlinear optical susceptibilities of molecular crystals within the experimental error bars. This is illustrated by considering two molecular crystals, namely: 2-methyl-4-nitroaniline and 4-(N,N-dimethylamino)-3-acetamidonitrobenzene. Three types of surrounding effects should be accounted for (i) the polarization due to the surrounding molecules, described here by static electric fields originating from their electric dipoles or charge distributions, (ii) the intermolecular interactions, which affect the geometry and particularly the molecular conformation, and (iii) the screening of the external electric field by the constitutive molecules. This study further highlights the role of electron correlation on the linear and nonlinear responses of molecular crystals and the challenge of describing frequency dispersion.
NASA Astrophysics Data System (ADS)
Bencheikh, F.; Sandanayaka, A. S. D.; Matsushima, T.; Ribierre, J. C.; Adachi, C.
2017-06-01
We report on the cavity numerical characterization of a second order one-dimensional distributed feedback organic laser. The gain medium containing 6 wt. % of 4,4'-bis[(N-carbazole)styryl]biphenyl) in a 4,4'-bis[9-dicarbazolyl]-2,2'-biphenyl) host is vacuum deposited to form an organic thin film on a SiO2 grating. The influence of the organic film thickness on the properties of the resonant cavity is investigated through numerical calculations of both the confinement factor Γ and the Q-factor. The Q-factor is obtained using two methods, one by calculating the eigenmodes of the resonant cavity and the other by calculating the reflection spectrum. It was found that while the Γ increases with the organic film thickness, the Q-factor shows a non-monotonic function with a maximum value for a thickness of 200 nm.
Marco, A Belén; Martínez de Baroja, Natalia; Franco, Santiago; Garín, Javier; Orduna, Jesús; Villacampa, Belén; Revuelto, Alejandro; Andreu, Raquel
2015-01-01
4H-Pyranylidene-containing push-pull chromophores built around a bithiophene (BT) π relay or a rigidified thiophene-based unit, namely cyclopenta[1,2-b:3,4-b']dithiophene (CPDT) or dithieno[3,2-b:2',3'-d]pyrrole (DTP), have been synthesized and characterized. The effect of these different relays on the polarization and the second-order nonlinear optical (NLO) properties has been studied. For the sake of comparison, the corresponding reported dithieno[3,2-b:2',3'-d]thiophene (DTT) derivatives have also been included in the discussion. Replacement of the BT core by a rigidified unit (CPDT, DTP) leads to more polarized systems. Calculated NBO charges and electrochemical measurements show that dithienopyrrole has a remarkable donor character that allows an important charge transfer between the donor and the acceptor. The influence of the rigidification of the BT relay on the NLO responses depends on the acceptor strength. For the weakest acceptor used (thiobarbituric acid), passing from the BT relay to the rigidified units always involves an increase in the μβ0 figure of merit. Nevertheless, for the strongest acceptor (2-dicyanomethylene-3-cyano-4,5,5-trimethyl-2,5-dihydrofuran (TCF)), a slight increase in μβ0 with respect to the BT chromophore is only observed for the DTP derivative. Thus, rigidification of the BT core is not enough to improve the second-order nonlinearity and the incorporation of a DTP moiety has proven to be the most efficient approach for this purpose.
Ma, Nana; Yan, Likai; Guan, Wei; Qiu, Yongqing; Su, Zhongmin
2012-04-28
We report a theoretical study based on density functional theory (DFT) on the geometric and electronic structure, linear optical and second-order nonlinear optical properties of a series of new inorganic-organic hybrid hexamolybdate-organoimido-(car)boranes. By the incorporation of borane/carborane at the end of the phenyl ring of the organoimido segment, the studied systems show excellent nonlinear optical (NLO) response than the organoimido-substituted hexamolybdate. The computed static first hyperpolarizability β(vec) value of [Mo(6)O(18)(NC(8)H(8))(B(12)H(11))](4-) (II) is largest, -167.2 × 10(-30) esu, and a higher β(vec) value of [Mo(6)O(18)(NC(8)H(8))(C(2)B(10)H(11))](2-) (III-2p) is 58.6 × 10(-30) esu. Moreover, the time-dependent (TD)DFT calculation illustrates that the maximum absorption, which is helpful for the large NLO responses, is mainly assigned to the charge transfer (CT) from (car)borane and organoimido segment to the hexamolybdate cluster. The density of density (DOS) calculations further illustrate the excitation from valence orbitals of boron atoms to that of Mo and O atoms in hexamolybdate can be responsible for larger NLO responses. The linear and nonlinear optical properties of species III both vary with the position of the vertex on the carborane. Furthermore, the order of the β(vec) values is consistent with the bathochromic shift of the maximum absorption for our studied systems, and the studied systems show a wider transparency range extending into the entire visible and infrared (IR) region.
NASA Astrophysics Data System (ADS)
Kiethe, Jan; Heuer, Axel; Jechow, Andreas
2017-08-01
We study the degree of second-order coherence of the emission of a high-power multi-quantum well superluminescent diode with a lateral tapered amplifier section with and without optical feedback. When operated in an external cavity, the degree of second-order coherence changed from the almost thermal case of g(2)(0)≈1.9 towards the mostly coherent case of g(2)(0)≈1.2 when the injection current at the tapered section was increased. We found good agreement with semi-classical laser theory near and below threshold while above laser threshold a slightly higher g (2)(0) was observed. As a free running device, the superluminescent diode yielded more than 400 mW of optical output power with good spatial beam quality of M^2_slow < 1.6 . In this case, the degree of second-order coherence dropped only slightly from 1.9 at low powers to 1.6 at the maximum output power. To our knowledge, this is the first investigation of a high-power tapered superluminescent diode concerning the degree of second-order coherence. Such a device might be useful for real-world applications probing the second order coherence function, such as ghost imaging.
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
Escudero, Daniel; Thiel, Walter; Champagne, Benoît
2015-07-15
In this communication we use the density functional theory-based multi-reference configuration interaction (DFT/MRCI) and the second-order algebraic diagrammatic construction (ADC(2)) methods to compute the spectroscopic and second-order nonlinear optical (NLO) properties of Ru(ii)-based NLO-phores. For some of the complexes, an appropriate treatment of doubly excited states is essential to correctly describe their spectroscopic and photochemical properties. Geometrical and solvent relaxation effects are also assessed. An adequate treatment of solvent effects seems critical for an accurate description of the NLO properties of these complexes.
Lematre, M; Domenjoud, M; Tran-Huu-Hue, L P
2011-12-01
In this study we develop the exact second order formalism of piezoelectric structures under an external mechanical stress. Indeed, previous models are approximated since they consist in deriving all the equations in the natural coordinate system (corresponding to the pre-stress free case). Hence, our exact formalism proposes to obtain the whole of equations in the current coordinate system (which is the coordinate system after the pre-deformation). Then, this exact formalism is used to derive the modified Christoffel equations and the modified KLM model. Finally, we quantify the correction with the approximate formalism on several transfer functions and electro-mechanical parameters for a non hysteretic material (lithium niobate). In conclusion, we show that for this material, significant corrections are obtained when studying the plane wave velocities and the electrical input impedance (about 4%), whereas other parameters such as coupling coefficient and impulse response are less influenced by the choice of coordinate systems (corrections less than 0.5%).
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.
Cuzinatto, R.R. . E-mail: rodrigo@ift.unesp.br; Melo, C.A.M. de . E-mail: cassius.anderson@gmail.com; Pompeia, P.J. . E-mail: pompeia@ift.unesp.br
2007-05-15
A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = {partial_derivative}F + fAF arises besides the one of the first order treatment, F = {partial_derivative}A - {partial_derivative}A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L {sub P} {proportional_to} G {sup 2}. In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.
NASA Astrophysics Data System (ADS)
Huang, Shuang; Yang, Bao-Zhu; Jiang, Xing-Fang; Guo, Jing-Fu; Ren, Ai-Min
2014-12-01
The static second-order nonlinear optical susceptibilities (β0) of a series of macrocyclic thiophene-based derivatives with strong donor/acceptor (D/A) substituents were studied in detail on the basis of the stability of the equilibrium geometries calculated at density functional theory (DFT) level. The research results show that the type of substituent, the pair number and the position of D/A group all have important influence on the value of β0. The molecule 4A1-4D5-8 with four pairs of electron donor (sbnd NH2) and acceptor (sbnd CN) located at contraposition has larger value of β0 (-338.88 × 10-30/esu), which is close to 50 times larger than that of SII. And the absolute value of β0 enlarges as increasing the ring size or the pair number. Moreover, the effects of BLA and charge transfer are analyzed to explain the significant enlargement of β0 for the molecules with stronger D/A group, besides the influence factors of ƒ, Δμ and W in the two-level approximation formula. In addition, it indicates an approximately proportional relationship between the values of β0 and δmax for most studied molecules.
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.
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.
Janjua, Muhammad Ramzan Saeed Ashraf; Guan, Wei; Yan, Likai; Su, Zhong-Min; Ali, Muhammad; Bukhari, Iftikhar Hussain
2010-06-01
We have explored an innovative, versatile, and novel molecular hybrid containing polyoxometalate (POM) cluster linked with terpyridine ligand via pi-bridged donor-acceptor (D-A) configuration. The dipole polarizabilities, density of states, and second-order nonlinear optical (NLO) properties of terpyridine-substituted hexamolybdates have been investigated by using time-dependent density functional response theory (TDDFT). This class of organic-inorganic hybrid compounds possesses a robustly large molecular second-order NLO response, especially [Mo(6)O(18)(N(4)C(25)H(16)I(2))](2-) (system 5) and [Mo(6)O(17)(N(4)C(25)H(16)(CN)(2))(N(4)C(25)H(16)(CN)(2))](2-) (system 10) with the static second-order polarizability (beta(vec)) computed to be 1209.25x10(-30)esu and 1622.67x10(-30)esu respectively. Thus, these systems have the possibility to be excellent second-order nonlinear optical materials. Analysis of the major contributions to the beta(vec) value suggests that the charge transfer (CT) from POM-cluster to terpyridine ligand (D-A) along the z-axis plays the key role in the NLO response, POM-cluster (hexamolybdates) acts as a donor (D) whereas terpyridine ligand acts as an acceptor (A) in all the studied systems. The computed beta(vec) values increase by the incorporation of electron acceptors (halogen=F, Cl, Br and I) at the terminus of terpyridine ligand. Furthermore, substitution of trifluoromethoxy (-OCF(3)), trifluoromethyl (-CF(3)), and cyanide (-CN) at the end of terpyridine ligand respectively enhances the optical nonlinearity. Orbital analysis shows that the degree of CT between POM and terpyridine segment was increased in 2D and organometallic/POM hybrid systems. The present investigation provides important and thought provoking insight into the robustly large NLO properties of terpyridine-substituted hexamolybdates. Copyright (c) 2010 Elsevier Inc. All rights reserved.
Yumura, Takashi; Yamamoto, Wataru
2017-09-20
We employed density functional theory (DFT) calculations with dispersion corrections to investigate energetically preferred alignments of certain p,p'-dimethylaminonitrostilbene (DANS) molecules inside an armchair (m,m) carbon nanotube (n × DANS@(m,m)), where the number of inner molecules (n) is no greater than 3. Here, three types of alignments of DANS are considered: a linear alignment in a parallel fashion and stacking alignments in parallel and antiparallel fashions. According to DFT calculations, a threshold tube diameter for containing DANS molecules in linear or stacking alignments was found to be approximately 1.0 nm. Nanotubes with diameters smaller than 1.0 nm result in the selective formation of linearly aligned DANS molecules due to strong confinement effects within the nanotubes. By contrast, larger diameter nanotubes allow DANS molecules to align in a stacking and linear fashion. The type of alignment adopted by the DANS molecules inside a nanotube is responsible for their second-order non-linear optical properties represented by their static hyperpolarizability (β0 values). In fact, we computed β0 values of DANS assemblies taken from optimized n × DANS@(m,m) structures, and their values were compared with those of a single DANS molecule. DFT calculations showed that β0 values of DANS molecules depend on their alignment, which decrease in the following order: linear alignment > parallel stacking alignment > antiparallel stacking alignment. In particular, a linear alignment has a β0 value more significant than that of the same number of isolated molecules. Therefore, the linear alignment of DANS molecules, which is only allowed inside smaller diameter nanotubes, can strongly enhance their second-order non-linear optical properties. Since the nanotube confinement determines the alignment of DANS molecules, a restricted nanospace can be utilized to control their second-order non-linear optical properties. These DFT findings can assist in the design
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.
Jalali-Heravi, M; Khandar, A A; Sheikshoaie, I
2000-07-01
A series of asymmetric three dentate salicylaldiminato Schiff base ligands 1-4 (Scheme 1) has been synthesized and their structures, electronic properties and second order nonlinearities are investigated using the AM1 Hamiltonian SCF-MO methods. The analysis of MOs indicates that the O(2) atom could be the coordination site if the ligands were monodentate. In addition, the atomic orbitals on the O(9) atom have no contributions to the frontier MOs of the anionic form of these three dentate ligands. The Mulliken populations reveal that the coordination sites N(6) and O(9) possess different character in generation of the Schiff base complexes. The molecular first-order hyperpolarizability value of ligands was calculated using finite field method. Generally the presence of the methoxy group as third dentate play a major role in increasing the second harmonic generation (SHG) responses of three dentate ligands. Comparison of the NLO properties of two dentate with three dentate salicylaldiminine-based ligands reveals that the presence of -NO2 and -OCH3 groups as R1 and R2 substituents enhance the second-order nonlinear optic properties of these type ligands.
NASA Astrophysics Data System (ADS)
Jalali-Heravi, M.; Khandar, A. A.; Sheikshoaie, I.
2000-07-01
A series of asymmetric three dentate salicylaldiminato Schiff base ligands 1- 4 ( Scheme 1) has been synthesized and their structures, electronic properties and second order nonlinearities are investigated using the AM1 Hamiltonian SCF-MO methods. The analysis of MOs indicates that the O(2) atom could be the coordination site if the ligands were monodentate. In addition, the atomic orbitals on the O(9) atom have no contributions to the frontier MOs of the anionic form of these three dentate ligands. The Mulliken populations reveal that the coordination sites N(6) and O(9) possess different character in generation of the Schiff base complexes. The molecular first-order hyperpolarizability value of ligands was calculated using finite field method. Generally the presence of the methoxy group as third dentate play a major role in increasing the second harmonic generation (SHG) responses of three dentate ligands. Comparison of the NLO properties of two dentate with three dentate salicylaldiminine-based ligands reveals that the presence of NO 2 and OCH 3 groups as R 1 and R 2 substituents enhance the second-order nonlinear optic properties of these type ligands.
NASA Astrophysics Data System (ADS)
Jalali-Heravi, M.; Khandar, A. A.; Sheikshoaie, I.
1999-10-01
A new series of asymmetric salicylaldiminato Schiff base ligands 1-9 has been synthesized and their structures, electronic properties and second-order nonlinearities are investigated. Three ligands of 1, 4 and 9 with different substituents were chosen as models for a theoretical investigation. Geometric parameters of model ligands and corresponding monoanions suggest that the substituents R 1 and R 2 have no significant effects on complex formation. The AM1 calculated changes in the bandgap indicate that the overall trend of variation of this parameter as a function of increase in the degree of nonplanarity is a red-to-blue transition. The analysis of low-electronic transitions of monoanions indicates that the MO more likely to combine with first-row transition metal orbitals is a orbital which is located on the O(2) atom. The Mulliken populations reveal that the influence of the R 1 and R 2 substituents on the population of the coordination sites is negligible. The molecular hyperpolarizability value of model ligands 1, 4, and 9 were calculated using field finite method. The ligand 1 showed a good second-order nonlinear optical (NLO) property. Although both R 1 and R 2 have effects on second harmonic generation (SHG) response, but R 2 plays a major role in designing of the NLO salicylaldiminiato Schiff base ligands.
Wang, Cun-Huan; Ma, Na Na; Sun, Xiu-Xin; Sun, Shi-Ling; Qiu, Yong-Qing; Liu, Peng-Jun
2012-11-01
The static second-order nonlinear optical (NLO) properties on a series of the two-dimensional (2D) pincer Ru(II) complexes with the substituted Tpy and H(2)SCS tridentate ligands (Tpy = 2,2':6',2″-terpyridyl and H(2)SCS = 2,6-bis(benzylaminothiocarbonyl)phenyl) have been investigated by density functional theory (DFT). Introducing different donor/acceptor substituents to two ligands has an influence on the static first hyperpolarizabilities (β(tot)) of the 2D systems. Compared to the reference system 1 [Ru(H(2)SCS)(Tpy)](+), introducing the branches with strong electron acceptor group (p-NO(2)-phenylethynyl) to the Tpy ligand or the branches with strong electron donor group (p-NH(2)-phenylethynyl) to the H(2)SCS ligand can effectively improve the β(tot) values. Time-dependent DFT (TDDFT) calculations indicate that the enhanced β(tot) values of the substituted systems are dominated by the intraligand charge transfer (ILCT), metal-to-ligand charge transfer (MLCT) and ligand-to-metal charge transfer (LMCT) transitions. Furthermore, the proton abstraction plays an important role in tuning the second-order NLO response. Particularly, for system 5 bearing the branches with NO(2) groups on H(2)SCS ligand, there is a dramatic enhancement in the β(tot) values for its deprotonated forms. The β(tot) values of the monodeprotonated system 5-H and the dideprotonated system 5-2H (58.712 × 10(-30) and 761.803 × 10(-30) esu) are about 7.58 times and 36.4 times larger than their diprotonated system 5, respectively. The second-order NLO responses based on substituent effect and proton abstraction switch are two-dimensional in characteristic with the large off-diagonal tensor values.
Ferreira-Valente, Alexandra; Costa, Patrício; Elorduy, Marta; Virumbrales, Montserrat; Costa, Manuel J; Palés, Jorge
2016-09-19
Empathy is a key aspect of the physician-patient interactions. The Jefferson Scale of Empathy (JSE) is one of the most used empathy measures of medical students. The development of cross-cultural empathy studies depends on valid and reliable translations of the JSE. This study sought to: (1) adapt and assess the psychometric properties in Spanish students of the Spanish JSE validated in Mexican students; (2) test a second order latent factor model. The Spanish JSE was adapted from the Spanish JSE-S, resulting in a final version of the measure. A non-probabilistic sample of 1104 medical students of two Spanish medical schools completed a socio-demographic and the Spanish JSE-S. Descriptive statistics, along with a confirmatory factor analysis, the average variance extracted (AVE), Cronbach's alphas and composite reliability (CR) coefficients were computed. An independent samples t-test was performed to access sex differences. The Spanish JSE-S demonstrated acceptable to good sensitivity (individual items - except for item 2 - and JSE-S total score: -2.72 < Sk < 0.35 and -0.77 < Ku < 7.85), convergent validity (AVE: between 0.28 and 0.45) and reliability (Cronbach's alphas: between 0.62 and 0.78; CR: between 0.62 and 0.87). The confirmatory factor analysis supported the three-factor solution and the second order latent factor model. The findings provide support for the sensitivity, construct validity and reliability of the adapted Spanish JSE-S with Spanish medical students. Data confirm the hypothesized second order latent factor model. This version may be useful in future research examining empathy in Spanish medical students, as well as in cross-cultural studies.
NASA Astrophysics Data System (ADS)
Karimi, M. J.; Vafaei, H.
2015-02-01
In this work, the optical rectification and the second harmonic generation coefficients in a strained InGaN/AlGaN quantum well are studied. Impacts of the spontaneous and piezoelectric polarization fields on the potential profile are taken into account. The energy levels and wave functions are calculated using the fourth-order Runge-Kutta method and optical properties are obtained using the compact density matrix approach. Effects of intense laser field, In composition, Al composition, the well width and barrier width on the second-order nonlinear optical properties are investigated. Results reveal that the confinement potential is considerably affected by the laser field and internal electric field. Results also indicate that the resonant peaks experience a red-shift with increasing the laser field strength and barrier width. Moreover, the resonant peaks suffer a blue-shift with the increase in In and Al compositions.
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
2015-09-24
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.
NASA Astrophysics Data System (ADS)
Shelkovnikov, Vladimir; Selivanova, Galina; Lyubas, Gleb; Korotaev, Sergey; Shundrina, Inna; Tretyakov, Evgeny; Zueva, Ekaterina; Plekhanov, Alexander; Mikerin, Sergey; Simanchuk, Andrey
2017-07-01
The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS-PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.
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).
NASA Astrophysics Data System (ADS)
Tang, Guo-Dong; Zhao, Jian-Ying; Li, Rong-Qing; Yuan-Cao; Zhang, Zai-Chao
2011-01-01
A series of asymmetric donor-acceptor substituted salen-type Schiff-bases have been synthesized and their structures, electronic properties and second order nonlinearities were investigated by DFT methods. In order to verify the stable of these Schiff-base derivates, the IR spectrum of these Schiff-base derivates were calculated, the result showed that these compounds are stable. The results of TD-DFT calculation indicate that the derivatives with the electron-donating group (CH 3, OCH 3 or N(C 2H 5) 2) have a red shift absorption compared to derivatives with the electron-withdrawing group (NO 2). The analysis of MOS indicates that the CN group has contribution to the LUMO orbital while the groups of OCH 3, N(C 2H 5) 2 and NO 2 have contribution to the HOMO orbital. OCH 3, N(C 2H 5) 2 as electron rich groups, made the derivates have a larger first static hyperpolarizability. However, the compound (II) with a NO 2 substituent, also has a large first static hyperpolarizability. This is probably because of the special transition model, namely the values of two oscillator strength f ( fHOMO-1-LUMO = 0.405, fHOMO-LUMO = 0.321) are almost equal. In order to understand the influence of the energy gap (Δ E) between the HOMO and the LUMO orbitals on the first static hyperpolarizability, we calculated the energy gap (Δ E) of all Schiff-base compounds. The results show that the smaller the HOMO-LUMO energy gap is, the larger the first static hyperpolarizability is.
Tang, Guo-Dong; Zhao, Jian-Ying; Li, Rong-Qing; Yuan-Cao; Zhang, Zai-Chao
2011-01-01
A series of asymmetric donor-acceptor substituted salen-type Schiff-bases have been synthesized and their structures, electronic properties and second order nonlinearities were investigated by DFT methods. In order to verify the stable of these Schiff-base derivates, the IR spectrum of these Schiff-base derivates were calculated, the result showed that these compounds are stable. The results of TD-DFT calculation indicate that the derivatives with the electron-donating group (CH3, OCH3 or N(C2H5)2) have a red shift absorption compared to derivatives with the electron-withdrawing group (NO2). The analysis of MOS indicates that the CN group has contribution to the LUMO orbital while the groups of OCH3, N(C2H5)2 and NO2 have contribution to the HOMO orbital. OCH3, N(C2H5)2 as electron rich groups, made the derivates have a larger first static hyperpolarizability. However, the compound (II) with a NO2 substituent, also has a large first static hyperpolarizability. This is probably because of the special transition model, namely the values of two oscillator strength f (fHOMO-1-LUMO=0.405, fHOMO-LUMO=0.321) are almost equal. In order to understand the influence of the energy gap (ΔE) between the HOMO and the LUMO orbitals on the first static hyperpolarizability, we calculated the energy gap (ΔE) of all Schiff-base compounds. The results show that the smaller the HOMO-LUMO energy gap is, the larger the first static hyperpolarizability is.
NASA Astrophysics Data System (ADS)
Zhu, Wei; Guan, Jian; Deng, Fu; Deng, Dongmei; Huang, Jiawei
2016-12-01
By using the transfer matrix method, the propagation of the first-order and the second-order Airy vortex (AiV) beams through strongly nonlocal nonlinear medium is exhibited. Based on the Huygens diffraction integral formula, we derive the analytical expressions of the first-order and the second-order AiV beams propagate through the paraxial ABCD system and present corresponding characteristic parameters such as propagation path, intensity, phase distributions, beam centers, the Poynting vector and angular momentum (AM) density flow. The propagation trajectory is periodical and looks like a sine wave. The AiV beam focuses two times in one period. The phase, energy flow and AM density flow distribution show a reversal when the beam propagates near the focusing point. Additionally, as the order increased, the vortex of the second-order AiV beam is stronger.
NASA Astrophysics Data System (ADS)
Dong, Guoping; Tao, Haizheng; Xiao, Xiudi; Lin, Changgui; Gong, Yueqiu; Zhao, Xiujian; Chu, Saisai; Wang, Shufeng; Gong, Qihuang
2007-03-01
Third-order optical nonlinearities, χ(3) of GeS2-Ga2S3-AgCl chalcohalide glasses have been studied systematically utilizing the femtosecond time-resolved optical Kerr effect (OKE) technique at 820nm, showing that the value of χ(3) enhances with increasing atomic ratio of (S+Cl/2)/(Ge+Ga). From the compositional dependence of glass structure by Raman spectra, a strong dependence of χ^(3) upon glass structure has been found, i.e. compared with [ClxS3-xGe(Ga)-Ge(Ga)S3-xClx] ethane-like s.u. as the structural defectiveness, [Ge(Ga)S4-xClx] mixed tetrahedra make greater contribution to the enhancement of χ(3). The maximum χ
NASA Astrophysics Data System (ADS)
Patra, Saroj Kanta; Schulz, Stefan
2017-09-01
In this work, we present a detailed analysis of the second-order piezoelectric effect in c-plane InxGa1-xN/GaN quantum dots and its consequences for electronic and optical properties of these systems. Special attention is paid to the impact of increasing In content x on the results. We find that in general the second-order piezoelectric effect leads to an increase in the electrostatic built-in field. Furthermore, our results show that for an In content ≥30%, this increase in the built-in field has a significant effect on the emission wavelength and the radiative lifetimes. For instance, at 40% In, the radiative lifetime is more than doubled when taking second-order piezoelectricity into account. Overall, our calculations reveal that when designing and describing the electronic and optical properties of c-plane InxGa1-xN/GaN quantum dot based light emitters with high In contents, second-order piezoelectric effects cannot be neglected.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C. H.
1993-01-01
This report presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design.
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.
Second-order superintegrable quantum systems
Miller, W.; Kalnins, E. G.; Kress, J. M.
2007-03-15
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n - 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schroedinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.
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.
Second-order nonlinearity induced transparency.
Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X
2017-04-01
In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.
An Analysis of Second-Order Autoshaping
ERIC Educational Resources Information Center
Ward-Robinson, Jasper
2004-01-01
Three mechanisms can explain second-order conditioning: (1) The second-order conditioned stimulus (CS2) could activate a representation of the first-order conditioned stimulus (CS1), thereby provoking the conditioned response (CR); The CS2 could enter into an excitatory association with either (2) the representation governing the CR, or (3) with a…
Second-Order Gravitational Self-Force
NASA Astrophysics Data System (ADS)
Pound, Adam
2012-08-01
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body’s mass (neglecting effects of internal structure). The motion is found to be geodesic in a certain locally defined regular geometry satisfying Einstein’s equation at second order. I outline a method of numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.
Second-Order Gravitational Self-Force
NASA Astrophysics Data System (ADS)
Pound, Adam
2015-01-01
In order to extract physical parameters from the waveform of an extreme-mass-ratio binary, one requires a second-order-accurate description of the motion of the smaller of the two objects in the binary. Using a method of matched asymptotic expansions, I derive the second-order equation of motion of a small, nearly spherical and non-rotating compact object in an arbitrary vacuum spacetime. I find that the motion is geodesic in a certain locally defined effective metric satisfying the vacuum Einstein equation through second order, and I outline a method of numerically determining this effective metric.
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.
Anitha, K; Balachandran, V
2015-07-05
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 (1)H and (13)C NMR chemical shifts have been calculated by gauge-indepedent atomic orbital (GIAO) method with B3LYP/6-311++G(d, p) approach. Copyright © 2015 Elsevier B.V. All rights reserved.
Understanding Second-Order Theory of Mind
2015-03-01
children develop the ability to perform second-order false - belief tasks [1]. We simulated five developing models...process of selection. Cognitive Psychology, 50:45–85, 2005. [7] H. W. Wellman, D. Cross, and J. Watson. Meta-analysis of theory -of- mind development: The truth about false belief . Child Development, 72(3):655–684, 2001. 168 ...second-order theory of mind task . Ultimately, this will provide robots with a deeper understanding of their human
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…
Urban Principals' Second Order Change Leadership
ERIC Educational Resources Information Center
Taylor, Rosemarye T.; La Cava, Gonzalo S.
2011-01-01
Urban school leaders have challenges in continually improving student achievement and making change as quickly as needed. To address this problem 37 non-Title I principals completed an on-line survey, Principal's Actions Survey (PAS), based on the seven responsibilities for second order change identified by Marzano, Waters, and McNulty (2005).…
Urban Principals' Second Order Change Leadership
ERIC Educational Resources Information Center
Taylor, Rosemarye T.; La Cava, Gonzalo S.
2011-01-01
Urban school leaders have challenges in continually improving student achievement and making change as quickly as needed. To address this problem 37 non-Title I principals completed an on-line survey, Principal's Actions Survey (PAS), based on the seven responsibilities for second order change identified by Marzano, Waters, and McNulty (2005).…
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…
Passman, S.L.
1982-08-01
The boundary-value problem associated with flow of a right circular cylinder of a second-order fluid under constant axial stress and lateral pressure is formulated. Closed-form solutions are given. Agreement with creep tests on natural rock salt is noted.
Second-order lower radial tangent derivatives and applications to set-valued optimization.
Xu, Bihang; Peng, Zhenhua; Xu, Yihong
2017-01-01
We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Some properties of second-order tangent derivatives are discussed, using which second-order necessary optimality conditions are established for a point pair to be a Henig efficient element of a set-valued optimization problem, and in the expressions the second-order tangent derivatives of the objective function and the constraint function are separated.
Trujillo, Alexander; Fuentealba, Mauricio; Carrillo, David; Manzur, Carolina; Ledoux-Rak, Isabelle; Hamon, Jean-René; Saillard, Jean-Yves
2010-03-15
The synthesis, spectroscopic and structural characterization, linear and nonlinear optical properties, as well as the electrochemical behavior of a series of robust neutral binuclear M[Fc-C(O)CH=C(CH(3))N-X-N=CH-(2-O,5-R-C(6)H(3))] (M = Ni (4), Cu (5), X = o-C(6)H(4), R = H; M = Ni (9), X = CH(2)CH(2), R = OH), and their corresponding ionic trinuclear [M{Fc-C(O)CH=C(CH(3))N-X-N=CH-(eta(6)-2-O,5-R-C(6)H(3))RuCp*}][PF(6)] (6, 7, 10), M[ONNO]-type unsymmetrical Salophen and salen complexes featuring ferrocenyl (Fc) donor and the mixed sandwich acceptor [Cp*Ru(eta(6)- salicylidene)](+) as a push-pull moiety are reported in this paper (Fc = CpFe(eta(5)-C(5)H(4)); Cp = eta(5)-C(5)H(5); Cp* = eta(5)-C(5)Me(5)). The single-crystal X-ray structure of the bimetallic iron-nickel derivative 4 indicates a bowed structure of the unsymmetrical Schiff base skeleton. The Ni(II) ion is tetracoordinated in a square planar environment, with two nitrogen atoms and two oxygen atoms as donors. The new metalloligand [Fc-C(O)CH=C(CH(3))N(H)CH(2)CH(2)N=CH-(2,5-(OH)(2)C(6)H(3))] (8) obtained from the Schiff base condensation of 2,5-dihydroxobenzaldehyde with the half-unit precursor, Fc-C(O)CH=C(CH(3))N(H)CH(2)CH(2)NH(2) (2), is reported with its crystal structure showing partial delocalization of the heteroconjugated [O-C-C-C-N] frameworks with a dihedral angle between the respective planes of 60.76 degrees. Second order nonlinear optical (NLO) measurements were achieved using the Harmonic Light Scattering technique to probe the role of the M[ONNO] chromophores and of the pi-complexation of the salicylidene ring in the nonlinearity. All the complexes exhibit a second-order nonlinear response increasing with the nuclearity, the hyperpolarizability (beta) value of the trinuclear complex 10 being 1.5 time larger than that of the metalloligand 8 (beta = 155 x 10(-30) esu). A rationalization of the structural, electronic, and redox properties of the title compounds is provided, based on a
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Ioffe, M. V. Kolevatova, E. V.
2016-08-15
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.
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.
Second-order gravitational self-force
Rosenthal, Eran
2006-10-15
We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveform templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational waves that are emitted from extreme mass-ratio binaries.
Beyond special relativity at second order
NASA Astrophysics Data System (ADS)
Carmona, J. M.; Cortés, J. L.; Relancio, J. J.
2016-10-01
The study of generic, nonlinear, deformations of special relativity parametrized by a high-energy scale M , which was carried out at first order in 1 /M in J. M. Carmona, J. L. Cortés, and F. Mercati, Phys. Rev. D 86, 084032 (2012), is extended to second order. This can be done systematically through a ("generalized") change of variables from momentum variables that transform linearly. We discuss the different perspectives on the meaning of the change of variables, obtain the coefficients of modified composition laws and Lorentz transformations at second order, and work out how κ -Poincaré, the most commonly used example in the literature, is reproduced as a particular case of the generic framework exposed here.
Second order Pseudo-gaussian shaper
Beche, Jean-Francois
2002-11-22
The purpose of this document is to provide a calculus spreadsheet for the design of second-order pseudo-gaussian shapers. A very interesting reference is given by C.H. Mosher ''Pseudo-Gaussian Transfer Functions with Superlative Recovery'', IEEE TNS Volume 23, p. 226-228 (1976). Fred Goulding and Don Landis have studied the structure of those filters and their implementation and this document will outline the calculation leading to the relation between the coefficients of the filter. The general equation of the second order pseudo-gaussian filter is: f(t) = P{sub 0} {center_dot} e{sup -3kt} {center_dot} sin{sup 2}(kt). The parameter k is a normalization factor.
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.
Second Order Bragg Scattering in a SAR,
1984-08-01
accept the notion that the short- wave components of the ship wake are slightly distorted versions of the Kelvin wake, then there is the possibility of...scattering, at a given place, from a spectrum of waves . The Dabob Bay data indicates that there is little energy in the wake having wave numbers capable...observations do show considerable enhancement of waves of twice the Bragg wavelength at the angle where a SAR wake is observed.. Second order Bragg
Second order Horner's syndrome in a cat.
De Risio, Luisa; Fraser McConnell, James
2009-08-01
This case report describes the clinical and magnetic resonance imaging (MRI) findings of a 3.5-year-old, male neutered, domestic shorthair cat with second order Horner's syndrome as the only clinical abnormality. The neuroanatomical pathway of the sympathetic innervation to the eye, differential diagnoses for Horner's syndrome in cats, and the interpretation of pharmacological testing are reviewed. The unusual MRI findings and the value of fat-suppressed MRI sequences are discussed.
Pole Assignment for Second-Order Systems
NASA Astrophysics Data System (ADS)
CHU, E. K.
2002-01-01
This paper contains some results for pole assignment problems for the second-order system M ẍ(t)+D ẋ(t)+K x (t)=B u (t) . Specifically, Algorithm 0 constructs feedback matrices F1 and F2 such that the closed-loop quadratic pencil Pc( λ)= λ2M+ λ ( D+ BF2)+( K+ BF1) has a desired set of eigenvalues and the associated eigenvectors are well-conditioned. The method is a modification of the SVD-based method proposed by Juang and Maghami [1, 2] which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. [3] for first-order systems. Robustness is achieved by minimising some not-so-well-known condition numbers of the eigenvalues of the closed-loop second-order pencil. We next consider the partial pole assignment problem. In 1997, Datta, Elhay and Ram proposed three biorthogonality relations for eigenvectors of symmetric definite quadratic pencils [4]. One of these relations was used to derive an explicit solution to the partial pole assignment problem by state feedback for the related single-input symmetric definite second-order control system. The solution shed new light on the stabilisation and control of large flexible space structures, for which only one small subset of the spectrum needs to be reassigned while retaining the complementary part of the spectrum. In this paper, the method has been generalised for multi-input and non-symmetric quadratic pencils. Finally, we discuss briefly the output feedback pole assignment problem.
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.
NASA Astrophysics Data System (ADS)
Frankowska, Hélène; Hoehener, Daniel
2017-06-01
This paper is devoted to pointwise second-order necessary optimality conditions for the Mayer problem arising in optimal control theory. We first show that with every optimal trajectory it is possible to associate a solution p (ṡ) of the adjoint system (as in the Pontryagin maximum principle) and a matrix solution W (ṡ) of an adjoint matrix differential equation that satisfy a second-order transversality condition and a second-order maximality condition. These conditions seem to be a natural second-order extension of the maximum principle. We then prove a Jacobson like necessary optimality condition for general control systems and measurable optimal controls that may be only ;partially singular; and may take values on the boundary of control constraints. Finally we investigate the second-order sensitivity relations along optimal trajectories involving both p (ṡ) and W (ṡ).
Anomalous transport in second order hydrodynamics
NASA Astrophysics Data System (ADS)
Megías, Eugenio; Valle, Manuel
2016-11-01
We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature. Talk given by E. Megías at the 4th International Conference on New Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Kolymbari, Crete, Greece.
Second-order conditioning in Drosophila
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 (SOC) protocol that further demonstrates the flexibility of fly behavior. In SOC, a previously conditioned stimulus (CS1) is used as reinforcement for a second conditioned stimulus (CS2) in associative learning. This higher-order context presents an opportunity for reassessing the roles of known learning and memory genes and neuronal networks in a new behavioral paradigm. PMID:21441302
Optical velocimeter by second order correlation
NASA Astrophysics Data System (ADS)
Suo, Yaji; Feng, Yaming; Xu, Da-xiao; Wan, Wenjie
2017-06-01
Motional information can be buried inside the temporal statistics of scattering light. Here we explore the second order correlation of scattering light to trace back the transverse velocity of objects, verifying the inverse relationship between the coherence time and the velocity. Based on this principle, a new type of optical velocimeter is demonstrated, which has been further applied to study the fluid flow inside a microfluidic channel. This new noninvasive and easy-to-implement velocimeter may offer a new avenue in many applications.
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.
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.
Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît
2014-05-13
The linear [χ((1))] and second-order nonlinear [χ((2))] optical susceptibilities of the 2-methyl-4-nitroaniline (MNA) crystal are calculated within the local field theory, which consists of first computing the molecular properties, accounting for the dressing effects of the surroundings, and then taking into account the local field effects. Several aspects of these calculations are tackled with the aim of monitoring the convergence of the χ((1)) and χ((2)) predictions with respect to experiment by accounting for the effects of (i) the dressing field within successive approximations, of (ii) the first-order ZPVA corrections, and of (iii) the geometry. With respect to the reference CCSD-based results, besides double hybrid functionals, the most reliable exchange-correlation functionals are LC-BLYP for the static χ((1)) and CAM-B3LYP (and M05-2X, to a lesser extent) for the dynamic χ((1)) but they strongly underestimate χ((2)). Double hybrids perform better for χ((2)) but not necessarily for χ((1)), and, moreover, their performances are much similar to MP2, which is known to slightly overestimate β, with respect to high-level coupled-clusters calculations and, therefore, χ((2)). Other XC functionals with less HF exchange perform poorly with overestimations/underestimations of χ((1))/χ((2)), whereas the HF method leads to underestimations of both. The first-order ZPVA corrections, estimated at the B3LYP level, are usually small but not negligible. Indeed, after ZPVA corrections, the molecular polarizabilities and first hyperpolarizabilities increase by 2% and 5%, respectively, whereas their impact is magnified on the macroscopic responses with enhancements of χ((1)) by up to 5% and of χ((2)) by as much as 10%-12% at λ = 1064 nm. The geometry plays also a key role in view of predicting accurate susceptibilities, particularly for push-pull π-conjugated compounds such as MNA. So, the geometry optimized using periodic boundary conditions is characterized
Nonlocal diffusion second order partial differential equations
NASA Astrophysics Data System (ADS)
Benedetti, I.; Loi, N. V.; Malaguti, L.; Taddei, V.
2017-02-01
The paper deals with a second order integro-partial differential equation in Rn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.
Cascaded Second-Order Nonlinearities in Waveguides.
NASA Astrophysics Data System (ADS)
Sundheimer, Michael Lee
The cascaded second-order nonlinearity arising from the second-harmonic generation process in noncentrosymmetric media is a novel approach to achieving the nonlinear phase shifts required for all-optical signal processing. The research presented in this dissertation demonstrated and measured the cascaded second-order nonlinearity for the first time in viable integrated optical waveguide formats. Cascaded self-phase modulation was measured in potassium titanyl phosphate (KTiOPO_4 or KTP) segmented quasi-phasematched waveguides at wavelengths near 855 nm and in the optical fiber telecommunications window near 1.585 μm using picosecond and femtosecond pulses, respectively. Spectral modulation and broadening were observed on the output fundamental spectrum and compared to predictions from pulsed second -harmonic generation theory under conditions of group-velocity mismatch (temporal walk-off) and group-velocity dispersion. Peak cascaded phase shifts of the fundamental of approximately pi at 855 nm were inferred with 690 W of peak guided power. Peak cascaded phase shifts of approximately pi/2 were inferred at 1.585 μm with 760 W of peak power in the guide. Direct interferometric measurements of the magnitude and sign of the cascaded nonlinear phase shift of the fundamental were performed in temperature-tuned lithium niobate (LiNbO _3) channel waveguides at 1.32 mum. The cascaded phase shift was shown to change sign upon passing through the phasematching condition, as required by theory. Peak cascaded phase shifts of +0.53 pi and -0.13 pi were measured for 86 W peak power in these waveguides. A non-uniform temperature profile along the waveguide led to a non-uniform wavevector-mismatch along the guide, resulting in an enhanced positive phase shift and an increased temperature bandwidth for the phase shift. The phase shifts achieved in this research are large enough to be suitable for some all-optical signal processing functions.
Second-order temporal modulation transfer functions.
Lorenzi, C; Soares, C; Vonner, T
2001-08-01
Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181
Second order optical nonlinearity in silicon by symmetry breaking
Cazzanelli, Massimo; Schilling, Joerg
2016-03-15
Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.
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.
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.
A second order derivative scheme based on Bregman algorithm class
NASA Astrophysics Data System (ADS)
Campagna, Rosanna; Crisci, Serena; Cuomo, Salvatore; Galletti, Ardelio; Marcellino, Livia
2016-10-01
The algorithms based on the Bregman iterative regularization are known for efficiently solving convex constraint optimization problems. In this paper, we introduce a second order derivative scheme for the class of Bregman algorithms. Its properties of convergence and stability are investigated by means of numerical evidences. Moreover, we apply the proposed scheme to an isotropic Total Variation (TV) problem arising out of the Magnetic Resonance Image (MRI) denoising. Experimental results confirm that our algorithm has good performance in terms of denoising quality, effectiveness and robustness.
Second-order type theory for first-class environment
NASA Astrophysics Data System (ADS)
Nishizaki, Shin-ya
2017-05-01
An environment is an assignment of variables to values, which is one of the fundamental notions in programming languages. A first-class entity is an object which can be passed to a function and returned as a result, such as an integer. We have studied an environment calculus, a lambda calculus with first-class environments for several years. We studied a simple type theory and ML-polymorphic type system for the environment calculus. In this paper, we propose an environment calculus with a Church-style second-order type system, and study its fundamental properties.
Adaptive suboptimal second-order sliding mode control for microgrids
NASA Astrophysics Data System (ADS)
Incremona, Gian Paolo; Cucuzzella, Michele; Ferrara, Antonella
2016-09-01
This paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary system becomes attractive. In the other two strategies, a suitable blend between two components, one mainly working during the reaching phase, the other being the predominant one in a vicinity of the sliding manifold, is generated, so as to reduce the control amplitude in steady state. The microgrid system in a grid-connected operation mode, controlled via the selected ASSOSM control strategies, exhibits appreciable stability properties, as proved theoretically and shown in simulation.
Second-order focusing parallel electron energy magnetic sector analyzer designs
NASA Astrophysics Data System (ADS)
Khursheed, Anjam
2011-07-01
This paper presents parallel magnetic sector analyzer designs that are predicted to have second-order or better focusing properties. Simulation results indicate that by reducing the gap between excitation plates in a compact parallel energy magnetic sector box design, second-order focusing regions in the detected energy spectrum can be obtained. A method for combining a first-order focusing magnetic box sector unit with a larger magnet sector unit is also presented in which, the field strength varies relatively slowly. Simulations predict that using a combination of such magnetic sector units, focusing properties better than second order can be achieved for most of the detected energy range.
Measurement of the second-order coherence of pseudothermal light
NASA Astrophysics Data System (ADS)
Kuusela, Tom A.
2017-04-01
We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.
"H"-shape second order NLO polymers: synthesis and characterization.
Li, Zhong'an; Hu, Pan; Yu, Gui; Zhang, Wei; Jiang, Zuoquan; Liu, Yunqi; Ye, Cheng; Qin, Jingui; Li, Zhen
2009-02-28
In this work, two "H"-shape and one "AB"-type second order nonlinear optical (NLO) polymers were prepared for the first time. The linkage positions of chromophores in the "H"-shape polymers were shoulder-to-shoulder, in which the chromophore moieties were part of the polymeric backbone. The subtle structure could be easily modified by the introduction of different isolation groups, to adjust the property of the resultant polymers. All the polymers exhibited good film-forming ability and thermal stability. The second harmonic generation (SHG) experiments demonstrated that the two "H"-shape polymers (P1 and P2) exhibited large SHG coefficients of d(33) values (up to 90 pm V(-1)), and P2 even demonstrated relatively good long-term temporal stability.
Second-order schedules and the problem of conditioned reinforcement
Stubbs, D. Alan
1971-01-01
Thirteen pigeons were exposed to a variety of second-order schedules in which responding under a component schedule was reinforced according to a schedule of reinforcement. Under different conditions, completion of each component resulted in either (1) the brief presentation of a stimulus also present during reinforcement (pairing operation), (2) the brief presentation of a stimulus not present during reinforcement (nonpairing operation), or (3) no brief stimulus presentation (tandem). Brief-stimulus presentations engendered a pattern of responding within components similar to that engendered by food. Patterning was observed when fixed-interval and fixed-ratio components were maintained under fixed- and variable-ratio and fixed- and variable-interval schedules. There were no apparent differences in performance under pairing and nonpairing conditions in any study. The properties of the stimuli presented in brief-stimulus operations produced different effects on response patterning. In one study, similar effects on performance were found whether brief-stimulus presentations were response-produced or delivered independently of responding. Response patterning did not occur when the component schedule under which a nonpaired stimulus was produced occurred independently of the food schedule. The results suggest a reevaluation of the role of conditioned reinforcement in second-order schedule performance. The similarity of behavior under pairing and nonpairing operations is consistent with two hypotheses: (1) the major effect is due to the discriminative properties of the brief stimulus; (2) the scheduling operation under which the paired or nonpaired stimulus is presented can establish it as a reinforcer. PMID:16811549
Galaxy bias and gauges at second order in general relativity
NASA Astrophysics Data System (ADS)
Bertacca, Daniele; Bartolo, Nicola; Bruni, Marco; Koyama, Kazuya; Maartens, Roy; Matarrese, Sabino; Sasaki, Misao; Wands, David
2015-09-01
We discuss the question of gauge choice when analysing relativistic density perturbations at second order. We compare Newtonian and general relativistic approaches. Some misconceptions in the recent literature are addressed. We show that the comoving-synchronous gauge is the unique gauge in general relativity that corresponds to the Lagrangian frame and is entirely appropriate to describe the matter overdensity at second order. The comoving-synchronous gauge is the simplest gauge in which to describe Lagrangian bias at second order.
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.
The effects of second-order hydrodynamics on a semisubmersible floating offshore wind turbine
NASA Astrophysics Data System (ADS)
Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A.
2014-06-01
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 a floating 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 Maritime Research Institute Netherlands (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 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 was applied to the Offshore Code Comparison Collaboration Continuation OC4-DeepCwind semisubmersible platform, supporting the National Renewable Energy Laboratory's 5-MW baseline wind turbine. In this paper, the loads and response of the system caused by the second-order hydrodynamics are analysed and compared to the first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads
Characterising the stabilisability for second-order linear switched systems
NASA Astrophysics Data System (ADS)
Cong, Shen
2013-03-01
The stabilisability of second-order linear switched systems is the topic focused on in a number of papers, however, some of its fundamental characteristics are still unrevealed. In this article, regarding a pair of subsystems, we are interested in characterising this problem from both the state-triggering and time-domain viewpoints and in revealing the inherent connection between them. To this end, we first use polar coordinates to represent the geometric property of switching and the dynamical behaviours caused by it, and then put the geometrised switching control into correspondence with the implicit stabilisation mechanism behind it. Doing this in a strong way relies on classifying switching control into two types intuitively, namely, chattering switching and spinning switching, and then clarifying their distinction and properties rigorously. Furthermore, the uniform convergence of the forced trajectory is shown by presenting estimation on its decay rate; and the limit cycles and sliding motions generated by switching are also accounted for. The results are illustrated by elaborate examples.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
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.
Smart structure control in matrix second order form
NASA Astrophysics Data System (ADS)
Diwekar, Anjali M.; Yedavalli, Rama K.
1995-05-01
Matrix second order systems arise in a variety of structural dynamics and control problems. The analysis and design of such systems is traditionally done in frequency domain or in time domain (state space framework). The formulation of the control design problem in matrix second order form (i.e., configuration space framework) has many advantages over first order state space form. In this paper, a novel approach for designing a stabilizing controller in a second-order model of piezoelectrically controlled flexible beam is proposed.
Smart structure control in matrix second-order form
NASA Astrophysics Data System (ADS)
Diwekar, Anjali M.; Yedavalli, Rama K.
1996-08-01
Matrix second-order systems arise in a variety of structural dynamics and control problems. The analysis and design of such systems is traditionally done in the frequency domain or in the time domain (state space framework). The formulation of the control design problem in matrix second-order form (i.e. configuration space framework) has many advantages over first-order state-space form. In this paper, a novel approach for designing a stabilizing controller in a second-order model of a piezoelectrically controlled flexible beam is proposed.
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.
Variational principles for multisymplectic second-order classical field theories
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
On the state estimation of structures with second order observers
NASA Technical Reports Server (NTRS)
Belvin, W. Keith; Park, K. C.
1989-01-01
The use of Linear Quadratic Regulator (LQR) control synthesis techniques implies the availability of full state feedback. For vibration control of structures, usually only a limited number of states are measured from which an observer model reconstructs the full state. It is shown that using second order observers is a viable technique for reconstructing the unmeasured states of structures under mildly restrictive conditions. Moreover, the computational advantages of the second order observer as compared to a first order observer indicate that significantly larger observer models may be utilized. Numerical examples are used to demonstrate the performance of second order observers. The implications of second order observers in the development of Controls-Structures Interaction (CSI) technology is discussed.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
NASA Astrophysics Data System (ADS)
Alloatti, L.; Kieninger, C.; Froelich, A.; Lauermann, M.; Frenzel, T.; Köhnle, K.; Freude, W.; Leuthold, J.; Wegener, M.; Koos, C.
2015-09-01
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al2O3, B = TiO2, and C = HfO2. The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths.
Second-order temporal interference of two independent light beams at an asymmetrical beam splitter
NASA Astrophysics Data System (ADS)
Liu, Jianbin; Wang, Jingjing; Xu, Zhuo
2017-01-01
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when asymmetrical beam splitter is employed.
Neural basis for stereopsis from second-order contrast cues.
Tanaka, Hiroki; Ohzawa, Izumi
2006-04-19
Humans and animals use visual cues such as brightness and color boundaries to identify objects and navigate through environments. However, even when these cues are not available, we can effortlessly perform these tasks by using second-order cues such as contrast variation (envelope) of patterns on surfaces. Previously, numerous psychophysical studies examined properties of binocular depth processing based on the contrast-envelope cues and suggested the existence of a stereo system that uses these cues. However, its physiological substrate has not been identified yet. Here, we show that a subset of cortical neurons in cat area 18 show binocular interactions for the contrast-envelope stimuli. These neurons are capable of representing a variety of depths in the three-dimensional space based on the information available from contrast cues alone. Furthermore, these neurons show similar disparity-tuning curves for borders defined by both luminance and contrast cues. This cue-invariant tuning is consistent with a linear binocular convergence model for monocular luminance and contrast-envelope processing pathways.
Polarization opposition effect and second-order ray tracing.
Videen, Gorden
2002-08-20
I develop a second-order ray-tracing model of the light scattered by a cloud of randomly oriented facets having sizes much larger than the incident wavelength. My results suggest that both symmetric and asymmetric branches of the polarization opposition effect can be produced by the same mechanism responsible for the photometric opposition effect, i.e., constructive interference of light rays traversing reciprocal paths that is associated with coherent backscattering enhancement. The model provides a greatly simplified representation of the physical phenomena to isolate the two mechanisms that may be responsible for the effect. The shapes and positions of the two branches of the polarization opposition effect calculated with the model are consistent with observation, so the model may provide a rapid technique to characterize the optical and physical properties of a scattering system. I note, however, that the model is a gross simplification containing only two physical mechanisms, Fresnel reflections and coherent interference, and it is possible that it represents a nonphysical description of particles smaller than the wavelength or that other mechanisms contributing to the polarization opposition effect are not included.
Second-Order Structured Deformations: Relaxation, Integral Representation and Applications
NASA Astrophysics Data System (ADS)
Barroso, Ana Cristina; Matias, José; Morandotti, Marco; Owen, David R.
2017-09-01
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications.
Second-order quasinormal mode of the Schwarzschild black hole
NASA Astrophysics Data System (ADS)
Nakano, Hiroyuki; Ioka, Kunihito
2007-10-01
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 ˜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.
NASA Astrophysics Data System (ADS)
Gallinato, Olivier; Poignard, Clair
2017-06-01
In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.
Deflection of light to second order in conformal Weyl gravity
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.
Spacecraft attitude determination using a second-order nonlinear filter
NASA Technical Reports Server (NTRS)
Vathsal, S.
1987-01-01
The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.
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 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.
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.
Second order closure for variable density free shear layer
NASA Astrophysics Data System (ADS)
Vandromme, D.; Kollmann, W.
A full second order closure turbulence model for the prediction of free shear flows with variable density is developed. The importance of density fluctuations due to inhomogeneities in fluid composition is emphasized. Some simplicity is achieved by using density weighted averaging to account implicitly for density fluctuation effects. Transport equations for various second order correlations - such as Reynolds stress, turbulent mass fluxes or density velocity correlations - are derived, modelled and solved, together with the mean equations for momentum and species conservation. Solutions of these equations are compared with the two different sets of experimental data for low speed free mixing layers (helium into nitrogen and freon 12 into air).
Second order limit language in variants of splicing system
NASA Astrophysics Data System (ADS)
Ahmad, Muhammad Azrin; Sarmin, Nor Haniza; Heng, Fong Wan; Yusof, Yuhani
2014-07-01
The cutting and pasting processes that occur in DNA molecules have led to the formulation of splicing system. Since then, there are few models used to model the splicing system. The splicing language, which is the product of splicing system, can be categorized into two, namely the adult and limit language. In this research, limit language is extended to the second order limit language. Few problems are approached which lead to the formation of second order limit language which is then analyzed using various types of splicing system.
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.
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
Human cooperation: second-order free-riding problem solved?
Fowler, James H
2005-09-22
Panchanathan and Boyd describe a model of indirect reciprocity in which mutual aid among cooperators can promote large-scale human cooperation without succumbing to a second-order free-riding problem (whereby individuals receive but do not give aid). However, the model does not include second-order free riders as one of the possible behavioural types. Here I present a simplified version of their model to demonstrate how cooperation unravels if second-round defectors enter the population, and this shows that the free-riding problem remains unsolved.
A uniformly second order fast sweeping method for eikonal equations
NASA Astrophysics Data System (ADS)
Luo, Songting
2013-05-01
A uniformly second order method with a local solver based on the piecewise linear discontinuous Galerkin formulation is introduced to solve the eikonal equation with Dirichlet boundary conditions. The method utilizes an interesting phenomenon, referred as the superconvergence phenomenon, that the numerical solution of monotone upwind schemes for the eikonal equation is first order accurate on both its value and gradient when the solution is smooth. This phenomenon greatly simplifies the local solver based on the discontinuous Galerkin formulation by reducing its local degrees of freedom from two (1-D) (or three (2-D), or four (3-D)) to one with the information of the gradient frozen. When considering the eikonal equation with point-source conditions, we further utilize a factorization approach to resolve the source singularities of the eikonal by decomposing it into two parts, either multiplicatively or additively. One part is known and captures the source singularities; the other part serves as a correction term that is differentiable at the sources and satisfies the factored eikonal equations. We extend the second order method to solve the factored eikonal equations to compute the correction term with second order accuracy, then recover the eikonal with second order accuracy. Numerical examples are presented to demonstrate the performance of the method.
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,…
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…
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.
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 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.
Second-order accurate difference schemes on highly irregular meshes
Manteuffel, T.A.; White, A.B. Jr.
1988-01-01
In this paper compact-as-possible second-order accurate difference schemes will be constructed for boundary-value problems of arbitrary order on highly irregular meshes. It will be shown that for equations of order (K) these schemes will have truncation error of order (3/endash/K). This phenomena is known as supraconvergence. 7 refs.
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…
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.
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…
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…
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.
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…
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,…
Digital second-order phase-locked loop
NASA Technical Reports Server (NTRS)
Holmes, J. K.; Carl, C. C.; Tagnelia, C. R.
1975-01-01
Actual tests with second-order digital phase-locked loop at simulated relative Doppler shift of 1x0.0001 produced phase lock with timing error of 6.5 deg and no appreciable Doppler bias. Loop thus appears to achieve subcarrier synchronization and to remove bias due to Doppler shift in range of interest.
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…
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…
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…
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.
Neumann problems for second order ordinary differential equations across resonance
NASA Astrophysics Data System (ADS)
Yong, Li; Huaizhong, Wang
1995-05-01
This paper deals with the existence-uniqueness problem to Neumann problems for second order ordinary differential equations probably across resonance. By the optimal control theory method, some global optimality results about the unique solvability for such boundary value problems are established.
Specificity of brain reactions to second-order visual stimuli.
Babenko, Vitaly V; Ermakov, Pavel N
2015-01-01
The second-order visual mechanisms perform the operation of integrating the spatially distributed local visual information. Their organization is traditionally considered within the framework of the filter-rectify-filter model. These are the second-order filters that provide the ability to detect texture gradients. However, the question of the mechanisms' selectivity to the modulation dimension remains open. The aim of this investigation is to answer the above question by using visual evoked potentials (VEPs). Stimuli were textures consisting of staggered Gabor patches. The base texture was nonmodulated (NM). Three other textures represented the base texture which was sinusoidally modulated in different dimensions: contrast, orientation, or spatial frequency. EEG was recorded with 20 electrodes. VEPs of 500 ms duration were obtained for each of the four textures. After that, VEP to the NM texture was subtracted from VEP to each modulated texture. As a result, three different waves (d-waves) were obtained for each electrode site. Each d-wave was then averaged across all the 48 observers. The revealed d-waves have a latency of about 200 ms and, in our opinion, reflect the second-order filters reactivation through the feedback connection. The d-waves for different modulation dimensions were compared with each other in time, amplitude, topography, and localization of the sources of activity that causes the d-wave (with sLORETA). We proceeded from the assumption that the d-wave (its first component) represents functioning of the second-order visual mechanisms and activity changes at the following processing stages. It was found that the d-waves for different modulation dimensions significantly differ in all parameters. The obtained results indicate that the spatial modulations of different texture parameters caused specific changes in the brain activity, which could be evidence supporting the specificity of the second-order visual mechanisms to modulation dimension.
Middelboe, Mathias; Holmfeldt, Karin; Riemann, Lasse; Nybroe, Ole; Haaber, Jakob
2009-08-01
Genetic, structural and physiological differences between strains of the marine bacterium Cellulophaga baltica MM#3 (Flavobacteriaceae) developing in response to the activity of two virulent bacteriophages, Phi S(M) and Phi S(T), was investigated during 3 weeks incubation in chemostat cultures. A distinct strain succession towards increased phage resistance and a diversification of the metabolic properties was observed. During the incubation the bacterial population diversified from a single strain, which was sensitive to 24 tested Cellulophaga phages, into a multistrain and multiresistant population, where the dominant strains had lost susceptibility to up to 22 of the tested phages. By the end of the experiment the cultures reached a quasi steady state dominated by Phi S(T)-resistant and Phi S(M) + Phi S(T)-resistant strains coexisting with small populations of phage-sensitive strains sustaining both phages at densities of > 10(6) plaque forming units (pfu) ml(-1). Loss of susceptibility to phage infection was associated with a reduction in the strains' ability to metabolize various carbon sources as demonstrated by BIOLOG assays. This suggested a cost of resistance in terms of reduced physiological capacity. However, there was no direct correlation between the degree of resistance and the loss of metabolic properties, suggesting either the occurrence of compensatory mutations in successful strains or that the cost of resistance in some strains was associated with properties not resolved by the BIOLOG assay. The study represents the first direct demonstration of phage-driven generation of functional diversity within a marine bacterial host population with significant implications for both phage susceptibility and physiological properties. We propose, therefore, that phage-mediated selection for resistant strains contributes significantly to the extensive microdiversity observed within specific bacterial species in marine environments.
NASA Astrophysics Data System (ADS)
Cariati, F.; Caruso, U.; Centore, R.; De Maria, A.; Fusco, M.; Panunzi, B.; Roviello, A.; Tuzi, A.
2004-10-01
Three new push-pull chromophores of potential interest in second order nonlinear optical applications were synthesized and characterized, also by EFISH determination of molecular second order NLO properties. The chromophores contain a phenyl-azo unit coupled with fluorenonic, stilbenic or 1,3,4-thia-diazolic groups and are OH-functionalized to prompt easy covalent insertion in polymer chains. The selective reduction of only one of the two chemically equivalent nitro groups in the starting precursors is the key step of the synthetic pathway affording the chromophores. These show good chemical and thermal stability. The X-ray structural determination of the fluorenone derived chromophore is also reported.
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.
The role of capture spiral silk properties in the diversification of orb webs
Tarakanova, Anna; Buehler, Markus J.
2012-01-01
Among a myriad of spider web geometries, the orb web presents a fascinating, exquisite example in architecture and evolution. Orb webs can be divided into two categories according to the capture silk used in construction: cribellate orb webs (composed of pseudoflagelliform silk) coated with dry cribellate threads and ecribellate orb webs (composed of flagelliform silk fibres) coated by adhesive glue droplets. Cribellate capture silk is generally stronger but less-extensible than viscid capture silk, and a body of phylogenic evidence suggests that cribellate capture silk is more closely related to the ancestral form of capture spiral silk. Here, we use a coarse-grained web model to investigate how the mechanical properties of spiral capture silk affect the behaviour of the whole web, illustrating that more elastic capture spiral silk yields a decrease in web system energy absorption, suggesting that the function of the capture spiral shifted from prey capture to other structural roles. Additionally, we observe that in webs with more extensible capture silk, the effect of thread strength on web performance is reduced, indicating that thread elasticity is a dominant driving factor in web diversification. PMID:22896566
Optimal second order sliding mode control for linear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-11-01
In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.
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.
On homogeneous second order linear general quantum difference equations.
Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M
2017-01-01
In this paper, we prove the existence and uniqueness of solutions of the β-Cauchy problem of second order β-difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β, defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β-difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β-difference equation.
Second-order centrality correlation in scale-free networks
NASA Astrophysics Data System (ADS)
Lv, Meilei; Guo, Xinling; Chen, Jiaquan; Lu, Zhe-Ming; Nie, Tingyuan
2015-02-01
Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree-degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC-SOC correlation in assortative network and neutral network behaves similarly to the degree-degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.
Phase transitions, inhomogeneous horizons and second-order hydrodynamics
NASA Astrophysics Data System (ADS)
Attems, Maximilian; Bea, Yago; Casalderrey-Solana, Jorge; Mateos, David; Triana, Miquel; Zilhão, Miguel
2017-06-01
We use holography to study the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order thermal phase transition. We place the theory on a cylinder in a set of homogeneous, unstable initial states. The dual gravity configurations are black branes afflicted by a Gregory-Laflamme instability. We numerically evolve Einstein's equations to follow the instability until the system settles down to a stationary, inhomogeneous black brane. The dual gauge theory states have constant temperature but non-constant energy density. We show that the time evolution of the instability and the final states are accurately described by second-order hydrodynamics. In the static limit, the latter reduces to a single, second-order, non-linear differential equation from which the inhomogeneous final states can be derived.
High T{sub c} superconducting second-order gradiometer
Kittel, A.; Kouznetsov, K.A.; McDermott, R.; Oh, B.; Clarke, J. |
1998-10-01
A planar, second-order gradiometer was fabricated from single-layer YBa{sub 2}Cu{sub 3}O{sub 7{minus}x} films. The gradiometer consists of a symmetric flux transformer with an overall length of 80 mm inductively coupled to a directly coupled magnetometer, and has a baseline of 31 mm. The mutual inductance between the flux transformer and the magnetometer is adjusted mechanically to reduce the response to a uniform magnetic field applied perpendicularly to the plane of the gradiometer to typically 50 ppm. From an independent measurement, the residual first-order gradient response was determined to be at most 1.4{percent} relative to the second-order gradient response. {copyright} {ital 1998 American Institute of Physics.}
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.
Second-order envelope equation of graphene electrons
NASA Astrophysics Data System (ADS)
Luo, Ji
2014-10-01
A treatment of graphene's electronic states based on the tight-binding method is presented. Like Dirac equation, this treatment uses envelope functions to eliminate crystal potential. Besides, a density-functional-theory Kohn-Sham (KS) orbital of an isolated carbon atom is employed. By locally expanding envelope functions into second-order polynomials and by involving up to third-nearest atoms in calculating orbital integrals, the second-order envelope equation is obtained. This equation does not contain any experimental data except graphene's crystal structure, and its coefficients are determined through several kinds of integrals of the carbon KS orbital. As an improvement, it leads to more accurate energy dispersion than Dirac equation including the triangular warping effect and asymmetry for electrons and holes, and gives the Fermi velocity which is in good agreement with the experimental value.
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.
Quasiparticle second-order viscous hydrodynamics from kinetic theory
NASA Astrophysics Data System (ADS)
Tinti, Leonardo; Jaiswal, Amaresh; Ryblewski, Radoslaw
2017-03-01
We present the derivation of second-order relativistic viscous hydrodynamics from an effective Boltzmann equation for a system consisting of quasiparticles of a single species. We consider temperature-dependent masses of the quasiparticles and devise a thermodynamically consistent framework to formulate second-order evolution equations for shear and bulk viscous pressure corrections. The main advantage of this formulation is that one can consistently implement a realistic equation of state of the medium within the framework of kinetic theory. Specializing to the case of a one-dimensional purely longitudinal boost-invariant expansion, we study the effect of this new formulation on the viscous hydrodynamic evolution of strongly interacting matter formed in relativistic heavy-ion collisions.
First and second order convex approximation strategies in structural optimization
NASA Technical Reports Server (NTRS)
Fleury, C.
1989-01-01
In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.
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.
Bounded solutions of a second order evolution equation and applications
NASA Astrophysics Data System (ADS)
Leiva, Hugo
2001-02-01
In this paper we study the following abstract second order differential equation with dissipation in a Hilbert space H: u″+cu'+dA u+kG(u)=P(t), u∈H, t∈R, where c, d and k are positive constants, G:H→H is a Lipschitzian function and P:R→H is a continuous and bounded function. A:D(A)⊂H→H is an unbounded linear operator which is self-adjoint, positive definite and has compact resolvent. Under these conditions we prove that for some values of d, c and k this system has a bounded solution which is exponentially asymptotically stable. Moreover; if P(t) is almost periodic, then this bounded solution is also almost periodic. These results are applied to a very well known second order system partial differential equations; such as the sine-Gordon equation, The suspension bridge equation proposed by Lazer and McKenna, etc.
Second order modeling of boundary-free turbulent shear flows
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Chen, Y.-Y.; Lumley, J. L.
1991-01-01
A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.
Thermoconvective Instability of a Second-Order Fluid
NASA Astrophysics Data System (ADS)
Dávalos, Luis Antonio O.; Manero, Octavio
1986-02-01
The non-linear three-dimensional thermoconvective instability of a second-order fluid layer between two parallel semi-infinite walls is analyzed under the fixed-heat flux boundary condition. In the analysis, the Boussinesq approximation is used to account for density changes in the system. It is shown that the non-linear time-dependent equation that governs the convective motion is of the same form as those obtained by Chapman and Proctor in the two-dimensional case and by Proctor (for infinitely thickwalls) in the three-dimensional case for Newtonian fluids. This result shows that the theorems of Tanner and Giesekus for planar, creeping flow of incompressible second-order fluids can be extended to three-dimensional, non-linear, time-dependent thermoconvective phenomena.
Bioethics as public discourse and second-order discipline.
Kopelman, Loretta M
2009-06-01
Bioethics is best viewed as both a second-order discipline and also part of public discourse. Since their goals differ, some bioethical activities are more usefully viewed as advancing public discourse than academic disciplines. For example, the "Universal Declaration on Bioethics and Human Rights" sponsored by the United Nations Educational, Scientific, and Cultural Organization seeks to promote ethical guidance on bioethical issues. From the vantage of philosophical ethics, it fails to rank or specify its stated principles, justify controversial principles, clarify key terms, or say what is meant by calling potentially conflicting norms "foundational." From the vantage of improving the public discourse about bioethical problems and seeking ethical solutions in the public arena, however, this document may have an important role. The goals and relations between bioethics as a second-order discipline and public discourse are explored.
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 long 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.
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 evaluations of orthogonal and symplectic Yangians
NASA Astrophysics Data System (ADS)
Karakhanyan, D. R.; Kirschner, R.
2017-08-01
Orthogonal or symplectic Yangians are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with the corresponding so( n) or sp(2 m) symmetry. We investigate the second-order solution conditions, where the expansion of L( u) in u -1 is truncated at the second power, and we derive the relations for the two nontrivial terms in L( u).
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.
Stabilisation of second-order nonlinear equations with variable delay
NASA Astrophysics Data System (ADS)
Berezansky, Leonid; Braverman, Elena; Idels, Lev
2015-08-01
For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilisation by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.
Asymptotic analysis of perturbed dust cosmologies to second order
NASA Astrophysics Data System (ADS)
Uggla, Claes; Wainwright, John
2013-08-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Λ >0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Λ >0 but logarithmic if Λ =0 and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if Λ >0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Λ =0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
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.
Superquantile/CVaR Risk Measures: Second-Order Theory
2015-07-31
superquantiles have recently been explored in some settings, but key parts of the theory have been lacking: descriptions of the associated risk en...2015 to 00-00-2015 4. TITLE AND SUBTITLE Superquantile/CVaR Risk Measures: Second-Order Theory 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...recently been explored in some settings, but key parts of the theory have been lacking: descriptions of the associated risk en- velopes and risk identi ers
Maintaining Limited-Range Connectivity Among Second-Order Agents
2016-07-07
we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are: (i) do...hoc networks of mobile autonomous agents. This loose ter- minology refers to groups of robotic agents with limited mobility and communica- tion...connectivity can be preserved. 3.1. Networks of robotic agents with second-order dynamics and the connectivity maintenance problem. We begin by
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.
Noise masking reveals channels for second-order letters
Oruç, İpek; Landy, Michael S.; Pelli, Denis G.
2009-01-01
We investigate the channels underlying identification of second-order letters using a critical-band masking paradigm. We find that observers use a single 1–1.5 octave-wide channel for this task. This channel’s best spatial frequency (c/letter) did not change across different noise conditions (indicating the inability of observers to switch channels to improve signal-to-noise ratio) or across different letter sizes (indicating scale invariance), for a fixed carrier frequency (c/letter). However, the channel’s best spatial frequency does change with stimulus carrier frequency (both in c/letter); one is proportional to the other. Following Majaj et al. (Majaj, N. J., Pelli, D. G., Kurshan, P., & Palomares, M. (2002). The role of spatial frequency channels in letter identification. Vision Research, 42, 1165–1184), we define “stroke frequency” as the line frequency (strokes/deg) in the luminance image. That is, for luminance-defined letters, stroke frequency is the number of lines (strokes) across each letter divided by letter width. For second-order letters, letter texture stroke frequency is the number of carrier cycles (luminance lines) within the letter ink area divided by the letter width. Unlike the nonlinear dependence found for first-order letters (implying scale-dependent processing), for second-order letters the channel frequency is half the letter texture stroke frequency (suggesting scale-invariant processing). PMID:16203023
Cue-invariant shape recognition in rats as tested with second-order contours.
De Keyser, Roxane; Bossens, Christophe; Kubilius, Jonas; Op de Beeck, Hans P
2015-01-01
Nonhuman primates are the main animal model to investigate high-level properties of human cortical vision. For one property, transformation-invariant object recognition, recent studies have revealed interesting and unknown capabilities in rats. Here we report on the ability of rats to rely upon second-order cues that are important to structure the incoming visual images into figure and background. Rats performed a visual shape discrimination task in which the shapes were not only defined by first-order luminance information but also by a variety of second-order cues such as a change in texture properties. Once the rats were acquainted with a first set of second-order stimuli, they showed a surprising degree of generalization towards new second-order stimuli. The limits of these capabilities were tested in various ways, and the ability to extract the shapes broke down only in extreme cases where no local cues were available to solve the task. These results demonstrate how rats are able to make choices based on fairly complex strategies when necessary.
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.
Adaptive second-order sliding mode control with uncertainty compensation
NASA Astrophysics Data System (ADS)
Bartolini, G.; Levant, A.; Pisano, A.; Usai, E.
2016-09-01
This paper endows the second-order sliding mode control (2-SMC) approach with additional capabilities of learning and control adaptation. We present a 2-SMC scheme that estimates and compensates for the uncertainties affecting the system dynamics. It also adjusts the discontinuous control effort online, so that it can be reduced to arbitrarily small values. The proposed scheme is particularly useful when the available information regarding the uncertainties is conservative, and the classical `fixed-gain' SMC would inevitably lead to largely oversized discontinuous control effort. Benefits from the viewpoint of chattering reduction are obtained, as confirmed by computer simulations.
Time regularity of the solutions to second order hyperbolic equations
NASA Astrophysics Data System (ADS)
Kinoshita, Tamotu; Taglialatela, Giovanni
2011-04-01
We consider the Cauchy problem for a second order weakly hyperbolic equation, with coefficients depending only on the time variable. We prove that if the coefficients of the equation belong to the Gevrey class γ^{s0} and the Cauchy data belong to γ^{s1}, then the Cauchy problem has a solution in γ^{s0}([0,T^{*}];γ^{s1}({R})) for some T *>0, provided 1≤ s 1≤2-1/ s 0. If the equation is strictly hyperbolic, we may replace the previous condition by 1≤ s 1≤ s 0.
Galaxy number counts to second order and their bispectrum
Dio, Enea Di; Durrer, Ruth; Marozzi, Giovanni; Montanari, Francesco E-mail: Ruth.Durrer@unige.ch E-mail: Francesco.Montanari@unige.ch
2014-12-01
We determine the number counts to second order in cosmological perturbation theory in the Poisson gauge and allowing for anisotropic stress. The calculation is performed using an innovative approach based on the recently proposed ''geodesic light-cone'' gauge. This allows us to determine the number counts in a purely geometric way, without using Einstein's equation. The result is valid for general dark energy models and (most) modified gravity models. We then evaluate numerically some relevant contributions to the number counts bispectrum. In particular we consider the terms involving the density, redshift space distortion and lensing.
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.
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.
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.
Octonic second-order equations of relativistic quantum mechanics
Mironov, Victor L.; Mironov, Sergey V.
2009-01-15
We demonstrate a generalization of relativistic quantum mechanics using eight-component value ''octons'' that generate an associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has a specific spatial structure that takes the form of an octonic oscillator with two spatial polarizations: longitudinal linear and transverse circular.
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.
A simple second-order digital phase-locked loop.
NASA Technical Reports Server (NTRS)
Tegnelia, C. R.
1972-01-01
A simple second-order digital phase-locked loop has been designed for the Viking Orbiter 1975 command system. Excluding analog-to-digital conversion, implementation of the loop requires only an adder/subtractor, two registers, and a correctable counter with control logic. The loop considers only the polarity of phase error and corrects system clocks according to a filtered sequence of this polarity. The loop is insensitive to input gain variation, and therefore offers the advantage of stable performance over long life. Predictable performance is guaranteed by extreme reliability of acquisition, yet in the steady state the loop produces only a slight degradation with respect to analog loop performance.
A framework for second-order parton showers
NASA Astrophysics Data System (ADS)
Li, Hai Tao; Skands, Peter
2017-08-01
A framework is presented for including second-order perturbative corrections to the radiation patterns of parton showers. The formalism allows to combine O (αs2)-corrected iterated 2 → 3 kernels for ;ordered; gluon emissions with tree-level 2 → 4 kernels for ;unordered; ones. The combined Sudakov evolution kernel is thus accurate to O (αs2). As a first step towards a full-fledged implementation of these ideas, we develop an explicit implementation of 2 → 4 shower branchings in this letter.
Langevin dynamics of financial systems: A second-order analysis
NASA Astrophysics Data System (ADS)
Canessa, E.
2001-07-01
We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat Cq, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that Cq can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point.
Second-order neutral impulsive stochastic evolution equations with delay
NASA Astrophysics Data System (ADS)
Ren, Yong; Sun, Dandan
2009-10-01
In this paper, we study the second-order neutral stochastic evolution equations with impulsive effect and delay (SNSEEIDs). We establish the existence and uniqueness of mild solutions to SNSEEIDs under non-Lipschitz condition with Lipschitz condition being considered as a special case by the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial data by means of corollary of the Bihari inequality. An application to the stochastic nonlinear wave equation with impulsive effect and delay is given to illustrate the theory.
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.
Stochastic evaluation of second-order Dyson self-energies.
Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So
2013-04-28
A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Green's function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 10(8) Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.
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
Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere.
Wang, Fei; Cai, Yangjian
2010-11-22
We present a detailed investigation of the second-order statistics of a twisted gaussian Schell-model (TGSM) beam propagating in turbulent atmosphere. Based on the extended Huygens-Fresnel integral, analytical expressions for the second-order moments of the Wigner distribution function of a TGSM beam in turbulent atmosphere are derived. Evolution properties of the second-order statistics, such as the propagation factor, the effective radius of curvature (ERC) and the Rayleigh range, of a TGSM beam in turbulent atmosphere are explored in detail. Our results show that a TGSM beam is less affected by the turbulence than a GSM beam without twist phase. In turbulent atmosphere the Rayleigh range doesn't equal to the distance where the ERC takes a minimum value, which is much different from the result in free space. The second-order statistics are closely determined by the parameters of the turbulent atmosphere and the initial beam parameters. Our results will be useful in long-distance free-space optical communications.
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.
Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal.
Shen, Yan; Liu, Lin; Zhao, Chengliang; Yuan, Yangsheng; Cai, Yangjian
2014-02-01
We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.
Eastaugh, Steven R
2005-01-01
Hospital diversification and its impact on the operating ratio are studied for 168 hospitals during the period from 1999 to 2004. Diversification and the operating ratio are modeled in a two-stage least squares (TSLS) framework as being jointly dependent. Institutional diversification is found to yield a better financial position, and the better operating ratio allows the institution the wherewithal to diversify. The impact of external government planning and hospital competition are also measured. An institution lifecycle hypothesis is advanced to explain hospital behavior: boom and bust, diversification and divestiture, occasionally leading to closure or merger. Management's attitude concerning risk and reward is considered.
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
Culzoni, María J; Damiani, Patricia C; García-Reiriz, Alejandro; Goicoechea, Héctor C; Olivieri, Alejandro C
2007-07-01
Three different experimental systems have been studied regarding the determination of analytes in complex samples, using non-linear second-order instrumental data, which are intrinsically able to provide the second-order advantage. This permits the quantitation of calibrated analytes in the presence of unexpected sample components, although a suitable algorithm is required. The recently described combination of artificial neural networks with post-training residual bilinearization has been applied to the three data sets, with successful results concerning prediction accuracy and precision, as well as profile recovery for the potential interferents in test samples. The studies involve: (1) the determination of two pharmaceuticals in the presence of an unexpected excipient by absorbance-pH matrix measurements, (2) the quantitation of iron(II) by its catalytic effect on the kinetics of the bromate oxidation of a colorant in the presence of a second interfering organic dye, and (3) the analysis of the antibiotic amoxicillin by fluorescence excitation-emission matrices in the presence of a fluorescent anti-inflammatory. The prediction results were compared and shown to be significantly better than those yielded by the unfolded partial least-squares/residual bilinearization model, due to the non-linear nature of the studied data.
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.
Gravitational Microlensing by Ellis Wormhole: Second Order Effects
NASA Astrophysics Data System (ADS)
Lukmanova, Regina; Kulbakova, Aliya; Izmailov, Ramil; Potapov, Alexander A.
2016-11-01
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.
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 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.
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
Second-Order Accurate Projective Integrators for Multiscale Problems
Lee, S L; Gear, C W
2005-05-27
We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution accuracy comparable to those obtained by implicit integrators. If the stiff differential equations are not directly available, our formulations and stability analysis are general enough to allow the combined outer-inner projective integrators to be applied to black-box legacy codes or perform a coarse-grained time integration of microscopic systems to evolve macroscopic behavior, for example.
Second order higher-derivative corrections in Double Field Theory
NASA Astrophysics Data System (ADS)
Lescano, Eric; Marqués, Diego
2017-06-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives O({α}^' 2}) for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
Communications: Ab initio second-order nonlinear optics in solids.
Luppi, Eleonora; Hübener, Hannes; Véniard, Valérie
2010-06-28
We present a first-principles theory for the calculation of the macroscopic second-order susceptibility chi((2)), based on the time-dependent density-functional theory approach. Our method allows to include straightforwardly the many-body effects, such as crystal local fields and excitons. We apply the theory to the computation of the second-harmonic generation spectroscopy. In order to demonstrate the accuracy of this approach we present spectra for the cubic semiconductor GaAs for which we obtain a very good agreement with the experimental results. We point out that crystal local fields are not sufficient to reproduce the experimental results. Only when we account for the excitonic effects we obtain a very good agreement with the experimental second-harmonic generation spectrum.
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.
Digital adaptive controllers using second order models with transport lag
NASA Technical Reports Server (NTRS)
Joshi, S.; Kaufman, H.
1975-01-01
Design of a discrete optimal regulator requires the a priori knowledge of a mathematical model for the system of interest. Because a second-order model with transport lag is very amenable to control computations and because this type of model has been used previously to represent certain high order single input-single output processes, an adaptive controller was designed based upon adjustment of controls computed for such a model. An extended Kalman filter was utilized for tracking the model parameters which were subsequently used to update a set of optimal control gains. Favorable results were obtained in applying this procedure to the control of several examples including a ninth order nonlinear process.
Digital second-order phase-locked loop
NASA Technical Reports Server (NTRS)
Holes, J. K.; Carl, C.; Tegnelia, C. R. (Inventor)
1973-01-01
A digital second-order phase-locked loop is disclosed in which a counter driven by a stable clock pulse source is used to generate a reference waveform of the same frequency as an incoming waveform, and to sample the incoming waveform at zero-crossover points. The samples are converted to digital form and accumulated over M cycles, reversing the sign of every second sample. After every M cycles, the accumulated value of samples is hard limited to a value SGN = + or - 1 and multiplied by a value delta sub 1 equal to a number of n sub 1 of fractions of a cycle. An error signal is used to advance or retard the counter according to the sign of the sum by an amount equal to the sum.
Second-order nonlinear optical effects of spin currents.
Wang, Jing; Zhu, Bang-Fen; Liu, Ren-Bao
2010-06-25
Pure spin currents carry information in spintronics and signify novel quantum spin phenomena such as topological insulators. Measuring pure spin currents, however, is difficult since they have no direct electromagnetic induction. Noticing that a longitudinal spin current, in which electrons move along their spin directions, is a chiral quantity, we envisage that it has a chiral sum-frequency optical effect. A systematic symmetry analysis confirms this idea and reveals the second-order optical effects of general spin currents with unique polarization dependence. Microscopic calculations based on the eight-band model of III-V compound semiconductors show that the susceptibility is sizable under realistic conditions. These findings form a basis for "seeing" spin currents where and while they flow with standard nonlinear optical spectroscopy, providing a toolbox to explore a wealth of physics connecting spins and photons.
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.
Perfectly matched layers for Maxwell's equations in second order formulation
Sjogreen, B; Petersson, A
2004-07-26
We consider the two-dimensional Maxwell's equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ''small-cell'' time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the parameters of the PML can be chosen to make the discrete solution of the PML equations converge to the solution of Maxwell's equations on the unbounded domain, as the grid size goes to zero. Several numerical examples are given.
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 L2 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.
WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS
MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN
2013-01-01
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 L2 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 O(h) to O(h1.5) 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 O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935
Perceptual learning of second order cues for layer decomposition.
Dövencioğlu, Dicle N; Welchman, Andrew E; Schofield, Andrew J
2013-01-25
Luminance variations are ambiguous: they can signal changes in surface reflectance or changes in illumination. Layer decomposition-the process of distinguishing between reflectance and illumination changes-is supported by a range of secondary cues including colour and texture. For an illuminated corrugated, textured surface the shading pattern comprises modulations of luminance (first order, LM) and local luminance amplitude (second-order, AM). The phase relationship between these two signals enables layer decomposition, predicts the perception of reflectance and illumination changes, and has been modelled based on early, fast, feed-forward visual processing (Schofield et al., 2010). However, while inexperienced viewers appreciate this scission at long presentation times, they cannot do so for short presentation durations (250 ms). This might suggest the action of slower, higher-level mechanisms. Here we consider how training attenuates this delay, and whether the resultant learning occurs at a perceptual level. We trained observers to discriminate the components of plaid stimuli that mixed in-phase and anti-phase LM/AM signals over a period of 5 days. After training, the strength of the AM signal needed to differentiate the plaid components fell dramatically, indicating learning. We tested for transfer of learning using stimuli with different spatial frequencies, in-plane orientations, and acutely angled plaids. We report that learning transfers only partially when the stimuli are changed, suggesting that benefits accrue from tuning specific mechanisms, rather than general interpretative processes. We suggest that the mechanisms which support layer decomposition using second-order cues are relatively early, and not inherently slow. Copyright © 2012 Elsevier Ltd. All rights reserved.
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.
One-electron density matrices and energy gradients in second-order electron propagator theory
NASA Astrophysics Data System (ADS)
Cioslowski, Jerzy; Ortiz, J. V.
1992-06-01
A formalism for evaluation of the effective first-order density matrices associated with second-order electron propagator theory is described. Computer implementation of this formalism affords first-order density properties, such as dipole moments, and energy gradients. Given an initial state with N electrons, this approach enables geometry optimization of the ground and excited electronic states of species with N-1 and N+1 electrons. The performance of the present method is assessed with test calculations on the formyl radical.
Attractivity theory for second order non-smooth dynamical systems with application to dry friction
NASA Astrophysics Data System (ADS)
Adly, Samir
2006-10-01
In this paper, we study the attractivity properties of the set of stationary solutions for a general class of second order non-smooth dynamical system involving friction term. Sufficient conditions for the local attractivity of the set of stationary solutions are given in the case of dry friction and negative viscous damping. An estimation of the attraction domain is also given in this case. Applications can be found in unilateral mechanics.
Hwang, Jai-chan; Noh, Hyerim
2007-11-15
velocity perturbations including the rotation coincide with the ones in Newton's gravity. All equations in this work include the cosmological constant in the background world model. We emphasize that our relativistic/Newtonian correspondences in several situations and pure general relativistic corrections in the context of Newtonian equations are mainly about the dynamic equations of density and velocity perturbations without using the gravitational potential (metric perturbations). Consequently, our relativistic/Newtonian correspondences do not imply the absence of many space-time (i.e., pure general relativistic) effects like frame dragging, and redshift and deflection of photons even in such cases. We also present the case of multiple minimally coupled scalar fields, and properly derive the large-scale conservation properties of curvature perturbation variable in various temporal gauge conditions to the second order.
NASA Astrophysics Data System (ADS)
Zieba, Jaroslaw W.; Zhang, Yue; Prasad, Paras N.; Casstevens, Martin K.; Burzynski, Ryszard
1992-12-01
A new class of promising composite materials consisting of sol-gel processed inorganic oxides and organic polymers has been developed over the last several years. These materials have been shown to be homogeneous, mechanically stable and have excellent optical properties. Second-order nonlinear optical properties are dependent upon the active chromophore being aligned within the structure. We report here the studies on the second-order nonlinear optical properties of a new oxide:polymer composite. A second-order chromophore, (N,N- diethylamino-((Beta) )-nitrostyrene or DEANST) has been doped into a sol-gel/polymer composite comprised of polyvinylpyrrolidone (PVP) and silica. The removal of solvent from a simple sol-gel preparation causes a tremendous shrinkage of the pores of the matrix. In addition, this particular polymer is capable of being crosslinked at elevated temperatures. These two effects were used to retain the alignment of the chromophores within this unique host material. The second-harmonic generation technique was used as a function of time to ascertain the utility of this approach and to determine the precise roles of processing conditions and components necessary to bring about this effect. The results of this work indicate that this composite can preserve the alignment of DEANST to satisfactory levels, making it an excellent candidate for device applications.
Contrast gain control in first- and second-order motion perception.
Lu, Z L; Sperling, G
1996-12-01
A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems' responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1-2% (5-10 x pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feedforward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.
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.
Second order gyrokinetic theory for particle-in-cell codes
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-15
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.
Second order evolution equations which describe pseudospherical surfaces
NASA Astrophysics Data System (ADS)
Catalano Ferraioli, D.; de Oliveira Silva, L. A.
2016-06-01
Second order evolution differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K = - 1, and can be seen as the compatibility condition of an associated sl (2 , R) -valued linear problem, also referred to as a zero curvature representation. Under the assumption that the linear problem is defined by 1-forms ωi =fi1 dx +fi2 dt, i = 1 , 2 , 3, with fij depending on (x , t , z ,z1 ,z2) and such that f21 = η, η ∈ R, we give a complete and explicit classification of equations of the form zt = A (x , t , z) z2 + B (x , t , z ,z1) . According to the classification, these equations are subdivided in three main classes (referred to as Types I-III) together with the corresponding linear problems. Explicit examples of differential equations of each type are determined by choosing certain arbitrary differentiable functions. Svinolupov-Sokolov equations admitting higher weakly nonlinear symmetries, Boltzmann equation and reaction-diffusion equations like Murray equation are some known examples of such equations. Other explicit examples are presented, as well.
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.
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.
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.
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.
Second order optimization for the inference of gene regulatory pathways.
Das, Mouli; Murthy, Chivukula A; De, Rajat K
2014-02-01
With the increasing availability of experimental data on gene interactions, modeling of gene regulatory pathways has gained special attention. Gradient descent algorithms have been widely used for regression and classification applications. Unfortunately, results obtained after training a model by gradient descent are often highly variable. In this paper, we present a new second order learning rule based on the Newton's method for inferring optimal gene regulatory pathways. Unlike the gradient descent method, the proposed optimization rule is independent of the learning parameter. The flow vectors are estimated based on biomass conservation. A set of constraints is formulated incorporating weighting coefficients. The method calculates the maximal expression of the target gene starting from a given initial gene through these weighting coefficients. Our algorithm has been benchmarked and validated on certain types of functions and on some gene regulatory networks, gathered from literature. The proposed method has been found to perform better than the gradient descent learning. Extensive performance comparison with the extreme pathway analysis method has underlined the effectiveness of our proposed methodology.
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
Second order anisotropy contribution in perpendicular magnetic tunnel junctions.
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 -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.
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 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. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
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.
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.
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
Bruschi, Maurizio; Fantucci, Piercarlo; Pizzotti, Maddalena
2005-10-27
In this work, we report an ab initio investigation of second-order nonlinear optical (NLO) properties and absorption electronic spectra of push-pull transition metal chromophores of the formula [M(CO)(5)L] (M = Cr, W; L = pyridine (Py), 4-formyl-pyridine (PyCHO), pyrazine (Pyz), trans-1,2-bis(4-pyridyl)ethylene (BPE)). Pyz and BPE are considered either with one nitrogen atom free or interacting with the strong acceptor BF(3). All of the molecular properties have been calculated using two different and methodologically independent approaches: the time dependent and coupled perturbed density functional theories (TDDFT and CPDFT) and the sum-over-states (SOS) approach, where the excited states are obtained via the single configuration interaction (SCI) ab initio method. DFT results are in acceptable agreement with the experimental energy values of electronic transitions (with the exception of chromophores with the large pi-delocalization, like BPE); SCI calculations overestimate excitation energies and produce an inversion in the order of d(M) --> pi(L) and d(M) --> pi(CO) transitions. The SCI-SOS approach gives first-order hyperpolarizabilities, basically in agreement as trend and values with the experiments and seems to be a tool generally suitable for the evaluation of these properties also for transition metal complexes. On the other hand, the first-order hyperpolarizabilities computed using the CPDFT approach are consistently overestimated in comparison with the experimental results, especially in the case of a ligand with large pi-delocalization. We also show that the "two-level" approximation taking into account only the lowest energy charge transfer excitation (e.g., d(M) --> pi(L)) is not applicable to chromophores with the extended pi-delocalized ligand (BPE) coordinated to a transition metal, due to significant contributions originating from intraligand pi(L) --> pi(L) transitions. This study reports a detailed analysis and comparison of electronic NLO
Second-order spatial correlation in the far-field: Comparing entangled and classical light sources
NASA Astrophysics Data System (ADS)
Zhang, Erfeng; Liu, Weitao; Lin, Huizu; Chen, Pingxing
2016-02-01
We consider second-order spatial correlation with entangled and classical light in the far-field. The quantum theory of second-order spatial correlation is analyzed, and the role of photon statistics and detection mode in the second-order spatial correlation are discussed. Meanwhile, the difference of second-order spatial correlation with entangled and classical light sources is deduced.
Forward and backward second-order Pavlovian conditioning in honeybees
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 inconclusive, and, therefore, we attempted to demonstrate SOC in the following three experiments: (Experiment 1) After differential conditioning (pairing odor A with US and presenting odor B without US), the bees experienced two pairs of partially overlapping odors, either a new odor C followed by a previously reinforced odor A (C-A) or a new odor C followed by a previously nonreinforced odor B (C-B). (Experiment 2) After differential conditioning, bees were presented with C-A or A-C. (Experiment 3) Bees were first presented with C-A or A-C before differential conditioning and were tested with odor C. We observed: (Experiment 1) 40% of the bees showed PER to the C-A presentation, but only 20% showed PER to the C-B presentation. (Experiment 2) 40% of the bees showed PER to the C-A presentation, while only 20% showed PER to the reversed sequence A-C. Experiments 1 and 2 showed that a previously reinforced odor can be a secondary reinforcer for excitatory SOC only with forward-pairing. (Experiment 3) PER toward C was lower (15%) in bees presented with A-C than with C-A (25%). This showed that backward SOC is not as effective as forward SOC. These results help to delineate different conditions that are critical for the phenomenon of SOC. PMID:17911371
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
Second order nonlinearity in Si by inhomogeneous strain and electric fields
NASA Astrophysics Data System (ADS)
Schilling, Jörg; Schriever, Clemens; Bianco, Federica; Cazzanelli, Massimo; Pavesi, Lorenzo
2015-08-01
The lack of a dipolar second order susceptibility (χ(2)) in silicon due to its centro-symmetric diamond lattice usually inhibits efficient second order nonlinear optical processes in the silicon bulk. Depositing stressed silicon nitride layers or growing a thermal oxide layer introduces an inhomogeneous strain into the silicon lattice and breaks the centro-symmetry of its crystal structure thereby creating a χ(2). This causes enhanced second harmonic generation and was observed in reflection and transmission measurements for wavelengths in the infrared. However strain is not the only means to break the structures symmetry. Fixed charges at the silicon nitride/silicon interface cause a high electric field close to the silicon interface which causes electric-field-induced-second-harmonic (EFISH) contributions too. The combination of both effects leads to χ(2) values which are estimated to be of the order as classic χ(2) materials like KDP or LiNiO3. This paves the way for the exploitation of other second order nonlinear processes in the area of silicon photonics and is an example how fundamental optical properties of materials can be altered by strain.
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
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.
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.
Gauge-invariant perturbations at second order: multiple scalar fields on large scales
NASA Astrophysics Data System (ADS)
Malik, Karim A.
2005-11-01
We derive the governing equations for multiple scalar fields minimally coupled to gravity in a flat Friedmann Robertson Walker background spacetime on large scales. We include scalar perturbations up to second order and write the equations in terms of physically transparent gauge-invariant variables at first and second order. This allows us to write the perturbed Klein Gordon equation at second order solely in terms of the field fluctuations on flat slices at first and second order.
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…
The Second-Order Factor Structure of the 16 PF: A Four Factor Solution.
ERIC Educational Resources Information Center
Marth, Joseph R.; Newman, Isadore
A review of the research into the second-order factor structure of the 16 Personality Factor Questionnaire (16 PF) indicates disagreement about the number and meaning of the second-order factors. However, repeated analyses of the second-order factor structure have consistently found fewer than the eight factors suggested by Catell (1973) and the…
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
Nanoengineering the second order susceptibility in semiconductor quantum dot heterostructures.
Zielinski, Marcin; Winter, Shoshana; Kolkowski, Radoslaw; Nogues, Claude; Oron, Dan; Zyss, Joseph; Chauvat, Dominique
2011-03-28
We study second-harmonic generation from single CdTe/CdS core/shell rod-on-dot nanocrystals with different geometrical parameters, which allow to fine tune the nonlinear properties of the nanostructure. These hybrid semiconductor-semiconductor nanoparticles exhibit extremely strong and stable second-harmonic emission, although the size of CdTe core is still within the strong quantum confinement regime. The orientation sensitive polarization response is analyzed by means of a pointwise additive model of the third-order tensors associated to the nanoparticle components. These findings prove that engineering of semiconducting complex heterostructures at the single nanoparticle scale can lead to extremely bright nanometric nonlinear light sources.
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.
A novel methodology to solve the CQLF problem for a finite set of stable second-order systems
NASA Astrophysics Data System (ADS)
Hernán Ordóñez-Hurtado, Rodrigo
2015-02-01
A new methodology to provide conclusive information about the existence/non-existence of a common quadratic Lyapunov function (CQLF) for a finite set of stable second-order systems is presented. Despite the high complexity of the CQLF problem, even in the case of N second-order systems, the results presented in this paper have a very simple and intuitive theoretical support, including topics such as classical intersection of convex sets and properties of convex linear combinations. Illustrative examples to show the performance of the proposed methodology are provided.
Klisch, Stephen M
2006-06-01
Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile-compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.
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.
SECOND-ORDER SOLUTIONS OF COSMOLOGICAL PERTURBATION IN THE MATTER-DOMINATED ERA
Hwang, Jai-chan; Noh, Hyerim; Gong, Jinn-Ouk
2012-06-10
We present the growing mode solutions of cosmological perturbations to the second order in the matter-dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in the most general fluid context. Based on these solutions, we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity, and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform-curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential that shows exact correspondence to the Newtonian one to the second order.
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.
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.
On the properness condition for modal analysis of non-symmetric second-order systems
NASA Astrophysics Data System (ADS)
Ouisse, Morvan; Foltête, Emmanuel
2011-02-01
Non-symmetric second-order systems can be found in several engineering contexts, including vibroacoustics, rotordynamics, or active control. In this paper, the notion of properness for complex modes is extended to the case of non-self-adjoint problems. The properness condition is related to the ability of a set of complex modes to represent in an exact way the behavior of a physical second-order system, meaning that the modes are the solutions of a quadratic eigenvalue problem whose matrices are those of a physical system. This property can be used to identify the damping matrices which may be difficult to obtain with mathematical modeling techniques. The first part of the paper demonstrates the properness condition for non symmetric systems in general. In the second part, the authors propose a methodology to enforce that condition in order to perform an optimal reconstruction of the "closest" physical system starting from a given basis complex modes. The last part is dedicated to numerical and experimental illustrations of the proposed methodology. A simulated academic test case is first used to investigate the numerical aspects of the method. A physical application is then considered in the context of rotordynamics. Finally, an experimental test case is presented using a structure with an active control feedback. An extension of the LSCF identification technique is also introduced to identify both left and right complex mode shapes from measured frequency response functions.
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.
Valiev, E. Z.
2009-02-15
The exchange striction model is invoked to derive an expression for the entropy of ferromagnetic materials undergoing first- and second-order magnetic phase transitions. The magnetocaloric and barocaloric effects are calculated for the ferromagnet La(Fe{sub 0.88}Si{sub 0.12}){sub 13} undergoing a first-order phase transition. The calculated results are in fair agreement with experimental data. The ferromagnet La(Fe{sub 0.88}Si{sub 0.12}){sub 13} is used as an example to predict the changes in magnetic and magnetocaloric properties associated with gradual increase in the magnetoelastic coupling constant (i.e., with passage from first- to second-order magnetic transition region). It is shown that stronger magnetoelastic coupling leads to stronger magnetocaloric effects and changes their dependence on magnetic field and pressure. Expressions are obtained for the maximum field- and pressure-induced entropy changes. An analysis is presented of the mechanism responsible for the increase in magnetocaloric and barocaloric effects associated with change from the second- to first-order magnetic phase transition.
Second-order integral sliding-mode control with experimental application.
Furat, Murat; Eker, İlyas
2014-09-01
In the present study, a second-order sliding-mode controller is proposed for single-input single-output (SISO) uncertain real systems. The proposed controller successively overcomes the variations caused by the uncertainties and external load disturbances although an approximate model of the system is used in the design procedure. An integral type sliding surface is used and the stability and robustness properties of the proposed controller are proved by means of Lyapunov stability theorem. The chattering phenomenon is significantly reduced adopting the switching gain with the known parameters of the system. Thus, the proposed controller is suitable for long-term application to the real systems. The performance of the proposed control scheme is validated by a real system experiments and the results are compared with the similar controllers presented in the literature.
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.
The structure of the second-order non-Born-Oppenheimer density matriz D2:
NASA Astrophysics Data System (ADS)
Ludena, Eduardo; Iza, Peter; Aray, Yosslen; Cornejo, Mauricio; Zambrano, Dik
Properties of the non-Born-Oppenheimer 2-matrix are examined. Using a coordinate system formed by internal translationally invariant plus the total center-of-mass coordinates it is shown that regardless of the point of reference selected, the operator for the reduced second order density matrix, 2-RDM, solely depends upon the translationally invariant internal coordinates. We apply this result to examine the nature of the 2-RDM extracted from the exact analytical solutions for model non-Born-Oppenheimer four-particle systems of the Coulomb-Hooke and Moshinsky types. We obtain for both these models explicit closed-form analytic expressions for the electron and nuclear 2-RDM. An explicit expression is also obtained for the electron-nuclear 2-RDM in the Moshinsky case, which shows coupling between the electron and nuclear coordinates. EVL and YA acknowledge support of SENESCYT's Prometheus Program.
Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field
NASA Astrophysics Data System (ADS)
Feng, Jinglang; Hou, Xiyun
2017-07-01
Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.
NASA Astrophysics Data System (ADS)
Nasilowski, Tomasz; Skorupski, Krzysztof; Makara, Mariusz; Statkiewicz-Barabach, Gabriela; Mergo, Pawel; Marc, Pawel; Jaroszewicz, Leszek
2011-05-01
Microstructured fibres (MSF) or photonic crystal fibres (PCF) possess a number of unique properties enabling a wide range of novel applications either in the telecommunication or in the sensing domain. In this paper we show that highly birefringent (HB) MSF with a dedicated design that allows inscribing fibre Bragg gratings in the MSF core can serve as pressure or stress transducers with extremely large sensitivity of second order mode, while exhibiting a low sensitivity to temperature drifts. Therefore, Bragg gratings inscribed in such MSF may offer a viable alternative to traditional optical fibre sensors of much lower stress sensitivity that require temperature compensation mechanisms and that are not intrinsically capable of distinguishing stress and temperature.
Intensity interferometry and the second-order correlation function g(2) in astrophysics
NASA Astrophysics Data System (ADS)
Foellmi, C.
2009-12-01
Most observational techniques in astronomy can be understood as exploiting the various forms of the first-order correlation function g(1). As demonstrated by the Narrabri stellar intensity interferometer back in the 1960s by Hanbury Brown & Twiss, the first experiment to measure the second-order correlation function g(2), light can carry more information than simply its intensity, spectrum, and polarization. Since this experiment, theoretical and laboratory studies of non-classical properties of light have become a very active field of research, called quantum optics. Despite the variety of results in this field, astrophysics remained focused essentially on first-order coherence. In this paper, we study the possibility that quantum properties of light could be observed in cosmic sources. We provide the basic mathematical ingredients about the first and the second order correlation functions, applied to the modern context of astronomical observations. We aim at replacing the Hanbury Brown & Twiss experiment in this context, and present two fundamental limitations of an intensity interferometer: the requirement of a chaotic light source and the rapid decrease of the amount of correlated fluctuations with the surface temperature. The first of these limitations paradoxically emphasizes that the exploitation of g(2) is richer than what a modern intensity interferometer could bring and is particularly interesting for sources of nonthermal light. We also discuss new photon-counting avalanche photodiodes currently being developed in Grenoble, and their impact on limiting magnitudes of an intensity interferometer. We conclude by briefly presenting why microquasars in our galaxy and their extragalactic parents can represent an excellent first target in the optical/near-infrared where to observe nonthermal light and to test the use of g(2) in astrophysical sources.
Real-time fringe pattern demodulation with a second-order digital phase-locked loop.
Gdeisat, M A; Burton, D R; Lalor, M J
2000-10-10
The use of a second-order digital phase-locked loop (DPLL) to demodulate fringe patterns is presented. The second-order DPLL has better tracking ability and more noise immunity than the first-order loop. Consequently, the second-order DPLL is capable of demodulating a wider range of fringe patterns than the first-order DPLL. A basic analysis of the first- and the second-order loops is given, and a performance comparison between the first- and the second-order DPLL's in analyzing fringe patterns is presented. The implementation of the second-order loop in real time on a commercial parallel image processing system is described. Fringe patterns are grabbed and processed, and the resultant phase maps are displayed concurrently.
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
The known unknowns: neural representation of second-order uncertainty, and ambiguity
Bach, Dominik R.; Hulme, Oliver; Penny, William D.; Dolan, Raymond J.
2011-01-01
Predictions provided by action-outcome probabilities entail a degree of (first-order) uncertainty. However, these probabilities themselves can be imprecise and embody second-order uncertainty. Tracking second-order uncertainty is important for optimal decision making and reinforcement learning. Previous functional magnetic resonance imaging investigations of second-order uncertainty in humans have drawn on an economic concept of ambiguity, where action-outcome associations in a gamble are either known (unambiguous) or completely unknown (ambiguous). Here, we relaxed the constraints associated with a purely categorical concept of ambiguity and varied the second-order uncertainty of gambles continuously, quantified as entropy over second-order probabilities. We show that second-order uncertainty influences decisions in a pessimistic way by biasing second-order probabilities, and that second-order uncertainty is negatively correlated with posterior cingulate cortex activity. The category of ambiguous (compared to non-ambiguous) gambles also biased choice in a similar direction, but was associated with distinct activation of a posterior parietal cortical area; an activation that we show reflects a different computational mechanism. Our findings indicate that behavioural and neural responses to second-order uncertainty are distinct from those associated with ambiguity and may call for a reappraisal of previous data. PMID:21451019
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.
Mansouri, Behzad; Allen, Harriet A; Hess, Robert F
2005-08-01
To better understand the nature of the cortical deficit in amblyopia we undertook a systematic investigation of second-order processing in 8 amblyopic and 8 normal observers. We investigated local detection, discrimination and global integration. Our local stimulus consisted of a Gaussian patch of fractal noise multiplied by a 1-d sinusoidal modulator. Our global stimulus consisted of an array of such elements. We revealed second-order detection deficits for stimuli with equi-visible carriers. Orientation discrimination for an isolated second-order patch was comparable in normal and amblyopic eyes. We showed that pure integration of second-order patterns can be normal in amblyopia.
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.
Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.
2017-09-01
High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemannmore » problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.« less
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. Copyright © 2011 Elsevier B.V. All rights reserved.
Second-order nonlinear optical response of zigzag BN single-walled nanotubes
NASA Astrophysics Data System (ADS)
Margulis, Vl. A.; Muryumin, E. E.; Gaiduk, E. A.
2010-12-01
A theory based on the two-band tight-binding approximation for π electrons is developed to describe the second-order nonlinear optical (NLO) properties of arrays of uniformly sized and well-aligned boron-nitride single-walled nanotubes (BN-SWNTs) with a zigzag achiral structure. It is assumed that the coherent light beam at frequency ω , incident upon the nanotube sample, is linearly polarized along the symmetry axis of the nanotubes. The long-axis NLO susceptibility χ(2)(ω) of those nanotubes is calculated within the independent nanotube approximation and in neglecting local-field effects. Using the perturbation-theory formalism in the crystal-momentum representation, we derive an explicit analytic expression for the χ(2)(ω) and apply it to study three distinct second-order NLO effects possible in the BN-SWNTs due to their noncentrosymmetric structure—namely, second-harmonic generation (SHG), linear electro-optical (LEO) effect, and nonlinear optical rectification (NOR). The theory is illustrated by numerical model calculations of the SHG, LEO, and NOR susceptibility spectra for several representative BN-SWNT ensembles consisting of large-diameter nanotubes. The calculated SHG spectra are found to be dominated by the highly peaked 2ω resonance at half the band-gap energy of the BN-SWNTs, where the absorption of light is negligible. Distinct features are also found in the LEO and NOR susceptibility spectra, e.g., a sudden switching of the susceptibility from a positive peak value to a negative peak one in the near vicinity of the fundamental absorption edge. A fairly large magnitude of those susceptibilities, reaching the order of 10-7esu under off-resonant conditions and up to 10-6esu in the resonant case, suggests that BN-SWNTs are a promising material for various electro-optical device applications.
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…
A Comparison Study of Second-Order Screening Designs and Their Extension
2013-12-01
40 vii Page III. Effect of Heredity and Sparsity on Second-Order Screening Design Performance...second- order screening designs with respect to the assumptions of both sparsity (factor or effect) and heredity (strong or weak). To date, evaluation of...screening design per- formance has assumed both factor sparsity and strong effect heredity . The article is currently under review for publication in
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…
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.
USDA-ARS?s Scientific Manuscript database
Adaptive waveform interpretation with Gaussian filtering (AWIGF) and second order bounded mean oscillation operator Z square 2(u,t,r) are TDR analysis methods based on second order differentiation. AWIGF was originally designed for relatively long probe (greater than 150 mm) TDR waveforms, while Z s...
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…
Cinque, Luigi
2013-01-01
Texture analysis is the process of highlighting key characteristics thus providing an exhaustive and unambiguous mathematical description of any object represented in a digital image. Each characteristic is connected to a specific property of the object. In some cases the mentioned properties represent aspects visually perceptible which can be detected by developing operators based on Computer Vision techniques. In other cases these properties are not visually perceptible and their computation is obtained by developing operators based on Image Understanding approaches. Pixels composing high quality medical images can be considered the result of a stochastic process since they represent morphological or physiological processes. Empirical observations have shown that these images have visually perceptible and hidden significant aspects. For these reasons, the operators can be developed by means of a statistical approach. In this paper we present a set of customized first and second order statistics based operators to perform advanced texture analysis of Magnetic Resonance Imaging (MRI) images. In particular, we specify the main rules defining the role of an operator and its relationship with other operators. Extensive experiments carried out on a wide dataset of MRI images of different body regions demonstrating usefulness and accuracy of the proposed approach are also reported. PMID:23840276
Assessing Stability and Change in a Second-Order Confirmatory Factor Model of Meaning in Life.
Krause, Neal; Hayward, R David
2014-04-01
Research indicates that meaning in life is an important correlate of health and well-being. However, relatively little is known about the way a sense of meaning may change over time. The purpose of this study is to explore two ways of assessing change in meaning within a second-order confirmatory factor analysis framework. First, tests are conducted to see if the first and second-order factor loadings and measurement error terms are invariant over time. Second, a largely overlooked technique is used to assess change and stability in meaning at the second-order level. Findings from a nationwide survey reveal that the first and second-order factor loadings are invariant of time. Moreover, the second-order measurement error terms, but not the first-order measurement error terms, are invariant, as well. The results further reveal that standard ways of assessing stability mask significant change in meaning that is due largely to regression to the mean.
Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets
Jimenez, Bienvenido Novo, Vicente
2004-03-15
We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Frechet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given.
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 diffraction forces on an array of vertical cylinders in bichromatic bidirectional waves
Vazquez, J.H.; Williams, A.N.
1995-02-01
A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.
Two-faced property of a market factor in asset pricing and diversification effect
NASA Astrophysics Data System (ADS)
Eom, Cheoljun
2017-04-01
This study empirically investigates the test hypothesis that a market factor acting as a representative common factor in the pricing models has a negative influence on constructing a well-diversified portfolio from the Markowitz mean-variance optimization function (MVOF). We use the comparative correlation matrix (C-CM) method to control a single eigenvalue among all eigenvalues included in the sample correlation matrix (S-CM), through the random matrix theory (RMT). In particular, this study observes the effect of the largest eigenvalue that has the property of the market factor. According to the results, the largest eigenvalue has the highest explanatory power on the stock return changes. The C-CM without the largest eigenvalue in the S-CM constructs a more diversified portfolio capable of improving the practical applicability of the MVOF. Moreover, the more diversified portfolio constructed from this C-CM has better out-of-sample performance in the future period. These results support the test hypothesis for the two-faced property of the market factor, defined by the largest eigenvalue.
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.
Optimal tuning of a control system for a second-order plant with time delay
NASA Astrophysics Data System (ADS)
Golinko, I. M.
2014-07-01
An engineering method for optimizing the parameters of PI and PID controllers for a second-order controlled plant with time delay is considered. An integral quality criterion involving minimization of the control output is proposed for optimizing the control system, which differs from the existing ones in that the effect the control output has on the technological process is taken into account in a correct way. The use of such control makes it possible to minimize the expenditure of material and/or energy resources, to limit the wear, and to increase the service life of the control devices. The unimodal nature of the proposed quality criterion for solving optimal controller tuning problems is numerically confirmed using the optimization theory. A functional correlation between the optimal controller parameters and dynamic properties of a controlled plant is determined for a single-loop control system with the use of calculation methods. The results from simulating the transients in the control system using the proposed and existing functional dependences are compared. The proposed calculation formulas differ from the existing ones by having simple structure, high accuracy of searching for the optimal controller parameters; they allow efficient control to be obtained and can be used for tuning automatic control systems in a wide range of controlled plant dynamic properties. The obtained calculation formulas are recommended for being used by engineers specializing in automation for designing new and optimizing the existing control systems.
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.
Second-order solution for determining density and velocity fields of galaxies
NASA Technical Reports Server (NTRS)
Gramann, Mirt
1993-01-01
In this Letter, I use second-order Lagrangian perturbation theory to calculate an analytical expression relating density to velocity in a gravitating system. This solution can be used to compare peculiar velocity field measurements with observations of large-scale structure. The predictions of both linear theory and second-order theory are compared with the results of N-body simulations. While linear theory systematically overestimates the velocity flows in high-density regions, the second-order corrections calculated herein remove this systematic error.
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.
Cheng, J L; Vermeulen, N; Sipe, J E
2017-03-06
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.
Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects
Cheng, J. L.; Vermeulen, N.; Sipe, J. E.
2017-01-01
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response. PMID:28262762
Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects
NASA Astrophysics Data System (ADS)
Cheng, J. L.; Vermeulen, N.; Sipe, J. E.
2017-03-01
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.
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.
Diversification: Far term (2000 - )
NASA Technical Reports Server (NTRS)
1975-01-01
Diversification, intended to underly the far term of the energy conservation program, was defined to imply conservation through substitution for scarce energy resources by maximizing the total number of viable energy system types in every sector. The following requirements or aspects of diversification that must be studied were given: fuel mix and end use patterns for various alternative diversification plans, current status of diversification, advantages and disadvantages of diversification, constraints and criteria, diversification actions and their controls, and means for implementing the chosen diversification strategy. The following advantages resulting from diversification were described: competition, crisis-related situations, local energy production, decentralized plant locations, long range energy policy, and environmental overloads. The major criteria by which a diversification program should be judged, the major constraints affecting the approaches, and the road to diversification, were elaborated.
Diversification: Far term (2000 - )
NASA Technical Reports Server (NTRS)
1975-01-01
Diversification, intended to underly the far term of the energy conservation program, was defined to imply conservation through substitution for scarce energy resources by maximizing the total number of viable energy system types in every sector. The following requirements or aspects of diversification that must be studied were given: fuel mix and end use patterns for various alternative diversification plans, current status of diversification, advantages and disadvantages of diversification, constraints and criteria, diversification actions and their controls, and means for implementing the chosen diversification strategy. The following advantages resulting from diversification were described: competition, crisis-related situations, local energy production, decentralized plant locations, long range energy policy, and environmental overloads. The major criteria by which a diversification program should be judged, the major constraints affecting the approaches, and the road to diversification, were elaborated.
Diversity spurs diversification in ecological communities
NASA Astrophysics Data System (ADS)
Calcagno, Vincent; Jarne, Philippe; Loreau, Michel; Mouquet, Nicolas; David, Patrice
2017-06-01
Diversity is a fundamental, yet threatened, property of ecological systems. The idea that diversity can itself favour diversification, in an autocatalytic process, is very appealing but remains controversial. Here, we study a generalized model of ecological communities and investigate how the level of initial diversity influences the possibility of evolutionary diversification. We show that even simple models of intra- and inter-specific ecological interactions can predict a positive effect of diversity on diversification: adaptive radiations may require a threshold number of species before kicking-off. We call this phenomenon DDAR (diversity-dependent adaptive radiations) and identify mathematically two distinct pathways connecting diversity to diversification, involving character displacement and the positive diversity-productivity relationship. Our results may explain observed delays in adaptive radiations at the macroscale and diversification patterns reported in experimental microbial communities, and shed new light on the dynamics of ecological diversity, the diversity-dependence of diversification rates, and the consequences of biodiversity loss.
Diversity spurs diversification in ecological communities.
Calcagno, Vincent; Jarne, Philippe; Loreau, Michel; Mouquet, Nicolas; David, Patrice
2017-06-09
Diversity is a fundamental, yet threatened, property of ecological systems. The idea that diversity can itself favour diversification, in an autocatalytic process, is very appealing but remains controversial. Here, we study a generalized model of ecological communities and investigate how the level of initial diversity influences the possibility of evolutionary diversification. We show that even simple models of intra- and inter-specific ecological interactions can predict a positive effect of diversity on diversification: adaptive radiations may require a threshold number of species before kicking-off. We call this phenomenon DDAR (diversity-dependent adaptive radiations) and identify mathematically two distinct pathways connecting diversity to diversification, involving character displacement and the positive diversity-productivity relationship. Our results may explain observed delays in adaptive radiations at the macroscale and diversification patterns reported in experimental microbial communities, and shed new light on the dynamics of ecological diversity, the diversity-dependence of diversification rates, and the consequences of biodiversity loss.
Application of a second-order projection method to the study of shear layers
Bell, J.B.; Glaz, H.M.; Solomon, J.M.; Szymczak, W.G.
1988-06-01
In this paper we apply a second-order projection method for the time-dependent, incompressible Navier-Stokes equations to the study of shear layers. The algorithm represents a higher-order extension of Chorin's projection algorithm. In Chorin's algorithm one first solves the Navier-Stokes equations ignoring the pressure term and then projects the resulting velocity field onto discretely divergence-free vector fields. Our method introduces more coupling between the diffusion-convection step and the projection to obtain second-order temporal accuracy. Furthermore, the algorithm incorporates a second-order Godunov method that provides a robust treatment of the nonlinear terms at high Reynolds number. These features combine to give a method that is second-order accurate for smooth flows and remains stable for singular initial data such as cortex sheets, even in the limit of vanishing viscosity. 9 refs., 2 figs.
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.
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.
On Picard boundary value problem for second order asymptotically homogeneous equations
NASA Astrophysics Data System (ADS)
Dong, Y.
Using the Leray-Schauder continuation principle we give some existence results for the Picard boundary value problem of second order asymptotically homogeneous equations. Some previous results by Tippett, Gaines-Mawhin, Lazer-Leach will be extended.
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)
Sensitivity to first- and second-order drifting gratings in 3-month-old infants
Armstrong, Vickie; Maurer, Daphne; Ellemberg, Dave; Lewis, Terri L
2011-01-01
In two experiments, we investigated 3-month-old infants' sensitivity to first- and second-order drifting gratings. In Experiment 1 we used forced-choice preferential looking with drifting versus stationary gratings to estimate depth modulation thresholds for 3-month-old infants and a similar task for a comparison group of adults. Thresholds for infants were more adult-like for second-order than first-order gratings. In Experiment 2, 3-month-olds dishabituated to a change in first-order orientation, but not to a change in direction of first- or second-order motion. Hence, results from Experiment 1 were likely driven by the perception of flicker rather than motion. Thus, infants' sensitivity to uniform motion is slow to develop and appears to be driven initially by flicker-sensitive mechanisms. The underlying mechanisms have more mature tuning for second-order than for first-order information. PMID:23145237
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)
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.
POSSIM: Parameterizing Complete Second-Order Polarizable Force Field for Proteins
2015-01-01
Previously, we reported development of a fast polarizable force field and software named POSSIM (POlarizable Simulations with Second order Interaction Model). The second-order approximation permits the speed up of the polarizable component of the calculations by ca. an order of magnitude. We have now expanded the POSSIM framework to include a complete polarizable force field for proteins. Most of the parameter fitting was done to high-level quantum mechanical data. Conformational geometries and energies for dipeptides have been reproduced within average errors of ca. 0.5 kcal/mol for energies of the conformers (for the electrostatically neutral residues) and 9.7° for key dihedral angles. We have also validated this force field by running Monte Carlo simulations of collagen-like proteins in water. The resulting geometries were within 0.94 Å root-mean-square deviation (RMSD) from the experimental data. We have performed additional validation by studying conformational properties of three oligopeptides relevant in the context of N-glycoprotein secondary structure. These systems have been previously studied with combined experimental and computational methods, and both POSSIM and benchmark OPLS-AA simulations that we carried out produced geometries within ca. 0.9 Å RMSD of the literature structures. Thus, the performance of POSSIM in reproducing the structures is comparable with that of the widely used OPLS-AA force field. Furthermore, our fitting of the force field parameters for peptides and proteins has been streamlined compared with the previous generation of the complete polarizable force field and relied more on transferability of parameters for nonbonded interactions (including the electrostatic component). The resulting deviations from the quantum mechanical data are similar to those achieved with the previous generation; thus, the technique is robust, and the parameters are transferable. At the same time, the number of parameters used in this work was
POSSIM: Parameterizing Complete Second-Order Polarizable Force Field for Proteins.
Li, Xinbi; Ponomarev, Sergei Y; Sigalovsky, Daniel L; Cvitkovic, John P; Kaminski, George A
2014-11-11
Previously, we reported development of a fast polarizable force field and software named POSSIM (POlarizable Simulations with Second order Interaction Model). The second-order approximation permits the speed up of the polarizable component of the calculations by ca. an order of magnitude. We have now expanded the POSSIM framework to include a complete polarizable force field for proteins. Most of the parameter fitting was done to high-level quantum mechanical data. Conformational geometries and energies for dipeptides have been reproduced within average errors of ca. 0.5 kcal/mol for energies of the conformers (for the electrostatically neutral residues) and 9.7° for key dihedral angles. We have also validated this force field by running Monte Carlo simulations of collagen-like proteins in water. The resulting geometries were within 0.94 Å root-mean-square deviation (RMSD) from the experimental data. We have performed additional validation by studying conformational properties of three oligopeptides relevant in the context of N-glycoprotein secondary structure. These systems have been previously studied with combined experimental and computational methods, and both POSSIM and benchmark OPLS-AA simulations that we carried out produced geometries within ca. 0.9 Å RMSD of the literature structures. Thus, the performance of POSSIM in reproducing the structures is comparable with that of the widely used OPLS-AA force field. Furthermore, our fitting of the force field parameters for peptides and proteins has been streamlined compared with the previous generation of the complete polarizable force field and relied more on transferability of parameters for nonbonded interactions (including the electrostatic component). The resulting deviations from the quantum mechanical data are similar to those achieved with the previous generation; thus, the technique is robust, and the parameters are transferable. At the same time, the number of parameters used in this work was
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.
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
Self-Consistent Second Order Perturbation Theory for the Hubbard Model in Two Dimensions
NASA Astrophysics Data System (ADS)
Nojiri, Hidekazu
1999-03-01
We apply self-consistent second order perturbation theory (SCSOPT)with respect to the on-site repulsive interaction Uto study the Hubbard model in two dimensions.We investigate single particle properties of the model over the entiredoping range at zero temperature.It is shown that as doping decreases toward half-fillingω-mass enhancement factor increases,while k-mass enhancement factor decreases.The increase in ω-mass enhancement factor is larger thanthe decrease in k-mass enhancement factor, so that total-mass is larger than that in the non-interacting case.When particle number density per unit cell n is given by0.64
Tomic, Slavisa; Beko, Marko; Dinis, Rui
2014-10-01
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.
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.
Random phase approximation with second-order screened exchange for current-carrying atomic states
NASA Astrophysics Data System (ADS)
Zhu, Wuming; Zhang, Liang; Trickey, S. B.
2016-12-01
The direct random phase approximation (RPA) and RPA with second-order screened exchange (SOSEX) have been implemented with complex orbitals as a basis for treating open-shell atoms. Both RPA and RPA+SOSEX are natural implicit current density functionals because the paramagnetic current density implicitly is included through the use of complex orbitals. We confirm that inclusion of the SOSEX correction improves the total energy accuracy substantially compared to RPA, especially for smaller-Z atoms. Computational complexity makes post self-consistent-field (post-SCF) evaluation of RPA-type expressions commonplace, so orbital basis origins and properties become important. Sizable differences are found in correlation energies, total atomic energies, and ionization energies for RPA-type functionals evaluated in the post-SCF fashion with orbital sets obtained from different schemes. Reference orbitals from Kohn-Sham calculations with semi-local functionals are more suitable for RPA+SOSEX to generate accurate total energies, but reference orbitals from exact exchange (non-local) yield essentially energetically degenerate open-shell atom ground states. RPA+SOSEX correlation combined with exact exchange calculated from a hybrid reference orbital set (half the exchange calculated from exact-exchange orbitals, the other half of the exchange from orbitals optimized for the Perdew-Burke-Ernzerhof (PBE) exchange functional) gives the best overall performance. Numerical results show that the RPA-like functional with SOSEX correction can be used as a practical implicit current density functional when current effects should be included.
NASA Astrophysics Data System (ADS)
Li, Xianyi
2007-10-01
By making use of inclusion theorem, we show in this paper the existence of solutions with a single semicycle for a general second-order rational difference equation. As a corollary, our results positively confirm Conjectures 4.8.3 and 5.4.6 in [M.R.S. Kulenovic, G. Ladas, Dynamics of Second-Order Rational Difference Equations, with Open Problems and Conjectures, Chapman and Hall/CRC, 2002].
An alternative assessment of second-order closure models in turbulent shear flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Gatski, Thomas B.
1994-01-01
The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.
A not so short note on the Klein Gordon equation at second order
NASA Astrophysics Data System (ADS)
Malik, Karim A.
2007-03-01
We give the governing equations for multiple scalar fields in a flat Friedmann Robertson Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein Gordon equation at second order in closed form in terms of gauge-invariant perturbations of the fields in the uniform curvature gauge. We also give a simplified form of the Klein Gordon equation using the slow-roll approximation.
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.
Third-order integrable difference equations generated by a pair of second-order equations
NASA Astrophysics Data System (ADS)
Matsukidaira, Junta; Takahashi, Daisuke
2006-02-01
We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel-Robert-Thomson (QRT) system, but in the other cases, they are irrelevant to the QRT system. We also discuss an ultradiscretization of the equations.
Second-order perturbation theory: a covariant approach involving a barotropic equation of state
NASA Astrophysics Data System (ADS)
Osano, Bob
2017-06-01
We present a covariant and gauge-invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor perturbations about the FLRW model having different kinds of equations of state. Our analysis of the radiation case suggests that it may be feasible to examine the CMB polarization arising from higher order perturbations.
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.
Can autistic children distinguish lies from jokes? A second look at second-order belief attribution.
Leekam, S R; Prior, M
1994-07-01
Previous studies show that autistic children fail tests of second-order belief attribution. They also fail tests of lying and deception. The present study used Leekam's (1988) joke-lie distinction task to test (a) understanding of second-order mental states (intention and belief) and (b) the ability to judge these acts as lies or jokes. Seventeen normal and 16 autistic children took part. Eight of the autistic children had previously passed a test of first-order false belief. Results showed that six autistic subjects (37.5%), all of whom are false belief "passers", gave consistently correct answers to second-order mental state questions. Neither normal nor autistic children found second-order intention easier than second-order belief. However, normal children found the ability to judge another person's mental state easier than labelling whether the person was lying or joking, supporting previous evidence. In contrast, there was no difference in these two judgements for autistic children. Overall these results qualify previous evidence by showing that autistic children can use second-order reasoning and can distinguish lies from jokes. Observational data on these children, however, suggest that their competence on the comprehension of these hypothetical situations was not matched by an ability to use lying and joking in real life. Methodological, language and diagnostic factors are discussed as providing possible explanations for the results.
Motion aftereffect of combined first-order and second-order motion.
van der Smagt, M J; Verstraten, F A; Vaessen, E B; van Londen, T; van de Grind, W A
1999-01-01
When, after prolonged viewing of a moving stimulus, a stationary (test) pattern is presented to an observer, this results in an illusory movement in the direction opposite to the adapting motion. Typically, this motion aftereffect (MAE) does not occur after adaptation to a second-order motion stimulus (i.e. an equiluminous stimulus where the movement is defined by a contrast or texture border, not by a luminance border). However, a MAE of second-order motion is perceived when, instead of a static test pattern, a dynamic test pattern is used. Here, we investigate whether a second-order motion stimulus does affect the MAE on a static test pattern (sMAE), when second-order motion is presented in combination with first-order motion during adaptation. The results show that this is indeed the case. Although the second-order motion stimulus is too weak to produce a convincing sMAE on its own, its influence on the sMAE is of equal strength to that of the first-order motion component, when they are adapted to simultaneously. The results suggest that the perceptual appearance of the sMAE originates from the site where first-order and second-order motion are integrated.
NASA Astrophysics Data System (ADS)
Svyatskiy, D.; Lipnikov, K.
2017-06-01
Richards's equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. We propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards' equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithms for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Numerical simulations show that the new preconditioner reduces computational cost up to 2-3 times in comparison with the conventional preconditioners.
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.
Svyatsky, Daniil; Lipnikov, Konstantin
2017-03-18
Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less
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.
First and second order semi-Markov chains for wind speed modeling
NASA Astrophysics Data System (ADS)
Prattico, F.; Petroni, F.; D'Amico, G.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. Semi-Markov processes (SMP) are a wide class of stochastic processes which generalize at the same time both Markov chains and renewal processes. Their main advantage is that of using whatever type of waiting time distribution for modeling the time to have a transition from one state to another one. This major flexibility has a price to pay: availability of data to estimate the parameters of the model which are more numerous. Data availability is not an issue in wind speed studies, therefore, semi-Markov models can be used in a statistical efficient way. In this work we present three different semi-Markov chain models: the first one is a first-order SMP where the transition probabilities from two speed states (at time Tn and Tn-1) depend on the initial state (the state at Tn-1), final state (the state at Tn) and on the waiting time (given by t=Tn-Tn-1), the second model is a second order SMP where we consider the transition probabilities as depending also on the state the wind speed was before the initial state (which is the state at Tn-2) and the last one is still a second order SMP where the transition probabilities depends on the three states at Tn-2,Tn-1 and Tn and on the waiting times t_1=Tn-1-Tn-2 and t_2=Tn-Tn-1. The three models are used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling
Assessing Stability and Change in a Second-Order Confirmatory Factor Model of Meaning in Life
Hayward, R. David
2013-01-01
Research indicates that meaning in life is an important correlate of health and well-being. However, relatively little is known about the way a sense of meaning may change over time. The purpose of this study is to explore two ways of assessing change in meaning within a second-order confirmatory factor analysis framework. First, tests are conducted to see if the first and second-order factor loadings and measurement error terms are invariant over time. Second, a largely overlooked technique is used to assess change and stability in meaning at the second-order level. Findings from a nationwide survey reveal that the first and second-order factor loadings are invariant of time. Moreover, the second-order measurement error terms, but not the first-order measurement error terms, are invariant, as well. The results further reveal that standard ways of assessing stability mask significant change in meaning that is due largely to regression to the mean. PMID:24778574
Spatial variances of wind fields and their relation to second-order structure functions and spectra
NASA Astrophysics Data System (ADS)
Vogelzang, Jur; King, Gregory P.; Stoffelen, Ad
2015-02-01
Kinetic energy variance as a function of spatial scale for wind fields is commonly estimated either using second-order structure functions (in the spatial domain) or by spectral analysis (in the frequency domain). Both techniques give an order-of-magnitude estimate. More accurate estimates are given by a statistic called spatial variance. Spatial variances have a clear interpretation and are tolerant for missing data. They can be related to second-order structure functions, both for discrete and continuous data. Spatial variances can also be Fourier transformed to yield a relation with spectra. The flexibility of spatial variances is used to study various sampling strategies, and to compare them with second-order structure functions and spectral variances. It is shown that the spectral sampling strategy is not seriously biased to calm conditions for scatterometer ocean surface vector winds. When the second-order structure function behaves like rp, its ratio with the spatial variance equals >(p+1>)>(p+2>). Ocean surface winds in the tropics have p between 2/3 and 1, so one-sixth to one-fifth of the second-order structure function value is a good proxy for the cumulative variance.
Hilbe, Christian; Traulsen, Arne; Röhl, Torsten; Milinski, Manfred
2014-01-01
Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all. PMID:24367116
Lateralization based on interaural differences in the second-order amplitude modulator.
Dietz, Mathias; Ewert, Stephan D; Hohmann, Volker
2012-01-01
Second-order amplitude modulation is a relatively slow variation of the modulation depth of a first-order amplitude modulation with higher frequency. In contrast to first-order modulation, which appears as a physical component in the stimulus spectrum after half-wave rectification, second-order modulation is not necessarily demodulated by the auditory periphery. For binaural processing of second-order amplitude modulated stimuli it is unknown whether interaural time differences (ITDs) in the second-order modulation result in a lateralized percept. Thus, second-order modulation can serve as a tool to investigate whether demodulation of interaurally delayed components is a prerequisite for lateralization. In most of the psychoacoustic experiments presented here, a 25 Hz sinusoidally amplitude-modulated (SAM) 160 Hz tone was either transposed to 4 kHz by half-wave rectifying this SAM waveform before multiplication with a 4 kHz tone (TSAM), or by adding an offset before multiplication (SAMAM). The experiments revealed an inability to lateralize the SAMAM based on ITDs in the 25 Hz component, whereas subjects could lateralize the TSAM. Given that only the TSAM results in a demodulated 25 Hz component after peripheral auditory processing, this result supports the hypothesis that demodulation is a prerequisite for lateralization, which has consequences for temporal modulation processing in models of binaural interaction. © 2012 Acoustical Society of America.
Rashed, Mohammed Abouelleil
2015-04-01
The centenary of Karl Jaspers' General Psychopathology was recognised in 2013 with the publication of a volume of essays dedicated to his work (edited by Stanghellini and Fuchs). Leading phenomenological-psychopathologists and philosophers of psychiatry examined Jaspers notion of empathic understanding and his declaration that certain schizophrenic phenomena are 'un-understandable'. The consensus reached by the authors was that Jaspers operated with a narrow conception of phenomenology and empathy and that schizophrenic phenomena can be understood through what they variously called second-order and radical empathy. This article offers a critical examination of the second-order empathic stance along phenomenological and ethical lines. It asks: (1) Is second-order empathy (phenomenologically) possible? (2) Is the second-order empathic stance an ethically acceptable attitude towards persons diagnosed with schizophrenia? I argue that second-order empathy is an incoherent method that cannot be realised. Further, the attitude promoted by this method is ethically problematic insofar as the emphasis placed on radical otherness disinvests persons diagnosed with schizophrenia from a fair chance to participate in the public construction of their identity and, hence, to redress traditional symbolic injustices.
Second-order fiber interleaving filter based on polarization-diversified loop
NASA Astrophysics Data System (ADS)
Park, Kyongsoo; Choi, Sungwook; Lee, Seul-Lee; Jeong, Jun Hyeok; Jeong, Sun Jae; Christian, Nouaze Joseph; Kim, Min Seok; Kim, Jihoon; Kang, Hyun Wook; Nam, Seung Yun; Oh, Junghwan; Lee, Yong Wook
2017-06-01
A second-order fiber interleaving filter that can provide a channel interleaving capability in second-order comb spectra is proposed and demonstrated on the basis of a polarization-diversified loop comprised of a four-port polarization beam splitter, four rotatable half-wave plates (HWPs), and three high birefringence fiber (HBF) segments. Each HBF segment is positioned between two adjoining HWPs, and two HWPs located among the three HBF segments determine the effective angular orientation difference among their principal axes, or fast and slow axes. At specific orientation angles of the four HWPs, second-order comb spectra such as flat-top and narrow-band ones could be obtained with a free spectral range (FSR) of ˜0.792 nm. In particular, the frequency interleaving of these second-order comb spectra, that is, a half FSR switching, could be implemented by controlling two out of four HWPs, which is the first demonstration of the interleaving operation in second-order comb spectra without expensive birefringence modulators. These spectral characteristics of the proposed filter were theoretically predicted and experimentally demonstrated.
Looking at faces: first-order and second-order features as determinants of facial appearance.
Rhodes, Gillian
2013-01-01
The encoding and relative importance of first-order (discrete) and second-order (configural) features in mental representations of unfamiliar faces have been investigated. Nonmetric multidimensional scaling (KYST) was carried out on similarity judgments of forty-one photographs of faces (homogeneous with respect to sex, race, facial expression, and, to a lesser extent, age). A large set of ratings, measurements, and ratios of measurements of the faces was regressed against the three-dimensional KYST solution in order to determine the first-order and second-order features used to judge similarity. Parameters characterizing both first-order and second-order features emerged as important determinants of facial similarity. First-order feature parameters characterizing the appearance of the eyes, eyebrows, and mouth, and second-order feature parameters characterizing the position of the eyes, spatial relations between the internal features, and chin shape correlated with the dimensions of the KYST solution. There was little difference in the extent to which first-order and second-order features were encoded. Two higher-level parameters, age and weight, were also used to judge similarity. The implications of these results for mental representations of faces are discussed.
Hilbe, Christian; Traulsen, Arne; Röhl, Torsten; Milinski, Manfred
2014-01-14
Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all.
Ethanol induces second-order aversive conditioning in adolescent and adult rats
Pautassi, Ricardo Marcos; Myers, Mallory; Spear, Linda Patia; Molina, Juan Carlos; Spear, Norman E.
2011-01-01
Alcohol abuse and dependence is considered a developmental disorder with etiological onset during late childhood and adolescence, and understanding age-related differences in ethanol sensitivity is important. Low to moderate ethanol doses (0.5 and 2.0 g/kg, i.g.) induce single-trial, appetitive second-order place conditioning (SOC) in adolescent, but not adult, rats. Recent studies have demonstrated that adolescents may be less sensitive than adults to the aversive properties of ethanol, reflected by conditioned taste aversion. The present study assessed the aversive motivational effects of high-dose ethanol (3.0 and 3.25 g/kg, i.g., for adolescent and adults, respectively) using SOC. These doses were derived from Experiment 1, which found similar blood and brain ethanol levels in adolescent and adult rats given 3.0 and 3.25 g/kg ethanol, respectively. In Experiment 2, animals received ethanol or vehicle paired with intraoral pulses of sucrose (conditioned stimulus 1 [CS1]). After one, two, or three conditioning trials, rats were presented with the CS1 while in a distinctive chamber (CS2). When tested for CS2 preference, ethanol-treated animals exhibited reduced preference for the CS2 compared with controls. This result, indicative of ethanol-mediated aversive place conditioning, was similar for adolescents and adults, for females and males, and after one, two, or three training trials. One finding, however, suggested that adolescents were less sensitive than adults to ethanol’s aversive effects at the intermediate level of training. In conjunction with previous results, the present study showed that in adolescent rats subjected to SOC, ethanol’s hedonic effects vary from appetitive to aversive as the ethanol dose increases. Adolescent and adult animals appear to perceive the post-ingestive effects of high-dose ethanol as similarly aversive when assessed by SOC. PMID:21187242
Second order incommensurate phase transition in 25L-Ta{sub 2}O{sub 5}
Audier, M.; Chenevier, B.; Roussel, H.; Lintanf Salauen, A.
2010-09-15
A new structural state 25L-Ta{sub 2}O{sub 5}, obtained from sintering and annealing treatments of a Ta{sub 2}O{sub 5} powder, is identified both by electron diffraction and high resolution imaging on a transmission electron microscope (TEM). According to general rules for the different L-Ta{sub 2}O{sub 5} structures proposed by Grey et al. (J. Solid State Chem. 178 (2005) 3308), a structural model is derived from their crystallographic data on 19L-Ta{sub 2}O{sub 5}. This model yields simulated images in agreement with high resolution TEM observations of the structure oriented along its [001] zone axis, but only for a very thin crystal thickness of less than 1.2 nm. Such a limitation is shown to be due to a modulation of the structure along its [001] axis. Actually, from an analysis of a diffuse scattering and of its evolution into satellites reflections as a function of the cooling rate, a second order incommensurate phase transition can be assumed to occur in this compound. The property of single phase samples observed by TEM is also verified by X-ray powder diffraction. In a discussion about studies performed by different authors on incommensurate structures in the system Ta{sub 2}O{sub 5}-WO{sub 3}, it is noticed that TEM results, similar to ours, indicate that phase transitions could be expected in these structures. - Graphical Abstract: Electron diffraction patterns of [100] zone axis, showing a structural change of the 25L-Ta{sub 2}O{sub 5} phase through a variation of the cooling rate from 1000 {sup o}C.
ElaStic: A tool for calculating second-order elastic constants from first principles
NASA Astrophysics Data System (ADS)
Golesorkhtabar, Rostam; Pavone, Pasquale; Spitaler, Jürgen; Puschnig, Peter; Draxl, Claudia
2013-08-01
Elastic properties play a key role in materials science and technology. The elastic tensors at any order are defined by the Taylor expansion of the elastic energy or stress in terms of the applied strain. In this paper, we present ElaStic, a tool that is able to calculate the full second-order elastic stiffness tensor for any crystal structure from ab initio total-energy and/or stress calculations. This tool also provides the elastic compliances tensor and applies the Voigt and Reuss averaging procedure in order to obtain an evaluation of the bulk, shear, and Young moduli as well as the Poisson ratio of poly-crystalline samples. In a first step, the space-group is determined. Then, a set of deformation matrices is selected, and the corresponding structure files are produced. In a next step, total-energy or stress calculations for each deformed structure are performed by a chosen density-functional theory code. The computed energies/stresses are fitted as polynomial functions of the applied strain in order to get derivatives at zero strain. The knowledge of these derivatives allows for the determination of all independent components of the elastic tensor. In this context, the accuracy of the elastic constants critically depends on the polynomial fit. Therefore, we carefully study how the order of the polynomial fit and the deformation range influence the numerical derivatives, and we propose a new approach to obtain the most reliable results. We have applied ElaStic to representative materials for each crystal system, using total energies and stresses calculated with the full-potential all-electron codes exciting and WIEN2k as well as the pseudo-potential code Quantum ESPRESSO.
Ethanol induces second-order aversive conditioning in adolescent and adult rats.
Pautassi, Ricardo Marcos; Myers, Mallory; Spear, Linda Patia; Molina, Juan Carlos; Spear, Norman E
2011-02-01
Alcohol abuse and dependence are considered public health problems, with an etiological onset often occurring during late childhood and adolescence, and understanding age-related differences in ethanol sensitivity is important. Low to moderate ethanol doses (0.5 and 2.0 g/kg, intragastrically [i.g.]) induce single-trial, appetitive second-order place conditioning (SOC) in adolescent, but not adult, rats. Recent studies have demonstrated that adolescents may be less sensitive than adults to the aversive properties of ethanol, reflected by conditioned taste aversion. The present study assessed the aversive motivational effects of high-dose ethanol (3.0 and 3.25 g/kg, i.g., for adolescents and adults, respectively) using SOC. Experiment 1 revealed similar blood and brain ethanol levels in adolescent and adult rats given 3.0 and 3.25 g/kg ethanol, respectively. In Experiment 2, animals received ethanol or vehicle paired with intraoral pulses of sucrose (conditioned stimulus 1 [CS1]). After one, two, or three conditioning trials, the rats were presented with the CS1 while in a distinctive chamber (CS2). When tested for CS2 preference, ethanol-treated animals exhibited reduced preference for the CS2 compared with controls. This result, indicative of ethanol-mediated aversive place conditioning, was similar for adolescents and adults; for females and males; and after one, two, or three training trials. In conjunction with previous results, the present study showed that, in adolescent rats subjected to SOC, ethanol's hedonic effects vary from appetitive to aversive as the ethanol dose increases. Adolescent and adult animals appear to perceive the postingestive effects of high-dose ethanol as similarly aversive when assessed by SOC.
Second-order perturbation theory for the single-impurity Anderson model of a BCS superconductor
NASA Astrophysics Data System (ADS)
Alastalo, Ari T.
2017-09-01
This paper presents a conserving approximation for a single magnetic impurity embedded in a BCS superconductor according to the Anderson model. The calculation generalizes the second-order selfenergy theory of a normal metal host into a superconducting medium. Within the second-order theory, both spin and pairing fluctuations contribute to the selfenergy. The second-order theory removes the unphysical spontaneous symmetry breaking of the Hartree-Fock approximation but results in a doubling of the bound-state spectrum within the energy gap. The HF bound states may be recovered in the small-U limit as the average of the two separate bound states. For increasing U, the novel pronounced low-energy bound states tend towards the center of the gap while the other bound states approach the gap edge and their spectral weights vanish.
Bell, J.B.; Solomon, J.M.; Szymczak, W.G.
1989-04-01
This paper describes a second-order projection method for the incompressible Navier-Stokes equations on a logically-rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to predict intermediate velocities which are then projected onto the space of divergence-free vector fields. The spatial discretization of the diffusion-convection equations is accomplished by formally transforming the equations to a uniform computational space. The diffusion terms are then discretized using standard finite-difference approximations. The convection terms are discretized using a second-order Godunov method that provides a robust discretization of these terms at high Reynolds number. The projection is approximated using a Galerkin procedure that uses a local basis for discretely divergence-free vector fields. Numerical results are presented illustrating the performance of the method. 13 refs., 5 figs.
Raman Scattering of Light in Silicon Nanostructures: First- and Second-Order Spectra
Kravets, V.G.; Kolmykova, V.Yu.
2005-07-15
First- and second-order Raman scattering spectra in Si nanocrystals have been studied. The shift to lower frequencies and the substantial broadening of first-order Raman scattering lines observed to occur with decreasing nanoparticle size were established to correlate with those in second-order spectra. It is shown that the experimentally observed shifts of peaks and their broadening cannot be predicted based only on the phenomenological model of strong phonon wave function localization. The anharmonic effect originating from the heating of the nanoparticle surface by laser radiation should also be included. Proper fitting of experimental data revealed that the anharmonic constants depend strongly on nanoparticle size. The shape and spectral positions of maxima in second-order Raman scattering spectra have been theoretically described.
The stability of numerical methods for second order ordinary differential equations
NASA Technical Reports Server (NTRS)
Gear, C. W.
1978-01-01
An important characterization of a numerical method for first order ODE's is the region of absolute stability. If all eigenvalues of the linear problem dy/dt = Ay are inside this region, the numerical method is stable. If the second order system d/dt(dy/dt) = 2Ady/dt - By is solved as a first order system, the same result applies to the eigenvalues of the generalized eigenvalue problem (lambda-squared)I 2(lambda)A + B. No such region exists for general methods for second order equations, but in some cases a region of absolute stability can be defined for methods for the single second order equation d/dt(dy/dt) = 2ady/dt - by. The absence of a region of absolute stability can occur when different members of a system of first order equations are solved by different methods.
BOTDA sensors enhanced using high-efficiency second-order distributed Brillouin amplification.
Jia, Xin-Hong; Chang, Han-Qing; Ao, Lei; Ji, Xiao-Ling; Xu, Cong; Zhang, Wei-Li
2016-06-27
A novel approach for long-distance sensing through Brillouin optical time-domain analysis (BOTDA) assisted by second-order distributed Brillouin amplification (DBA) was proposed and experimentally demonstrated. To the best of our knowledge, this is the first BOTDA study that used second-order DBA. Compared with BOTDA assisted by first-order DBA, the proposed approach enhanced the signal-to-noise ratio of the Brillouin trace by ~3 dB for a range featuring minimum sensing intensity. Long-distance sensing with ~5 m spatial resolution and ± 1.6°C measurement uncertainty over ~99 km fiber was successfully realized by employing high-efficiency pumping using ~6 dBm second-order and ~1.5 dBm first-order pumps.
Chen, Jiale; Gao, Zhe
2013-08-15
The second-order velocity distribution function was calculated from the second-order rf kinetic theory [Jaeger et al., Phys. Plasmas 7, 641 (2000)]. However, the nonresonant ponderomotive force in the radial direction derived from the theory is inconsistent with that from the fluid theory. The inconsistency arises from that the multiple-timescale-separation assumption fails when the second-order Vlasov equation is directly integrated along unperturbed particle orbits. A slowly ramped wave field including an adiabatic turn-on process is applied in the modified kinetic theory in this paper. Since this modification leads only to additional reactive/nonresonant response relevant with the secular resonant response from the previous kinetic theory, the correct nonresonant ponderomotive force can be obtained while all the resonant moments remain unchanged.
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
NASA Astrophysics Data System (ADS)
Nakamura, K.
2009-06-01
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.
Encoding and estimation of first- and second-order binocular disparity in natural images
Hibbard, Paul B.; Goutcher, Ross; Hunter, David W.
2016-01-01
The first stage of processing of binocular information in the visual cortex is performed by mechanisms that are bandpass-tuned for spatial frequency and orientation. Psychophysical and physiological evidence have also demonstrated the existence of second-order mechanisms in binocular processing, which can encode disparities that are not directly accessible to first-order mechanisms. We compared the responses of first- and second-order binocular filters to natural images. We found that the responses of the second-order mechanisms are to some extent correlated with the responses of the first-order mechanisms, and that they can contribute to increasing both the accuracy, and depth range, of binocular stereopsis. PMID:26731646
Second-Order Belief Attribution in Williams Syndrome: Intact or Impaired?
Sullivan, Kate; Tager-Flusberg, Helen
2005-01-01
Second-order mental state attribution in a group of children with Williams syndrome was investigated. The children were compared to age, IQ, and language-matched groups of children with Prader-Willi syndrome or nonspecific mental retardation. Participants were given two trials of a second-order reasoning task. No significant differences between the Williams syndrome and Prader-WiIli or mentally retarded groups on any of the test questions were found. Results contrast with the view that individuals with Williams syndrome have an intact theory of mind and suggest that in their attributions of second-order mental states, children with Williams syndrome perform no better than do other groups of children with mental retardation. PMID:10587733
Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width
NASA Technical Reports Server (NTRS)
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro
2006-01-01
Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.
Second order gauge invariant measure of a tidally deformed black hole
Ahmadi, Nahid
2012-08-01
In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.
Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence
Li, Yang; Gao, Zhe; Chen, Jiale
2016-08-15
A second order kinetic model for turbulent ion parallel momentum transport is presented. A new nonresonant second order parallel momentum flux term is calculated. The resonant component of the ion parallel electrostatic force is the momentum source, while the nonresonant component of the ion parallel electrostatic force compensates for that of the nonresonant second order parallel momentum flux. The resonant component of the kinetic momentum flux can be divided into three parts, including the pinch term, the diffusive term, and the residual stress. By reassembling the pinch term and the residual stress, the residual stress can be considered as a pinch term of parallel wave-particle resonant velocity, and, therefore, may be called as “resonant velocity pinch” term. Considering the resonant component of the ion parallel electrostatic force is the transfer rate between resonant ions and waves (or, equivalently, nonresonant ions), a conservation equation of the parallel momentum of resonant ions and waves is obtained.
Feasibility of a second-order gravitational red-shift experiment
NASA Technical Reports Server (NTRS)
Jaffe, J.; Vessot, R. F. C.
1976-01-01
The number of gravitation experiments undertaken since the advent of Einstein's theory of gravitation is quite small, with, so far, only the famous perihelion-advance experiment and a recent lunar-laser-ranging experiment being capable of measuring a nonlinear, second-order effect. It now appears that another distinct test of the second-order term may be feasible through the use of very stable atomic clocks. This experiment, which would measure the second-order gravitational red-shift, is a bona fide test of the field equations of gravity, not just a test of the underlying principle of equivalence. The nature of such an experiment, the basic equations, model-orbit calculations, and some tracking-accuracy requirements are presented. It is concluded that current space-probe tracking capabilities cannot determine all the necessary orbital parameters with sufficient accuracy for this experiment at the present time.
First- or second-order transition in the melting of repeat sequence DNA.
Chen, Y Z; Prohofsky, E W
1994-01-01
Both theoretical analysis and observation of the continuity of the melted fraction of base pairs indicate that the melting transition in DNA is second order. Analysis of the salt dependence of the transition by polyelectrolyte limiting laws, however, has first-order dynamics imbedded in the analysis. This paper proposes that the observation taken to be a latent heat of melting in the limiting law analysis could instead be a specific heat anomaly associated with a second-order transition. The limiting laws can be reconstructed based on a second-order transition with a specific heat anomaly. The T2M dependence of this excess heat is also consistent with its being a specific heat anomaly of a system displaying classical critical behavior. Classical critical behavior indicates that theoretical mean field approaches such as MSPA should be particularly appropriate to helix melting studies. PMID:8130338
Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width
NASA Technical Reports Server (NTRS)
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro
2006-01-01
Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.
New second order Mumford-Shah model based on Γ-convergence approximation for image processing
NASA Astrophysics Data System (ADS)
Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li
2016-05-01
In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.
Part A: Nonprincipal-plane scattering from flat plates: Second-order and corner diffractions
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.
1989-01-01
Two models of a flat plate for nonprincipal-plane scattering are explored. The first is a revised version of the Physical Optics/Physical Theory of Diffraction (PO/PTD) model with second-order PTD equivalent currents included to account for second-order interactions among the plate edges. The second model uses a heurisitcally derived corner diffraction coefficient to account for the corner scattering mechanism. The patterns obtained using the newer models were compared to the data of previously reported models, the Moment Method (MM), and experimental results. Near normal incidence, all the models agreed; however, near grazing incidence a need for higher-order and corner diffraction mechanisms was noted. In many instances the second-order and corner-scattered fields which were formulated improved the results.
Feasibility of a second-order gravitational red-shift experiment
NASA Technical Reports Server (NTRS)
Jaffe, J.; Vessot, R. F. C.
1976-01-01
The number of gravitation experiments undertaken since the advent of Einstein's theory of gravitation is quite small, with, so far, only the famous perihelion-advance experiment and a recent lunar-laser-ranging experiment being capable of measuring a nonlinear, second-order effect. It now appears that another distinct test of the second-order term may be feasible through the use of very stable atomic clocks. This experiment, which would measure the second-order gravitational red-shift, is a bona fide test of the field equations of gravity, not just a test of the underlying principle of equivalence. The nature of such an experiment, the basic equations, model-orbit calculations, and some tracking-accuracy requirements are presented. It is concluded that current space-probe tracking capabilities cannot determine all the necessary orbital parameters with sufficient accuracy for this experiment at the present time.
Nie, Xiaobing; Cao, Jinde
2011-11-01
In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.
Stabilization and PID tuning algorithms for second-order unstable processes with time-delays.
Seer, Qiu Han; Nandong, Jobrun
2017-03-01
Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.
Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry.
Broch, Laurent; En Naciri, Aotmane; Johann, Luc
2010-06-10
We investigate the systematic errors at the second order for a Mueller matrix ellipsometer in the dual rotating compensator configuration. Starting from a general formalism, we derive explicit second-order errors in the Mueller matrix coefficients of a given sample. We present the errors caused by the azimuthal inaccuracy of the optical components and their influences on the measurements. We demonstrate that the methods based on four-zone or two-zone averaging measurement are effective to vanish the errors due to the compensators. For the other elements, it is shown that the systematic errors at the second order can be canceled only for some coefficients of the Mueller matrix. The calibration step for the analyzer and the polarizer is developed. This important step is necessary to avoid the azimuthal inaccuracy in such elements. Numerical simulations and experimental measurements are presented and discussed.
Vogt, Leslie; Olivares-Amaya, Roberto; Kermes, Sean; Shao, Yihan; Amador-Bedolla, Carlos; Aspuru-Guzik, Alan
2008-03-13
The modification of a general purpose code for quantum mechanical calculations of molecular properties (Q-Chem) to use a graphical processing unit (GPU) is reported. A 4.3x speedup of the resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) execution time is observed in single point energy calculations of linear alkanes. The code modification is accomplished using the compute unified basic linear algebra subprograms (CUBLAS) library for an NVIDIA Quadro FX 5600 graphics card. Furthermore, speedups of other matrix algebra based electronic structure calculations are anticipated as a result of using a similar approach.
NASA Astrophysics Data System (ADS)
Kashchenko, Sergey A.
2016-12-01
The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Espa, D; Pilia, L; Marchiò, L; Artizzu, F; Di Carlo, G; Marinotto, D; Serpe, A; Tessore, F; Deplano, P
2016-11-01
A film of [Pd(R2pipdt)(dmit)] (1), where R2pipdt = 1,4-didodecyl-piperazine-2,3-dithione (acceptor) and dmit = 2-thioxo-1,3-dithiole-4,5-dithiolate (donor) incorporated into a polymethylmethacrylate (PMMA) matrix, showing a good second-harmonic generation, has been prepared for the first time in the class of dithione-dithiolate 2nd order NLO-chromophores. Moreover full characterization of 1, including molecular second-order NLO properties in solution, is reported.
NASA Astrophysics Data System (ADS)
Gushchin, A. K.
2016-10-01
The paper is concerned with the properties of the solution to a Dirichlet problem for a homogeneous second-order elliptic equation with L_p-boundary function, p>1. The same conditions are imposed on the coefficients of the equation and the boundary of the bounded domain as were used to establish the solvability of this problem. The L_p-norm of the nontangential maximal function is estimated in terms of the L_p-norm of the boundary value. This result depends on a new estimate, proved below, for the nontangential maximal function in terms of an analogue of the Lusin area integral. Bibliography: 31 titles.
NASA Technical Reports Server (NTRS)
Yee, H. C.; Kutler, P.
1983-01-01
A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.
Perceived timing of first- and second-order changes in vision and hearing.
Arrighi, Roberto; Alais, David; Burr, David
2005-10-01
Simultaneous changes in visual stimulus attributes (such as motion or color) are often perceived to occur at different times, a fact usually attributed to differences in neural processing times of those attributes. However, other studies suggest that perceptual misalignments are not due to stimulus attributes, but to the type of change, first- or second-order. To test whether this idea generalizes across modalities, we studied perceptual synchrony of acoustic and of audiovisual cross-modal stimuli, which varied in a first- or second-order fashion. First-order changes were abrupt changes in tone intensity or frequency (auditory), or spatial position (visual), while second-order changes were an inversion of the direction of change, such as a turning point when a rising tone starts falling or a translating visual blob reverses. For both pure acoustic and cross-modal stimuli, first-order changes were systematically perceived before second-order changes. However, when both changes were first-order, or both were second-order, little or no difference in perceptual delay was found between them, regardless of attribute or modality. This shows that the type of attribute change, as well as latency differences, is a strong determinant of subjective temporal alignments. We also performed an analysis of reaction times (RTs) to the first- and second-order attribute changes used in these temporal alignment experiments. RT differences between these stimuli did not correspond with our temporal alignment data, suggesting that subjective alignments cannot be accounted for by a simple latency-based explanation.
Diversification of energy sources
NASA Technical Reports Server (NTRS)
1975-01-01
The concept of energy source diversification was introduced as a substitution conservation action. The current status and philosophy behind a diversification program is presented in the context of a national energy policy. Advantages, disadvantages (constraints), and methods of implementation for diversification are discussed. The energy source systems for diversification are listed and an example impact assessment is outlined which deals with the water requirements of the specific energy systems.
Diversification of energy sources
NASA Technical Reports Server (NTRS)
1975-01-01
The concept of energy source diversification was introduced as a substitution conservation action. The current status and philosophy behind a diversification program is presented in the context of a national energy policy. Advantages, disadvantages (constraints), and methods of implementation for diversification are discussed. The energy source systems for diversification are listed and an example impact assessment is outlined which deals with the water requirements of the specific energy systems.
Radiation effects on stagnation point flow with melting heat transfer and second order slip
NASA Astrophysics Data System (ADS)
Mabood, F.; Shafiq, A.; Hayat, T.; Abelman, S.
This article examines the effects of melting heat transfer and thermal radiation in stagnation point flow towards a stretching/shrinking surface. Mathematical formulation is made in the presence of mass transfer and second order slip condition. Numerical solutions to the resulting nonlinear problems are obtained by Runge-Kutta fourth fifth order method. Physical quantities like velocity, temperature, concentration, skin friction, Nusselt and Sherwood number are analyzed via sundry parameters for stretching/shrinking, first order slip, second order slip, radiation, melting, Prandtl and Schmidt. A comparative study with the previously published results in limiting sense is made.
Robust controller designs for second-order dynamic system: A virtual passive approach
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh
1990-01-01
A robust controller design is presented for second-order dynamic systems. The controller is model-independent and itself is a virtual second-order dynamic system. Conditions on actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gains are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the physical meaning of this controller design.
Anti-Stokes luminescence in the light of second order perturbation theory
Bhattacharya, Rupak Pal, Bipul Bansal, Bhavtosh
2014-11-10
Anti-Stokes photoluminescence is measured in high-quality GaAs quantum wells. The primary pathway for interband optical absorption and hence emission under subbandgap photoexcitation is the optical phonon-mediated second-order electric dipole transition. This conclusion is drawn from the remarkable agreement between predictions of second-order perturbation calculation and the measured intensity of anti-Stokes photoluminescence, both as function of the detuning wavelength and temperature. The results are of direct relevance to laser cooling of solids where phonon-assisted upconversion is a necessary condition.
2011-06-22
C. Hofmann, Z. Liu, A. Wang, J. R. Heflin , and Y. Xu, “Demonstration of a cylindrically symmetric second-order nonlinear fiber with self-assembled...organic surface layers,” Opt. Express, 19 (11), 10326-10335 (2011). Y. Xu, M. Han, A. Wang, Z. Liu, and J. R. Heflin , “Second order parametric...processes in nonlinear silica microspheres,” Phys. Rev. Lett., 100, Art#163905, (2008). Y. Xu, A. Wang, J. R. Heflin , and Z. Liu, “Proposal and
Regularization of the second-order gravitational perturbations produced by a compact object
Rosenthal, Eran
2005-12-15
The equations for the second-order gravitational perturbations produced by a compact object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill defined. Here we construct well defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the expected gravitational waves. Construction of templates with desired accuracy for extreme mass-ratio binaries, in which a compact object inspirals towards a supermassive black hole, requires calculation of the second-order gravitational perturbations produced by the compact object.
NASA Astrophysics Data System (ADS)
Yang, Xiaofeng; Han, Daozhi
2017-02-01
In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank-Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.
NASA Astrophysics Data System (ADS)
Plyushchay, Mikhail S.
2017-02-01
A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.
Second-order Cosmological Perturbations Engendered by Point-like Masses
NASA Astrophysics Data System (ADS)
Brilenkov, Ruslan; Eingorn, Maxim
2017-08-01
In the ΛCDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second-order scalar, vector, and tensor metric corrections are suitable at arbitrary distances, including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfillment of all Einstein equations, as well as self-consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological back-reaction manifestations by means of relativistic simulations are also outlined.
Contributions to the second order dielectric response of an electron liquid
NASA Astrophysics Data System (ADS)
Bachlechner, Martina E.; Miesenboeck, Helga M.; Macke, Wilhelm
1988-06-01
The dielectric response function χ of a uniform electron gas is investigated up to the second order of the Coulomb interaction with different methods. When examining all polarisation diagrams with two interaction lines, it is confirmed that previous work in the Green's function formalism does not contain all second order processes and the importance of the corrections is pointed out. It is further shown, how the evaluation of χ with Green's function can be greatly simplified when taking into account the symmetry of the expressions.
First- and second-order backscattering from clouds illuminated by finite beams.
Anderson, R C; Browell, E V
1972-06-01
Calculations have been carried out for first- and second-order backscattering from water clouds illuminated by a continuous 0.9-micro beam with a finite divergence angle. In the single-scattering calculations several cloud types were used, while only an approximation to fair weather cumulus clouds was used for double scattering. It was found that the intensity and hence the reflectivity varied with the transceiver-cloud distance for both orders of scattering. Second-order backscattering also varied with field of view. From these results a criterion is suggested for determining when the plane parallel atmosphere theories can be used with finite beams.
Stable Second-Order Nonlinear Optical Materials Based on Interpenetrating Polymer Networks
1994-03-17
0IJUN93 to 31MAY94 4. 1I1Lk ANDLSUBI1ILIE D. ?-UNUING NUMBERS •’• Stable Second-Order Nonlinear Optical Materials Based On C:N00014-90-J-1148...release and sale; its distribution is unlimited. I Stable Second-Order Nonlinear Optical Materials Based On Interpenetrating Polymer Networks S... Optical Materials Based On Interpenetrating Polymer Networks by S. Marturunkakul, J. I. Chen, L. Li, X. L. Jiang, R. J. Jeng, S. K. Sengupta, J. Kumar
NASA Astrophysics Data System (ADS)
Wang, Zhengzi
2015-08-01
The influence of ambient temperature is a big challenge to robust infrared face recognition. This paper proposes a new ambient temperature normalization algorithm to improve the performance of infrared face recognition under variable ambient temperatures. Based on statistical regression theory, a second order polynomial model is learned to describe the ambient temperature's impact on infrared face image. Then, infrared image was normalized to reference ambient temperature by the second order polynomial model. Finally, this normalization method is applied to infrared face recognition to verify its efficiency. The experiments demonstrate that the proposed temperature normalization method is feasible and can significantly improve the robustness of infrared face recognition.
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
Discontinuous deformation analysis with second-order finite element meshed block
NASA Astrophysics Data System (ADS)
Grayeli, Roozbeh; Mortazavi, Ali
2006-12-01
The discontinuous deformation analysis (DDA) with second-order displacement functions was derived based on six-node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second-order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright
Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles
Sabitov, I Kh
2014-12-31
We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.
Observed galaxy number counts on the lightcone up to second order: I. Main result
Bertacca, Daniele; Maartens, Roy; Clarkson, Chris E-mail: roy.maartens@gmail.com
2014-09-01
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
Second-order discrete Kalman filtering equations for control-structure interaction simulations
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.
1991-01-01
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.
Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M
2013-01-01
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.
Employment of Second Order Ruled Surfaces in Design of Sheet Beam Guns
Krasnykh, Anatoly; /SLAC
2007-03-05
A novel 3D method of sheet beam gun design has recently been developed. Second order ruled surfaces (SORS) can be used to define the geometry of the gun electrodes. The gun design process is made simpler if SORS are derived from analytical formulas. A proposed method is discussed and illustrated.
Keep Your Distance! Using Second-Order Ordinary Differential Equations to Model Traffic Flow
ERIC Educational Resources Information Center
McCartney, Mark
2004-01-01
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…
Second-order hot image from a scatterer in high-power laser systems
Xie Liangping; Zhao Jianlin; Jing Feng
2005-05-01
A theory is developed for predicting a second-order hot-image formation in high-power laser systems. Light diffracted from a small optical scatterer interferes with an intense original wave in the nonlinear medium to produce a hologram like a Fresnel-zone plate. The theoretical model shows that the hologram produces a negative first-order diffractive wave focused to the traditional hot image and negative second-order diffraction that causes another intense image, namely, a second-order hot image. It is found by analysis that the location of the second-order hot image arises in a downstream plane with a half-distance from the medium to the scatterer. Results of the numerical calculations show that the peak intensity of the nonlinear image may reach a level high enough to damage optical components with the increase of the breakup integral (B integral), indicating that the image may also potentially damage expensive optical components in high-power laser systems.
Xu, Enhua; Zhao, Dongbo; Li, Shuhua
2015-10-13
A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.
ERIC Educational Resources Information Center
Facao, M.; Lopes, A.; Silva, A. L.; Silva, P.
2011-01-01
We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for…
ERIC Educational Resources Information Center
Facao, M.; Lopes, A.; Silva, A. L.; Silva, P.
2011-01-01
We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for…
Time domain reflectometry waveform analysis with second order bounded mean oscillation
USDA-ARS?s Scientific Manuscript database
Tangent-line methods and adaptive waveform interpretation with Gaussian filtering (AWIGF) have been proposed for determining reflection positions of time domain reflectometry (TDR) waveforms. However, the accuracy of those methods is limited for short probe TDR sensors. Second order bounded mean osc...
A novel unsplit perfectly matched layer for the second-order acoustic wave equation.
Ma, Youneng; Yu, Jinhua; Wang, Yuanyuan
2014-08-01
When solving acoustic field equations by using numerical approximation technique, absorbing boundary conditions (ABCs) are widely used to truncate the simulation to a finite space. The perfectly matched layer (PML) technique has exhibited excellent absorbing efficiency as an ABC for the acoustic wave equation formulated as a first-order system. However, as the PML was originally designed for the first-order equation system, it cannot be applied to the second-order equation system directly. In this article, we aim to extend the unsplit PML to the second-order equation system. We developed an efficient unsplit implementation of PML for the second-order acoustic wave equation based on an auxiliary-differential-equation (ADE) scheme. The proposed method can benefit to the use of PML in simulations based on second-order equations. Compared with the existing PMLs, it has simpler implementation and requires less extra storage. Numerical results from finite-difference time-domain models are provided to illustrate the validity of the approach.
Concurrent Second-Order Schedules: Some Effects of Variations in Response Number and Duration
ERIC Educational Resources Information Center
Sealey, Diane M.; Sumpter, Catherine E.; Temple, W.; Foster, T. Mary
2005-01-01
To examine the effects on concurrent performance of independent manipulations of response-unit duration and number, 6 hens were exposed to concurrent second- order schedules of reinforcement. Each first-order operant unit required completion of a fixed-ratio schedule within the time specified by a fixed- interval schedule, with one further…
Second-Order Theoretical Analysis: A Method for Constructing Theoretical Explanation
ERIC Educational Resources Information Center
Shkedi, Asher
2004-01-01
In this paper a model is offered that allows for the construction of a theoretical explanation on the basis of data accumulated in the field for the purpose of constructing a meaningful description. In this endeavour a distinction is proposed between two methods of theoretical analysis: first-order analysis and second-order analysis. First-order…
First-Order or Second-Order Kinetics? A Monte Carlo Answer
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2005-01-01
Monte Carlo computational experiments reveal that the ability to discriminate between first- and second-order kinetics from least-squares analysis of time-dependent concentration data is better than implied in earlier discussions of the problem. The problem is rendered as simple as possible by assuming that the order must be either 1 or 2 and that…
Boyko, Vyacheslav M.; Popovych, Roman O.; Shapoval, Nataliya M.
2013-01-01
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach. PMID:23564972
Temporal Frequency Modulates Reaction Time Responses to First-Order and Second-Order Motion
ERIC Educational Resources Information Center
Hutchinson, Claire V.; Ledgeway, Tim
2010-01-01
This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily…
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
ERIC Educational Resources Information Center
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1
NASA Technical Reports Server (NTRS)
Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany
1990-01-01
A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.
Sample Sizes for Two-Group Second-Order Latent Growth Curve Models
ERIC Educational Resources Information Center
Wanstrom, Linda
2009-01-01
Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…
NASA Astrophysics Data System (ADS)
Higuera, A. V.; Cary, J. R.
2017-05-01
Time-centered, hence second-order, methods for integrating the relativistic momentum of charged particles in an electromagnetic field are derived. A new method is found by averaging the momentum before use in the magnetic rotation term, and an implementation is presented that differs from the relativistic Boris Push only in the method for calculating the Lorentz factor. This is shown to have the same second-order accuracy in time as that found by splitting the electric acceleration and magnetic rotation (Boris Push) and that found by averaging the velocity in the magnetic rotation term (Vay's method) [J.-L. Vay, Phys. Plasmas 15, 056701 (2008)]. All three methods are shown to conserve energy when there is no electric field. The Boris Push and the current method are shown to be volume-preserving, while Vay's method and the current method preserve the E →×B → velocity. Thus, of these second-order relativistic momentum integrations, only the integrator introduced here both preserves volume and gives the correct E →×B → velocity. While all methods have error that is second-order in time, they deviate from each other by terms that increase as the motion becomes relativistic. Numerical results show that Vay's method develops energy errors near resonant orbits of a test problem that neither volume-preserving integrator does.
Concurrent Second-Order Schedules: Some Effects of Variations in Response Number and Duration
ERIC Educational Resources Information Center
Sealey, Diane M.; Sumpter, Catherine E.; Temple, W.; Foster, T. Mary
2005-01-01
To examine the effects on concurrent performance of independent manipulations of response-unit duration and number, 6 hens were exposed to concurrent second- order schedules of reinforcement. Each first-order operant unit required completion of a fixed-ratio schedule within the time specified by a fixed- interval schedule, with one further…
Conservation of Autonomy: Toward a Second-Order Perspective on Psychosomatic Symptoms.
ERIC Educational Resources Information Center
Fourie, David P.
1993-01-01
Considers families of people suffering from psychosomatic disorders from perspective of second-order cybernetics in which emphasis is on autonomy of various levels of system. Describes psychosomatic symptoms and illustrates symptoms as expression of ideas aimed at conservation of autonomy, both at individual and family level. Highlights…
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
ERIC Educational Resources Information Center
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
A New Approach to Design of Cross-Linked Second-Order Nonlinear Optical Polymers
1990-09-01
PERSONI L ,UTH R(S) Skant rpa ty, Braja K. Mandal and Jayant Kumer 1. TYPE OFREPORT 13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) 15. PAGE...Processing of NLO Materials. VIITIT; I A NEW APPROACH TO DESIGN OF CROSS-LINKED SECOND-ORDER NONLINEAR OPTICAL POLYMERS BRAJA K. MANDAL, JUN Y. LEE
Robust eigensystem assignment for state estimators using second-order models
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Maghami, Peiman G.
1990-01-01
A novel design of a state estimator is presented using second-order dynamic equations of mechanical systems. The eigenvalues and eigenvectors of the state estimator are assigned by solving the second-order eigenvalue problem of the structural system. Three design method for the state estimator are given in this paper. The first design method uses collocated sensors to measure the desired signals and their derivatives. The second design method uses prefilters to shift signal phases to obtain estimates of the signal derivatives. These two methods are used to build a second-order state estimator model. The third design method is the conventional one which converts a typical second-order dynamic model to a first-order model, and then builds a state estimator based on the first-order model. It is shown that all the three designs for state estimation are similar. A numerical example representing a large space structure is given for illustration of the design methods presented in this paper.
NASA Astrophysics Data System (ADS)
Zainuddin, N.; Ibrahim, Z. B.; Othman, K. I.
2014-10-01
The three point block method for solving second order ordinary differential equations (ODEs) directly using constant step size is derived. The reliability of this new method is verified in the numerical results with the improved performance in terms of computation time while maintaining the accuracy. The comparison is presented between the new method and classical backward differentiation formulas (BDF) of order 3.
Control by Contextual Stimuli in Novel Second-Order Conditional Discriminations
ERIC Educational Resources Information Center
Perez-Gonzalez, Luis Antonio; Martinez, Hector
2007-01-01
Eighteen undergraduates participated in studies designed to examine the factors that produce transfer of contextual functions to novel stimuli in second-order conditional discriminations. In Study 1, participants selected comparison B1 given sample A1 and comparison B2 given sample A2 in a matching-to-sample procedure. Contextual stimuli X1 or X2…
A Primary- and Second-Order Component Analysis of the Organizational Identification Questionnaire.
ERIC Educational Resources Information Center
Johnson, William L.; Johnson, Annabel M.; Heimberg, Felix
1999-01-01
Examined the factor structure of the Organizational Identification Questionnaire (G. Cheney, 1982), widely used to assess organizational identification. Analysis of results from 369 social-service employers yields four first-order and two second-order components. Contains 33 references. (SLD)
Validity of the Quality of School Life Scale: A Primary and Second-Order Factor Analysis.
ERIC Educational Resources Information Center
Johnson, William L.; Johnson, Annabel M.
1993-01-01
Primary and second-order principal components analyses were performed on the Quality of School Life Scale (QSL), a measure of elementary school climate, for responses of 141 fourth through sixth graders. Findings suggest three general factors, but item composition of subscales differs somewhat from that proposed by the QSL's developers. (SLD)
NASA Astrophysics Data System (ADS)
Breil, J.; Maire, P.-H.; Nicolaï, P.; Schurtz, G.
2008-05-01
In laser produced plasmas large self-generated magnetic fields have been measured. The classical formulas by Braginskii predict that magnetic fields induce a reduction of the magnitude of the heat flux and its rotation through the Righi-Leduc effect. In this paper a second order tensorial diffusion method used to correctly solve the Righi-Leduc effect in multidimensional code is presented.
The Development of Perceptual Sensitivity to Second-Order Facial Relations in Children
ERIC Educational Resources Information Center
Baudouin, Jean-Yves; Gallay, Mathieu; Durand, Karine; Robichon, Fabrice
2010-01-01
This study investigated children's perceptual ability to process second-order facial relations. In total, 78 children in three age groups (7, 9, and 11 years) and 28 adults were asked to say whether the eyes were the same distance apart in two side-by-side faces. The two faces were similar on all points except the space between the eyes, which was…
Matheson, H E; Bilsbury, T G; McMullen, P A
2012-03-01
A large body of research suggests that faces are processed by a specialized mechanism within the human visual system. This specialized mechanism is made up of subprocesses (Maurer, LeGrand, & Mondloch, 2002). One subprocess, called second- order relational processing, analyzes the metric distances between face parts. Importantly, it is well established that other-race faces and contrast-reversed faces are associated with impaired performance on numerous face processing tasks. Here, we investigated the specificity of second-order relational processing by testing how this process is applied to faces of different race and photographic contrast. Participants completed a feature displacement discrimination task, directly measuring the sensitivity to second-order relations between face parts. Across three experiments we show that, despite absolute differences in sensitivity in some conditions, inversion impaired performance in all conditions. The presence of robust inversion effects for all faces suggests that second-order relational processing can be applied to faces of different race and photographic contrast.
The Development of Perceptual Sensitivity to Second-Order Facial Relations in Children
ERIC Educational Resources Information Center
Baudouin, Jean-Yves; Gallay, Mathieu; Durand, Karine; Robichon, Fabrice
2010-01-01
This study investigated children's perceptual ability to process second-order facial relations. In total, 78 children in three age groups (7, 9, and 11 years) and 28 adults were asked to say whether the eyes were the same distance apart in two side-by-side faces. The two faces were similar on all points except the space between the eyes, which was…
Second-Order Schedules of Token Reinforcement with Pigeons: Implications for Unit Price
ERIC Educational Resources Information Center
Bullock, Christopher E.; Hackenberg, Timothy D.
2006-01-01
Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio).…
Second-order dipolar order in magic-angle spinning nuclear magnetic resonance.
van Beek, Jacco D; Hemmi, Adrian; Ernst, Matthias; Meier, Beat H
2011-10-21
Generating dipolar order under magic-angle spinning (MAS) conditions is explored for different pulse sequences and dipolar-coupling networks. It is shown that under MAS second-order dipolar order can be generated reliably with 10% to 30% efficiency using the Jeener-Broekaert sequence in systems where the second-order average Hamiltonian is a (near) constant of the motion. When using adiabatic demagnetization and remagnetization, second-order dipolar order can be generated and reverted back to Zeeman order with up to 60% efficiency. This requires a maximum field strength with a nutation frequency that is less than one-quarter of the rotor frequency, and that the spin system can be properly spinlocked under such conditions. A simple coherent description accounts for the principal features of the spin dynamics, even using the smallest possible system of three coupled spins. For the systems investigated, the lifetime of second-order dipolar order under MAS was found to be on the order of T(1). © 2011 American Institute of Physics
UV Curable Epoxy-Based Second Order Nonlinear Optical Materials; Synthesis and Characterization
1992-05-14
01JUN91 to 31MAY92 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS UV Curable Epoxy-Based Second Order Nonlinear Optical Materials ; C: N00014-90-J- 1148 Svnthesis... Nonlinear Optical Materials ; Synthesis and Characterization by R.J. Jeng, Y.M. Chen, B.K. Mandal, J. Kumar and S.K. Tripathy to be published in
ERIC Educational Resources Information Center
Papa, Frank J.; And Others
1997-01-01
Chest pain was identified as a specific medical problem space, and disease classes were modeled to define it. Results from a test taken by 628 medical residents indicate a second-order factor structure that suggests that chest pain is a multidimensional problem space. Implications for medical education are discussed. (SLD)
NASA Astrophysics Data System (ADS)
Kharzeev, Dmitri E.; Yee, Ho-Ung
2011-08-01
We present two new results on relativistic hydrodynamics with anomalies and external electromagnetic fields, “chiral magnetohydrodynamics” (CMHD). First, we study CMHD in four dimensions at second order in the derivative expansion assuming the conformal/Weyl invariance. We classify all possible independent conformal second order viscous corrections to the energy-momentum tensor and to the U(1) current in the presence of external electric and/or magnetic fields, and identify 18 terms that originate from the triangle anomaly. We then propose and motivate the following guiding principle to constrain the CMHD: the anomaly-induced terms that are even under the time-reversal invariance should not contribute to the local entropy production rate. This allows us to fix 13 out of the 18 transport coefficients that enter the second order formulation of CMHD. We also relate one of our second order transport coefficients to the chiral shear waves. Our second subject is hydrodynamics with (N+1)-gon anomaly in an arbitrary 2N dimensions. The effects from the (N+1)-gon anomaly appear in hydrodynamics at (N-1)th order in the derivative expansion, and we identify precisely N such corrections to the U(1) current. The time-reversal constraint is powerful enough to allow us to find the analytic expressions for all transport coefficients. We confirm the validity of our results (and of the proposed guiding principle) by an explicit fluid/gravity computation within the AdS/CFT correspondence.
Kharzeev, D.E.; Yee, H.-U.
2011-08-25
We present two new results on relativistic hydrodynamics with anomalies and external electromagnetic fields, 'chiral magnetohydrodynamics' (CMHD). First, we study CMHD in four dimensions at second order in the derivative expansion assuming the conformal/Weyl invariance. We classify all possible independent conformal second order viscous corrections to the energy-momentum tensor and to the U(1) current in the presence of external electric and/or magnetic fields, and identify 18 terms that originate from the triangle anomaly. We then propose and motivate the following guiding principle to constrain the CMHD: the anomaly-induced terms that are even under the time-reversal invariance should not contribute to the local entropy production rate. This allows us to fix 13 out of the 18 transport coefficients that enter the second order formulation of CMHD. We also relate one of our second order transport coefficients to the chiral shear waves. Our second subject is hydrodynamics with (N+1)-gon anomaly in an arbitrary 2N dimensions. The effects from the (N+1)-gon anomaly appear in hydrodynamics at (N-1)th order in the derivative expansion, and we identify precisely N such corrections to the U(1) current. The time-reversal constraint is powerful enough to allow us to find the analytic expressions for all transport coefficients. We confirm the validity of our results (and of the proposed guiding principle) by an explicit fluid/gravity computation within the AdS/CFT correspondence.
Second-Order Schedules of Token Reinforcement with Pigeons: Implications for Unit Price
ERIC Educational Resources Information Center
Bullock, Christopher E.; Hackenberg, Timothy D.
2006-01-01
Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio).…
Control by Contextual Stimuli in Novel Second-Order Conditional Discriminations
ERIC Educational Resources Information Center
Perez-Gonzalez, Luis Antonio; Martinez, Hector
2007-01-01
Eighteen undergraduates participated in studies designed to examine the factors that produce transfer of contextual functions to novel stimuli in second-order conditional discriminations. In Study 1, participants selected comparison B1 given sample A1 and comparison B2 given sample A2 in a matching-to-sample procedure. Contextual stimuli X1 or X2…
Independence of First- and Second-Order Memories in Newborn Rabbits
ERIC Educational Resources Information Center
Coureaud, Gerard; Languille, Solene; Joly, Virginie; Schaal, Benoist; Hars, Bernard
2011-01-01
The mammary pheromone promotes the acquisition of novel odorants (CS1) in newborn rabbits. Here, experiments pinpoint that CS1 becomes able to support neonatal learning of other odorants (CS2). We therefore evaluated whether these first- and second-order memories remained dependent after reactivation. Amnesia induced after CS2 recall selectively…
Second-order magnetic critical points at finite magnetic fields: Revisiting Arrott plots
NASA Astrophysics Data System (ADS)
Bustingorry, S.; Pomiro, F.; Aurelio, G.; Curiale, J.
2016-06-01
The so-called Arrott plot, which consists in plotting H /M against M2, with H the applied magnetic field and M the magnetization, is used to extract valuable information in second-order magnetic phase transitions. Besides, it is widely accepted that a negative slope in the Arrott plot is indicative of a first-order magnetic transition. This is known as the Banerjee criterion. In consequence, the zero-field transition temperature T* is reported as the characteristic first-order transition temperature. By carefully analyzing the mean-field Landau model used for studying first-order magnetic transitions, we show in this work that T* corresponds in fact to a triple point where three first-order lines meet. More importantly, this analysis reveals the existence of two symmetrical second-order critical points at finite magnetic field (Tc,±Hc) . We then show that a modified Arrott plot can be used to obtain information about these second-order critical points. To support this idea we analyze experimental data on La2 /3Ca1 /3MnO3 and discuss an estimate for the location of the triple point and the second-order critical points.
Independence of First- and Second-Order Memories in Newborn Rabbits
ERIC Educational Resources Information Center
Coureaud, Gerard; Languille, Solene; Joly, Virginie; Schaal, Benoist; Hars, Bernard
2011-01-01
The mammary pheromone promotes the acquisition of novel odorants (CS1) in newborn rabbits. Here, experiments pinpoint that CS1 becomes able to support neonatal learning of other odorants (CS2). We therefore evaluated whether these first- and second-order memories remained dependent after reactivation. Amnesia induced after CS2 recall selectively…
SMITE - A Second Order Eulerian Code for Hydrodynamic and Elastic-Plastic Problems
1975-08-01
et al Mathematical Applications Group, Incorporated Prepared for: Ballistic Research Laboratories August 1975 DISTRIBI,TED BY: mi] National...SMITE - A SECOND ORDER EULERIAN CODE FOR HYDRODYNAMIC AND ELASTIC-PLASTIC PROBLEMS Prepared by Mathematical Applications Group, Inc. 3...AODRcis jMathematical Applications Group, Inc. 13 Westchester Plaza IFlmsford, New York 10523 10. PROGRAM ELEMENT, PROJECT, TASK AREA t WORK
On types of the resolvent of a complete second order differential operator
Ospanov, Kordan Nauryzkhanovich
2015-09-18
In this work we consider the complete second order differential operator, the intermediate coefficient of which is growing rapidly. We find the conditions when its resolvent is compact or belongs to Schatten class, in particular, it is a nuclear operator. The most accurate results are obtained when the coefficient oscillates weakly. In this case we shown that the operator is separable.
Comparison of methods for determining the second-order detection efficiency of a VUV spectrometer
NASA Astrophysics Data System (ADS)
Kendrick, Richard L.; McPherson, Armon; Rouze, N.; Westerveld, W. B.; Risley, John S.
1987-05-01
Four independent procedures were developed and tested to measure the apparatus response function of a VUV spectrometer-detector system for unpolarized 46-nm radiation dispersed in second order. These measurements were made to allow the use of continuum synchrotron radiation for the calibration of the response of the spectrometer-detector system for dispersion of 92-nm radiation in first order with full correction for the effects of synchrotron radiation dispersed in second order. In the first method, synchrotron radiation was used in combination with a thin Al foil to block out synchrotron radiation at 92 nm while allowing 46-nm radiation to enter the spectrometer. In the second as well as the third method, Ne II 46-nm line radiation was used to measure the response function in first and second order. The line radiation was produced by: (1) an electron beam exciting a Ne gas target for which the resulting VUV light illuminated the entire grating; and (2) a duoplasmatron VUV light source operating with Ne gas producing a small spot of radiation that was scanned across the surface of the spectrometer grating. In the fourth method the difference in the spectral distributions of synchrotron radiation produced by electrons with different kinetic energies was employed to deduce the second-order detection efficiency. The ratio of the second-order to first-order response function for 56-nm radiation could be determined to a precision of 6 percent using the bandpass filter and electron-beam methods, 10 percent using the duoplasmatron method, and 250 percent using the multiple electron energy method.
On the second order effect of the springing response of large blunt ship
NASA Astrophysics Data System (ADS)
Kim, Yooil; Park, Sung-Gun
2015-09-01
The springing response of a large blunt ship was considered to be influenced by a second order interaction between the incoming irregular wave and the blunt geometry of the forebody of the ship. Little efforts have been made to simulate this complicated fluid-structure interaction phenomenon under irregular waves considering the second order effect; hence, the above mentioned premise still remains unproven. In this paper, efforts were made to quantify the second order effect between the wave and vibrating flexible ship structure by analyzing the experimental data obtained through the model basin test of the scaled-segmented model of a large blunt ship. To achieve this goal, the measured vertical bending moment and the wave elevation time history were analyzed using a higher order spectral analysis technique, where the quadratic interaction between the excitation and response was captured by the cross bispectrum of two randomly oscillating variables. The nonlinear response of the vibrating hull was expressed in terms of a quadratic Volterra series assuming that the wave excitation is Gaussian. The Volterra series was then orthogonalized using Barrett's procedure to remove the interference between the kernels of different orders. Both the linear and quadratic transfer functions of the given system were then derived based on a Fourier transform of the orthogonalized Volterra series. Finally, the response was decomposed into a linear and quadratic part to determine the contribution of the second order effect using the obtained linear and quadratic transfer functions of the system, combined with the given wave spectrum used in the experiment. The contribution of the second order effect on the springing response of the analyzed ship was almost comparable to the linear one in terms of its peak power near the resonance frequency.
Second order distorted born approximation for backscattering from a layer of discrete random medium
NASA Technical Reports Server (NTRS)
Lang, Roger H.; Saatchi, Sasan S.
1993-01-01
In recent years there has been increasing interest in scattering and depolarization characteristics of the vegetation canopies. Scattering models applied to the microwave remote sensing of vegetation canopies showed that multiple scattering effects can be important in simulating the backscattering coefficients correctly. In particular, in most applications, the cross-polarized backscattering coefficients are often underestimated by single scattering models. Recently, there have been concerted efforts to include the second order terms in the radiative transfer models of vegetation canopies in order to account for multiple scattering within the canopy. The coherent wave theory approach is extended to include multiple scattering effects to predict the coherent and incoherent backscattering contributions from a layer of vegetation canopy. The problem is initially formulated in terms of the exact equation for the correlation function of the field, i.e., the Bethe-Salpeter equation. Using fractional volume as a small parameter, a Foldy type approximation is made to obtain a more manageable correlation equation. This equation is iterated to obtain first and second order solutions. The iteration procedure assumes the variance of the field fluctuations are small compared to the coherent intensity. This assumption proved to be particularly successful in computing backscattering coefficients. First and second order backscattering coefficients are calculated from the iterants of the correlation equation. It is shown that the first order coefficients are the same as the distorted Born results used previously by the authors. These results contained enhancement terms in the direct-reflected contributions. The important contributions to second order backscattering are examined and interpreted in terms of scattering diagrams. Examples of situations in which second order backscattering coefficients are important are given.
Second order root control of self-ligating brackets and traditional brackets: a "typodont" study.
Butti, A C; Mangiacapra, R; Saporito, I; Augusti, G; Salvato, A; Re, D
2014-03-01
Aim of the study was to evaluate if self-ligating brackets (SLB) and conventional brackets (CB) have the same degree of second order root control in closing extraction spaces. Two resin models, left and right sides of an upper arch, with two wells in the premolar area, were used. Wells have been filled with wax and resin premolars with anatomic root structure were placed in them. Resin premolars were bonded with CB and SLB. We performed 20 pairwise runs: CB on one side against SLB on the other side. We tested 0.018 and 0.016x0.022 stainless steel arches. Models were put in warm water to allow teeth to move in the softened wax by the force excerpted by NiTi coils. Root control in the second order was evaluated with the aid of metallic markers on the roots and digital radiographies taken before and after each run. On 0.018 wires CB moved 4.0 mm (SD 1.06 mm), mean root control angle was 14.8° (SD 9.15°), while SLB moved 4.1 mm (SD 1.33 mm), mean angle in the second order was 11.8° (SD 5.01°). On 0.016x0.022 wires CB moved 3.6 mm (SD 1.24 mm), mean angle in the second order was 9.7° (SD 5.48°) while SLB moved 3.4 mm (SD 1.05 mm), mean angle was 10.7° (SD 3.92°). It seems that, on typodont, CB and SLB are equally efficient in moving teeth crowns and have the same degree of second order root control, both when 0.018 and 0.016x0.022 stainless steel wires are used.
NASA Astrophysics Data System (ADS)
Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng
2016-12-01
In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we first propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite-element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML. Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: (1) for an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; (2) unlike the M-PML with high-order damping profile, the M-PML with second-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; (3) in an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with second-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.
Tuer, Adam E; Akens, Margarete K; Krouglov, Serguei; Sandkuijl, Daaf; Wilson, Brian C; Whyne, Cari M; Barzda, Virginijus
2012-11-21
The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, <δ>. A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.
Tuer, Adam E.; Akens, Margarete K.; Krouglov, Serguei; Sandkuijl, Daaf; Wilson, Brian C.; Whyne, Cari M.; Barzda, Virginijus
2012-01-01
The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = χZZZ(2)′/χZXX(2)′; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, 〈δ〉. A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented. PMID:23200043
Boixel, Julien; Guerchais, Véronique; Le Bozec, Hubert; Jacquemin, Denis; Amar, Anissa; Boucekkine, Abdou; Colombo, Alessia; Dragonetti, Claudia; Marinotto, Daniele; Roberto, Dominique; Righetto, Stefania; De Angelis, Roberta
2014-04-09
Novel photochromic dithienylethene-based platinum(II) complexes (C^N^N)Pt(C≡C-DTE-C6H4-D) ((C^N^N) = 4,4'-di(n-hexyl)-6-phenyl-2,2'-bipyridine; D = H, NMe2) were prepared and characterized. Their excellent photochromic properties allow the photoinduced switching of their second-order nonlinear optical properties in solution, as measured by the EFISH technique, due to formation of an extended π-conjugated ligand upon suitable electromagnetic radiation. Insights into the electronic structures of the complexes and the nature of their excited states have been obtained by DFT and TD-DFT calculations. These novel Pt(II) complexes were nanoorganized in polymer films which were poled, affording new materials characterized by a good second-order NLO response that can be easily switched, with an excellent NLO contrast. To the best of our knowledge, our compounds allowed designing the very first examples of switchable NLO polymer films based on metal complexes.
ERIC Educational Resources Information Center
Borrello, Gloria M.; Thompson, Bruce
The calculation of second-order results in the validity assessment of measures and some useful interpretation aids are presented. First-order and second-order results give different and informative pictures of data dynamics. Several aspects of good practice in interpretation of second-order results are presented using data from 487 subjects…
Long-wavelength properties of phase-field-crystal models with second-order dynamics.
Heinonen, V; Achim, C V; Ala-Nissila, T
2016-05-01
The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.
Long-wavelength properties of phase-field-crystal models with second-order dynamics
NASA Astrophysics Data System (ADS)
Heinonen, V.; Achim, C. V.; Ala-Nissila, T.
2016-05-01
The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.
Gu, Jianmin; Yan, Yongli; Zhao, Yong Sheng; Yao, Jiannian
2012-05-02
The transparent bulk polymer nanocomposites blended with rare earth nanoparticles are prepared through the radical polymerization of trimethylolpropane trimethylacrylate (TMPTMA). These materials produce continuously tunable second harmonic (SH) radiation under illumination of a wide spectral range of fundamental waves (750-850 nm). The SHG efficiency can be controlled well by altering the Tb(3+) doping content in the nanoparticles.
The Relationship Between Second-Order Nonlinear Optical Properties and Ground-State Polarization
NASA Technical Reports Server (NTRS)
Bourhil, G.; Cheng, L-T.; Lee, G.; Marder, S. R.; Perry, J. W.; Perry, M. J.; Tienmann, B. G.
1993-01-01
A review is presented describing our recent work to correlate the first hyperpolarizability, of organic materials with the molecular parameter bond length alternation (BLA). Donor-acceptor polyenes displaying a wide BLA range were synthesized.
NASA Astrophysics Data System (ADS)
Ferhat, Ipar
With increasing advancement in material science and computational power of current computers that allows us to analyze high dimensional systems, very light and large structures are being designed and built for aerospace applications. One example is a reflector of a space telescope that is made of membrane structures. These reflectors are light and foldable which makes the shipment easy and cheaper unlike traditional reflectors made of glass or other heavy materials. However, one of the disadvantages of membranes is that they are very sensitive to external changes, such as thermal load or maneuvering of the space telescope. These effects create vibrations that dramatically affect the performance of the reflector. To overcome vibrations in membranes, in this work, piezoelectric actuators are used to develop distributed controllers for membranes. These actuators generate bending effects to suppress the vibration. The actuators attached to a membrane are relatively thick which makes the system heterogeneous; thus, an analytical solution cannot be obtained to solve the partial differential equation of the system. Therefore, the Finite Element Model is applied to obtain an approximate solution for the membrane actuator system. Another difficulty that arises with very flexible large structures is the dimension of the discretized system. To obtain an accurate result, the system needs to be discretized using smaller segments which makes the dimension of the system very high. This issue will persist as long as the improving technology will allow increasingly complex and large systems to be designed and built. To deal with this difficulty, the analysis of the system and controller development to suppress the vibration are carried out using vector second order form as an alternative to vector first order form. In vector second order form, the number of equations that need to be solved are half of the number equations in vector first order form. Analyzing the system for control
Liu, Chun-Guang; Guan, Wei; Song, Ping; Yan, Li-Kai; Su, Zhong-Min
2009-07-20
The redox-active tetrathiafulvalene (TTF) is a good electron donor, and porphyrin is highly delocalized in cyclic pi-conjugated systems. The direct combination of the two interesting building units into the same molecule provides an intriguing molecular system for designing nonlinear optical (NLO) molecular materials. In the present paper, the second-order NLO properties of a series of monoTTF-porphyrins and metalloporphyrins have been calculated by density functional theory (DFT) combined with the finite field (FF) method. Our calculations show that these compounds possess considerably large static first hyperpolarizabilities, approximately 400 x 10(-30) esu. Since the TTF unit is able to exist in three different stable redox states (TTF, TTF(*+), and TTF(2+)), the redox switching of the NLO response of the zinc(II) derivative of monoTTF-metalloporphyrin has been studied, and a substantial enhancement in static first hyperpolarizability has been obtained in its oxidized species according to our DFT-FF calculations. The beta values of one- and two-electron-oxidized species are 3.6 and 8.7 times as large as that of the neutral compound, especially for two-electron-oxidized species, with a value of 3384 x 10(-30) esu. This value is about 3 times that for a push-pull metalloporphyrin, which has an exceptionally large hyperpolarizability among reported organic NLO chromophores. Meanwhile, to give a more intuitive description of band assignments of the electron spectrum and trends in NLO behavior of these compounds, the time-dependent (TD)DFT method has been adopted to calculate the electron spectrum. The TDDFT calculations well-reproduce the soret band and Q-type bands of the monoTTF-porphyrin, and these absorption bands can be assigned to the pi --> pi* transition of the porphyrin core. On the other hand, the oxidized process significantly affects the geometrical structures of the TTF unit and porphyrin ring, and the two-electron-oxidized species has a planar TTF unit
Explorations of new second-order nonlinear optical materials in the potassium vanadyl iodate system.
Sun, Chuan-Fu; Hu, Chun-Li; Xu, Xiang; Yang, Bing-Ping; Mao, Jiang-Gao
2011-04-13
Four new potassium vanadyl iodates based on lone-pair-containing IO(3) and second-order Jahn-Teller distorted VO(5) or VO(6) asymmetric units, namely, α-KVO(2)(IO(3))(2)(H(2)O) (Pbca), β-KVO(2)(IO(3))(2)(H(2)O) (P2(1)2(1)2(1)), K(4)[(VO)(IO(3))(5)](2)(HIO(3))(H(2)O)(2)·H(2)O (P1), and K(VO)(2)O(2)(IO(3))(3) (Ima2) have been successfully synthesized by hydrothermal reactions. α-KVO(2)(IO(3))(2)(H(2)O) and β-KVO(2)(IO(3))(2)(H(2)O) exhibit two different types of 1D [VO(2)(IO(3))(2)](-) anionic chains. Neighboring VO(6) octahedra in the α-phase are corner-sharing into a 1D chain with the IO(3) groups attached on both sides of the chain in a uni- or bidentate bridging fashion, whereas those of VO(5) polyhedra in the β-phase are bridged by IO(3) groups into a right-handed helical chain with remaining IO(3) groups being grafted unidentately on both sides of the helical chain. The structure of K(4)[(VO)(IO(3))(5)](2)(HIO(3))(H(2)O)(2)·H(2)O contains novel isolated [(VO)(IO(3))(5)](2-) units composed of one VO(6) octahedron linked to five IO(3) groups and one terminal O(2-) anion. The structure of K(VO)(2)O(2)(IO(3))(3) exhibits a 1D [(VO)(2)O(2)(IO(3))(3)](-) chain in which neighboring VO(6) octahedra are interconnected by both oxo and bridging iodate anions. Most interestingly, three of four compounds are noncentrosymmetric (NCS), and K(VO)(2)O(2)(IO(3))(3) displays a very strong second-harmonic generation response of about 3.6 × KTP, which is phase matchable. It also has high thermal stability, a wide transparent region and moderate hardness as well as an excellent growth habit. Thermal analyses and optical and ferroelectric properties as well as theoretical calculations have also been performed.
Parallel Computation of Air Pollution Using a Second-Order Closure Model
NASA Astrophysics Data System (ADS)
Pai, Prasad Prabhakar
1991-02-01
Rational analysis, prediction and policy making of air pollution problems depend on our understanding of the individual processes that govern the atmospheric system. In the past, computational constraints have prohibited the incorporation of detailed physics of many individual processes in air pollution models. This has resulted in poor model performance for realistic situations. Recent advances in computing capabilities make it possible to develop air pollution models which capture the essential physics of the individual processes. The present study uses a three -dimensional second-order closure diffusion model to simulate dispersion from ground level and elevated point sources in convective (daytime) boundary layers. The model uses mean and turbulence variables simulated with a one-dimensional second-order closure fluid dynamic model. The calculated mean profiles of wind and temperature are found to be in good agreement with the observed Day 33 Wangara data, whereas the calculated vertical profiles of turbulence variables agree well with those estimated from other numerical models and laboratory experiments. The three-dimensional second -order closure diffusion model can capture the plume behavior in daytime atmospheric boundary layer remarkably well in comparison with laboratory data. We also compare the second -order closure diffusion model with the commonly used K -diffusion model for the same meteorological conditions. In order to reduce the computational requirements for second -order closure models, we propose a parallel algorithm of a time-splitting finite element method for the numerical solution of the governing equations. The parallel time -splitting finite element method substantially reduces the model wallclock or turnaround time by exploiting the vector and parallel capabilities of modern supercomputers. The plethora of supercomputers in the market today made it important for us to study the key issue of algorithm "portability". In view of this, we
Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection
NASA Astrophysics Data System (ADS)
Meyer, Bettina; Schneider, Tapio
2017-04-01
There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the
Mice Can Use Second-Order, Contrast-Modulated Stimuli to Guide Visual Perception.
Khastkhodaei, Zeinab; Jurjut, Ovidiu; Katzner, Steffen; Busse, Laura
2016-04-20
Visual processing along the primate ventral stream takes place in a hierarchy of areas, characterized by an increase in both complexity of neuronal preferences and invariance to changes of low-level stimulus attributes. A basic type of invariance is form-cue invariance, where neurons have similar preferences in response to first-order stimuli, defined by changes in luminance, and global features of second-order stimuli, defined by changes in texture or contrast. Whether in mice, a now popular model system for early visual processing, visual perception can be guided by second-order stimuli is currently unknown. Here, we probed mouse visual perception and neural responses in areas V1 and LM using various types of second-order, contrast-modulated gratings with static noise carriers. These gratings differ in their spatial frequency composition and thus in their ability to invoke first-order mechanisms exploiting local luminance features. We show that mice can transfer learning of a coarse orientation discrimination task involving first-order, luminance-modulated gratings to the contrast-modulated gratings, albeit with markedly reduced discrimination performance. Consistent with these behavioral results, we demonstrate that neurons in area V1 and LM are less responsive and less selective to contrast-modulated than to luminance-modulated gratings, but respond with broadly similar preferred orientations. We conclude that mice can, at least in a rudimentary form, use second-order stimuli to guide visual perception. To extract object boundaries in natural scenes, the primate visual system does not only rely on differences in local luminance but can also take into account differences in texture or contrast. Whether the mouse, which has a much simpler visual system, can use such second-order information to guide visual perception is unknown. Here we tested mouse perception of second-order, contrast-defined stimuli and measured their neural representations in two areas of
Helquat Dyes: Helicene-like Push-Pull Systems with Large Second-Order Nonlinear Optical Responses.
Coe, Benjamin J; Rusanova, Daniela; Joshi, Vishwas D; Sánchez, Sergio; Vávra, Jan; Khobragade, Dushant; Severa, Lukáš; Císařová, Ivana; Šaman, David; Pohl, Radek; Clays, Koen; Depotter, Griet; Brunschwig, Bruce S; Teplý, Filip
2016-03-04
Helquat dyes combine a cationic hemicyanine with a helicene-like motif to form a new blueprint for chiral systems with large and tunable nonlinear optical (NLO) properties. We report a series of such species with characterization, including determination of static first hyperpolarizabilities β0 via hyper-Rayleigh scattering and Stark spectroscopy. The measured β0 values are similar to or substantially larger than that of the commercial chromophore E-4'-(dimethylamino)-N-methyl-4-stilbazolium. Density functional theory (DFT) and time-dependent DFT calculations on two of the new cations are used to probe their molecular electronic structures and optical properties. Related molecules are expected to show bulk second-order NLO effects in even nonpolar media, overcoming a key challenge in developing useful materials.
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
NASA Astrophysics Data System (ADS)
Basin, Michael; Bharath Panathula, Chandrasekhara; Shtessel, Yuri
2016-09-01
This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.
NASA Astrophysics Data System (ADS)
Logan, Dylan F.; Alamin Dow, Ali B.; Stepanov, Dmitri; Abolghasem, Payam; Kherani, Nazir P.; Helmy, Amr S.
2013-02-01
We demonstrate multi-layer silicon-oxy-nitride (SiON) waveguides as a platform for broadband tunable phase-matching of second-order nonlinear interactions arising at material interfaces. Second-harmonic generation (SHG) is measured with a 2 ps pulsed pump of 1515-1535 nm wavelength, where 6 nW power is generated by an average pump power of 30 mW in a 0.92 mm long device. The wavelength acceptance bandwidth of the SHG is as broad as 20 nm due to the low material dispersion of SiON waveguides. The waveguide structure provides a viable method for utilizing second order nonlinearity for light generation and manipulation in silicon photonic circuits.
Second-order nonlinear susceptibility in quantum dot structure under applied electric field
NASA Astrophysics Data System (ADS)
Abdullah, M.; Noori, Farah T. Mohammed; Al-Khursan, Amin H.
2015-06-01
A model for quantum dot (QD) subbands, when the dots are in the form of quantum disks, under applied electric field was stated. Then, subbands of dots with different disk radii and heights were calculated under applied field. The competition between the shift due to confinement by field and the size was shown for subbands. Second-order nonlinear susceptibility in quantum dots (QDs) was derived using density matrix theory which is, then, simulated using the calculated subbands. Both interband (IB) and intersubband (ISB) transitions were discussed. High second-order susceptibility in QDs was predicted. The results show a reduction in the susceptibility with the applied field while the peak wavelength was mainly relates to energy difference between subbands. A good match between theory and laboratory experiments was observed. Laboratory experiments at terahertz region might be possible using valence intersubband which is important in many device applications.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
Second-order decoherence mechanisms of a transmon qubit probed with thermal microwave states
NASA Astrophysics Data System (ADS)
Goetz, J.; Deppe, F.; Eder, P.; Fischer, M.; Müting, M.; Puertas Martínez, J.; Pogorzalek, S.; Wulschner, F.; Xie, E.; Fedorov, K. G.; Marx, A.; Gross, R.
2017-06-01
Thermal microwave states are omnipresent noise sources in superconducting quantum circuits covering all relevant frequency regimes. We use them as a probe to identify three second-order decoherence mechanisms of a superconducting transmon qubit. First, we quantify the efficiency of a resonator filter in the dispersive Jaynes-Cummings regime and find evidence for parasitic loss channels. Second, we probe second-order noise in the low-frequency regime and demonstrate the expected T 3 temperature dependence of the qubit dephasing rate. Finally, we show that qubit parameter fluctuations due to two-level states are enhanced under the influence of thermal microwave states. In particular, we experimentally confirm the T 2-dependence of the fluctuation spectrum expected for noninteracting two-level states.
NASA Astrophysics Data System (ADS)
Jensen, Robert
1988-03-01
We prove that viscosity solutions in W 1,∞ of the second order, fully nonlinear, equation F( D 2 u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D 2 u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.
A second-order closure analysis of turbulent diffusion flames. [combustion physics
NASA Technical Reports Server (NTRS)
Varma, A. K.; Fishburne, E. S.; Beddini, R. A.
1977-01-01
A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Error analysis of exponential integrators for oscillatory second-order differential equations
NASA Astrophysics Data System (ADS)
Grimm, Volker; Hochbruck, Marlis
2006-05-01
In this paper, we analyse a family of exponential integrators for second-order differential equations in which high-frequency oscillations in the solution are generated by a linear part. Conditions are given which guarantee that the integrators allow second-order error bounds independent of the product of the step size with the frequencies. Our convergence analysis generalizes known results on the mollified impulse method by García-Archilla, Sanz-Serna and Skeel (1998, SIAM J. Sci. Comput. 30 930-63) and on Gautschi-type exponential integrators (Hairer E, Lubich Ch and Wanner G 2002 Geometric Numerical Integration (Berlin: Springer), Hochbruck M and Lubich Ch 1999 Numer. Math. 83 403-26).
Second-order perturbation theory: The problem of infinite mode coupling
NASA Astrophysics Data System (ADS)
Miller, Jeremy; Wardell, Barry; Pound, Adam
2016-11-01
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in Pound [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
Relativistic second-order dissipative fluid dynamics at finite chemical potential
NASA Astrophysics Data System (ADS)
Jaiswal, Amaresh; Friman, Bengt; Redlich, Krzysztof
2016-07-01
We employ a Chapman-Enskog like expansion for the distribution function close to equilibrium to solve the Boltzmann equation in the relaxation time approximation and subsequently derive second-order evolution equations for dissipative charge currentand shear stress tensor for a system of massless quarks and gluons. We use quantum statistics for the phase space distribution functions to calculate the transport coefficients. We show that, the second-order evolution equations for the dissipative charge current and the shear stress tensor can be decoupled. We find that, for large chemical potential, the charge conductivity is small compared to the shear viscosity. Moreover, we demonstrate that the limiting behaviour of the ratio of heat conductivity to shear viscosity is identicalto that obtained for a strongly coupled conformal plasma.
Second-order equation of motion for electromagnetic radiation back-reaction
NASA Astrophysics Data System (ADS)
Matolcsi, T.; Fülöp, T.; Weiner, M.
2017-09-01
We take the viewpoint that the physically acceptable solutions of the Lorentz-Dirac equation for radiation back-reaction are actually determined by a second-order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second-order equation of motion exactly in the non-relativistic regime via each of these three methods, leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.
The second-order luminosity-redshift relation in a generic inhomogeneous cosmology
Ben-Dayan, Ido; Marozzi, Giovanni; Veneziano, Gabriele; Nugier, Fabien E-mail: giovanni.marozzi@unige.ch E-mail: gabriele.veneziano@cern.ch
2012-11-01
After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed 'geodesic light-cone' gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for the computation of the effects of stochastic inhomogeneities on precision dark-energy cosmology whose results we have anticipated in a recent letter. More generally, it can be used in connection with any physical information carried by light-like signals traveling along our past light-cone.
Modeling of manometer-based oscillations with a second-order accurate scheme
Petelin, S.; Tiselj, I.
1997-12-01
Modeling of manometer-type oscillations by the computer codes RELAP5 and TRAC represents a difficult problem because of the two-fluid models used in both codes and because of the numerical damping of the first-order accurate numerical schemes. Separate liquid-level-tracking models are suggested to improve the accuracy of the solutions. This paper summarizes the results of a new approach. RELAP5/MOD3.2 calculations with a first-order accurate numerical scheme, with and without level tracking, were compared with the results of the 2F code with a second-order accurate numerical scheme for a six-equation two-fluid model. As an assessment case, U-tube liquid oscillations were simulated. The main objective of the work is to study the behavior of the second-order accurate schemes in the modeling of the vertically stratified flows.
Application of graphene second-order nonlinearity in THz plasmons excitation
NASA Astrophysics Data System (ADS)
Jamalpoor, Kamal; Zarifkar, Abbas; Miri, Mehdi
2017-09-01
In this paper, the phase-matching condition, the excited electric field formula, and the nonlinear susceptibility tensor elements conditions required for excitation of surface plasmon polaritons (SPPs) on flat graphene are derived. The second-order nonlinearity is utilized for compensation of the free-space and SPPs wave vectors mismatch. In order to excite SPPs on graphene, the phase matching condition is investigated for the second-order effects including the difference frequency generation (DFG), the second harmonic generation (SHG), and the sum-frequency generation (SFG). In addition, since the incident waves polarizations play an important role in the excitation of the SPPs, the realization of the susceptibility tensor elements conditions, the effect of TE, TM, not polarized and perpendicularly polarized incident waves are investigated using the Green's function theory.
Bioethics in Denmark. Moving from first- to second-order analysis?
Nielsen, Morten Ebbe Juul; Andersen, Martin Marchman
2014-07-01
This article examines two current debates in Denmark--assisted suicide and the prioritization of health resources--and proposes that such controversial bioethical issues call for distinct philosophical analyses: first-order examinations, or an applied philosophy approach, and second-order examinations, what might be called a political philosophical approach. The authors argue that although first-order examination plays an important role in teasing out different moral points of view, in contemporary democratic societies, few, if any, bioethical questions can be resolved satisfactorily by means of first-order analyses alone, and that bioethics needs to engage more closely with second-order enquiries and the question of legitimacy in general.
Scaled Group Consensus in Multiagent Systems With First/Second-Order Continuous Dynamics.
Yu, Junyan; Shi, Yang
2017-08-29
We investigate scaled group consensus problems of multiagent systems with first/second-order linear continuous dynamics. For a complex network consisting of two subnetworks with different physical quantities or task distributions, it is concerned with this case that the agents' states in one subnetwork converge to a consistent value asymptotically, while the states in the other subnetwork approach another value with a ratio of the former. For the case of the information exchange being directed, novel consensus protocols are designed for both first-order and second-order dynamics to solve the scaled group consensus problems. By utilizing algebra theory, graph theory, and Lyapunov stability theory, several necessary and sufficient conditions are established to guarantee the agents' states reaching the scaled group consensus asymptotically. Finally, several simulation results are presented to demonstrate the effectiveness of the theoretical results.
Background first- and second-order modeling for point target detection.
Genin, Laure; Champagnat, Frédéric; Le Besnerais, Guy
2012-11-01
This paper deals with point target detection in nonstationary backgrounds such as cloud scenes in aerial or satellite imaging. We propose an original spatial detection method based on first- and second-order modeling (i.e., mean and covariance) of local background statistics. We first show that state-of-the-art nonlocal denoising methods can be adapted with minimal effort to yield edge-preserving background mean estimates. These mean estimates lead to very efficient background suppression (BS) detection. However, we propose that BS be followed by a matched filter based on an estimate of the local spatial covariance matrix. The identification of these matrices derives from a robust classification of pixels in classes with homogeneous second-order statistics based on a Gaussian mixture model. The efficiency of the proposed approaches is demonstrated by evaluation on two cloudy sky background databases.
A weak second order tau-leaping method for chemical kinetic systems
NASA Astrophysics Data System (ADS)
Hu, Yucheng; Li, Tiejun; Min, Bin
2011-07-01
Recently Anderson and Mattingly [Comm. Math. Sci. 9, 301 (2011)] proposed a method which can solve chemical Langevin equations with weak second order accuracy. We extend their work to the discrete chemical jump processes. With slight modification, the method can also solve discrete chemical kinetic systems with weak second order accuracy in the large volume scaling. Especially, this method achieves higher order accuracy than both the Euler τ-leaping and mid-point τ-leaping methods in the sense that the local truncation error for the covariance is of order τ3V-1 when τ = V-β (0 < β < 1) and the system size V → ∞. We present the convergence analysis, numerical stability analysis, and numerical examples. Overall, in the authors' opinion, the new method is easy to be implemented and good in performance, which is a good candidate among the highly accurate τ-leaping type schemes for discrete chemical reaction systems.
A weak second order tau-leaping method for chemical kinetic systems.
Hu, Yucheng; Li, Tiejun; Min, Bin
2011-07-14
Recently Anderson and Mattingly [Comm. Math. Sci. 9, 301 (2011)] proposed a method which can solve chemical Langevin equations with weak second order accuracy. We extend their work to the discrete chemical jump processes. With slight modification, the method can also solve discrete chemical kinetic systems with weak second order accuracy in the large volume scaling. Especially, this method achieves higher order accuracy than both the Euler τ-leaping and mid-point τ-leaping methods in the sense that the local truncation error for the covariance is of order τ(3)V(-1) when τ = V(-β) (0 < β < 1) and the system size V → ∞. We present the convergence analysis, numerical stability analysis, and numerical examples. Overall, in the authors' opinion, the new method is easy to be implemented and good in performance, which is a good candidate among the highly accurate τ-leaping type schemes for discrete chemical reaction systems.
The second order effects on commercial shipping of restrictions on the use of TBT.
Strandenes, S P
2000-08-21
Increased hull roughness reduces vessel speed and increases fuel consumption. These are first order effects of restricting or prohibiting the use of antifouling paints. Reduced transport capacity and increased capital costs are frequently recognised as second order effects of such reductions in fleet efficiency. This paper focuses on other second order effects of prohibiting or restricting the use of TBT-based antifoulings. The potential cost increases will affect high-speed vessels most severely. These vessels are the segment of the shipping industry that is most relevant to the political drive in Europe towards shifting the balance of transport of goods towards sea rather than road transport for environmental reasons. Any decision to restrict or prohibit these paints would tend also to induce a shift from local to global environmental problems, which would be more difficult to manage.
Inconsistent channel bandwidth estimates suggest winner-take-all nonlinearity in second-order vision
Westrick, Zachary M.; Henry, Christopher A.; Landy, Michael S.
2013-01-01
The processing of texture patterns has been characterized by a model that postulates a first-stage linear filter to highlight a component texture, a pointwise rectification stage to convert contrast for the highlighted texture into mean response strength, followed by a second-stage linear filter to detect the texture-defined pattern. We estimated the spatial-frequency bandwidth of the second-stage filter mediating orientation-discrimination of orientation-modulated second-order gratings by measuring threshold elevation in the presence of filtered noise added to the modulation signal. This experiment yielded no evidence for frequency tuning. A second experiment, in which subjects had to detect similar second-order gratings while judging their modulation frequency, produced bandwidth estimates of 1–1.5 octaves, similar to estimated bandwidths of first-order channels. We propose that an additional dominant-response-selection nonlinearity can account for these apparently contradictory results. PMID:23416867
Long-distance fiber sensor system based on the second-order Raman pump and amplification
NASA Astrophysics Data System (ADS)
Dong, B.; Hu, J.; Chen, Z.; Yu, C.
2012-07-01
We demonstrate a novel technique to realize a long-distance fiber sensor system based on the second-order Raman pump and amplification. With the second-order Raman pump and amplification, a gain spectrum around 1582-nm is achieved. It serves as not only the optical source for the remote fiber sensor but also the filter to intensity modulated the wavelength shift of the fiber sensor. A long-distance fiber strain sensor system is demonstrated by adopting a fiber Fabry-Pérot sensor. Experimental results show that the wavelength shift of the sensor in response to the strain is simultaneously intensity modulated by the steep slope with a high sensitivity, while it is temperature insensitive. With the side gain spectrum served as a quasi-linear filter, the sensor can also be quasi-linearly intensity-modulated.
Sustainable institutionalized punishment requires elimination of second-order free-riders
NASA Astrophysics Data System (ADS)
Perc, Matjaž
2012-03-01
Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the ``punishment pool'' from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.
Quasidegenerate second-order perturbation corrections to single excitation configuration interaction
NASA Astrophysics Data System (ADS)
Head-Gordon, Martin
1999-02-01
A family of quasidegenerate second-order perturbation theories that correct excitation energies from single-excitation configuration interaction (CIS) are introduced which generalize the earlier non-degenerate second-order method, CIS(D). The new methods are termed CIS(D), where n ranges from 0 to x, according to the number of terms retained in a doubles denominator expansion. Truncation at either n = 0 or n = 1 yields methods which involve the diagonalization of a dressed singles-only response matrix, where the dressing is state-independent. Hence CIS(D0) and CIS(D1) can be implemented efficiently using semidirect methods, which are discussed. Test calculations on formaldehyde, ethylene, chlorine nitrate, styrene, benzaldehyde, and chalcone are presented to assess the performance of these methods. CIS(D0) and CIS(D1) both show significant improvements relative to CIS(D) in cases of near-degeneracy.
Direct method for second-order sensitivity analysis of modal assurance criterion
NASA Astrophysics Data System (ADS)
Lei, Sheng; Mao, Kuanmin; Li, Li; Xiao, Weiwei; Li, Bin
2016-08-01
A Lagrange direct method is proposed to calculate the second-order sensitivity of modal assurance criterion (MAC) values of undamped systems. The eigenvalue problem and normalizations of eigenvectors, which augmented by using some Lagrange multipliers, are used as the constraints of the Lagrange functional. Once the Lagrange multipliers are determined, the sensitivities of MAC values can be evaluated directly. The Lagrange direct method is accurate, efficient and easy to implement. A simply supported beam is utilized to check the accuracy of the proposed method. A frame is adopted to validate the predicting capacity of the first- and second-order sensitivities of MAC values. It is shown that the computational costs of the proposed method can be remarkably reduced in comparison with those of the indirect method without loss of accuracy.
Beyond the G W approximation: A second-order screened exchange correction
NASA Astrophysics Data System (ADS)
Ren, Xinguo; Marom, Noa; Caruso, Fabio; Scheffler, Matthias; Rinke, Patrick
2015-08-01
Motivated by the recently developed renormalized second-order perturbation theory for ground-state energy calculations, we propose a second-order screened exchange correction (SOSEX) to the G W self-energy. This correction follows the spirit of the SOSEX correction to the random-phase approximation for the electron correlation energy and can be clearly represented in terms of Feynman diagrams. We benchmark the performance of the perturbative G0W0 +SOSEX scheme for a set of molecular systems, including the G2 test set from quantum chemistry as well as benzene and tetracyanoethylene. We find that G0W0 +SOSEX improves over G0W0 for the energy levels of the highest occupied and lowest unoccupied molecular orbitals. In addition, it can resolve some of the difficulties encountered by the G W method for relative energy positions as exemplified by benzene where the energy spacing between certain valence orbitals is severely underestimated.
NASA Astrophysics Data System (ADS)
Revathi, P.; Sakthivel, R.; Song, D.-Y.; Ren, Yong; Zhang, Pei
2013-09-01
Fractional Brownian motion has been widely used to model a number of phenomena in diverse fields of science and engineering. In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of second-order nonautonomous neutral stochastic evolution equations with infinite delay driven by fractional Brownian motion (fBm) with Hurst parameter H ∈ (1/2, 1) in Hilbert spaces. More precisely, using semigroup theory and successive approximation approach, we establish a set of sufficient conditions for obtaining the required result under the assumption that coefficients satisfy non-Lipschitz condition with Lipschitz condition being considered as a special case. Further, the result is deduced to study the second-order autonomous neutral stochastic equations with fBm. The results generalize and improve some known results. Finally, as an application, stochastic wave equation with infinite delay driven by fractional Brownian motion is provided to illustrate the obtained theory.
Linear ion trap for second-order Doppler shift reduction in frequency standard applications
NASA Technical Reports Server (NTRS)
Prestage, John D.; Janik, Gary R.; Dick, G. John; Maleki, Lute
1990-01-01
The authors have designed and are presently testing a novel linear ion trap that permits storage of a large number of ions with reduced susceptibility to the second-order Doppler effect caused by the RF confining fields. This new trap should store about 20 times the number of ions as a conventional RF trap with no corresponding increase in second-order Doppler shift from the confining field. In addition, the sensitivity of this shift to trapping parameters, i.e., RF voltage, RF frequency, and trap size, is greatly reduced. The authors have succeeded in trapping mercury ions and xenon ions in the presence of helium buffer gas. Trap times as long as 2000 s have been measured.
NASA Astrophysics Data System (ADS)
Yajima, Takahiro; Yamasaki, Kazuhito
2016-03-01
Geometric structures of dynamical systems are investigated based on a differential geometric method (Jacobi stability of KCC-theory). This study focuses on differences of Jacobi stability of two-dimensional second-order differential equation from that of one-dimensional second-order differential equation. One of different properties from a one-dimensional case is the Jacobi unstable condition given by eigenvalues of deviation curvature with different signs. Then, this geometric theory is applied to an overhead crane system as a two-dimensional dynamical system. It is shown a relationship between the Hopf bifurcation of linearized overhead crane and the Jacobi stability. Especially, the Jacobi stable trajectory is found for stable and unstable spirals of the two-dimensional linearized system. In case of the linearized overhead crane system, the Jacobi stable spiral approaches to the equilibrium point faster than the Jacobi unstable spiral. This means that the Jacobi stability is related to the resilience of deviated trajectory in the transient state. Moreover, for the nonlinear overhead crane system, the Jacobi stability for limit cycle changes stable and unstable over time.
NASA Astrophysics Data System (ADS)
Li, Wei; Bashan, Amir; Buldyrev, Sergey; Stanley, Eugene; Havlin, Shlomo
2012-02-01
We study a system composed of two interdependent lattice networks A and B, where nodes in network A depend on a node within a certain shuffling distance r of its corresponding counterpart in network B and vice versa. We find, using numerical simulation that percolation in the two interdependent lattice networks system shows that for small r the phase transition is second order while for larger r it is a first order.
Second-order Born approximation for the ionization of molecules by electron and positron impact
Dal Cappello, C.; Rezkallah, Z.; Houamer, S.; Charpentier, I.; Hervieux, P. A.; Ruiz-Lopez, M. F.; Dey, R.; Roy, A. C.
2011-09-15
Second-order Born approximation is applied to study the ionization of molecules. The initial and final states are described by single-center wave functions. For the initial state a Gaussian wave function is used while for the ejected electron it is a distorted wave. Results of the present model are compared with recent (e,2e) experiments on the water molecule. Preliminary results are also presented for the ionization of the thymine molecule by electrons and positrons.
Dal Cappello, C.; Champion, C.; Kada, I.; Mansouri, A.
2011-06-15
The double ionization of isolated water molecules fixed in space is investigated within a theoretical approach based on the second-order Born approximation. Electron angular distributions have been studied for specific kinematical conditions. The three usual mechanisms, the shake-off and the two two-step mechanisms, have been identified. A significant contribution of the two-step mechanism is clearly visible for some particular kinematics.
Finite amplitude instability of second-order fluids in plane Poiseuille flow.
NASA Technical Reports Server (NTRS)
Mcintire, L. V.; Lin, C. H.
1972-01-01
The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.
First and second-order features for detection of masses in digital breast tomosynthesis
NASA Astrophysics Data System (ADS)
Samala, Ravi K.; Wei, Jun; Chan, Heang-Ping; Hadjiiski, Lubomir; Cha, Kenny; Helvie, Mark A.
2016-03-01
We are developing novel methods for prescreening of mass candidates in computer-aided detection (CAD) system for digital breast tomosynthesis (DBT). With IRB approval and written informed consent, 186 views from 94 breasts were imaged using a GE GEN2 prototype DBT system. The data set was randomly separated into training and test sets by cases. Gradient field convergence features based on first-order features were used to select the initial set of mass candidates. Eigenvalues based on second-order features from the Hessian matrix were extracted for the mass candidate locations in the DBT volume. The features from the first- and second-order analysis form the feature vector that was input to a linear discriminant analysis (LDA) classifier to generate a candidate-likelihood score. The likelihood scores were ranked and the top N candidates were passed onto the subsequent detection steps. The improvement between using only first-order features and the combination of first and second-order features was analyzed using a rank-sensitivity plot. 3D objects were obtained with two-stage 3D clustering followed by active contour segmentation. Morphological, gradient field, and texture features were extracted and feature selection was performed using stepwise feature selection. A combination of LDA and rule-based classifiers was used for FP reduction. The LDA classifier output a masslikelihood score for each object that was used as a decision variable for FROC analysis. At breast-based sensitivities of 70% and 80%, prescreening using first-order and second-order features resulted in 0.7 and 1.0 FPs/DBT.
Estimates of solutions of certain classes of second-order differential equations in a Hilbert space
Artamonov, N V
2003-08-31
Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained.
On the basic equations for the second-order modeling of compressible turbulence
NASA Technical Reports Server (NTRS)
Liou, W. W.; Shih, T.-H.
1991-01-01
Equations for the mean and turbulent quantities for compressible turbulent flows are derived. Both the conventional Reynolds average and the mass-weighted, Favre average were employed to decompose the flow variable into a mean and a turbulent quality. These equations are to be used later in developing second order Reynolds stress models for high speed compressible flows. A few recent advances in modeling some of the terms in the equations due to compressibility effects are also summarized.
A second-order characteristic line scheme for solving a juvenile-adult model of amphibians.
Deng, Keng; Wang, Yi
2015-01-01
In this paper, we develop a second-order characteristic line scheme for a nonlinear hierarchical juvenile-adult population model of amphibians. The idea of the scheme is not to follow the characteristics from the initial data, but for each time step to find the origins of the grid nodes at the previous time level. Numerical examples are presented to demonstrate the accuracy of the scheme and its capability to handle solutions with singularity.
Second-Order Far Field Computational Boundary Conditions for Inviscid Duct Flow Problems
1990-03-01
COMPUTATIONAL BOUNDARY CONDITIONS INTERNAL FLOW COMPUTATIONS EULER METHODS 19. ABSTRACT (Continue on reverse if necessary and identify by block number...SOLUTIONS OF THE LINEARIZED, SECOND-ORDER EULER EQUATIONS. THE EULER EQUATIONS ARE LINEARIZED ABOUT A CONSTANT PRESSURE, RECTILINEAR FLOW C)NDITION...THE BOUNDARY PROCEDURE CAN BE USED WITH ANY NUMERICAL EULER SOLUTION METHOD AND ALLOWS COMPUTATIONAL BOUNDARIES TO BE LOCATED EXTREMELY CLOSE TO THE
Navier-Stokes computation of compressible turbulent flows with a second order closure
NASA Technical Reports Server (NTRS)
Dingus, C.; Kollmann, W.
1991-01-01
The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.
Second-order motion perception in peripheral vision: limits of early filtering.
Wang, Y Z; Hess, R F; Baker, C L
1997-12-01
Spatial and temporal analysis of contrast-modulated sine-wave gratings reveals that the second-order motion stimulus contains two sidebands, with equal energy but moving in opposite directions, flanking a stationary carrier. Any early linear spatial filtering process in the visual system that attenuates one sideband more than the other will be detrimental to the balance between the two sidebands, so that the perceived direction of the carrier might be opposite to that of the envelope motion. We tested this hypothesis by using contrast-modulated gratings presented centrally or at 20 deg in the horizontal nasal field with a two-alternative forced-choice staircase paradigm. We found that when the envelope frequency was close to that of the carrier, a second-order stimulus whose envelope motion direction was correctly identified in the fovea appeared to drift in the opposite direction in the periphery. Further increasing the envelope spatial frequency resulted in a reversed motion percept in both central and peripheral viewing conditions. For subjects to identify correctly the direction of motion of the envelope, the spatial frequency ratio of the carrier to the envelope had to be more than 2 in the fovea and more than 6 in the periphery. These phenomena in second-order motion perception can be explained by a linear model of motion detection with an early spatial filtering process. Further experiments and computer simulation show that undersampling of the carrier has little effect on second-order motion perception in the periphery, as long as the carrier is detectable.
Second-order few-mode Raman amplifier for mode-division multiplexed optical communication systems.
Li, Jiaxiong; Du, Jiangbing; Ma, Lin; Li, Ming-Jun; Xu, Ke; He, Zuyuan
2017-01-23
We experimentally demonstrate and investigate, for first time to our best knowledge, a second-order few-mode Raman amplifier for low noise distributed fiber amplification. The 1455 and 1360 nm pumps are both injected into the few-mode fiber (FMF) in the forms of two degenerate LP_{11} modes in the backward direction. Within the band from 1542 to 1558 nm, maximum on-off gains of 4 dB are achieved for both LP_{01} and LP_{11} modes, and the differential modal gain (DMG) is less than 0.4 dB. The noise figure (NF) improvements at 1550 nm for LP_{01} and LP_{11} modes are 1.2 dB and 1.1 dB, respectively, compared with the conventional first-order pumping scheme. The lowest NFs of less than -2 dB are achieved for both modes. We build an optical time-domain reflectometer (OTDR) in the few-mode distributed Raman amplifier (FM-DRA) to measure the signal evolutions, and the results indicate a proof-of-concept low noise amplification for second-order pumping with respect to the conventional first-order pumping case. Due to the second-order pumping, broadened Raman amplification band has been observed with improved gain flatness for both LP_{01} and LP_{11} modes, which is also of great importance in the optical communication systems. The second-order FM-DRA can be used potentially in future high capacity mode-division multiplexing (MDM) optical communication systems.
Static multipole polarisabilities and second-order Stark shift in francium.
Khan, F; Khandelwal, G S; Wilson, J W
1988-01-01
The multipole polarisability of the ground state of francium is calculated by utilising both the variational technique of Davison and the quantum defect theory underlying the Bates-Damgaard method. This approach is also shown to yield reasonable results for other alkali atoms. Second-order Stark shift for the ground state of francium is presented as a function of field strength for possible future experimental comparison.
Static multipole polarisabilities and second-order Stark shift in francium
NASA Technical Reports Server (NTRS)
Khan, F.; Khandelwal, G. S.; Wilson, J. W.
1988-01-01
The multipole polarizability of the ground state of francium is calculated by utilizing both the variational technique of Davison and the quantum defect theory underlying the Bates-Damgaard method. This approach is also shown to yield reasonable results for other alkali atoms. Second-order Stark shift for the ground state of francium is presented as a function of field strength for possible future experimental comparison.
The Formation of the Second-Order Nonlinearity in Thermally Poled Fused Silica Glass
2007-11-02
NONIINEARITY IN THERMALLY POLED FUSED SILICA GLASS 6. AUTHOR(S) THOMAS GUSTAVE ALLEY 5. FUNDING NUMBERS 7. PERFORMING ORGANIZATION NAME(S) AND...ADDRESS(ES) The University of New Mexico 8. PERFORMING ORGANIZATION REPORT NUMBER 98-020D 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES...self- organized , photoinduced, second-order nonlinearity. The most widely accepted explanation attributes the nonlinearity to an asymmetric
Haupert, Levi; Simpson, Garth
2011-01-01
Second order nonlinear optical imaging of chiral crystals (SONICC) is a promising new method for the sensitive and selective detection of protein crystals. Relevant general principles of second harmonic generation, which underpins SONICC, are reviewed. Instrumentation and methods for SONICC measurements are described and critically assessed in terms of performance trade-offs. Potential origins of false-positives and false-negatives are also discussed. PMID:22101350
Finite-time consensus for leader-following second-order multi-agent system
NASA Astrophysics Data System (ADS)
Sun, Fenglan; Guan, Zhi-Hong
2013-04-01
The finite-time consensus problems of second-order multi-agent system under fixed and switching network topologies are studied in this article. Based on the graph theory, LaSalle's invariance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. The leader-following finite-time consensus is analysed in detail. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Finite amplitude instability of second-order fluids in plane Poiseuille flow.
NASA Technical Reports Server (NTRS)
Mcintire, L. V.; Lin, C. H.
1972-01-01
The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.