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.
Second order nonlinear optical properties of In-doped lithium niobate
NASA Astrophysics Data System (ADS)
Xue, D.; Betzler, K.; Hesse, H.
2001-01-01
Second order nonlinear optical properties of In-doped lithium niobate crystals have been quantitatively studied from the chemical bond viewpoint. The results show that the second order nonlinear optical response of In-doped lithium niobate crystals at 1079 nm decreases remarkably with increasing In concentration in the crystal. This approximately linear composition-property correlation in In-doped lithium niobate crystals is quantitatively expressed in the current work. Furthermore, the different influences of Mg, Zn, and In dopants, respectively, on the nonlinear susceptibility of lithium niobate single crystals are also compared in the present work.
Second-order and third-order elastic properties of diamond: An ab initio study
NASA Astrophysics Data System (ADS)
Clerc, Daryl G.; Ledbetter, Hassel
2005-10-01
Diamond's second-order elastic properties, and several third-order properties associated with uniform deformation, were calculated using ab initio all-electron density-functional theory. The predicted second-order elastic properties and equilibrium lattice parameter, in units of GPa and nm, are c11=1043(5), c12=128(5), c44=534(17), bulk modulus B=433(5), shear modulus G=502(10), Poisson ratio μ=0.082(5), and a=0.35569(2), where the parenthetic number is the uncertainty. The second-order force constants, in units of GPa, are kI=3843(108), kII=2346(17), kIII=2847(35), and kIV=5635(45). Here, subscripts I IV denote four strains whose tensor elements are [ɛ, ɛ, ɛ, 0, 0, 0], [ɛ, ɛ, 0, 0, 0, 0], [ɛ, ɛ, -ɛ, 0, 0, 0], and [ɛ, ɛ, ɛ, ɛ, ɛ, ɛ], respectively, using 6-component notation in the format [ɛ1, ɛ2, ɛ3, ɛ4, ɛ5, ɛ6]. Predicted inelastic properties include the third-order force constant corresponding to uniform dilation gI=-55,000(3,500) GPa, the bulk-modulus pressure derivative ∂B/∂P=4.7(3), and the overall Gruneisen parameter γG=0.85(15). Both our second-order and third-order properties agree well with measured values obtained by ultrasonics and by Raman spectroscopy.
NASA Astrophysics Data System (ADS)
Harding, Michael E.; Vázquez, Juana; Stanton, John F.; Diezemann, Gregor; Gauss, Jürgen
2011-06-01
For a small set of linear and non-linear molecules, a detailed comparison of two different procedures for predicting vibrationally averaged molecular properties, i.e., second-order vibrational perturbation theory (VPT2) and a variational approach, is carried out. Results for vibrational corrections to dipole and quadrupole moments, nuclear quadrupole moments, static electric-dipole polarizabilities, NMR chemical shielding tensors, nuclear spin-rotation tensors, magnetizabilities, and rotational g-tensors are reported.
Properties of the internal clock: first- and second-order principles of subjective time.
Allman, Melissa J; Teki, Sundeep; Griffiths, Timothy D; Meck, Warren H
2014-01-01
Humans share with other animals an ability to measure the passage of physical time and subjectively experience a sense of time passing. Subjective time has hallmark qualities, akin to other senses, which can be accounted for by formal, psychological, and neurobiological models of the internal clock. These include first-order principles, such as changes in clock speed and how temporal memories are stored, and second-order principles, including timescale invariance, multisensory integration, rhythmical structure, and attentional time-sharing. Within these principles there are both typical individual differences--influences of emotionality, thought speed, and psychoactive drugs--and atypical differences in individuals affected with certain clinical disorders (e.g., autism, Parkinson's disease, and schizophrenia). This review summarizes recent behavioral and neurobiological findings and provides a theoretical framework for considering how changes in the properties of the internal clock impact time perception and other psychological domains.
Ismagilov, Timur Z.
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
NASA Astrophysics Data System (ADS)
Umezawa, Hirohito; Jackson, Matthew; Lebel, Olivier; Nunzi, Jean-Michel; Sabat, Ribal Georges
2016-10-01
The second-order nonlinear optical coefficients of thin films of mexylaminotriazine-functionalized azobenzene molecular glass derivatives were measured using second harmonic generation. The thin films were poled using a custom corona poling set-up and the second harmonic light from a pulsed 1064-nm laser was detected. Four out of the six tested compounds showed optical nonlinearity and a maximum coefficient of 75 pm/V was obtained. The time dependence of the nonlinear coefficients was studied under ambient light and under dark; the second harmonic generation intensity stayed constant for thiazole-containing derivatives while a significant decay was measured for the other compounds.
NASA Astrophysics Data System (ADS)
Sadybekov, Makhmud A.; Sarsenbi, Abdizhahan; Tengayeva, Aizhan
2016-08-01
In this paper, we consider a spectral problem for a model differential operator of the second order with involution. The operator is given by a differential expression ℓu = -u″(-x) and boundary conditions of the general form. A criterion of the basis property of systems of eigenfunctions of the operator is set in the sense of coefficients of the boundary conditions.
NASA Astrophysics Data System (ADS)
Karakas, Asli; Unver, Huseyin; Elmali, Ayhan
To investigate the microscopic second-order nonlinear optical (NLO) behavior of the 1-salicylidene-3-thio-semicarbazone Schiff base compound, the electric dipole moments (μ), linear static polarizabilities (α) and first static hyperpolarizabilites (β) have been calculated using finite field second-order Møller-Plesset perturbation (FF MP2) theory. The ab-initio results on (hyper)polarizabilities show that the investigated molecule might have microscopic NLO properties with non-zero values. To understand the NLO behavior in the context of molecular orbital structure, we have also examined the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the HOMO-LUMO gap in the same theoretical framework as the (hyper)polarizability calculations. In addition to the NLO properties, the electronic transition spectra have been computed using a semi-empirical method (ZINDO). ZINDO calculation results show that the electronic transition wavelengths have been estimated to be shorter than 400 nm.
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.
NASA Astrophysics Data System (ADS)
Belardini, A.; Dominici, L.; Larciprete, M. C.; Michelotti, F.; Rousseau, A.; Ratsimihety, A.
2006-12-01
In this work the authors investigated the second order nonlinear optical properties of a group of Disperse Red 1 based electro-optic fluorinated copolymers, synthesized with two fluorinated monomers: the α-fluoroacrylate monomer bearing an adamantane side group and the α-fluoroacrylate monomer bearing the Disperse Red 1 chromophore. By means of nonlinear ellipsometry at λ =1550nm, the poling induced electro-optic tensor main component r33 was determined. The polymer's thermostability was investigated by means of the temperature scanning and isothermal relaxation techniques, leading to the determination of the depolarization temperature Tdep=136°C, corresponding to an activation energy for the relaxation of the orientational distribution of the active chromophores EA=105kcal/mol. The increased thermostability of the copolymer, given by the adamantane side group, is then compared with that of other two groups of fluorinated copolymers.
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
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
2014-03-21
We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with χ{sub eff}{sup (2)} ∼ 0.6 pm V{sup −1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
Monago-Maraña, Olga; Durán-Merás, Isabel; Galeano-Díaz, Teresa; Muñoz de la Peña, Arsenio
2016-04-01
The influence of pH on the fluorescence of flavonoid compounds was investigated and the highest fluorescence emission was obtained in basic medium. Selected conditions to improve this signal were: pH 9.5, 0.14 M Britton Robinson buffer and methanol between 5% and 10%. The excitation-emission fluorescence matrices of a set of 36 samples of Spanish paprika were analyzed by means of parallel factor analysis (PARAFAC). Thus, the profiles of possible fluorescence components (PARAFAC loadings) were obtained. One of these profiles was identified by matching PARAFAC scores with LC analysis on the same samples. Two clusters of samples were obtained when score values were plotted against each other. Spectrofluorimetry coupled to second order multivariate calibration methods, as unfolded-partial least squares with residual bilinearization (U-PLS/RBL) and multidimensional-partial least-squares with residual bilinearization (N-PLS/RBL), was investigated to quantify quercetin and kaempferol in those samples. Good results were obtained for quercetin by this approach.
Monago-Maraña, Olga; Durán-Merás, Isabel; Galeano-Díaz, Teresa; Muñoz de la Peña, Arsenio
2016-04-01
The influence of pH on the fluorescence of flavonoid compounds was investigated and the highest fluorescence emission was obtained in basic medium. Selected conditions to improve this signal were: pH 9.5, 0.14 M Britton Robinson buffer and methanol between 5% and 10%. The excitation-emission fluorescence matrices of a set of 36 samples of Spanish paprika were analyzed by means of parallel factor analysis (PARAFAC). Thus, the profiles of possible fluorescence components (PARAFAC loadings) were obtained. One of these profiles was identified by matching PARAFAC scores with LC analysis on the same samples. Two clusters of samples were obtained when score values were plotted against each other. Spectrofluorimetry coupled to second order multivariate calibration methods, as unfolded-partial least squares with residual bilinearization (U-PLS/RBL) and multidimensional-partial least-squares with residual bilinearization (N-PLS/RBL), was investigated to quantify quercetin and kaempferol in those samples. Good results were obtained for quercetin by this approach. PMID:26593589
NASA Technical Reports Server (NTRS)
Stiegman, A. E.; Graham, Eva; Khundkar, Lutfur R.; Perry, Joseph W.; Cheng, L.-T.; Perry, Kelly J.
1991-01-01
A series of donor-acceptor acetylene compounds was synthesized in which systematic changes in both the conjugation length and the donor-acceptor strength were made. The effect of these structural changes on the spectroscopic and electronic properties of the molecules and, ultimately, on the measured second-order molecular hyperpolarizabilities (beta) was investigated. It was found that increases in the donor-acceptor strength resulted in increases in the magnitude of beta. For this class of molecules, the increase is dominated by the energy of the intramolecular charge-transfer transition, while factors such as the ground to excited-state dipole moment change and the transition-moment integral are much less important. Increasing the conjugation length from one to two acetylene linkers did not result in an increase in the value of beta; however, beta increased sharply in going from two acetylenes to three. This increase is attributed to the superposition of several nearly isoenergetic excited states.
Feng, Xiaoxiao; Zhang, Junjie; Gao, Zeliang; Zhang, Shaojun; Sun, Youxuan; Tao, Xutang
2014-02-24
The complete set of second-order nonlinear optical (NLO) coefficients of Cs{sub 2}TeMo{sub 3}O{sub 12} single crystals were obtained using the Maker Fringe techniques. The NLO coefficients d{sub 32} and d{sub 33} were measured to be on the order of 6.8 and 6.5 pm/V, respectively. Irradiated by 1064 nm laser, the crystal is phase-matchable, and its effective nonlinear coefficient is 4.6 pm/V for type I phase matching at θ = 42.7°. The relationship between the second-order nonlinear properties and the crystal structure is also discussed. Considering its wide transmission range, phase matching, and large effective NLO coefficient, Cs{sub 2}TeMo{sub 3}O{sub 12} is a good candidate for IR NLO application.
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.
Second-Order Algebraic Theories
NASA Astrophysics Data System (ADS)
Fiore, Marcelo; Mahmoud, Ola
Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
Bondu, Flavie; Quertinmont, Jean; Rodriguez, Vincent; Pozzo, Jean-Luc; Plaquet, Aurélie; Champagne, Benoît; Castet, Frédéric
2015-12-14
The nonlinear optical (NLO) properties of a double photochrome molecular switch are reported for the first time by considering the four trans forms of a dithienylethene-indolinooxazolidine hybrid. The four forms are characterized by means of hyper-Rayleigh scattering (HRS) experiments and quantum chemical calculations. Experimental measurements provide evidence that the pH- and light-triggered transformations between the different forms of the hybrid are accompanied by large variations of the first hyperpolarizability, which makes this compound an effective multistate NLO switch. Quantum chemical calculations conducted at the time-dependent Hartree-Fock and time-dependent DFT levels agree with the experimental data and allow a complete rationalization of the NLO responses of the different forms. The HRS signal of the forms with an open indolinooxazolidine moiety are more than one order of magnitude larger than that measured for the other forms, whereas the open/closed status of the dithienylethene subunit barely influences the dynamic NLO properties. However, extrapolation of the NLO responses to the static limit leads to univocally distinguishable intrinsic responses for three of the various forms. This hybrid system thus acts as a highly efficient multistate NLO switch for eventual exploitation in optical memory systems with multiple storage and nondestructive readout capacity. PMID:26560091
Willow, Soohaeng Yoo; Salim, Michael A.; Kim, Kwang S.; Hirata, So
2015-01-01
A direct, simultaneous calculation of properties of a liquid using an ab initio electron-correlated theory has long been unthinkable. Here we present structural, dynamical, and response properties of liquid water calculated by ab initio molecular dynamics using the embedded-fragment spin-component-scaled second-order many-body perturbation method with the aug-cc-pVDZ basis set. This level of theory is chosen as it accurately and inexpensively reproduces the water dimer potential energy surface from the coupled-cluster singles, doubles, and noniterative triples with the aug-cc-pVQZ basis set, which is nearly exact. The calculated radial distribution function, self-diffusion coefficient, coordinate number, and dipole moment, as well as the infrared and Raman spectra are in excellent agreement with experimental results. The shapes and widths of the OH stretching bands in the infrared and Raman spectra and their isotropic-anisotropic Raman noncoincidence, which reflect the diverse local hydrogen-bond environment, are also reproduced computationally. The simulation also reveals intriguing dynamic features of the environment, which are difficult to probe experimentally, such as a surprisingly large fluctuation in the coordination number and the detailed mechanism by which the hydrogen donating water molecules move across the first and second shells, thereby causing this fluctuation. PMID:26400690
Willow, Soohaeng Yoo; Salim, Michael A; Kim, Kwang S; Hirata, So
2015-01-01
A direct, simultaneous calculation of properties of a liquid using an ab initio electron-correlated theory has long been unthinkable. Here we present structural, dynamical, and response properties of liquid water calculated by ab initio molecular dynamics using the embedded-fragment spin-component-scaled second-order many-body perturbation method with the aug-cc-pVDZ basis set. This level of theory is chosen as it accurately and inexpensively reproduces the water dimer potential energy surface from the coupled-cluster singles, doubles, and noniterative triples with the aug-cc-pVQZ basis set, which is nearly exact. The calculated radial distribution function, self-diffusion coefficient, coordinate number, and dipole moment, as well as the infrared and Raman spectra are in excellent agreement with experimental results. The shapes and widths of the OH stretching bands in the infrared and Raman spectra and their isotropic-anisotropic Raman noncoincidence, which reflect the diverse local hydrogen-bond environment, are also reproduced computationally. The simulation also reveals intriguing dynamic features of the environment, which are difficult to probe experimentally, such as a surprisingly large fluctuation in the coordination number and the detailed mechanism by which the hydrogen donating water molecules move across the first and second shells, thereby causing this fluctuation.
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).
Second-Order Footsteps Illusions.
Kitaoka, Akiyoshi; Anstis, Stuart
2015-12-01
In the "footsteps illusion", light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures-even though luminance-based neural motion detectors are blind to such edges. PMID:27551366
Second-order coherence of supercontinuum light.
Genty, Goëry; Surakka, Minna; Turunen, Jari; Friberg, Ari T
2010-09-15
We analyze the coherence properties of supercontinuum generated in photonic crystal fibers by applying the second-order coherence theory of nonstationary light. Using an ensemble of simulated realizations, we construct two-frequency cross-spectral density and two-time mutual coherence functions. This allows us to introduce measures of temporal and spectral coherence. We show that, in the long-pulse regime, supercontinuum light can be decomposed into a sum of coherent and quasi-stationary contributions. Our approach and findings are also applicable in the short-pulse regime. PMID:20847777
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.
Lacroix, P.G.; Di Bella, S.; Ledoux, I.
1996-02-01
A new Schiff-base ligand based on the condensation of diaminomaleonitrile and 4-(diethylamino)salicylaldehyde is reported with its copper, nickel, and zinc complexes. Their second-order nonlinear optical properties are investigated by electric field induced second harmonic (EFISH) and ZINDO quantum-chemical calculation to probe the role of the metal center in the nonlinearity. All of the complexes exhibit a second-order nonlinear response that is larger than that of the ligand with an hyperpolarizability {beta} value of 400 ({+-}100) 10{sup -30} cm{sup 5} esu{sup -1} for the zinc derivative at 1.34 {mu}m. Theoretical calculations indicate that the two-level model is inadequate to describe the nonlinearity in such systems. 41 refs., 3 figs., 2 tabs.
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.
Anitha, K; Balachandran, V
2015-07-01
Vibrational spectral analysis and quantum chemical computations based on density functional theory have been performed on the N-(2-cyanoethyl)-N-butylaniline. The geometry, structural properties, intermolecular hydrogen bond, and harmonic vibrational frequencies of the title molecule have been investigated with the help of DFT (B3LYP) and LC-DFT (CAM-B3LYP) method. Molecular electrostatic potential (MEP) have been performed. The various intramolecular interactions have been exposed by natural bond orbital analysis. The distribution of atomic charges and bending of natural hybrid orbitals also reflect the presence of intramolecular hydrogen bonding. Global reactivity and local reactivity descriptors of the title molecule have been calculated. The analysis of the electron density of HOMO and LUMO gives an idea of the delocalization and low value of energy gap indicated the electron transport in the molecule and thereby NLO activity. The effect of solvent on second-order NLO properties has been studied using polarized continuum model (PCM) in the tetrahydrofuran (THF) solution. The solvent leads to a slight enhancement of the NLO responses for the studied complexes relevant to their NLO responses in gas phase. The electronic absorption spectra were investigated by the TDDFT methods. The frequency-dependent first hyperpolarizabilities of the N-(2-cyanoethyl)-N-butylaniline were also evaluated. The (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.
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 corrected Hadamard formulas
NASA Astrophysics Data System (ADS)
Epele, L. N.; Fanchiotti, H.; Canal, C. A. García
1985-08-01
The second-order correction to the Hadamard formulas for the Green's function, harmonic measures, and period matrix of a two-dimensional domain is obtained in the context of the domain-variational theory.
Selfishness as second-order altruism.
Eldakar, Omar Tonsi; Wilson, David Sloan
2008-05-13
Selfishness is seldom considered a group-beneficial strategy. In the typical evolutionary formulation, altruism benefits the group, selfishness undermines altruism, and the purpose of the model is to identify mechanisms, such as kinship or reciprocity, that enable altruism to evolve. Recent models have explored punishment as an important mechanism favoring the evolution of altruism, but punishment can be costly to the punisher, making it a form of second-order altruism. This model identifies a strategy called "selfish punisher" that involves behaving selfishly in first-order interactions and altruistically in second-order interactions by punishing other selfish individuals. Selfish punishers cause selfishness to be a self-limiting strategy, enabling altruists to coexist in a stable equilibrium. This polymorphism can be regarded as a division of labor, or mutualism, in which the benefits obtained by first-order selfishness help to "pay" for second-order altruism. PMID:18448681
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…
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…
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.
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.
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.
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.
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.
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.
Experimental Measurement of the Second-Order Coherence of Supercontinuum.
Närhi, Mikko; Turunen, Jari; Friberg, Ari T; Genty, Goëry
2016-06-17
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources. PMID:27367389
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.
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
Espa, Davide; Pilia, Luca; Makedonas, Christodoulos; Marchiò, Luciano; Mercuri, M Laura; Serpe, Angela; Barsella, Alberto; Fort, Alain; Mitsopoulou, Christiana A; Deplano, Paola
2014-01-21
The mixed-ligand complexes [M(II)(Et2dazdt)(mnt)] (M = Ni, 1; Pd, 2; Pt, 3) [Et2dazdt = N,N'-diethyl-perhydrodiazepine-2,3-dithione; mnt = maleonitrile-2,3-dithiolate] have been prepared and fully characterized. X-ray diffractometric studies on 1-3 (the structure of 1 was already known) show that the crystals are isostructural (triclinic, P-1), and two independent molecular entities are present in the unit cell. These entities differ in the orientation of the ethyl substituents with respect to the epta-atomic ring. In the C2S2MS2C2 dithiolene core the four sulfur atoms define a square-planar coordination environment of the metal where the M-S bond distances involving the two ligands are similar, while the C-S bond distances in the C2S2 units exhibit a significant difference in Et2dazdt (dithione) and mnt (dithiolato) ligands. 1-3 show in the visible region one or two moderately strong absorption peaks, having ligand-to-ligand charge-transfer (CT) character with some contribution of the metal, and show negative solvatochromism and molecular quadratic optical nonlinearity, which was determined by the EFISH (electric-field-induced second-harmonic generation) technique. These complexes are redox active and show two reversible reduction waves and one irreversible oxidation wave. Theoretical calculations based on DFT and TD-DFT calculations on complexes 1-3 as well as on [Pt(Bz2pipdt)(mnt)] (4) and [Pt(Bz2pipdt)(dmit)] (5) highlight the factors which affect the optical properties of these second-order redox-active NLO chromophores. Actually, the torsion angle of the dithione system (δ2) inversely correlates either with the oscillator strengths of the main transition of the complexes or with their beta values. The high beta value of 5 can be attributed both to its lowest torsion angles and to the extent of the π system of its dithiolate ligand, dmit. PMID:24405208
Analysis of implicit second-order upwind-biased stencils
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Warren, Gary P.
1993-01-01
Truncation error and stability properties of several implicit upwind schemes for the two-dimensional Euler equations are examined. The schemes use linear data reconstruction methods to achieve second-order flux integrations where the implicit Jacobian operators are first order. The stability properties of the schemes are examined by a Von Neumann analysis of the linearized, constant-coefficient Euler equations. The choice of the data reconstruction method used to evaluate the flux integral has a dramatic effect on the convergence properties of the implicit solution method. In particular, the typical one-dimensional data reconstruction methods used with structured grids exhibit poor convergence properties compared to the unstructured grid method considered. Of the schemes examined, the one with the superior convergence properties is well-suited for both unstructured and structured grids, which has important implications for the design of implicit methods.
Entanglement in a second-order quantum phase transition
Vidal, Julien; Palacios, Guillaume; Mosseri, Remy
2004-02-01
We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point {lambda}{sub c} in the thermodynamical limit. We also show that there exists a value {lambda}{sub 0}{>=}{lambda}{sub c} above which the ground state is not spin squeezed despite a nonvanishing concurrence.
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.
Stress-dependent second-order grain statistics of polycrystals.
Kube, Christopher M; Turner, Joseph A
2015-10-01
In this article, the second-order statistics of the elastic moduli of randomly oriented grains in a polycrystal are derived for the case when an initial stress is present. The initial stress can be either residual stress or stresses generated from external loading. The initial stress is shown to increase or decrease the variability of the grain's elastic moduli from the average elastic moduli of the polycrystal. This variation in the elastic properties of the individual grains causes acoustic scattering phenomenon in polycrystalline materials to become stress-dependent. The influence of the initial stress on scattering is shown to be greater than the influence on acoustic phase velocities, which defines the acoustoelastic effect. This work helps the development of scattering based tools for the nondestructive analysis of material stresses in polycrystals.
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
Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine: Preprint
Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A.
2014-07-01
The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at the MARIN offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST in the future. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method has been applied to the OC4-DeepCwind semisubmersible platform, supporting the NREL 5-MW baseline wind turbine. The loads and response of the system due to the second-order hydrodynamics are analysed and compared to first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads and induced response data are compared to the loads and motions induced by aerodynamic loading as solved by FAST.
Second order guiding-center Vlasov-Maxwell equations
Madsen, Jens
2010-08-15
Second order gyrogauge invariant guiding-center coordinates with strong ExB-flow are derived using the Lie transformation method. The corresponding Poisson bracket structure and equations of motion are obtained. From a variational principle the explicit Vlasov-Maxwell equations are derived including second order terms. The second order contributions contain the lowest order finite-Larmor-radius corrections to the electromagnetic field. Therefore, the model is capable of describing situations where strong ExB-flows and finite-Larmor-radius effects are mutually important.
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.
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.
Second-order model selection in mixture experiments
Redgate, P.E.; Piepel, G.F.; Hrma, P.R.
1992-07-01
Full second-order models for q-component mixture experiments contain q(q+l)/2 terms, which increases rapidly as q increases. Fitting full second-order models for larger q may involve problems with ill-conditioning and overfitting. These problems can be remedied by transforming the mixture components and/or fitting reduced forms of the full second-order mixture model. Various component transformation and model reduction approaches are discussed. Data from a 10-component nuclear waste glass study are used to illustrate ill-conditioning and overfitting problems that can be encountered when fitting a full second-order mixture model. Component transformation, model term selection, and model evaluation/validation techniques are discussed and illustrated for the waste glass example.
Second-order spatial analysis of epidermal nerve fibers.
Waller, Lance A; Särkkä, Aila; Olsbo, Viktor; Myllymäki, Mari; Panoutsopoulou, Ioanna G; Kennedy, William R; Wendelschafer-Crabb, Gwen
2011-10-15
Breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. Preliminary neurologic studies indicate qualitative differences in the spatial patterns of nerve fibers based on pathophysiologic conditions in the subjects. Of particular interest is the evolution of spatial patterns observed in the progression of diabetic neuropathy. It appears that the spatial distribution of nerve fibers becomes more 'clustered' as neuropathy advances, suggesting the possibility of diagnostic prediction based on patterns observed in skin biopsies. We consider two approaches to establish statistical inference relating to this observation. First, we view the set of locations where the nerves enter the epidermis from the dermis as a realization of a spatial point process. Secondly, we treat the set of fibers as a realization of a planar fiber process. In both cases, we use estimated second-order properties of the observed data patterns to describe the degree and scale of clustering observed in the microscope images of blister biopsies. We illustrate the methods using confocal microscopy blister images taken from the thigh of one normal (disease-free) individual and two images each taken from the thighs of subjects with mild, moderate, and severe diabetes and report measurable differences in the spatial patterns of nerve entry points/fibers associated with disease status.
a Second Order Born Calculation for Charge Transfer.
NASA Astrophysics Data System (ADS)
Simony, Paul Richard
Charge transfer cross sections, from the ground state of the target to the ground state of the projectile, have been computed in a second order Born approximation for protons incident upon hydrogen at energies of 1, 10, and 50 MeV. The exact second order matrix element is evaluated numerically, and the results are compared to a standard peaking approximation (SP), as well as to a new peaking approximation (LP) developed herein. At 50 MeV two distinct second order effects are evident in the differential cross section. For very small (center of mass) scattering angles ((theta) (DBLTURN) .032(DEGREES)) the second order cross section is smaller than the first order cross section, while at larger angles ((theta) (DBLTURN) .054(DEGREES)) a second Born peak occurs. This peak can be kinematically associated with a classical two step process which gives rise to the well known dominating v('-11) asymptotic velocity dependence of the total cross section. The reduction of the differential cross section at smaller angles serves to decrease the total cross section, as is predicted by the asymptotic expression. At 10 MeV second order effects become less important, and at 1 MeV the kinematic peak has all but disappeared, while the second order cross section has here become larger than the first order cross section. At intermediate energies experimental results indicate that the first order cross section used here is itself too large.
[Second-order retrospective revaluation in human contingency learning].
Numata, Keitaro; Shimazaki, Tsuneo
2009-04-01
We demonstrated second-order retrospective revaluation with three cues (T1, T2, and C) and an outcome, in human contingency learning. Experimental task, PC-controlled video game in which participants were required to observe about the relations between firing missiles and the tank destruction, consisted of three training phases and two rating phases. Groups C+ and C- consisted of same first two training phases, CT+ (cues C and T with an outcome) and T1T2+ followed by C+, or C- training for Groups C+, C-, respectively. In rating phases, it is clearly demonstrated that the judgment of predictive value for the outcome of the T2 were higher by C+ training (second-order unovershadowing) and lowered by C- training (second-order backward blocking). The results for Groups RC+ and RC-, in which the orders of the first two training phase for Groups C+ and C- were interchanged, also showed second-order unovershadowing and second-order backward blocking. These results, the robustness of second-order retrospective revaluation against the order of the first training phases, can be explained by the extended comparator hypothesis and probabilistic contrast model. However, these results cannot be explained by traditional associative learning models. PMID:19489431
Second-order conditioning with and without unconditioned stimulus presentation.
Holland, P C
1980-07-01
The effects of presenting various episodes after serial presentation of two conditioned stimuli (CS2-CS1 sequences) on second-order conditioning to CS2 were examined in three experiments using rat subjects in an appetitive conditioning situation. In Experiment 1, presentation of food unconditioned stimuli (USs) immediately after CS2-CS1 sequences interfered with second-order conditioning of CS2. In Experiment 2, postsequence presentation of a "surprising" US interfered with second-order conditioning more than did presentation of an "expected" US; similarly, less second-order conditioning of CS2 was observed when postsequence nonpresentation of a US was surprising than when US omission was expected. In Experiment 3, the interfering effect of US presentation on second-order conditioning was smaller when a brief delay was introduced between presentation of the CS2-CS-1 sequence and the US. The results are discussed in terms of an information-processing theory recently proposed by Wagner and his colleagues.
Deflection of light to second order in conformal Weyl gravity
NASA Astrophysics Data System (ADS)
Sultana, Joseph
2013-04-01
We reexamine the deflection of light in conformal Weyl gravity obtained in Sultana and Kazanas (2010), by extending the calculation based on the procedure by Rindler and Ishak, for the bending angle by a centrally concentrated spherically symmetric matter distribution, to second order in M/R, where M is the mass of the source and R is the impact parameter. It has recently been reported in Bhattacharya et al. (JCAP 09 (2010) 004; JCAP 02 (2011) 028), that when this calculation is done to second order, the term γr in the Mannheim-Kazanas metric, yields again the paradoxical contribution γR (where the bending angle is proportional to the impact parameter) obtained by standard formalisms appropriate to asymptotically flat spacetimes. We show that no such contribution is obtained for a second order calculation and the effects of the term γr in the metric are again insignificant as reported in our earlier work.
Some restrictions on the existence of second order limit language
NASA Astrophysics Data System (ADS)
Ahmad, Muhammad Azrin; Sarmin, Nor Haniza; Yusof, Yuhani; Fong, Wan Heng
2015-10-01
The cut and paste phenomenon on DNA molecules with the presence of restriction enzyme and appropriate ligase has led to the formalism of mathematical modelling of splicing system. A type of splicing system named Yusof-Goode splicing system is used to present the transparent behaviour of the DNA splicing process. The limit language that is defined as the leftover molecules after the system reaches its equilibrium point has been extended to a second order limit language. The non-existence of the second order limit language biologically has lead to this study by using mathematical approach. In this paper, the factors that restrict the formation of the second order limit language are discussed and are presented as lemmas and theorem using Y-G approach. In addition, the discussion focuses on Yusof- Goode splicing system with at most two initial strings and two rules with one cutting site and palindromic crossing site and recognition sites.
Weak value amplification via second-order correlated technique
NASA Astrophysics Data System (ADS)
Ting, Cui; Jing-Zheng, Huang; Xiang, Liu; Gui-Hua, Zeng
2016-02-01
We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification (WVA) experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed. Project supported by the Union Research Centre of Advanced Spaceflight Technology (Grant No. USCAST2013-05), the National Natural Science Foundation of China (Grant Nos. 61170228, 61332019, and 61471239), and the High-Tech Research and Development Program of China (Grant No. 2013AA122901).
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.
Controlling flexible structures with second order actuator dynamics
NASA Technical Reports Server (NTRS)
Inman, Daniel J.; Umland, Jeffrey W.; Bellos, John
1989-01-01
The control of flexible structures for those systems with actuators that are modeled by second order dynamics is examined. Two modeling approaches are investigated. First a stability and performance analysis is performed using a low order finite dimensional model of the structure. Secondly, a continuum model of the flexible structure to be controlled, coupled with lumped parameter second order dynamic models of the actuators performing the control is used. This model is appropriate in the modeling of the control of a flexible panel by proof-mass actuators as well as other beam, plate and shell like structural numbers. The model is verified with experimental measurements.
Kubo Formulas for Second-Order Hydrodynamic Coefficients
Moore, Guy D.; Sohrabi, Kiyoumars A.
2011-03-25
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity {eta} and on five additional ''second-order'' hydrodynamical coefficients {tau}{sub {Pi}}, {kappa}, {lambda}{sub 1}, {lambda}{sub 2}, and {lambda}{sub 3}. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient {lambda}{sub 3} can be evaluated directly by Euclidean means and does not in general vanish.
The Poisson equation at second order in relativistic cosmology
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A. E-mail: Adam.Christopherson@nottingham.ac.uk
2013-08-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.
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
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 variational equations for N-body simulations
NASA Astrophysics Data System (ADS)
Rein, Hanno; Tamayo, Daniel
2016-07-01
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.
Second-order accurate 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.
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.
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…
Maximum principles for second order dynamic equations on time scales
NASA Astrophysics Data System (ADS)
Stehlik, Petr; Thompson, Bevan
2007-07-01
This paper establishes some new maximum principles for second order dynamic equations on time scales, including: a strong maximum principle; a generalized maximum principle; and a boundary point lemma. The new results include, as special cases, well-known ideas for ordinary differential equations and difference equations.
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…
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.
Pecuniary Effects, Second-Order Conditions, and the LRAC Curve.
ERIC Educational Resources Information Center
Comolli, Paul M.
2000-01-01
Explores the importance of second-order conditions in the cost-minimization problem confronting the monopsonistic employer of factor inputs. Describes an alternative approach to the presence of pecuniary effects that does not depend on the assumption that firms are monopsonistic in factor markets. (CMK)
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,…
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…
Green's function of the second order differential operator with involution
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sarsenbi, Abdisalam A.
2016-08-01
In the present paper, the Green's function of the second order differential operator L defined by formula L u =α u″ (x ) -u″ (-x ) =λ u (x ) ,-1
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.
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.
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.
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
A Second-Order Achromat Design Based on FODO Cell
Sun, Yipeng; /SLAC
2011-08-19
Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first order dispersion and provide betatron focusing. Similarly a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to generate an isochronous section, quadrupoles are again needed to tune the first order transfer matrix element R{sub 56} equaling zero. Usually sextupoles are needed to correct second order dispersion in the bending plane, for both the dogleg optics and the chicane (with quad) optics. In this paper, an alternative optics design is introduced, which is based on a simple FODO cell and does not need sextupoles assistance to form a second-order achromat. It may provide a similar function of either a dogleg or a bypass, by using 2 or 4 of such combined supercells.
Compressible turbulence transport equations for generalized second order closure
Cloutman, L D
1999-05-01
Progress on the theory of second order closure in turbulence models of various types requires knowledge of the transport equations for various turbulence correlations. This report documents a procedure that provides such equations for a wide variety of turbulence averages for compressible flows of a multicomponent fluid. Generalizing some work by Germano for incompressible flows, we introduce an appropriate extension of his generalized second order correlations and use a generalized mass-weighted averaging procedure to derive transport equations for the correlations. The averaging procedure includes all of the commonly used averages as special cases. The resulting equations provide an internally consistent starting point for future work in developing single-point statistical turbulence transport models for fluid flows. The form invariance of the in-compressible equations also holds for the compressible case, and we discuss some of the closure issues and frequently ignored complications of statistical turbulence models of compressible flows.
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.
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.
Using of "pseudo-second-order model" in adsorption.
Ho, Yuh-Shan
2014-01-01
A research paper's contribution exists not only in its originality and creativity but also in its continuity and development for research that follows. However, the author easily ignores it. Citation error and quotation error occurred very frequently in a scientific paper. Numerous researchers use secondary references without knowing the original idea from authors. Sulaymon et al. (Environ Sci Pollut Res 20:3011-3023, 2013) and Spiridon et al. (Environ Sci Pollut Res 20:6367-6381, 2013) presented wrong pseudo-second-order models in Environmental Science and Pollution Research, vol. 20. This comment pointed the errors of the kinetic models and offered information for citing original idea of pseudo-second-order kinetic expression. In order to stop the proliferation of the mistake, it is suggested to cite the original paper for the kinetic model which provided greater accuracy and more details about the kinetic expression.
Transport equations with second-order differential collision operators
Cosner, C.; Lenhart, S.M.; Protopopescu, V.
1988-07-01
This paper discusses existence, uniqueness, and a priori estimates for time-dependent and time-independent transport equations with unbounded collision operators. These collision operators are described by second-order differential operators resulting from diffusion in the velocity space. The transport equations are degenerate parabolic-elliptic partial differential equations, that are treated by modifications of the Fichera-Oleinik-Radkevic Theory of second-order equations with nonnegative characteristic form. They consider weak solutions in spaces that are extensions of L/sup rho/ to include traces on certain parts of the boundary. This extension is necessary due to the nonclassical boundary conditions imposed by the transport problem, which requires a specific analysis of the behavior of our weak solutions.
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.
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.
Asymptotic stability of second-order neutral stochastic differential equations
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ren, Yong; Kim, Hyunsoo
2010-05-01
In this paper, we study the existence and asymptotic stability in pth moment of mild solutions to second-order nonlinear neutral stochastic differential equations. Further, this result is extended to establish stability criterion for stochastic equations with impulsive effects. With the help of fixed point strategy, stochastic analysis technique, and semigroup theory, a set of novel sufficient conditions are derived for achieving the required result. Finally, an example is provided to illustrate the obtained result.
Second-order (2 +1 ) -dimensional anisotropic hydrodynamics
NASA Astrophysics Data System (ADS)
Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
2014-11-01
We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.
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.
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.
Second order distorted wave calculations for electron impact ionization processes
NASA Astrophysics Data System (ADS)
Chen, Zhangjin
Electron impact ionization of atoms provides a fundamental test of the current understanding of atomic structure as well as our understanding of the three body problem. Triple differential cross sections (TDCS), measured in the coincidence experiment, provide the most sensitive test of the theory of electron impact ionization processes. It was found two decades ago that second-order effects were crucial in explaining both the positions and magnitudes of the binary and recoil peaks in the TDCS. However, the existing theoretical calculations of second-order amplitudes typically resort to simplifying approximations, such as the closure approximation or neglecting the real part of the Green's function, to make the calculation tractable. In this work, we have developed a second-order distorted wave (DWB2) theory for atomic ionization which does not make these approximations. The DWB2 theory has been used to calculate the TDCS for electron impact ionization of hydrogen. It is found that the DWB2 results are in good agreement with absolute experimental measurements for incident energy greater than 100 eV. We have also performed DWB2 calculations for electron impact ionization of helium with the residual ion left in the n=1 and 2 states at intermediate energies in coplanar asymmetric geometry. Both the neutral and ionic distorting potentials are employed for the projectile in the final state. It has been found that the DWB2 results with the ionic distorting potential are in better agreement with experiment for the case in which the residual ion is left in the excited states. We have also performed the calculations to check the validity of the closure approximation and the simplified Green's function approximation and found that these approximations are not accurate for non-coplanar geometry and low incident energies.
Determination of robust stability margin for second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.; Kau, C.-T.; Juang, Jer-Nan
1992-01-01
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
NASA Astrophysics Data System (ADS)
Pokharel, Rajendra K.
Relativistic heavy ion collision experiments show clear evidence of creation of a very short-lived phase of nuclear matter consisting of color-deconfined quarks and gluons. This matter is known as the quark-gluon plasma (QGP). Fluctuation and correlation measurements of the detected particles have played a very important role in revealing the properties of QGP. In particular, these measurements have shown that the QGP behaves like a nearly perfect liquid. Relativistic hydrodynamics has been successfully used to study how the QGP evolves before the system hadronizes and ultimately produces the final state particles. Transport properties like shear viscosity constitute an important part in such studies. This work is focused on developing a second order hydrodynamic theory for the evolution of two-particle transverse momentum correlations. We use general temperature dependent transport and relaxation coefficients as well as the latest information on equations of state and use both first and second order relativistic viscous hydrodynamics to compute experimentally measurable observables. We will show that our computations using the second order viscous hydrodynamics are in good agreement with experimental data. We also highlight some features that distinguish the second order viscous hydrodynamic evolution of QGP from the first order.
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.
Detection of a diffusive cloak via second-order statistics
NASA Astrophysics Data System (ADS)
Koirala, Milan; Yamilov, Alexey
2016-08-01
We propose a scheme to detect the diffusive cloak proposed by Schittny et al [Science 345, 427 (2014)]. We exploit the fact that diffusion of light is an approximation that disregards wave interference. The long-range contribution to intensity correlation is sensitive to locations of paths crossings and the interference inside the medium, allowing one to detect the size and position, including the depth, of the diffusive cloak. Our results also suggest that it is possible to separately manipulate the first- and the second-order statistics of wave propagation in turbid media.
Local second-order boundary methods for lattice Boltzmann models
Ginzbourg, I.; d`Humieres, D.
1996-09-01
A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.
Finite difference schemes for second order systems describing black holes
Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.
2006-06-15
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.
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.
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.
The role of capture spiral silk properties in the diversification of orb webs.
Tarakanova, Anna; Buehler, Markus J
2012-12-01
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.
Second-order analytic solutions for re-entry trajectories
NASA Astrophysics Data System (ADS)
Kim, Eun-Kyou
1993-01-01
With the development of aeroassist technology, either for near-earth orbital transfer with or without a plane change or for planetary aerocapture, it is of interest to have accurate analytic solutions for reentry trajectories in an explicit form. Starting with the equations of motion of a non-thrusting aerodynamic vehicle entering a non-rotating spherical planetary atmosphere, a normalization technique is used to transform the equations into a form suitable for an analytic integration. Then, depending on the type of planar entry modes with a constant angle-of-attack, namely, ballistic fly-through, lifting skip, and equilibrium glide trajectories, the first-order solutions are obtained with the appropriate simplification. By analytic continuation, the second-order solutions for the altitude, speed, and flight path angle are derived. The closed form solutions lead to explicit forms for the physical quantities of interest, such as the deceleration and aerodynamic heating rates. The analytic solutions for the planar case are extended to three-dimensional skip trajectories with a constant bank angle. The approximate solutions for the heading and latitude are developed to the second order. In each type of trajectory examined, explicit relations among the principal variables are in a form suitable for guidance and navigation purposes. The analytic solutions have excellent agreement with the numerical integrations. They also provide some new results which were not reported in the existing classical theory.
Phillips, Steven; Wilson, William H.
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other “structurally related” cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
Phillips, Steven; Wilson, William H
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other "structurally related" cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castañeda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work.
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.
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.
Compact Two-State-Variable Second-Order Memristor Model.
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2016-06-01
A key requirement for using memristors in functional circuits is a predictive physical model to capture the resistive switching behavior, which shall be compact enough to be implemented using a circuit simulator. Although a number of memristor models have been developed, most of these models (i.e., first-order memristor models) have utilized only a one-state-variable. However, such simplification is not adequate for accurate modeling because multiple mechanisms are involved in resistive switching. Here, a two-state-variable based second-order memristor model is presented, which considers the axial drift of the charged vacancies in an applied electric field and the radial vacancy motion caused by the thermophoresis and diffusion. In particular, this model emulates the details of the intrinsic short-term dynamics, such as decay and temporal heat summation, and therefore, it accurately predicts the resistive switching characteristics for both DC and AC input signals. PMID:27152649
Second-order analysis of semiparametric recurrent event processes.
Guan, Yongtao
2011-09-01
A typical recurrent event dataset consists of an often large number of recurrent event processes, each of which contains multiple event times observed from an individual during a follow-up period. Such data have become increasingly available in medical and epidemiological studies. In this article, we introduce novel procedures to conduct second-order analysis for a flexible class of semiparametric recurrent event processes. Such an analysis can provide useful information regarding the dependence structure within each recurrent event process. Specifically, we will use the proposed procedures to test whether the individual recurrent event processes are all Poisson processes and to suggest sensible alternative models for them if they are not. We apply these procedures to a well-known recurrent event dataset on chronic granulomatous disease and an epidemiological dataset on meningococcal disease cases in Merseyside, United Kingdom to illustrate their practical value.
Gravitational Microlensing by Ellis Wormhole: Second Order Effects
NASA Astrophysics Data System (ADS)
Lukmanova, Regina; Kulbakova, Aliya; Izmailov, Ramil; Potapov, Alexander A.
2016-07-01
Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.
Nonoscillation for second order sublinear dynamic equations on time scales
NASA Astrophysics Data System (ADS)
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009-10-01
Consider the Emden-Fowler sublinear dynamic equation x[Delta][Delta](t)+p(t)f(x([sigma](t)))=0, where , is a time scale, , where ai>0, 0<[beta]i<1, with [beta]i the quotient of odd positive integers, 1<=i<=m. When m=1, and , (0.1) is the usual sublinear Emden-Fowler equation which has attracted the attention of many researchers. In this paper, we allow the coefficient function p(t) to be negative for arbitrarily large values of t. We extend a nonoscillation result of Wong for the second order sublinear Emden-Fowler equation in the continuous case to the dynamic equation (0.1). As applications, we show that the sublinear difference equation has a nonoscillatory solution, for b>0, c>[alpha], and the sublinear q-difference equation has a nonoscillatory solution, for , q>1, b>0, c>1+[alpha].
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.
Compact Two-State-Variable Second-Order Memristor Model.
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2016-06-01
A key requirement for using memristors in functional circuits is a predictive physical model to capture the resistive switching behavior, which shall be compact enough to be implemented using a circuit simulator. Although a number of memristor models have been developed, most of these models (i.e., first-order memristor models) have utilized only a one-state-variable. However, such simplification is not adequate for accurate modeling because multiple mechanisms are involved in resistive switching. Here, a two-state-variable based second-order memristor model is presented, which considers the axial drift of the charged vacancies in an applied electric field and the radial vacancy motion caused by the thermophoresis and diffusion. In particular, this model emulates the details of the intrinsic short-term dynamics, such as decay and temporal heat summation, and therefore, it accurately predicts the resistive switching characteristics for both DC and AC input signals.
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.
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.
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.
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.
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action
NASA Astrophysics Data System (ADS)
Bettoni, Dario; Liberati, Stefano
2013-10-01
The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and properties are worth analyzing along the experience accumulated in the latter context. Here, we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for scalar-tensor theories a là Brans-Dicke. We identify the most general transformation preserving second-order field equations and discuss the issue of viable frames for this kind of theory, in particular, the possibility to cast the action in the so-called Einstein frame. Interestingly, we find that only for a subset of the Horndeski Lagrangian such a frame exists. Finally, we investigate the transformation properties of such frames under field redefinitions and frame transformations and their reciprocal relationship.
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.
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.
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.
On computing first and second order derivative spectra
NASA Astrophysics Data System (ADS)
Roy, Indrajit G.
2015-08-01
Enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis. First and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing. But high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data. An algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed. The algorithm is formalized in the framework of an inverse problem, where based on the fundamental theorem of calculus a matrix equation is formed using a Volterra type integral equation of first kind. A regularization technique, where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra. The higher order derivative spectra are obtained while using the algorithm in sequel. The algorithm is tested successfully with synthetically generated spectral data contaminated with additive white Gaussian noise, and also with real absorbance and reflectance spectral data for fresh and sea water respectively.
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.
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.
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
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 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.
Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation
Petersson, N A; Sjogreen, B
2012-03-26
second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a
Second order multidimensional sign-preserving remapping for ALE methods
Hill, Ryan N; Szmelter, J.
2010-12-15
A second-order conservative sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods is developed utilising concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The algorithm is inherently multidimensional, and so does not introduce splitting errors. The remapping is implemented in a two-dimensional, finite element ALE solver employing staggered quadrilateral meshes. The MPDATA remapping uses a finite volume discretization developed for volume coordinates. It is applied for the remapping of density and internal energy arranged as cell centered, and velocity as nodal, dependent variables. In the paper, the advection of scalar fields is examined first for test cases with prescribed mesh movement. A direct comparison of MPDATA with the performance of the van Leer MUSCL scheme indicates advantages of a multidimensional approach. Furthermore, distinctly different performance between basic MPDATA and the infinite gauge option is illustrated using benchmarks involving transport of a sign changing velocity field. Further development extends the application of MPDATA remapping to the full ALE solver with a staggered mesh arrangement for density, internal energy and momentum using volume coordinates. At present, two options of the algorithm - basic and infinite gauge - are implemented. To ensure a meaningful assessment, an identical Lagrangian solver and computational mesh update routines are used with either MPDATA or van Leer MUSCL remapping. The evaluation places particular focus on the abilities of both schemes to accurately model multidimensional problems. Theoretical considerations are supported with numerical examples. In addition to the prescribed mesh movement cases for advection of scalars, the demonstrations include two-dimensional Eulerian and ALE flow simulations on quadrilateral meshes with both fixed and variable timestep control. The key comparisons include the standard test cases of Sod and Noh
Second-order estimates for the effective behaviour of viscoplastic polycrystalline materials
NASA Astrophysics Data System (ADS)
Bornert, M.; Masson, R.; Castañeda, P. Ponte; Zaoui, A.
2001-11-01
This paper is concerned with the application of the "second-order" nonlinear homogenisation procedure (Ponte Castañeda, J. Mech. Phys. Solids 44 (6) (1996) 827) to generate estimates of the self-consistent type for the effective behaviour of fcc and hcp viscoplastic polycrystals. The method has the distinctive property that it leads to estimates that are exact to second-order in the heterogeneity contrast, and which are expected to be more accurate, particularly when compared to rigorous bounds, than those resulting from earlier homogenisation schemes such as the Hill "incremental" method or its "total" formulation (Hutchinson) for pure power-law viscous materials. Special attention is paid to large grain anisotropy leading to correspondingly large heterogeneity contrast, and to highly nonlinear behaviour. Comparisons are also carried out with estimates derived from other more recent homogenisation schemes such as the "tangent" and "affine" methods. The results, illustrated for zirconium- and ice-type polycrystals, show that the second-order procedure offers the potential for significantly improved results, at least relative to the Hill incremental formulation.
Second-order bosonic Kadanoff-Baym equations for plasmon-accompanied optical absorption
NASA Astrophysics Data System (ADS)
Schüler, Michael; Pavlyukh, Yaroslav
2016-03-01
The availability of ultra-short and strong light sources opens the door for a variety of new experiments such as transient absorption, where optical properties of systems can be studied in extreme nonequilibrium situations. The nonequilibrium Green's function formalism is an efficient approach to investigate these processes theoretically. Here we apply the method to the light-matter interaction of the magnesium 2p core level accompanied by electron-plasmon interaction due to collective excitations in the conduction band. The plasmons are described as massive bosonic quasi-particle excitations, leading to a second-order equations of motion, requiring a new approach for their propagation.
Cascaded second-order contribution to the third-order nonlinear susceptibility
NASA Astrophysics Data System (ADS)
Kolleck, Christian
2004-05-01
Cascading of second-order nonlinear effects leads to an effective third-order nonlinearity. In addition to the macroscopic electric field at the intermediate frequencies another term has to be taken into account which is due to the locality of the intermediate polarization sources. Combining the correction terms at the three intermediate frequencies gives rise to a third-order susceptibility tensor, which exhibits the same symmetry properties as an intrinsic susceptibility. This particularly applies to the contributions from the rectified and the second-harmonic fields to the degenerate susceptibility.
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.
Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta
NASA Astrophysics Data System (ADS)
Giovannini, Massimo
2011-01-01
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.
Zhao, J.M.; Tan, J.Y.; Liu, L.H.
2013-01-01
A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.
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
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
A second order residual based predictor-corrector approach for time dependent pollutant transport
NASA Astrophysics Data System (ADS)
Pavan, S.; Hervouet, J.-M.; Ricchiuto, M.; Ata, R.
2016-08-01
We present a second order residual distribution scheme for scalar transport problems in shallow water flows. The scheme, suitable for the unsteady cases, is obtained adapting to the shallow water context the explicit Runge-Kutta schemes for scalar equations [1]. The resulting scheme is decoupled from the hydrodynamics yet the continuity equation has to be considered in order to respect some important numerical properties at discrete level. Beyond the classical characteristics of the residual formulation presented in [1,2], we introduce the possibility to iterate the corrector step in order to improve the accuracy of the scheme. Another novelty is that the scheme is based on a precise monotonicity condition which guarantees the respect of the maximum principle. We thus end up with a scheme which is mass conservative, second order accurate and monotone. These properties are checked in the numerical tests, where the proposed approach is also compared to some finite volume schemes on unstructured grids. The results obtained show the interest in adopting the predictor-corrector scheme for pollutant transport applications, where conservation of the mass, monotonicity and accuracy are the most relevant concerns.
Effects of Deception on Children's Understanding of Second-Order False Belief
ERIC Educational Resources Information Center
Miller, Scott A.
2013-01-01
This research examined two questions: effects of deception on children's understanding of second-order false belief, and possible effects of number of siblings on second-order performance. Kindergarten children responded to 3 second-order problems that varied in the presence and the nature of deception. Performance was better on the problems…
Robustness improvement of hyperspectral image unmixing by spatial second-order regularization.
Bauer, Sebastian; Stefan, Johannes; Michelsburg, Matthias; Laengle, Thomas; León, Fernando Puente
2014-12-01
The acquisition of hundreds of images of a scene, each at a different wavelength, is known as hyperspectral imaging. This high amount of data allows the extraction of much more information from hyperspectral images compared with conventional color images. The forward-looking imaging approach emerged from remote sensing, but is still not very widespread in industrial and other practical applications. Spectral unmixing, in particular, aims at the determination of the components present in a scene as well as the abundance to which each component contributes. This information is valuable, for instance, when discrimination tasks are to be performed. Involving not only spectral, but also spatial information was found to have the potential to improve the unmixing results. Several publications use spatial first-order regularization (closely related to the total variation approach) to incorporate this spatial information. Like in classical image processing, this approach favors piecewise constant pixel transitions. This is why it was proposed in the literature to use second-order regularization instead of first order to approach piecewise-linear transitions. Therefore, we introduce Hessian-based regularization to hyperspectral unmixing and propose an algorithm to calculate the regularized result. We use simulated data and images measured in our laboratory to show that both the first- and second-order approaches share many properties and produce similar results. The second-order approach, however, is more robust and thus more accurate in finding the minimum. Both methods smoothen the images in the case of supervised unmixing (i.e., the component spectra are known beforehand) and enhance unsupervised unmixing (when the spectra are not known).
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.
ERIC Educational Resources Information Center
Fuchs, Susanne; Perrier, Pascal; Hartinger, Mariam
2011-01-01
Purpose: Linear second-order models have often been used to investigate properties of speech production. However, these models are inaccurate approximations of the speech apparatus. This study aims at assessing how reliably stiffness can be estimated from kinematics with these models. Method: Articulatory movements were collected for 9 speakers of…
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.
Uniformly second-order-accurate essentially nonoscillatory schemes for the Euler equations
NASA Astrophysics Data System (ADS)
Yang, J. Y.
1990-12-01
Two time-level explicit and implicit finite-difference shock-capturing schemes based on the characteristic flux difference splitting method and the modified flux approach with the essentially nonoscillatory (ENO) property of Harten and Osher have been developed for the two-dimensional Euler equations. The methods are conservative, uniformly second-order accurate in time and space, even at local extrema. General coordinate systems are used to treat complex geometries. Standard alternating direction implicit approximate factorization is used for constructing implicit schemes. Numerical results have been obtained for unsteady shock wave reflection around general two-dimensional blunt bodies and for steady transonic flows over a circular arc bump in a channel. Properties of ENO schemes as applied to two-dimensional flows with multiple embedded discontinuities are discussed. Comparisons of the performance between the present ENO schemes and the previous total variation diminishing schemes is also included.
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.
NASA Astrophysics Data System (ADS)
Castro Díaz, M. J.; Fernández-Nieto, E. D.; Narbona-Reina, G.; de la Asunción, M.
2014-04-01
In this work we propose a second order flux limiter finite volume method, named PVM-2U-FL, that only uses information of the two external waves of the hyperbolic system. This method could be seen as a natural extension of the well known WAF method introduced by E.F. Toro in [23]. We prove that independently of the number of unknowns of the 1D system, it recovers the second order accuracy at regular zones, while in presence of discontinuities, the scheme degenerates to PVM-2U method, which can be seen as an improvement of the HLL method (see [6,10]). Another interesting property of the method is that it does not need any spectral decomposition of the Jacobian or Roe matrix associated to the flux function. Therefore, it can be easily applied to systems with a large number of unknowns or in situations where no analytical expression of the eigenvalues or eigenvectors are known. In this work, we apply the proposed method to magnetohydrodynamics and to stratified multilayer flows. Comparison with the two-waves WAF and HLL-MUSCL methods are also presented. The numerical results show that PVM-2U-FL is the most efficient and accurate among them.
Fast and efficient second-order method for training radial basis function networks.
Xie, Tiantian; Yu, Hao; Hewlett, Joel; Rózycki, Paweł; Wilamowski, Bogdan
2012-04-01
This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.
Li, Yuan-Na; Wu, Hai-Long; Qing, Xiang-Dong; Nie, Chong-Chong; Li, Shu-Fang; Yu, Yong-Jie; Zhang, Shu-Rong; Yu, Ru-Qin
2011-07-15
A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L(-1) sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL(-1), respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices. PMID:21645706
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.
Second-order optical effects in several pyrazolo-quinoline derivatives
NASA Astrophysics Data System (ADS)
Makowska-Janusik, M.; Gondek, E.; Kityk, I. V.; Wisła, J.; Sanetra, J.; Danel, A.
2004-11-01
Using optical poling of several pyazolo-quinoline (PAQ) derivatives we have found an existence of sufficiently high second order optical susceptibility at wavelength 1.76 μm varying in the range 0.9-2.8 pm/V. The performed quantum chemical simulations of the UV-absorption for isolated, solvated and incorporated into the polymethacrylate (PMMA) polymer films have shown that the PM3 method is the best among the semi-empirical ones to simulate the optical properties. The calculations of the hyperpolarizabilites have shown a good correlation with experimentally measured susceptibilities obtained from the optical poling. We have found that experimental susceptibility depends on linear molecular polarizability and photoinducing changes of the molecular dipole moment. It is clearly seen for the PAQ4-PAQ6 molecules possessing halogen atoms with relatively large polarizabilities.
Unbalanced and Minimal Point Equivalent Estimation Second-Order Split-Plot Designs
NASA Technical Reports Server (NTRS)
Parker, Peter A.; Kowalski, Scott M.; Vining, G. Geoffrey
2007-01-01
Restricting the randomization of hard-to-change factors in industrial experiments is often performed by employing a split-plot design structure. From an economic perspective, these designs minimize the experimental cost by reducing the number of resets of the hard-to- change factors. In this paper, unbalanced designs are considered for cases where the subplots are relatively expensive and the experimental apparatus accommodates an unequal number of runs per whole-plot. We provide construction methods for unbalanced second-order split- plot designs that possess the equivalence estimation optimality property, providing best linear unbiased estimates of the parameters; independent of the variance components. Unbalanced versions of the central composite and Box-Behnken designs are developed. For cases where the subplot cost approaches the whole-plot cost, minimal point designs are proposed and illustrated with a split-plot Notz design.
Fisher information of special functions and second-order differential equations
NASA Astrophysics Data System (ADS)
Yáñez, R. J.; Sánchez-Moreno, P.; Zarzo, A.; Dehesa, J. S.
2008-08-01
We investigate a basic question of analytic information theory, namely, the evaluation of the Fisher information and the relative Fisher information with respect to a non-negative function, for the probability distributions obtained by squaring the special functions of mathematical physics which are solutions of second-order differential equations. We obtain explicit expressions for these information-theoretic properties via the expectation values of the coefficients of the differential equation. We illustrate our approach for various nonrelativistic D-dimensional wavefunctions and some special functions of physicomathematical interest. Emphasis is made in the Nikiforov-Uvarov hypergeometric-type functions, which include and generalize the Hermite functions and the Gauss and Kummer hypergeometric functions, among others.
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.
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.
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.
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.
The Second Order Approximation to Sample Influence Curve in Canonical Correlation Analysis.
ERIC Educational Resources Information Center
Fung, Wing K.; Gu, Hong
1998-01-01
A second order approximation to the sample influence curve (SIC) has been derived in the literature. This paper presents a more accurate second order approximation, which is exact for the SIC of the squared multiple correction coefficient. An example is presented. (SLD)
Increasing stimulus size impairs first- but not second-order motion perception.
Glasser, Davis M; Tadin, Duje
2011-11-23
As stimulus size increases, the direction of high-contrast moving stimuli becomes increasingly difficult to perceive. This counterintuitive effect, termed spatial suppression, is believed to reflect antagonistic center-surround interactions--mechanisms that play key roles in tasks requiring sensitivity to relative motion. It is unknown, however, whether second-order motion also exhibits spatial suppression. To test this hypothesis, we measured direction discrimination thresholds for first- and second-order stimuli of varying sizes. The results revealed increasing thresholds with increasing size for first-order stimuli but demonstrated no spatial suppression of second-order motion. This selective impairment of first-order motion predicts increasing predominance of second-order cues as stimulus size increases. We confirmed this prediction by utilizing compound stimuli that contain first- and second-order information moving in opposite directions. Specifically, we found that for large stimuli, motion perception becomes increasingly determined by the direction of second-order cues. Overall, our findings show a lack of spatial suppression for second-order stimuli, suggesting that the second-order system may have distinct functional roles, roles that do not require high sensitivity to relative motion.
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
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…
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.
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.
Interactions between first- and second-order motion revealed by optokinetic nystagmus.
Harris, L R; Smith, A T
2000-01-01
A previous study has suggested that second-order motion is ineffective at driving optokinetic nystagmus (OKN) when presented alone. First- and second-order motion cues interact in creating the perception of motion. Is there an interaction between first- and second-order cues in the control of eye movements? We presented combinations of first- and second-order cues moving in the same or opposite directions and measured the eye movements evoked, to look for a modification of the oculomotor response to first-order motion by simultaneously presented second-order cues. Dynamic random noise was used as a carrier for first- and second-order drifting gratings (13.4 degrees/s; 0.25 cycles/degree; 64 x 48 degrees screen viewed at 28.5 cm). Second-order gratings were defined by spatial modulation of the luminance flicker frequency of noise pixels of constant contrast (50%). A first-order, luminance-defined grating (13.4 degrees/s; 0.25 cycles/degree; variable contrast from 4-50%) was moved in either the same or the opposite direction. Eye movements were recorded by video-oculography from six subjects as they looked straight ahead. The gain (eye velocity/stimulus velocity) of first-order-evoked OKN increased with contrast. The presence of flicker-defined second-order motion in the opposite direction attenuated this OKN below a first-order contrast of 15%, although it had little effect at higher contrasts. When first- and second-order motion were in the same direction, there was an enhancement of the OKN response. We conclude that second-order motion can modify the optokinetic response to simultaneously presented first-order motion. PMID:10638442
NASA Astrophysics Data System (ADS)
Idiart, M. I.; Moulinec, H.; Ponte Castañeda, P.; Suquet, P.
2006-05-01
This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417-1423], while the theoretical estimates follow from the so-called "second-order" procedure [Ponte Castañeda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. J. Mech. Phys. Solids 50, 737-757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding "second-order" estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the "second-order" estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the "second-order" method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites.
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. PMID:27618513
Second-order schedules of drug self-administration in animals.
Schindler, Charles W; Panlilio, Leigh V; Goldberg, Steven R
2002-10-01
On a second-order schedule, a subject responds according to one schedule (the unit schedule) for a brief presentation of a stimulus such as a light. Responding by the subject on this unit schedule is then reinforced according to another schedule of reinforcement. Second-order schedules of drug injection allow the study of more complex behavioral sequences than do simple schedules and may more accurately reflect the human drug-abuse situation. Much of the early work in this area used primates as subjects and focused on the behavioral variables controlling responding. It was shown that long sequences of behavior could be maintained on second-order schedules with relatively infrequent injections of drug and that the second-order, brief-stimulus presentations were critical to the acquisition and maintenance of responding. Also, the continued presentation of the brief stimulus in extinction often led to prolonged extinction behavior. These studies clearly showed that environmental stimuli greatly influence drug self-administration behavior under second-order schedules. The focus of much of the more recent work with second-order schedules has been on the evaluation of pharmacological treatments for drug addiction, both as antagonist and substitution therapies. Both types of potential therapies have shown promise in these preclinical models of addictive behavior. The recent extension of second-order self-administration studies to rats as subjects has facilitated the investigation of neural mechanisms involved in this behavior. While this use of second-order schedules is a relatively recent phenomenon, significant contributions have already been made in identifying neural mechanisms critical to second-order schedule drug self-administration. This active area of research holds great promise for delineating specific brain regions critical to different aspects of drug addiction.
NASA Astrophysics Data System (ADS)
Grima, Ramon
2015-10-01
It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.
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.
First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
Bonnans, J. Frederic; Silva, Francisco J.
2012-06-15
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
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.
Jung, Yousung; Lochan, Rohini C; Dutoi, Anthony D; Head-Gordon, Martin
2004-11-22
A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Møller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite-spin second order energy (SOS-MP2), where MP2 is Møller-Plesset theory, yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the fifth order computational steps associated with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.
Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.
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.
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)
Second-order conditioning of the pigeon's key-peck using an autoshaping procedure.
Green, L; Schweitzer, L
1980-03-01
Second-order conditioning of the pigeon's key-peck was established using an autoshaping procedure. In the first experiment, pigeons came to peck a response key, the second-order conditioned stimulus (CS2), when it was paired with another key (CS1) that had previously been paired with food delivery. In the second experiment, pigeons again came to peck a key (CS2) when it was followed by a clicker (CS1) which had been paired with food delivery, even though the clicker itself had not evoked pecking. Responses to a second-order stimulus, therefore, need not resemble responses to the first-order CS. Furthermore, in both experiments, extinction of the first-order IS led to reduction in pecking CS2. These results were discussed in terms of the nature of the associations being formed during second-order conditioning.
A second order accurate embedded boundary method for the wave equation with Dirichlet data
Kreiss, H O; Petersson, N A
2004-03-02
The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.
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.
Algorithms and design for a second-order automatic differentiation module
Abate, J.; Bischof, C.; Roh, L.; Carle, A.
1997-07-01
This article describes approaches to computing second-order derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given that show the speedup possible with these techniques relative to existing approaches. The authors also describe a new source transformation AD module for computing second-order derivatives of C and Fortran codes and the underlying infrastructure used to create a language-independent translation tool.
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.
Exponential stability of second-order stochastic evolution equations with Poisson jumps
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ren, Y.
2012-12-01
This paper is concerned with the exponential stability problem of second-order nonlinear stochastic evolution equations with Poisson jumps. By using the stochastic analysis theory, a set of novel sufficient conditions are derived for the exponential stability of mild solutions to the second-order nonlinear stochastic differential equations with infinite delay driven by Poisson jumps. An example is provided to demonstrate the effectiveness of the proposed result.
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.
Second-order many-body perturbation theory: an eternal frontier.
Hirata, So; He, Xiao; Hermes, Matthew R; Willow, Soohaeng Y
2014-01-30
Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation.
Second-order many-body perturbation study of ice Ih
NASA Astrophysics Data System (ADS)
He, Xiao; Sode, Olaseni; Xantheas, Sotiris S.; Hirata, So
2012-11-01
Ice Ih is arguably the most important molecular crystal in nature, yet our understanding of its structural and dynamical properties is still far from complete. We present embedded-fragment calculations of the structures and vibrational spectra of the three-dimensional, proton-disordered phase of ice Ih performed at the level of second-order many-body perturbation theory with a basis-set superposition error correction. Our calculations address previous controversies such as the one related to the O-H bond length as well as the existence of two types of hydrogen bonds with strengths differing by a factor of two. For the latter, our calculations suggest that the observed spectral features arise from the directionality or the anisotropy of collective hydrogen-bond stretching vibrations rather than the previously suggested vastly different force constants. We also report a capability to efficiently compute infrared and Raman intensities of a periodic solid. Our approach reproduces the infrared and Raman spectra, the variation of inelastic neutron scattering spectra with deuterium concentration, and the anomaly of heat capacities at low temperatures for ice Ih.
Synaptic transmission of baro- and chemoreceptors afferents in the NTS second order neurons.
Accorsi-Mendonça, Daniela; Machado, Benedito H
2013-04-01
Second order neurons in the nucleus tractus solitarius (NTS) process and integrate the afferent information from arterial baroreceptors with high fidelity and precise timing synaptic transmission. Since 2nd-order NTS neurons receiving baroreceptors inputs are relatively well characterized, their electrophysiological profile has been accepted as a general characteristic for all 2nd-order NTS neurons involved with the processing of different sensorial inputs. On the other hand, the synaptic properties of other afferent systems in NTS, such as the peripheral chemoreceptors, are not yet well understood. In this context, in previous studies we demonstrated that in response to repetitive afferents stimulation, the chemoreceptors 2nd-order NTS neurons also presented high fidelity of synaptic transmission, but with a large variability in the latency of evoked responses. This finding is different in relation to the precise timing transmission for baroreceptor 2nd-order NTS neurons, which was accepted as a general characteristic profile for all 2nd order neurons in the NTS. In this brief review we discuss this new concept as an index of complexity of the sensorial inputs to NTS with focus on the synaptic processing of baro- and chemoreceptor afferents.
Second-order many-body perturbation theory: an eternal frontier.
Hirata, So; He, Xiao; Hermes, Matthew R; Willow, Soohaeng Y
2014-01-30
Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation. PMID:24328153
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.
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.
Second-Order Inference for the Mean of a Variable Missing at Random.
Díaz, Iván; Carone, Marco; van der Laan, Mark J
2016-05-01
We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator. PMID:27227727
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.
NASA Astrophysics Data System (ADS)
Reina, Borja; Vera, Raül
2015-08-01
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in general relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function m0 (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass δ M needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.
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.
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. PMID:24367116
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
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
Beneke, M.; Fidler, C.
2010-09-15
Non-Gaussianity and B-mode polarization are particularly interesting features of the cosmic microwave background, as--at least in the standard model of cosmology--their only sources to first order in cosmological perturbation theory are primordial, possibly generated during inflation. If the primordial sources are small, the question arises how large is the non-Gaussianity and B-mode background induced in second order from the initially Gaussian and scalar perturbations. In this paper we derive the Boltzmann hierarchy for the microwave background photon phase-space distributions at second order in cosmological perturbation theory including the complete polarization information, providing the basis for further numerical studies. As an aside we note that the second-order collision term contains new sources of B-mode polarization and that no polarization persists in the tight-coupling limit.
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.
NASA Astrophysics Data System (ADS)
Farahani, K.; Bahai, H.
2004-07-01
This paper extends the first order formulations presented in Part I to second order methods for relocation of structural natural frequencies from their initial design values to new modified frequencies. The method is based on an inverse formulation and solution algorithm of the eigenvalue problem. Using the second order Taylor's expansion series, the required parameter variation to achieve a desired natural frequency shift for the structure is computed through second order differential or binomial equations. The proposed technique can also incorporate the design constraints or objective functions in the system equations. The formulations are quite generic and applicable to all finite element structures. The accuracy of the proposed methods is tested by conducting several case studies, the results of which demonstrate the validity of the technique for a wide range of practical problems.
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
Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence
NASA Astrophysics Data System (ADS)
Li, Yang; Gao, Zhe; Chen, Jiale
2016-08-01
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.
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
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.
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.
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.
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.
Use of the particle swarm optimization algorithm for second order design of levelling networks
NASA Astrophysics Data System (ADS)
Yetkin, Mevlut; Inal, Cevat; Yigit, Cemal Ozer
2009-08-01
The weight problem in geodetic networks can be dealt with as an optimization procedure. This classic problem of geodetic network optimization is also known as second-order design. The basic principles of geodetic network optimization are reviewed. Then the particle swarm optimization (PSO) algorithm is applied to a geodetic levelling network in order to solve the second-order design problem. PSO, which is an iterative-stochastic search algorithm in swarm intelligence, emulates the collective behaviour of bird flocking, fish schooling or bee swarming, to converge probabilistically to the global optimum. Furthermore, it is a powerful method because it is easy to implement and computationally efficient. Second-order design of a geodetic levelling network using PSO yields a practically realizable solution. It is also suitable for non-linear matrix functions that are very often encountered in geodetic network optimization. The fundamentals of the method and a numeric example are given.
Mean-value second-order uncertainty analysis method: application to water quality modelling
NASA Astrophysics Data System (ADS)
Mailhot, Alain; Villeneuve, Jean-Pierre
Uncertainty analysis in hydrology and water quality modelling is an important issue. Various methods have been proposed to estimate uncertainties on model results based on given uncertainties on model parameters. Among these methods, the mean-value first-order second-moment (MFOSM) method and the advanced mean-value first-order second-moment (AFOSM) method are the most common ones. This paper presents a method based on a second-order approximation of a model output function. The application of this method requires the estimation of first- and second-order derivatives at a mean-value point in the parameter space. Application to a Streeter-Phelps prototype model is presented. Uncertainties on two and six parameters are considered. Exceedance probabilities (EP) of dissolved oxygen concentrations are obtained and compared with EP computed using Monte Carlo, AFOSM and MFOSM methods. These results show that the mean-value second-order method leads to better estimates of EP.
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.
Spectral methods for the wave equation in second-order form
Taylor, Nicholas W.; Teukolsky, Saul A.; Kidder, Lawrence E.
2010-07-15
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semidiscrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multidomain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.
NASA Astrophysics Data System (ADS)
Jayabalan, J.; Singh, Manoranjan P.; Banerjee, Arup; Rustagi, K. C.
2008-01-01
In this paper, we present results of calculations of linear and second-order nonlinear polarizabilities of sector-shaped metallic nanoparticles (hemisphere is a special case) using free electron theory. The dependences of the ground state electron density distribution and polarizabilities on various shape parameters of sector are analyzed. The ground state electron densities near the corners and edges of sector-shaped nanoparticle are very low and do not contribute to the linear and second-order polarizabilities. The second-order polarizability is found to depend strongly on the angle of the sector and is shown to be proportional to the product of an appropriately defined asymmetric volume of the particle and the third power of the electron cloud length.
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Guha, Partha; de Lucas, Javier
2013-03-01
A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geometric way. This allows us to study the transformation of these equations into simpler canonical forms, which solves a gap in the previous literature, and other relevant differential equations, which leads to derive new constants of motion for families of second-order Gambier equations. Additionally, we describe general solutions of certain second-order Gambier equations in terms of particular solutions of Riccati equations, linear systems, and t-dependent frequency harmonic oscillators.
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.
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 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.
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.
Effective second-order susceptibility in photonic crystals mode of centrosymmetric materials
NASA Astrophysics Data System (ADS)
Feigel, A.; Kotler, Z.; Sfez, B.
2002-02-01
A technique for obtaining efficient bulk second-order susceptibility in noncentrosymmetric photonic crystals (PC) made of centrosymmetric materials is discussed. The effect is based on the electric quadrupole effect, strong electromagnetic mode deformation, and nonhomogeneous contribution to volume polarization from different parts of the PC. The required symmetry breaking is introduced on the macroscale of the PC unit cell. The obtained structural χ(2)str is comparable with the second-order susceptibility of ordinary nonlinear materials. Phase matching can be achieved by introducing symmetry modulation (quasi-phase-matching) during fabrication of the PC.
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.
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.
NASA Astrophysics Data System (ADS)
Moore, R. L.; Thompson, M. C.; Robbins, T. S.
1990-03-01
An analysis is presented to calculate scalar permittivity and tensor permeability for ferrite materials from waveguide transmission cavity data. A correct measurement of the permittivity of ferrites and other high dielectric constant materials, requires an extension of current techniques to a second-order perturbational analysis. This second-order correction offsets an apparent frequency dependent dielectric behavior measured during a multimode cavity measurement. The analysis implies that dimensions of ferrite samples to be used in various waveguides (X-Ka bands) must be reduced to a near 0.015-in. cross-sections to eliminate a coupling of permittivity and permeability measurements.
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.
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.
Observation of a motional Stark effect to determine the second-order Doppler effect.
Hagel, G; Battesti, R; Nez, F; Julien, L; Biraben, F
2002-11-11
The high resolution two-photon spectroscopy of hydrogen is often limited by the second-order Doppler effect. To determine this effect, we apply a magnetic field perpendicular to the atomic beam. This field induces a quadratic motional Stark shift proportional, as the second-order Doppler effect, to v(2) (v atomic velocity). For some magnetic field, these two effects are opposite and the total shift due to the atomic velocity is reduced. We present the first observation of this effect for the 1S-3S transition in hydrogen.
First- and second-order error estimates in Monte Carlo integration
NASA Astrophysics Data System (ADS)
Bakx, R.; Kleiss, R. H. P.; Versteegen, F.
2016-11-01
In Monte Carlo integration an accurate and reliable determination of the numerical integration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In contrast to the usual (first-order) error estimator, this second-order estimator can be shown to be not necessarily positive in an actual Monte Carlo computation. We propose an alternative and indicate how this can be computed in linear time without risk of large rounding errors. In addition, we comment on the relatively very slow convergence of the second-order error estimate.
Imaging of biological tissues with pixel-level analysis of second-order susceptibility
NASA Astrophysics Data System (ADS)
Hu, Po-Sheng; Ghazaryan, Ara; Hovhannisyan, Vladimir; Chen, Shean-Jen; Chen, Yang-Fang; Kim, Chang-Seok; Tsai, Tsung-Hua; Dong, Chen-Yuan
2013-03-01
We discuss the recent advances in the development and applications of second-order susceptibility as a contrast mechanism in optical microscopy for biological tissues. We review nonlinear optical methods and approaches for differentiation of tissue structures and discrimination of normal and pathological skin tissues, which have been demonstrated for the potential use in clinical diagnosis. In addition, the potential of second-order susceptibility imaging, encompassing applications in differentiating various types of collagen molecules for clinical diagnosis, is demonstrated. Finally, we discuss future development and application of this technique.
Approximate Controllability of Second-Order Stochastic Differential Equations with Impulsive Effects
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Ren, Yong; Mahmudov, N. I.
Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.
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.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
NASA Astrophysics Data System (ADS)
Jameel, A. F.; Ismail, Ahmad Izani Md
2014-07-01
In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The effectiveness of the algorithm is demonstrated by solving nonlinear second order fuzzy Riccati equation. The results indicate that the method is very effective and simple to apply.
Robust controller designs for second-order dynamic systems - A virtual passive approach
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh
1991-01-01
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 gians 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.
Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass.
Choi, Jiyeon; Bellec, Matthieu; Royon, Arnaud; Bourhis, Kevin; Papon, Gautier; Cardinal, Thierry; Canioni, Lionel; Richardson, Martin
2012-03-15
We demonstrate that direct femtosecond laser writing in silver-containing zinc and gallium phosphate glass enables generation of three-dimensional (3D) optical second-order nonlinear microstructures having an χ(2) value about 2.5 times that of quartz. The proposed physical model involves photo-reduction, photo-dissociation, and migration of silver species within the glass matrix. 3D laser-written second-order nonlinear structures could become a new class of nonlinear optical components. PMID:22446213
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.
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.
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
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)
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…
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 Factor Structure of the MBTI: A Construct Validity Assessment.
ERIC Educational Resources Information Center
Thompson, Bruce; Borrello, Gloria M.
1986-01-01
Factor adequacy and other results based on data from college students (N=359) provided positive evidence regarding the construct validity of the Myers-Briggs Type Indicator (MBTI). Second order factor analysis supported the appropriateness of the MBTI item weighting procedures. (Author/ABB)
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…
Second-order cascading in third-order nonlinear optical processes
NASA Astrophysics Data System (ADS)
Meredith, Gerald R.
1982-12-01
Because cascaded second-order processes make substantial qualitative and quanitative differences to the results of third-order nonlinear optical experiments, a formalism for their treatment is presented. The symmetry dictates concerning the occurrence and relationships of magnitudes of cascading are tabulated for the higher symmetry crystal classes. Angular momentum considerations are applied to the situations allowing circularly polarized light waves.
Do Children with Autism Perceive Second-Order Relational Features? The Case of the Thatcher Illusion
ERIC Educational Resources Information Center
Rouse, Helen; Donnelly, Nick; Hadwin, Julie A.; Brown, Tony
2004-01-01
Background: This study presents two experiments that investigated whether children with autism were susceptible to the Thatcher illusion. Perception of the Thatcher illusion requires being able to compute second-order configural relations for facial stimuli. Method: In both experiments children with autism were matched for non-verbal and verbal…
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…
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.
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…
Validity of a Measure of Children's Health Locus of Control: A Second-Order Factor Analysis.
ERIC Educational Resources Information Center
Thompson, Bruce; And Others
The study reported in this paper investigated the structure of the health locus of control beliefs of elementary school children using second-order factor analysis and the measurement characteristics of the Multidimensional Health Locus of Control (MHLC) Scales. Changes of wording were made in 10 of the MHLC Scales items in order to improve the…
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).…
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…
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…
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
NASA Technical Reports Server (NTRS)
Pflaum, Christoph
1996-01-01
A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.
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…
Multidimensional first and second order symmetric strang splitting for hyperbolic systems
Kucharik, Milan; Wendroff, Burton
2008-01-01
We propose an algebraic basis for symmetric Strang splitting for first and second order accurate schemes for hyperbolic systems in N dimensions. Examples are given for two and three dimensions. Optimal stability is shown for symmetric systems. Lack of strong stability is shown for a non-symmetric example. Some numerical examples are presented for some Euler-like constant coefficient problems.
NASA Astrophysics Data System (ADS)
Sun, Yuan Gong; Wong, James S. W.
2007-10-01
We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities: where , p(t) is positive and differentiable, [alpha]1>...>[alpha]m>1>[alpha]m+1>...>[alpha]n. No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n=1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993) 813-817], Wong [J.S.W. Wong, Oscillation criteria for a forced second linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240], Sun, Ou and Wong [Y.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a linear second order differential equation, Comput. Math. Appl. 48 (2004) 1693-1699] for the linear equation, Nazr [A.H. Nazr, Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for the superlinear equation, and Sun and Wong [Y.G. Sun, J.S.W. Wong, Note on forced oscillation of nth-order sublinear differential equations, JE Math. Anal. Appl. 298 (2004) 114-119] for the sublinear equation.
Enhancement of linear and second-order hyperpolarizabilities in wedge-shaped nanostructures
NASA Astrophysics Data System (ADS)
Jayabalan, J.; Singh, Manoranjan P.; Rustagi, K. C.
2003-08-01
Analytical solutions for the wave functions for free electrons inside a wedge-shaped quantum dot are reported. For silver wedge-shaped quantum dots, linear and second-order hyperpolarizabilities are calculated for various apex angles. It is found that linear and nonlinear hyperpolarizabilities both increase with decreasing apex angle.
Time domain reflectometry waveform analysis with second order bounded mean oscillation
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
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
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.
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
2014-04-01
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.
Cheng, Juan; Shu, Chi-Wang
2014-09-01
In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.
Deffayet, C.; Deser, S.; Esposito-Farese, G.
2009-09-15
We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.
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.
Second-order nonlinear optical property and crystal growth of chalcone derivatives
NASA Astrophysics Data System (ADS)
Goto, Yoshitaka; Hayashi, Akio; Zhang, G. J.; Nakayama, M.; Kitaoka, Yasuo; Sasaki, Takatomo; Watanabe, Toshiyuki; Miyata, Seizo; Honda, K.; Goto, Midori
1990-12-01
300 types of "chalcone" derivatives excellent in blue light region transparency were synthesized to investigate on second harmonic generation(SHG). The results of investigation suggested that an alkoxy group, an alkylthio group and halogen were effective as a substituent. Besides, a single crystal with respect to 4-ethoxy-4 ' -methoxychalcone(C-607) and 1- (2-thienyl ) -3- (4- fflethylphenyl)propene-l-one(TC-28) were grown. The obtained crystals were high quality and large size over 5 cm. We also had the first success in continuous SHG on a intracavity of the microchip laser using this single crystal "chalcone".
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.
NASA Astrophysics Data System (ADS)
Morshed, Khandakar Niaz; Dasi, Lakshmi Prasad
2013-05-01
We study the variations in second-order velocity structure functions (SFs) in the strongly anisotropic turbulent flow past a backward facing step. Time-resolved particle image velocimetry measurements were taken in a stationary turbulent flow past a backward facing step at Reynolds numbers 13,600, 9,000, and 5,500 based on the maximum velocity and step size. Large-scale anisotropic properties of the flow along with local small-scale turbulence characteristics were characterized in detail. Seven interrogation points distributed along points of different large-scale anisotropic characteristics systematically probed the influence of large-scale anisotropy on the second-order SFs. The velocity SFs at each interrogation point represent variance of velocity increments in the streamwise, transverse (wall normal), and the two principle directions of local deformation field. Logarithmic derivatives of the SFs captured the scale-dependent scaling characteristics at the small scales. Measurements revealed a strongly anisotropic large-scale flow with an intense turbulent free-shear layer downstream of the step. Comparison among second-order SFs reveals a mechanistic relationship between the mean flow deformation field, defined by the principle axis of deformation and the magnitude of eigenvalues, to the characteristic influence on SF scaling in the dissipative and non-dissipative scales. Specifically, we report that non-dissipative scaling between orthogonal directions does not differentially saturate if these directions are aligned with the principle axis of deformation. We also show that the relative root mean square of velocity components influences the level of exponent saturation in the dissipative scale regime.
NASA Astrophysics Data System (ADS)
Li, Zhi-Hui; Ma, Qiang; Cui, Junzhi
2016-06-01
The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment.
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.
Comprehensive investigation about the second order term of thermodynamic perturbation expansion
NASA Astrophysics Data System (ADS)
Zhou, Shiqi; Solana, J. R.
2009-10-01
Monte Carlo simulations are carried out for the second order term in the thermodynamic perturbation expansion around a hard sphere reference fluid. The sample potentials considered cover a wide spectrum: From two frequently employed, namely hard sphere plus square well potential and hard core attractive Yukawa potential, to two kinds of repulsive potentials, namely hard sphere plus square shoulder potential and hard sphere plus triangle shoulder potential; the investigated potential range also extends from extremely short range to rather long range. The obtained simulation data are used to evaluate performance of two theoretical approaches, i.e., a traditional macroscopic compressibility approximation (MCA) and a recent coupling parameter expansion. Extensive comparison shows that the coupling parameter expansion provides a reliable method for accurately calculating the second order term of the high temperature series expansion, while the widely accepted MCA fails quantitatively or even qualitatively for most of the situations investigated.
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.
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.
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.
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.
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 cone programming formulation for consolidation analysis of saturated porous media
NASA Astrophysics Data System (ADS)
Zhang, Xue; Sheng, Daichao; Sloan, Scott W.; Krabbenhoft, Kristian
2016-07-01
In this paper, the incremental problem for consolidation analysis of elastoplastic saturated porous media is formulated and solved using second-order cone programming. This is achieved by the application of the Hellinger-Reissner variational theorem, which casts the governing equations of Biot's consolidation theory as a min-max optimisation problem. The min-max problem is then discretised using the finite element method and converted into a standard second-order cone programming problem that can be solved efficiently using modern optimisation algorithms (such as the primal-dual interior-point method). The proposed computational formulation is verified against a number of benchmark examples and also applied to simulate the construction of a road embankment on soft clay.
Stable surface relief grating with second-order nonlinearity on urethane urea copolymer film
NASA Astrophysics Data System (ADS)
Che, Yanlong; Sugihara, Okihiro; Fujimura, Hisashi; Okamoto, Naomichi; Egami, Chikara; Kawata, Yoshimasa; Tsuchimori, Masaaki; Watanabe, Osamu
2003-01-01
Surface relief gratings (SRGs) on azobenzene-contained urethane-urea copolymer film with second-order nonlinearity are fabricated by laser-interferometric method. The surface relief structures are obtained upon exposure an interference pattern of a CW Ar + laser and a single-pulse UV laser. The SRG is thermally stable even at Tg of the copolymer. The mechanism of the stability is investigated by comparing the pulse UV laser inscribed SRG. It is suggested that laser ablation of the copolymer surface by the high-power laser irradiation is taken into account. Second-order nonlinearity is induced by corona-poling process after grating formation. Diffraction of second-harmonic generation (SHG) is observed by inserting a fundamental beam, which is in agreement with vector diagram.
Improved Global Soft Decision Incorporating Second-Order Conditional MAP in Speech Enhancement
NASA Astrophysics Data System (ADS)
Kum, Jong-Mo; Chang, Joon-Hyuk
In this paper, we propose a novel method based on the second-order conditional maximum a posteriori (CMAP) to improve the performance of the global soft decision in speech enhancement. The conventional global soft decision scheme is found through investigation to have a disadvantage in that the global speech absence probability (GSAP) in that scheme is adjusted by a fixed parameter, which could be a restrictive assumption in the consecutive occurrences of speech frames. To address this problem, we devise a method to incorporate the second-order CMAP in determining the GSAP, which is clearly different from the previous approach in that not only current observation but also the speech activity decisions of the previous two frames are exploited. Performances of the proposed method are evaluated by a number of tests in various environments and show better results than previous work.
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.
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.
Second-order two-scale method for bending behaviors of composite plate with periodic configuration
NASA Astrophysics Data System (ADS)
Zhu, Guoqing; Cui, Junzhi
2010-06-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
Second-Order Two-Scale Method for Bending Behaviors of Composite Plate with Periodic Configuration
NASA Astrophysics Data System (ADS)
Zhu, Guoqing; Cui, Junzhi
2010-05-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator
NASA Astrophysics Data System (ADS)
Doron, A.; Tamir, I.; Mitra, S.; Zeltzer, G.; Ovadia, M.; Shahar, D.
2016-02-01
In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.
Yield criteria for porous media in plane strain: second-order estimates versus numerical results
NASA Astrophysics Data System (ADS)
Pastor, Joseph; Ponte Castañeda, Pedro
2002-11-01
This Note presents a comparison of some recently developed "second-order" homogenization estimates for two-dimensional, ideally plastic porous media subjected to plane strain conditions with corresponding yield analysis results using a new linearization technique and systematically optimized finite elements meshes. Good qualitative agreement is found between the second-order theory and the yield analysis results for the shape of the yield surfaces, which exhibit a corner on the hydrostatic axis, as well as for the dependence of the effective flow stress in shear on the porosity, which is found to be non-analytic in the dilute limit. Both of these features are inconsistent with the predictions of the standard Gurson model. To cite this article: J. Pastor, P. Ponte Castañeda, C. R. Mecanique 330 (2002) 741-747.
Second-order discretization in space and time for radiation hydrodynamics
Edwards, J. D.; Morel, J. E.; Lowrie, R. B.
2013-07-01
We present a method for solving the equations of radiation hydrodynamics that is second-order accurate in space and time. This method combines the MUSCL-Hancock method for solving the Euler equations with the TR/BDF2 scheme in time for solving the equations of radiative transfer. We use an LDFEM to discretize the radiative transfer equations in space, which, though uncommon for radiation diffusion calculations, is a standard for radiation transport applications. We address the challenges inherent to using different spatial discretizations for the hydrodynamics and radiation and demonstrate how these may be overcome. We define our method for a 1-D model of compressible fluid dynamics coupled with grey radiation diffusion. Using the method of manufactured solutions, we show that the method is second-order accurate in space and time for both the equilibrium diffusion and streaming limit. (authors)
NASA Astrophysics Data System (ADS)
Shay, W. A.; Schultz, D. H.
1985-05-01
The present investigation is concerned with a problem described by Schultz (1973), who provided a numerical solution for the flow of a fluid in a heated closed cavity. The procedures employed by various investigators to obtain numerical results for this problem are evaluated. No evidence is found that any one of the considered methods have produced results for large Rayleigh numbers and small Prandtl numbers with small grids and second order boundary approximations. The current investigation provides a method which produces such results. The selected procedure involves the use of a rectangular array of nodes which is placed over the region considered in the problem. The solution of the obtained difference equations is discussed, and the results are presented in a number of tables and graphs. It is found that the employed second-order method is superior to the method used by Schultz.
Atmospheric Effects of Second Order on Cosmic Rays Intensity Measured at the South Hemisphere
NASA Astrophysics Data System (ADS)
Alvarez-Castillo, Jesús; Francisco Valdes-Galicia, Jose
In this work, we show atmospheric effects of second order on the cosmic rays intensity observed in the South Hemisphere; analysis is using meteorologic data of the TRMM satelite and others of the NOAA, and free data of the surface detectors from Pierre Auger Observatory with a resolution of 15 minutes. The time period analized was from 2006-2011. The methodology consisted in analize the anomalies in atmospheric pressure and in the corrected cosmic rays data for barometric effects considering a sigma level >|2|, the results reflecting a second order variation in the atmospheric pressure, applying digital filters and the spectrum of the data showed a trend that correspond to periodicities of the rain and electric field.
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.
Temporal second-order coherence function for displaced-squeezed thermal states
NASA Astrophysics Data System (ADS)
Alexanian, Moorad
2016-05-01
We calculate the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz. a displaced-squeezed thermal state. The calculation involves first dynamical generation at time t of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time ? apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on ?, via ?, for the given Gaussian state parameters, Gaussian state preparation time t, and average number ? of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in ? rather than an exponential one as is the case for general, displaced-squeezed thermal states.
Optical implementation of a second-order translation-invariant network algorithm
NASA Astrophysics Data System (ADS)
Horan, Paul; Jennings, Andrew; Kelly, Brian; Hegarty, John
1993-03-01
Higher-order networks, particularly second-order translation-invariant networks, are introduced, and their suitability for optical implementation is outlined. The algorithm is implemented with a conventional liquid-crystal display, permitting on-line learning and updating of weights. The basic operation of the optical system is demonstrated, and the ability of the system to adapt to system nonuniformities is illustrated. The implementation with an integrated optoelectronic array of asymmetric Fabry-Perot modulators containing a GaAs/AlGaAs multiple-quantum-well active region is described. The principles of operation and operating characteristics of the device array are outlined. The use of the array in an optical system to calculate the autocorrelation matrix necessary for a second-order network is demonstrated.
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.
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.
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
2016-03-01
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. PMID:26844587
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.
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. PMID:11539071
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.
Singh, Sanjay; Caron, Luana; D'Souza, Sunil Wilfred; Fichtner, Tina; Porcari, Giacomo; Fabbrici, Simone; Shekhar, Chandra; Chadov, Stanislav; Solzi, Massimo; Felser, Claudia
2016-05-01
In contrast to rare-earth-based materials, cheaper and more environmentally friendly candidates for cooling applications are found within the family of Ni-Mn Heusler alloys. Initial interest in these materials is focused on the first-order magnetostructural transitions. However, large hysteresis makes a magnetocaloric cycle irreversible. Alternatively, here it is shown how the Heusler family can be used to optimize reversible second-order magnetic phase transitions for magnetocaloric applications. PMID:26928954
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.
Observation of second-order kinetic damage in sodium salicylate due to soft x rays
NASA Astrophysics Data System (ADS)
Husk, D. E.; Tarrio, C.; Benitez, E. L.; Schnatterly, S. E.
1991-10-01
We have observed the dose dependence of the bulk quantum efficiency for luminescence of sodium salicylate as a function of the photon energy from 7 to 150 eV. We show that the damage is a second-order or higher kinetic process in the number of electron-hole pairs and is not reversible. We predict that the threshold for damage occurs at 7.2 eV, or twice the band gap of sodium salicylate.
Singh, Sanjay; Caron, Luana; D'Souza, Sunil Wilfred; Fichtner, Tina; Porcari, Giacomo; Fabbrici, Simone; Shekhar, Chandra; Chadov, Stanislav; Solzi, Massimo; Felser, Claudia
2016-05-01
In contrast to rare-earth-based materials, cheaper and more environmentally friendly candidates for cooling applications are found within the family of Ni-Mn Heusler alloys. Initial interest in these materials is focused on the first-order magnetostructural transitions. However, large hysteresis makes a magnetocaloric cycle irreversible. Alternatively, here it is shown how the Heusler family can be used to optimize reversible second-order magnetic phase transitions for magnetocaloric applications.
An approach for generation of second order RC-active filters.
NASA Technical Reports Server (NTRS)
Dunn, W. R., Jr.
1972-01-01
It is shown that node (or loop) matrix equations can be written which yield second order low-pass, band-pass, and high-pass network functions. Networks corresponding to the equations can in turn be formulated by inspection of the equations. The networks employ ideal VCT or CVT sources which can be physically realized using transistors and/or operational amplifiers. The technique yields several structures which are believed to be new.
Solution of second-order linear system by matched asymptotic expansions
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1982-01-01
Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also 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.
Sherman, L.L.; Taylor, A.C. III; Hou, G.W.; Korivi, V.M.
1996-12-01
The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained. The basic equations for second-order sensitivity derivatives are presented, which results in a comparison of four different methods. Each of these four schemes for second-order derivatives requires that large systems are solved first for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first-order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent-flow example. In each of these two sample problems, three dependent variables (coefficients of lift, drag, and pitching-moment) and six independent variables (three geometric-shape and three flow-condition design variables) are considered. Several different procedures are tested, and results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method. Furthermore, it is at least two to four times faster than central finite differences, without an overwhelming penalty in computer memory. 23 refs., 14 tabs.
Mitigation of Second-Order Ionospheric Error for Real-Time PPP Users in Europe
NASA Astrophysics Data System (ADS)
Abdelazeem, Mohamed
2016-07-01
Currently, the international global navigation satellite system (GNSS) real-time service (IGS-RTS) products are used extensively for real-time precise point positioning and ionosphere modeling applications. The major challenge of the dual frequency real-time precise point positioning (RT-PPP) is that the solution requires relatively long time to converge to the centimeter-level accuracy. This relatively long convergence time results essentially from the un-modeled high-order ionospheric errors. To overcome this challenge, a method for the second-order ionospheric delay mitigation, which represents the bulk of the high-order ionospheric errors, is proposed for RT-PPP users in Europe. A real-time regional ionospheric model (RT-RIM) over Europe is developed using the IGS-RTS precise satellite orbit and clock products. GPS observations from a regional network consisting of 60 IGS and EUREF reference stations are processed using the Bernese 5.2 software package in order to extract the real-time vertical total electron content (RT-VTEC). The proposed RT-RIM has spatial and temporal resolution of 1º×1º and 15 minutes, respectively. In order to investigate the effect of the second-order ionospheric delay on the RT-PPP solution, new GPS data sets from another reference stations are used. The examined stations are selected to represent different latitudes. The GPS observations are corrected from the second-order ionospheric errors using the extracted RT-VTEC values. In addition, the IGS-RTS precise orbit and clock products are used to account for the satellite orbit and clock errors, respectively. It is shown that the RT-PPP convergence time and positioning accuracy are improved when the second-order ionospheric delay is accounted for.
Second-order virial expansion for an atomic gas in a harmonic waveguide
NASA Astrophysics Data System (ADS)
Kristensen, Tom; Leyronas, Xavier; Pricoupenko, Ludovic
2016-06-01
The virial expansion for cold two-component Fermi and Bose atomic gases is considered in the presence of a waveguide and in the vicinity of a Feshbach resonance. The interaction between atoms and the coupling with the Feshbach molecules is modeled using a quantitative separable two-channel model. The scattering phase shift in an atomic waveguide is defined. This permits us to extend the Beth-Uhlenbeck formula for the second-order virial coefficient to this inhomogeneous case.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps.
NASA Astrophysics Data System (ADS)
Johnson, Aaron P.; Kingdom, Frederick A. A.; Baker, Curtis L.
2005-10-01
Spatial filters that mimic receptive fields of visual cortex neurons provide an efficient representation of achromatic image structure, but the extension of this idea to chromatic information is at an early stage. Relatively few studies have looked at the statistical relationships between the modeled responses to natural scenes of the luminance (LUM), red-green (RG), and blue-yellow (BY) postreceptoral channels of the primate visual system. Here we consider the correlations among these channel responses in terms of pixel, first-order, and second-order information. First-order linear filtering was implemented by convolving the cosine-windowed images with oriented Gabor functions, whose gains were scaled to give equal amplitude response across spatial frequency to random fractal images. Second-order filtering was implemented via a filter-rectify-filter cascade, with Gabor functions for both first- and second-stage filters. Both signed and unsigned filter responses were obtained across a range of filter parameters (spatial frequency, 2-64 cycles/image orientation, 0-135°). The filter responses to the LUM channel images were larger than those for either RG or BY channel images. Cross correlations between the first-order channel responses and between the first- and second-order channel responses were measured. Results showed that the unsigned correlations between first-order channel responses were higher than expected on the basis of previous studies and that first-order channel responses were highly correlated with LUM, but not with RG or BY, second-order responses. These findings imply that course-scale color information correlates well with course-scale changes of fine-scale texture.
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.
A second-order pressure-correction method for viscous incompressible flow
NASA Astrophysics Data System (ADS)
Vankan, J.
An ADI scheme with pressure correction which is second order consistent in space and time is presented. It is shown that the pressure correction method in a system of constrained ordinary differential equations under reasonably weak assumptions leads to a solution with 0 (Delta t sq) accuracy. It is proved that in a linearized simplified case pressure correction does not affect the unconditional stability of the underlying scheme. Application to flow in a glass furnace is illustrated.
A preliminary compressible second-order closure model for high speed flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1989-01-01
A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.
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.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps. PMID:27410804
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.
Assessment of the second-order perturbative corrections to PNOF5
NASA Astrophysics Data System (ADS)
Piris, M.; Ruipérez, F.; Matxain, J. M.
2014-03-01
In a recent paper (J. Chem. Phys. 139, 064111, 2013), an antisymmetrised product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by means of the occupation numbers was used to generate the Piris natural orbital functional 5 (PNOF5). This functional describes most of the non-dynamical effects, but also an important part of the intrapair (intrageminal) electron correlation. Second-order corrections to the generating PNOF5 wave function were derived using the multiconfigurational perturbation theory size consistent at the second order (SC2-MCPT) to include the missing interpair (intergeminal) electron correlation. A modified version of the SC2-MCPT involving double excitations only from different geminals was introduced and denoted as PNOF5-PT2. In this paper, the ground-state energies of 36 closed-shell species belonging to the G2/97 test set of molecules are studied by the PNOF5-PT2 and PNOF5-SC2-MCPT methods. The numerical performance of both methods on eight dimers, with different strength of hydrogen bonds, and 13 isogyric reactions is also assessed. The results are in reasonable agreement with those obtained using the complete active space second-order perturbation theory and coupled-cluster method with singles, doubles, and noniterative triples corrections.
NASA Astrophysics Data System (ADS)
Sigalotti, L. Di G.; Klapp, J.
1997-03-01
A new second-order Eulerian code is compared with a version of the TREESPH code formulated by Hernquist and Katz (1989) for the standard isothermal collapse test. The results indicate that both codes produce a very similar evolution ending with the formation of a protostellar binary system. Contrary to previous first-order calculations, the binary forms by direct fragmentation, i.e. without the occurrence of an intermediate bar configuration. A similar trend was also found in second-order Eulerian calculations (Myhill and Boss 1993), suggesting that it is a result of the decreased numerical diffusion associated with the new second-order schemes. The results have also implications on the differences between the finite difference methods and the particle method SPH, raised by Monaghan and Lattanzio (1986) for this problem. In particular, the Eulerian calculation does not result in a run-away collapse of the fragments, and as found in the TREESPH evolution, they also show a clear tendency to get closer together. In agreement with previous SPH calculations (Monaghan and Lattanzio 1986), the results of the long term evolution with code TREESPH show that the gravitational interaction between the two fragments may become important, and eventually induce the binary to coalesce. However, SPH calculations by Bate, Bonnell and Price (1995) indicate that the two fragments, after having reached a minimum separation distance, do not merge but continue to orbit each other.
An Eulerian scheme for the second-order approximation of subsurface transport moments
NASA Astrophysics Data System (ADS)
Naff, R. L.
1994-05-01
The moments of a conservative tracer cloud migrating in a mean uniform flow field are estimated using an operator approximation scheme; results are presented for the second, third, and fourth central moments in the mean flow direction. It is assumed that the spatially variable flow field, and therefore the tracer migration problem itself, is amenable to a probabilistic description; the effects of local dispersion on cloud migration are neglected in this study. Variation in the flow field is assumed to be the result of spatial variation in the hydraulic conductivity; spatial variation in porosity is assumed negligible. The operator approximation scheme, as implemented in this study, is second-order correct, which requires a second-order correct approximation of the velocity field correlation structure. Because estimation of the velocity correlation structure is decidedly the most difficult aspect of second-order analysis, an ad hoc extension of the imperfectly stratified approximation developed earlier is implemented for this purpose. The first-order approximation resulting from the operator expansion scheme is equivalent to small perturbation Eulerian results presented earlier (Naff, 1990, 1992). The infinite-order approximation resulting from this scheme is equivalent to the exponential operator results obtained by Van Kampen (1976).
Second-order autoshaped key pecking based on an auditory stimulus.
Burt, J S; Westbrook, R F
1980-11-01
In Experiment 1, pigeons were exposed either to paired or to unpaired presentations of a tone and grain, and then to paired presentations of a keylight with the tone. Substantial second-order conditioned pecking to the keylight was produced in the birds that had received paired presentations of tone and grain. In Experiment 2, second-order pecking to the keylight increased in probability across four groups that had received, respectively, 20, 80, 140, or 200 paired presentations of tone and grain. In Experiment 3, the amount of pecking directed towards a keylight which predicted the first-order, tone CS was as substantial in birds without a prior history of key pecking as in birds with such a history. A further experiment failed to discover any significant differences in the levels of second-order pecking to a keylight paired with a first-order tone CS or with a first-order keylight CS. Thus, an auditory signal that does not itself support pecking may enable a localized visual stimulus to evoke key pecking.
NASA Astrophysics Data System (ADS)
Ahn, Kyoung-Pyo; Ishikawa, Ryo; Saitou, Akira; Honjo, Kazuhiko
This paper describes the characteristic of negative group delay (NGD) circuits for various configurations including first-order, distributed, and second-order RC circuit configurations. This study includes locus, magnitude, and phase characteristics of the NGD circuits. The simplest NGD circuit is available using first-order RC or RL configuration. As an example of distributed circuit configuration, it is verified that losses in a distributed line causes NGD characteristic at higher cut-off band of a coupled four-line bandpass filter. Also, novel wideband NGD circuits using second-order RC configuration, instead of conventional RLC configuration, are proposed. Adding a parallel resistor to a parallel-T filter enables NGD characteristic to it. Also, a Wien-Robinson bridge is modified to have NGD characteristic by controlling the voltage division ratio. They are fabricated on MMIC substrate, and their NGD characteristics are verified with measured results. They have larger insertion loss than multi-stage RLC NGD circuits, however they can realize second-order NGD characteristic without practical implementation of inductors.
Chen, Chao-Yin; Bonham, Ann C; Dean, Caron; Hopp, Francis A; Hillard, Cecilia J; Seagard, Jeanne L
2010-12-01
In prior studies, we found that activation of cannabinoid-1 receptors in the nucleus tractus solitarii (NTS) prolonged baroreflex-induced sympathoinhibition in rats. In many regions of the central nervous system, activation of cannabinoid-1 receptors presynaptically inhibits γ-aminobutyric acid (GABA) release, disinhibiting postsynaptic neurons. To determine if cannabinoid-1 receptor-mediated presynaptic inhibition of GABA release occurs in the NTS, we recorded miniature inhibitory postsynaptic currents in anatomically identified second-order baroreceptive NTS neurons in the presence of ionotropic glutamate receptor antagonists and tetrodotoxin. The cannabinoid-1 receptor agonists, WIN 55212-2 (0.3-30 μM) and methanandamide (3 μM) decreased the frequency of miniature inhibitory postsynaptic currents in a concentration-dependent manner, an effect that was blocked by the cannabinoid-1 receptor antagonist, N-(piperidin-1-yl)-5-(4-iodophenyl)-1-(2,4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide (AM 251, 5 μM). Importantly, depolarization of second-order baroreceptive neurons decreased the frequency of miniature inhibitory postsynaptic currents; an effect which was blocked by the cannabinoid-1 receptor antagonist. The data indicate that depolarization of second-order baroreceptive NTS neurons induces endocannabinoid release from the neurons, leading to activation of presynaptic cannabinoid-1 receptors, inhibition of GABA release and subsequent enhanced baroreflex signaling in the NTS. The data suggest that endocannabinoid signaling in the NTS regulates short-term synaptic plasticity and provide a mechanism for endocannabinoid modulation of central baroreflex control.
Effects of Second-Order Hydrodynamic Forces on Floating Offshore Wind Turbines
Duarte, T.; Sarmento, A. J. N. A.; Jonkman, J.
2014-04-01
Relative to first-order, second-order wave-excitation loads are known to cause significant motions and additional loads in offshore oil and gas platforms. The design of floating offshore wind turbines was partially inherited from the offshore oil and gas industry. Floating offshore wind concepts have been studied with powerful aero-hydro-servo-elastic tools; however, most of the existing work on floating offshore wind turbines has neglected the contribution of second-order wave-excitation loads. As a result, this paper presents a computationally efficient methodology to consider these loads within FAST, a wind turbine computer-aided engineering tool developed by the National Renewable Energy Laboratory. The method implemented was verified against the commercial OrcaFlex tool, with good agreement, and low computational time. A reference floating offshore wind turbine was studied under several wind and wave load conditions, including the effects of second-order slow-drift and sum-frequency loads. Preliminary results revealed that these loads excite the turbine's natural frequencies, namely the surge and pitch natural frequencies.
Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene.
Wu, Sanfeng; Mao, Li; Jones, Aaron M; Yao, Wang; Zhang, Chuanwei; Xu, Xiaodong
2012-04-11
Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, and optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here, we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable second order nonlinear susceptibility χ((2)) once an in-plane electric field is applied. χ((2)) can be electrically tuned from 0 to ~10(5) pm/V, 3 orders of magnitude larger than the widely used nonlinear crystal AgGaSe(2). We show that the unusually large χ((2)) arise from two different quantum enhanced two-photon processes thanks to the unique electronic spectrum of BLG. The tunable electronic bandgap of BLG adds additional tunability on the resonance of χ((2)), which corresponds to a tunable wavelength ranging from ~2.6 to ~3.1 μm for the up-converted photon. Combined with the high electron mobility and optical transparency of the atomically thin BLG, our scheme suggests a new regime of nonlinear photonics based on BLG. PMID:22369519
Treatment of Second Order Structures of Protein on Medical Equipments Using Oxygen Plasma
NASA Astrophysics Data System (ADS)
Hayashi, Nobuya; Kitazaki, Satoshi; Goto, Masaaki; Yagyu, Yoshihito; Yonesu, Akira
2009-10-01
Removal of proteins from the surface of medical equipments are attempted using an RF plasma. Oxygen gas is introduced into a vacuum chamber with dimensions of 450 mm in length, 200 mm in diameter and 20L of capacity. When an RF power (13.56 MHz, 60W) is applied to an ICP type antenna, oxygen radicals (atomic oxygen and excited oxygen molecule) are produced below the antenna. The characteristics of removing protein from the medical equipments was investigated using casein and heat-resistive keratin proteins. Initial concentration of the proteins on a CaF2 substrate is several mg/cm2. The treatment effect of proteins is determined by the peak height of chemical bonds in amide and second order structures appeared on FTIR spectra. The second order structure of a protein such as alpha-helix and beta-sheet are decomposed with the treatment period. Complete treatment of proteins including the second order structure requires several hours avoiding the damage to medical equipments.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
In Part I of this work, an improved "second-order" homogenization theory was developed. This new theory makes use of generalized secant moduli that are intermediate between the standard secant and tangent moduli of the nonlinear phases, and that depend not only on the averages, or first-moments of the fields in the phases, but also on the second-moments of the field fluctuations, or phase covariance tensors. In this article, the theory, which is known to be exact to second-order in the heterogeneity contrast, is applied to the special cases of rigidly reinforced and porous materials. These are cases corresponding to infinite contrast where fairly explicit analytical expressions of the Hashin-Shtrikman and self-consistent-type may be generated for nonlinear composites. The results show that the new theory improves on the earlier theory (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) in at least two ways. First, the new theory satisfies rigorous bounds, even near the percolation limit, where field fluctuations become important, and the earlier second-order theory had been found to fail. Second, the new theory predicts fully compressible behavior for porous materials with an incompressible matrix phase, where the earlier theory had also been found to fail. In addition, the new estimates are found to be in better agreement with numerical simulations available from the literature.
Second-order theory for nonlinear composites and application to isotropic constituents
NASA Astrophysics Data System (ADS)
Idiart, Martín I.; Danas, Kostas; Ponte Castañeda, Pedro
2006-10-01
New prescriptions are proposed for the 'reference' fields in the context of the 'second-order' nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737-757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, 'second-order' estimates of the Hashin-Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered. To cite this article: M.I. Idiart et al., C. R. Mecanique 334 (2006).
Effect of Second-Order Hydrodynamics on Floating Offshore Wind Turbines: Preprint
Roald, L.; Jonkman, J.; Robertson, A,; Chokani, N.
2013-07-01
Offshore winds are generally stronger and more consistent than winds on land, making the offshore environment attractive for wind energy development. A large part of the offshore wind resource is however located in deep water, where floating turbines are the only economical way of harvesting the energy. The design of offshore floating wind turbines relies on the use of modeling tools that can simulate the entire coupled system behavior. At present, most of these tools include only first-order hydrodynamic theory. However, observations of supposed second-order hydrodynamic responses in wave-tank tests performed by the DeepCwind consortium suggest that second-order effects might be critical. In this paper, the methodology used by the oil and gas industry has been modified to apply to the analysis of floating wind turbines, and is used to assess the effect of second-order hydrodynamics on floating offshore wind turbines. The method relies on combined use of the frequency-domain tool WAMIT and the time-domain tool FAST. The proposed assessment method has been applied to two different floating wind concepts, a spar and a tension-leg-platform (TLP), both supporting the NREL 5-MW baseline wind turbine. Results showing the hydrodynamic forces and motion response for these systems are presented and analysed, and compared to aerodynamic effects.
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.
Wang, Jing; Zhu, Shijun; Wang, Haiyan; Cai, Yangjian; Li, Zhenhua
2016-05-30
Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications. PMID:27410089
Ethanol Self-Administration in Mice under a Second-Order Schedule
Lamb, Richard J.; Pinkston, Jonathan W.; Ginsburg, Brett C.
2015-01-01
Long Fixed-Interval (FI) schedules, particularly second-order schedules, can engender substantial responding before drug or ethanol delivery that is uninfluenced by the direct effects of the drug or ethanol. Thus, these schedules can be used to study the effects of medications upon drug- or ethanol-seeking, uninfluenced by the direct effects of the self-administered drug or ethanol. Long FI second-order schedules are frequently used in primates and occasionally in rats. Under second-order schedules, completion of one response requirement, e.g., a Fixed Ratio 10 (FR10:S), produces a brief stimulus presentation, e.g., a 1-sec 80-dB 4-kHZ tone, and this FR10:S serves as the response unit under another schedule, e.g., a FI 1800-sec. Thus, the first FR10 completed after 1800 sec would result in delivery both of the tone and of reinforcement, e.g., 10 × 0.01 mL 16% (w/v) ethanol. To examine if such schedules could be effectively used in mice, which have advantages in neurobiological and genetic studies, we trained eight C57BL/6J mice to respond under the schedule just described. This schedule maintained substantial responding. The temporal pattern of behavior was typical of an FI schedule with responding accelerating across the interval. We also examined the effects of acute and chronic administration of fluvoxamine on this responding, and these were modest. Finally, we examined responding when alcohol and/or tone deliveries were withheld, and found that extinction occurred most rapidly when both were withheld. This work demonstrates that long FI schedules of ethanol delivery may be useful in studying ethanol seeking in mice. PMID:26254963
NASA Astrophysics Data System (ADS)
Di G. Sigalotti, L.; Klapp, J.
1997-03-01
A new second-order Eulerian code is compared with a version of the TREESPH code formulated by Hernquist & Katz (1989ApJS...70..419H) for the standard isothermal collapse test. The results indicate that both codes produce a very similar evolution ending with the formation of a protostellar binary system. Contrary to previous first-order calculations, the binary forms by direct fragmentation, i.e., without the occurrence of an intermediate bar configuration. A similar trend was also found in recent second-order Eulerian calculations (Myhill & Boss 1993ApJS...89..345M), suggesting that it is a result of the decreased numerical diffusion associated with the new second-order schemes. The results have also implications on the differences between the finite difference methods and the particle method SPH, raised by Monaghan & Lattanzio (1986A&A...158..207M) for this problem. In particular, the Eulerian calculation does not result in a run-away collapse of the fragments, and as found in the TREESPH evolution, they also show a clear tendency to get closer together. In agreement with previous SPH calculations (Monaghan & Lattanzio 1986A&A...158..207M), the results of the long term evolution with code TREESPH show that the gravitational interaction between the two fragments may become important, and eventually induce the binary to coalesce. However, most recent SPH calculations (Bate, Bonnell & Price 1995MNRAS.277..362B ) indicate that the two fragments, after having reached a minimum separation distance, do not merge but continue to orbit each other.
NASA Astrophysics Data System (ADS)
Ren, Xinguo; Rinke, Patrick; Scuseria, Gustavo E.; Scheffler, Matthias
2013-07-01
We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as ``renormalization'' of the second-order direct, exchange, and single-excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on a KS reference. In this work, we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well-balanced performance [J. Paier , New J. Phys.1367-263010.1088/1367-2630/14/4/043002 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to noncovalent interactions, including the rare-gas dimers, and the S22 and S66 test sets, as well as the cohesive energy of small copper clusters, and the equilibrium geometry of 10 diatomic molecules. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different electronic situations, and is a promising step towards a generally applicable electronic-structure approach.
NASA Astrophysics Data System (ADS)
Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng
2016-09-01
In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we firstly 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 (ADEPML). 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 2nd-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 2nd-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.
Enhancing second-order conditioning with lesions of the basolateral amygdala.
Holland, Peter C
2016-04-01
Because the occurrence of primary reinforcers in natural environments is relatively rare, conditioned reinforcement plays an important role in many accounts of behavior, including pathological behaviors such as the abuse of alcohol or drugs. As a result of pairing with natural or drug reinforcers, initially neutral cues acquire the ability to serve as reinforcers for subsequent learning. Accepting a major role for conditioned reinforcement in everyday learning is complicated by the often-evanescent nature of this phenomenon in the laboratory, especially when primary reinforcers are entirely absent from the test situation. Here, I found that under certain conditions, the impact of conditioned reinforcement could be extended by lesions of the basolateral amygdala (BLA). Rats received first-order Pavlovian conditioning pairings of 1 visual conditioned stimulus (CS) with food prior to receiving excitotoxic or sham lesions of the BLA, and first-order pairings of another visual CS with food after that surgery. Finally, each rat received second-order pairings of a different auditory cue with each visual first-order CS. As in prior studies, relative to sham-lesioned control rats, lesioned rats were impaired in their acquisition of second-order conditioning to the auditory cue paired with the first-order CS that was trained after surgery. However, lesioned rats showed enhanced and prolonged second-order conditioning to the auditory cue paired with the first-order CS that was trained before amygdala damage was made. Implications for an enhanced role for conditioned reinforcement by drug-related cues after drug-induced alterations in neural plasticity are discussed. (PsycINFO Database Record PMID:26795578
Ethanol self-administration in mice under a second-order schedule.
Lamb, Richard J; Pinkston, Jonathan W; Ginsburg, Brett C
2015-09-01
Long Fixed-Interval (FI) schedules, particularly second-order schedules, can engender substantial responding before drug or ethanol delivery that is uninfluenced by the direct effects of the drug or ethanol. Thus, these schedules can be used to study the effects of medications upon drug- or ethanol-seeking, uninfluenced by the direct effects of the self-administered drug or ethanol. Long FI second-order schedules are frequently used in primates and occasionally in rats. Under second-order schedules, completion of one response requirement, e.g., a Fixed Ratio 10 (FR10:S), produces a brief stimulus presentation, e.g., a 1-s 80-dB 4-kHZ tone, and this FR10:S serves as the response unit under another schedule, e.g., an FI 1800-s. Thus, the first FR10 completed after 1800 s would result in delivery both of the tone and of reinforcement, e.g., 10 × 0.01 mL 16% (w/v) ethanol. To examine if such schedules could be effectively used in mice, which have advantages in neurobiological and genetic studies, we trained eight C57BL/6J mice to respond under the schedule just described. This schedule maintained substantial responding. The temporal pattern of behavior was typical of an FI schedule with responding accelerating across the interval. We also examined the effects of acute and chronic administration of fluvoxamine on this responding, and these were modest. Finally, we examined responding when alcohol and/or tone deliveries were withheld, and found that extinction occurred most rapidly when both were withheld. This work demonstrates that long FI schedules of ethanol delivery may be useful in studying ethanol seeking in mice.
Comparison of Second-Order Loads on a Semisubmersible Floating Wind Turbine: Preprint
Gueydon, S.; Duarte, T.; Jonkman, J.; Bayati, I.; Sarmento, A.
2014-03-01
As offshore wind projects move to deeper waters, floating platforms become the most feasible solution for supporting the turbines. The oil and gas industry has gained experience with floating platforms that can be applied to offshore wind projects. This paper focuses on the analysis of second-order wave loading on semisubmersible platforms. Semisubmersibles, which are being chosen for different floating offshore wind concepts, are particularly prone to slow-drift motions. The slack catenary moorings usually result in large natural periods for surge and sway motions (more than 100 s), which are in the range of the second-order difference-frequency excitation force. Modeling these complex structures requires coupled design codes. Codes have been developed that include turbine aerodynamics, hydrodynamic forces on the platform, restoring forces from the mooring lines, flexibility of the turbine, and the influence of the turbine control system. In this paper two different codes are employed: FAST, which was developed by the National Renewable Energy Laboratory, and aNySIM, which was developed by the Maritime Research Institute Netherlands. The hydrodynamic loads are based on potential-flow theory, up to the second order. Hydrodynamic coefficients for wave excitation, radiation, and hydrostatic forces are obtained with two different panel codes, WAMIT (developed by the Massachusetts Institute of Technology) and DIFFRAC (developed by MARIN). The semisubmersible platform, developed for the International Energy Agency Wind Task 30 Offshore Code Comparison Collaboration Continuation project is used as a reference platform. Irregular waves are used to compare the behavior of this platform under slow-drift excitation loads. The results from this paper highlight the effects of these loads on semisubmersible-type platforms, which represent a promising solution for the commercial development of the offshore deepwater wind resource.
Second-order Poisson-Nernst-Planck solver for ion transport
NASA Astrophysics Data System (ADS)
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
2011-06-01
The Poisson-Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second-order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are
Thellamurege, Nandun M; Si, Dejun; Cui, Fengchao; Li, Hui
2014-05-01
A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.
Wang, Shiwei; Zhao, Lisha; Zhang, Xiaolong; Shi, Zuosen; Cui, Zhanchen; Yang, Yanqiang
2009-08-15
This work focused on the development of a novel method for molecular level assembly and processing of inorganic-organic hybrid second-order nonlinear optical (SONLO) multilayer films. Aromatic diazo group linked silicon sol was first synthesized and used as a polycation. This oligomer was assembled into inorganic-organic hybrid SONLO multilayer films by electric-field-induced layer-by-layer assembly technique with a low molecular weight chromophore molecule as an anion. After UV irradiation, the electrostatic interaction between layers converted to covalent bonds. Large second-harmonic generation signal of the assembled film was observed, which confirmed that the chromophore in the film had a high degree of molecular orientation as assembled under the electric field. As the cross-linked structure and silicon oxygen meshwork in the films, the resulting inorganic-organic hybrid multilayer films displayed good thermal and chemical stability, and excellent NLO properties. PMID:19433327
Nontrivial Bloch oscillations in waveguide arrays with second-order coupling.
Wang, Gang; Huang, Ji Ping; Yu, Kin Wah
2010-06-01
Under the influence of the next-nearest-neighbor interaction, we theoretically investigate the occurrence of Bloch oscillations in zigzag waveguide arrays. Because of the special topological configuration of the lattice itself, the second-order coupling (SOC) can be enhanced significantly and leads to the band alteration beyond the nearest-neighbor model, i.e., the offset of minimum value from the band edge. Contrary to the behavior in the vanishing SOC, the oscillation patterns exhibit new features, namely, a double turning-back occurs when the beam approaches the band edge. Our results can be applied to some ordered-lattice systems.
Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity
NASA Astrophysics Data System (ADS)
Gerace, Dario; Savona, Vincenzo
2014-03-01
It is shown that noncentrosymmetric materials with bulk second-order nonlinear susceptibility can be used to generate strongly antibunched radiation at an arbitrary wavelength, solely determined by the resonant behavior of suitably engineered coupled microcavities. The proposed scheme exploits the unconventional photon blockade of a coherent driving field at the input of a coupled cavity system, where one of the two cavities is engineered to resonate at both fundamental and second harmonic frequencies, respectively. Remarkably, the unconventional blockade mechanism occurs with reasonably low quality factors at both harmonics, and does not require a sharp doubly resonant condition for the second cavity, thus proving its feasibility with current semiconductor technology.
An invariant asymptotic formula for solutions of second-order linear ODE's
NASA Technical Reports Server (NTRS)
Gingold, H.
1988-01-01
An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).
Kim, Sungho; Du, Chao; Sheridan, Patrick; Ma, Wen; Choi, ShinHyun; Lu, Wei D
2015-03-11
Memristors have been extensively studied for data storage and low-power computation applications. In this study, we show that memristors offer more than simple resistance change. Specifically, the dynamic evolutions of internal state variables allow an oxide-based memristor to exhibit Ca(2+)-like dynamics that natively encode timing information and regulate synaptic weights. Such a device can be modeled as a second-order memristor and allow the implementation of critical synaptic functions realistically using simple spike forms based solely on spike activity. PMID:25710872
Kohn–Sham exchange-correlation potentials from second-order reduced density matrices
Cuevas-Saavedra, Rogelio; Staroverov, Viktor N.; Ayers, Paul W.
2015-12-28
We describe a practical algorithm for constructing the Kohn–Sham exchange-correlation potential corresponding to a given second-order reduced density matrix. Unlike conventional Kohn–Sham inversion methods in which such potentials are extracted from ground-state electron densities, the proposed technique delivers unambiguous results in finite basis sets. The approach can also be used to separate approximately the exchange and correlation potentials for a many-electron system for which the reduced density matrix is known. The algorithm is implemented for configuration-interaction wave functions and its performance is illustrated with numerical examples.
A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes
NASA Technical Reports Server (NTRS)
Carpenter, Russell; Lee, Taesul
2008-01-01
Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.
Reconstruction of discontinuous parameters in a second order impedance boundary operator
NASA Astrophysics Data System (ADS)
Chaabane, S.; Charfi, B.; Haddar, H.
2016-10-01
We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Kohn-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of an unknown number of discontinuity points.
Solution of second order quasi-linear boundary value problems by a wavelet method
Zhang, Lei; Zhou, Youhe; Wang, Jizeng
2015-03-10
A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.
Second-order Bragg gratings in single-mode chalcogenide fibres
Bernier, M; Asatryan, K E; Vallee, R; Galstian, T M; Vasil'ev, Sergei A; Medvedkov, O I; Plotnichenko, V G; Gnusin, P I; Dianov, Evgenii M
2011-05-31
Bragg gratings with a second-order resonance wavelength in the near-IR spectral region have been inscribed into single-mode chalcogenide (As{sub 2}S{sub 3}) glass fibre by a He - Ne laser beam using a configuration typical of Bragg grating fabrication in germanosilicate fibre, with the use of a phase mask that ensures effective diffraction of the writing light into the +1 and -1 orders. The spectra of the inscribed gratings show no resonances due to cladding mode excitation because the cladding material is photosensitive. (fibre optics)
Second-order nonlinear optical susceptibilities of AIIBVI and AIIIBV semiconductors
NASA Astrophysics Data System (ADS)
Kumar, V.; Sinha, Anita; Singh, B. P.; Chandra, S.
2016-10-01
The second-order nonlinear optical (NLO) susceptibilities χ123(2) of AIIBVI and AIIIBV groups of semiconductors with zincblende (ZB) structure have been studied. Two relations have been proposed for the calculation of χ123(2) (0) at zero frequency. One is based on bond charge model of Levine and the other is based on plasma oscillations theory of solids. Calculated values of χ123(2) (0) for all compounds are in fair agreement with the available experimental and reported values.
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Tetikoglu, Fatih Sabahattin
2015-09-01
In this study, the Green's function of the second order differential operator Ax defined by the formula Axu =-a (x )ux x(x )+δ u (x ), δ ≥0 , a (x )=a (x +2 π ), x ∈ℝ1 with domain D (Ax)={ u (x ):u (x ),u '(x ),u″(x )∈C (ℝ1),u (x )=u (x +2 π ), x ∈ℝ1,∫0 2 π u (x )d x =0 } is presented. The estimates for the Green's function and it's derivative are obtained. The positivity of the operator Ax is proved.
The decoupling of second-order linear systems with a singular mass matrix
NASA Astrophysics Data System (ADS)
Kawano, Daniel T.; Morzfeld, Matthias; Ma, Fai
2013-12-01
It was demonstrated in earlier work that a nondefective, linear dynamical system with an invertible mass matrix in free or forced motion may be decoupled in the configuration space by a real and isospectral transformation. We extend this work by developing a procedure for decoupling a linear dynamical system with a singular mass matrix in the configuration space, transforming the original differential-algebraic system into decoupled sets of real, independent, first- and second-order differential equations. Numerical examples are provided to illustrate the application of the decoupling procedure.
Second-order time delay by a radially moving Kerr-Newman black hole
NASA Astrophysics Data System (ADS)
He, Guansheng; Lin, Wenbin
2016-09-01
We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Schäfer's formulation which is based on the retarded Liénard-Wiechert potential.
Ultra-fast digital holography of the femto-second order
NASA Astrophysics Data System (ADS)
Zhai, Hongchen; Wang, Xiaolei; Mu, Guoguang
2007-01-01
We report on pulsed digital micro holographic systems recording ultra-fast process of the femto-second order, by spatially angular division multiplexing (SADM) and wavelength division multiplexing (WDM), respectively. Both intensity and phase images of the digitally reconstructed images are obtained through Fourier transformation and digital filtering, which show clearly the plasma forming and propagating dynamic process of laser induced ionization of ambient air at the wavelength of 800 nm, with a time resolution of 50 fs and frame intervals of 300 to 550 fs.
Action approach to cosmological perturbations: the second-order metric in matter dominance
Boubekeur, Lotfi; Creminelli, Paolo; Vernizzi, Filippo; Norena, Jorge
2008-08-15
We study nonlinear cosmological perturbations during post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-({partial_derivative}{phi}){sup 2}]{sup (1+w)/2w}. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second-order metric during matter dominance in the comoving gauge directly as a function of the primordial inflationary perturbation {zeta}. Going to Poisson gauge, we recover the metric previously derived in the literature.
Kim, Sungho; Du, Chao; Sheridan, Patrick; Ma, Wen; Choi, ShinHyun; Lu, Wei D
2015-03-11
Memristors have been extensively studied for data storage and low-power computation applications. In this study, we show that memristors offer more than simple resistance change. Specifically, the dynamic evolutions of internal state variables allow an oxide-based memristor to exhibit Ca(2+)-like dynamics that natively encode timing information and regulate synaptic weights. Such a device can be modeled as a second-order memristor and allow the implementation of critical synaptic functions realistically using simple spike forms based solely on spike activity.
Treatment Characteristics of Second Order Structure of Proteins Using Low-Pressure Oxygen RF Plasma
NASA Astrophysics Data System (ADS)
Hayashi, Nobuya; Nakahigashi, Akari; Kawaguchi, Ryutaro; Goto, Masaaki
2010-10-01
Removal of proteins from the surface of medical equipments is attempted using oxygen plasma produced by RF discharge. FTIR spectra indicate that the bonding of C-H and N-H in the casein protein is reduced after irradiation of oxygen plasma. Also, the second order structure of a protein such as α-helix and β-sheet are modified by the oxygen plasma. Complete removal of casein protein with the concentration of 0.016 mg/cm2 that is equivalent to remnants on the medical equipment requires two hours avoiding the damage to medical equipments.
Treatment Characteristics of Second Order Structure of Proteins Using Low-Pressure Oxygen RF Plasma
Hayashi, Nobuya; Nakahigashi, Akari; Kawaguchi, Ryutaro; Goto, Masaaki
2010-10-13
Removal of proteins from the surface of medical equipments is attempted using oxygen plasma produced by RF discharge. FTIR spectra indicate that the bonding of C-H and N-H in the casein protein is reduced after irradiation of oxygen plasma. Also, the second order structure of a protein such as {alpha}-helix and {beta}-sheet are modified by the oxygen plasma. Complete removal of casein protein with the concentration of 0.016 mg/cm{sup 2} that is equivalent to remnants on the medical equipment requires two hours avoiding the damage to medical equipments.
Creating second-order nonlinearity in pure synthetic silica optical fibers by thermal poling.
An, Honglin; Fleming, Simon
2007-04-01
A twin-hole optical fiber with pure synthetic silicate glass between the two electrode holes was thermally poled. The induced second-order nonlinearity (SON) was located at the core-cladding interface sections that were nearly parallel to the poling electric field. The polarization dependence of the induced SON suggests that nonlinearity was due to the presence of a space-charge field, which was probably formed by electron migration among the defects located at the core-cladding interface. The magnitude of the induced SON was measured to be approximately 0.06 pm /V.
Thermal poling induced second-order nonlinearity in femtosecond- laser-modified fused silica
An Honglin; Fleming, Simon; McMillen, Benjamin W.; Chen, Kevin P.; Snoke, David
2008-08-11
Thermal poling was utilized to induce second-order nonlinearity in regions of fused silica modified by 771 nm femtosecond laser pulses. With second-harmonic microscopy, it was found that the nonlinearity in the laser-modified region was much lower than that in nonmodified regions. This is attributed to a more rigid glass network after irradiation by the femtosecond laser pulses and/or lack of mobile alkali ions. Measurement of the distribution of chemical elements in the femtosecond-laser-modified region in a soda lime glass revealed a lower level of sodium ions.
Analysis and design of a second-order digital phase-locked loop
NASA Technical Reports Server (NTRS)
Blasche, P. R.
1979-01-01
A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.
Effect of Second-Order Hydrodynamics on a Floating Offshore Wind Turbine
Roald, L.; Jonkman, J.; Robertson, A.
2014-05-01
The design of offshore floating wind turbines uses design codes that can simulate the entire coupled system behavior. At the present, most codes include only first-order hydrodynamics, which induce forces and motions varying with the same frequency as the incident waves. Effects due to second- and higher-order hydrodynamics are often ignored in the offshore industry, because the forces induced typically are smaller than the first-order forces. In this report, first- and second-order hydrodynamic analysis used in the offshore oil and gas industry is applied to two different wind turbine concepts--a spar and a tension leg platform.
Non-iterative local second order Møller-Plesset theory
NASA Astrophysics Data System (ADS)
Maslen, P. E.; Head-Gordon, M.
1998-01-01
Second order Møller-Plesset perturbation theory (MP2) is formulated in terms of atom-centred occupied and virtual orbitals. Both the occupied and the virtual orbitals are non-orthogonal. A new parameter-free atoms-in-molecules local approximation is employed to reduce the cost of the calculation to cubic scaling, and a quasi-canonical two-particle basis is introduced to enable the solution of the local MP2 equations via explicit matrix diagonalisation rather than iteration.
Second-order shaped pulsed for solid-state quantum computation
Sengupta, Pinaki
2008-01-01
We present the construction and detailed analysis of highly optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semianalytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analyzing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.
Constraints on general second-order scalar-tensor models from gravitational Cherenkov radiation
Kimura, Rampei; Yamamoto, Kazuhiro E-mail: kazuhiro@hiroshima-u.ac.jp
2012-07-01
We demonstrate that the general second-order scalar-tensor theories, which have attracted attention as possible modified gravity models to explain the late time cosmic acceleration, could be strongly constrained from the argument of the gravitational Cherenkov radiation. To this end, we consider the purely kinetic coupled gravity and the extended galileon model on a cosmological background. In these models, the propagation speed of tensor mode could be less than the speed of light, which puts very strong constraints from the gravitational Cherenkov radiation.
Fast curvature matrix-vector products for second-order gradient descent.
Schraudolph, Nicol N
2002-07-01
We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this approach. Since both were originally derived by very different routes, this offers fresh insight into their operation, resulting in further improvements to SMD.
Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker.
Yang, Jun; Sha, Kan; Gan, Woon-Seng; Tian, Jing
2005-04-01
The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer.
Assessment of Patellar Tendon Reflex Responses Using Second-Order System Characteristics
Steineman, Brett D.; Karra, Pavan; Park, Kiwon
2016-01-01
Deep tendon reflex tests, such as the patellar tendon reflex (PTR), are widely accepted as simple examinations for detecting neurological disorders. Despite common acceptance, the grading scales remain subjective, creating an opportunity for quantitative measures to improve the reliability and efficacy of these tests. Previous studies have demonstrated the usefulness of quantified measurement variables; however, little work has been done to correlate experimental data with theoretical models using entire PTR responses. In the present study, it is hypothesized that PTR responses may be described by the exponential decay rate and damped natural frequency of a theoretical second-order system. Kinematic data was recorded from both knees of 45 subjects using a motion capture system and correlation analysis found that the mean R2 value was 0.99. Exponential decay rate and damped natural frequency ranges determined from the sample population were −5.61 to −1.42 and 11.73 rad/s to 14.96 rad/s, respectively. This study confirmed that PTR responses strongly correlate to a second-order system and that exponential decay rate and undamped natural frequency are novel measurement variables to accurately measure PTR responses. Therefore, further investigation of these measurement variables and their usefulness in grading PTR responses is warranted. PMID:27041981
Accuracy of second order perturbation theory in the polaron and variational polaron frames
NASA Astrophysics Data System (ADS)
Lee, Chee Kong; Moix, Jeremy; Cao, Jianshu
2012-05-01
In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.
Transport coefficients in second-order non-conformal viscous hydrodynamics
NASA Astrophysics Data System (ADS)
Ryblewski, Radoslaw
2015-05-01
Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory.
Second-Order Controllability of Multi-Agent Systems with Multiple Leaders
NASA Astrophysics Data System (ADS)
Liu, Bo; Shi, Yun-Tao; Su, Hou-Sheng; Han, Xiao
2016-05-01
This paper proposes a new second-order continuous-time multi-agent model and analyzes the controllability of second-order multi-agent system with multiple leaders based on the asymmetric topology. This paper considers the more general case: velocity coupling topology is different from location coupling topology. Some sufficient and necessary conditions are presented for the controllability of the system with multiple leaders. In addition, the paper studies the controllability of the system with velocity damping gain. Simulation results are given to illustrate the correctness of theoretical results. Supported by the National Natural Science Foundation of China under Grant Nos. 61473129, 61304049, 61104140, 61473002, the Beijing Natural Science Foundation Program under Grant No. 4132021, the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215, “The-Great-Wall-Scholar” Candidate Training-Plan of North China University of Technology (NX130), and the Plan Training Project of Excellent Young Teacher of North China University of Technology (NX132), the Fundamental Research Funds for the Central Universities, (HUST: Grant No. 2015TS025), the Fundamental Research Funds for the Central Universities (WUT: Grant No. 2015VI015)
Analysis of heart rate variability signal in meditation using second-order difference plot
NASA Astrophysics Data System (ADS)
Goswami, Damodar Prasad; Tibarewala, Dewaki Nandan; Bhattacharya, Dilip Kumar
2011-06-01
In this article, the heart rate variability signal taken from subjects practising different types of meditations have been investigated to find the underlying similarity among them and how they differ from the non-meditative condition. Four different groups of subjects having different meditation techniques are involved. The data have been obtained from the Physionet and also collected with our own ECG machine. For data analysis, the second order difference plot is applied. Each of the plots obtained from the second order differences form a single cluster which is nearly elliptical in shape except for some outliers. In meditation, the axis of the elliptical cluster rotates anticlockwise from the cluster formed from the premeditation data, although the amount of rotation is not of the same extent in every case. This form study reveals definite and specific changes in the heart rate variability of the subjects during meditation. All the four groups of subjects followed different procedures but surprisingly the resulting physiological effect is the same to some extent. It indicates that there is some commonness among all the meditative techniques in spite of their apparent dissimilarity and it may be hoped that each of them leads to the same result as preached by the masters of meditation. The study shows that meditative state has a completely different physiology and that it can be achieved by any meditation technique we have observed. Possible use of this tool in clinical setting such as in stress management and in the treatment of hypertension is also mentioned.
Seeing the unseen: Second-order correlation learning in 7- to 11-month-olds.
Yermolayeva, Yevdokiya; Rakison, David H
2016-07-01
We present four experiments with the object-examining procedure that investigated 7-, 9-, and 11-month-olds' ability to associate two object features that were never presented simultaneously. In each experiment, infants were familiarized with a number of 3D objects that incorporated different correlations among the features of those objects and the body of the objects (e.g., Part A and Body 1, and Part B and Body 1). Infants were then tested with objects with a novel body that either possessed both of the parts that were independently correlated with one body during familiarization (e.g., Part A and B on Body 3) or that were attached to two different bodies during familiarization. The experiments demonstrate that infants as young as 7months of age are capable of this kind of second-order correlation learning. Furthermore, by at least 11months of age infants develop a representation for the object that incorporates both of the features they experienced during training. We suggest that the ability to learn second-order correlations represents a powerful but as yet largely unexplored process for generalization in the first years of life.
Enhancement of Second-Order Nonlinear-Optical Signals by Optical Stimulation
NASA Astrophysics Data System (ADS)
Goodman, A. J.; Tisdale, W. A.
2015-05-01
Second-order nonlinear optical interactions such as sum- and difference-frequency generation are widely used for bioimaging and as selective probes of interfacial environments. However, inefficient nonlinear optical conversion often leads to poor signal-to-noise ratio and long signal acquisition times. Here, we demonstrate the dramatic enhancement of weak second-order nonlinear optical signals via stimulated sum- and difference-frequency generation. We present a conceptual framework to quantitatively describe the interaction and show that the process is highly sensitive to the relative optical phase of the stimulating field. To emphasize the utility of the technique, we demonstrate stimulated enhancement of second harmonic generation (SHG) from bovine collagen-I fibrils. Using a stimulating pulse fluence of only 3 nJ /cm2 , we obtain an SHG enhancement >104 relative to the spontaneous signal. The stimulation enhancement is greatest in situations where spontaneous signals are the weakest—such as low laser power, small sample volume, and weak nonlinear susceptibility—emphasizing the potential for this technique to improve signal-to-noise ratios in biological imaging and interfacial spectroscopy.
Increasing returns to scale: The solution to the second-order social dilemma
Ye, Hang; Chen, Shu; Luo, Jun; Tan, Fei; Jia, Yongmin; Chen, Yefeng
2016-01-01
Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms. PMID:27535087
Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
Boubekeur, Lotfi; Creminelli, Paolo; D'Amico, Guido; Noreña, Jorge; Vernizzi, Filippo E-mail: creminel@ictp.it E-mail: norena@sissa.it
2009-08-01
We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result δT/T = Φ/3. The calculation is done in Poisson gauge. Besides intrinsic contributions calculated at last scattering, one must consider integrated effects. These are associated to lensing, and to the time dependence of the potentials (Rees-Sciama) and of the vector and tensor components of the metric generated at second order. The bispectrum is explicitly computed in the flat-sky approximation. It scales as l{sup −4} in the scale invariant limit and the shape dependence of its various contributions is represented in 3d plots. Although all the contributions to the bispectrum are parametrically of the same order, the full bispectrum is dominated by lensing. In the squeezed limit it corresponds to f{sub NL}{sup local} = −1/6−cos(2θ), where θ is the angle between the short and the long modes; the angle dependent contribution comes from lensing. In the equilateral limit it corresponds to f{sub NL}{sup equil} ≅ 3.13.
First and second order derivatives for optimizing parallel RF excitation waveforms
NASA Astrophysics Data System (ADS)
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.
First and second order derivatives for optimizing parallel RF excitation waveforms.
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. PMID:26232364
Seeing the unseen: Second-order correlation learning in 7- to 11-month-olds.
Yermolayeva, Yevdokiya; Rakison, David H
2016-07-01
We present four experiments with the object-examining procedure that investigated 7-, 9-, and 11-month-olds' ability to associate two object features that were never presented simultaneously. In each experiment, infants were familiarized with a number of 3D objects that incorporated different correlations among the features of those objects and the body of the objects (e.g., Part A and Body 1, and Part B and Body 1). Infants were then tested with objects with a novel body that either possessed both of the parts that were independently correlated with one body during familiarization (e.g., Part A and B on Body 3) or that were attached to two different bodies during familiarization. The experiments demonstrate that infants as young as 7months of age are capable of this kind of second-order correlation learning. Furthermore, by at least 11months of age infants develop a representation for the object that incorporates both of the features they experienced during training. We suggest that the ability to learn second-order correlations represents a powerful but as yet largely unexplored process for generalization in the first years of life. PMID:27038738
Increasing returns to scale: The solution to the second-order social dilemma.
Ye, Hang; Chen, Shu; Luo, Jun; Tan, Fei; Jia, Yongmin; Chen, Yefeng
2016-01-01
Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms.
Increasing returns to scale: The solution to the second-order social dilemma.
Ye, Hang; Chen, Shu; Luo, Jun; Tan, Fei; Jia, Yongmin; Chen, Yefeng
2016-01-01
Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms. PMID:27535087
Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation
Mannheim, P.D. ); Kazanas, D. )
1994-04-01
In this work, the authors study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. It is found, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. The authors present the solutions of this fourth order equation and find that they are able to recover all of the standard Newton-Euler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, the authors make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales for outside of fundamental sources, or on the very smallest ones within their interiors. This study enables the deduction that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary. 17 refs., 1 fig.
Cascante, M; Sorribas, A; Franco, R; Canela, E I
1991-04-21
Models based on the power-law formalism provide a useful tool for analyzing metabolic systems. Within this methodology, the S-system variant furnishes the best strategy. In this paper we explore an extension of this formalism by considering second-order derivative terms of the Taylor series which the power-law is based upon. Results show that the S-system equations which include second-order Taylor coefficients give better accuracy in predicting the response of the system to a perturbation. Hence, models based on this new approach could provide a useful tool for quantitative purposes if one is able to measure the required derivatives experimentally. In particular we show the utility of this approach when it comes to discriminating between two mechanisms that are equivalent in the S-system a representation based on first-order coefficients. However, the loss of analytical tractability is a serious disadvantage for using this approach as a general tool for studying metabolic systems.
Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker.
Yang, Jun; Sha, Kan; Gan, Woon-Seng; Tian, Jing
2005-04-01
The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer. PMID:16060510
Implementing the Second-Order Fermi Process in a Kinetic Monte-Carlo Simulation
NASA Astrophysics Data System (ADS)
Summerlin, E. J.
2010-12-01
Kinetic Monte-Carlo test-particle simulations require a way to simulate the effects of turbulence on particles. One way to do this is to prescribe a phenomenological scattering mechanism based on an empirical and/or qualitative description of turbulent scattering. Previous incarnations of the simulation presented here parameterize a scattering mean free path proportional to some power of the particle’s momentum in agreement with observational evidence from many sources. The scattering itself was done by scattering of the particle’s local fluid frame velocity onto a sphere of radius |v| via either large of small angle scattering. However, in real plasmas the scattering centers (turbulent plasma waves) are not stationary in the local fluid frame and particle velocities should, instead, be randomized in the frame of the moving scattering centers (which presumably move with the Alfvén speed) to more accurately represent the effects of turbulence on particles. Allowing scattering centers to move introduces heating as particles now diffuse in momentum as well as space (receiving a random kick of order the Alfvén speed at each scattering event). In 1965, Eugene Parker considered this effect (then called fermi acceleration) for cosmic ray particles and (correctly) concluded that it was negligible for those highly energetic particles because the particle speed was so much larger than the Alfvén speed kick which it received. However, doing the same calculation for thermal particles embedded in the solar wind (for whom a single kick of an Alfvén speed is significant) yields a very different result and it becomes clear that this process, now called second-order Fermi acceleration, must be included to get an accurate picture of particle acceleration in the heliosphere. This presentation will highlight the theoretical argument for the importance of second-order fermi acceleration in both the solar wind and shock environs as well as problems in heliophysics to which it
ERIC Educational Resources Information Center
Hayden, Angela; Bhatt, Ramesh S.; Reed, Andrea; Corbly, Christine R.; Joseph, Jane E.
2007-01-01
Sensitivity to second-order relational information (i.e., spatial relations among features such as the distance between eyes) is a vital part of achieving expertise with face processing. Prior research is unclear on whether infants are sensitive to second-order differences seen in typical human populations. In the current experiments, we examined…
NASA Astrophysics Data System (ADS)
Man, Yiu-Kwong
2010-10-01
In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.
Relaxation approximations to second-order traffic flow models by high-resolution schemes
Nikolos, I.K.; Delis, A.I.; Papageorgiou, M.
2015-03-10
A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.
NASA Astrophysics Data System (ADS)
Bauer, S. H.; Lazaar, K. I.
1983-09-01
The usually quoted expression for the second order rate constant, for a unimolecular reaction at the low pressure limit, is valid only for strictly irreversible processes. Its application to isomerization reactions (which are to some extent reversible) is demonstrably in error; corrected expressions have been published. Attention is directed to intramolecular conversions over low barriers, for which the inappropriateness of the unidirectional expression becomes obvious. For such isomerizations we propose a model which incorporates only operationally observable states, so that an essential conceptual ambiguity is avoided. Use of this model is illustrated for the syn⇄anti conversions of methyl nitrite, derived from a gas phase NMR coalescence curve (Mc:Tc). The present data suggest that during isomerization the alkyl nitrites may not be completely ergodic on a time scale of 10-9 s. A regional phase-space model is proposed which has the appropriate formalism to account for this behavior.
NASA Astrophysics Data System (ADS)
Pei, Yongquan; Sun, Jitao
2016-11-01
This paper investigates the stationary average consensus problem for second-order discrete-time multi-agent systems (SDMAS). A stationary consensus problem is to find a control algorithm that brings the state of a group of agents to a common constant value which is called the collective decision. We introduce the concept of stationary average consensus of SDMAS and propose a consensus algorithm. Based on the polynomial stability and the graph theory, we obtain two necessary and sufficient conditions of stationary average consensus of SDMAS. The last theorem provides an algebraic criterion of stationary average consensus, and can help us to determine the parameters in the consensus algorithm. Furthermore, in this consensus algorithm, only the states of the agents are transferred among the agents. Therefore, this algorithm can not only solve the stationary average consensus problem but also reduce the amount of transferred data. A numerical example is provided to illustrate the efficiency of our results.
First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients
NASA Technical Reports Server (NTRS)
Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard
1996-01-01
The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.
Approximated optimum condition of second order response surface model with correlated observations
NASA Astrophysics Data System (ADS)
Somayasa, Wayan
2016-06-01
In the present paper we establish an inference procedure for the eigenvalues of the model matrix of the second-order response surface model (RSM). In contrast to the classical treatment where the sample are assumed to be independently distributed, in this work we do not need such distributional simplification. The confidence region for the unknown vector of the eigenvalues is derived by means of delta method. The finite sample behavior of the convergence result is discussed by Monte Carlo Simulation. We get the approximated distribution of the pivotal quantity of the population eigenvalues as a chi-square distribution model. Next we attempt to apply the method to a real data provided by a mining industry. The data represents the percentage of cobalt (Co) observed over the exploration region.
The lattice Boltzmann model for the second-order Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2010-04-01
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin-Ono equation. With the Taylor expansion and the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations.
A second-order Budkyo-type parameterization of landsurface hydrology
NASA Technical Reports Server (NTRS)
Andreou, S. A.; Eagleson, P. S.
1982-01-01
A simple, second order parameterization of the water fluxes at a land surface for use as the appropriate boundary condition in general circulation models of the global atmosphere was developed. The derived parameterization incorporates the high nonlinearities in the relationship between the near surface soil moisture and the evaporation, runoff and percolation fluxes. Based on the one dimensional statistical dynamic derivation of the annual water balance, it makes the transition to short term prediction of the moisture fluxes, through a Taylor expansion around the average annual soil moisture. A comparison of the suggested parameterization is made with other existing techniques and available measurements. A thermodynamic coupling is applied in order to obtain estimations of the surface ground temperature.
A Second Order JFNK-based IMEX Method for Single and Multi-phase Flows
Samet Kadioglu; Dana Knoll; Mark Sussman; Richard Martineau
2010-07-01
Abstract We present a second order time accurate IMplicit/EXplicit (IMEX) method for solving single and multi-phase flow problems. The algorithm consists of a combination of an explicit and an implicit blocks. The explicit block solves the non-stiff parts of the governing system whereas the implicit block operates on the stiff terms. In our self-conisstent IMEX implementation, the explicit part is always executed inside the implicit block as part of the nonlinear functions evaluation making use of the Jacobian-freeNewton Krylov (JFNK) method [7]. This leads to an implicitly balanced algorithm in that all non-linearities due to the coupling of different time terms are consistently converged. In this paper, we present computational results when this IMEX strategy is applied to single/multi-phase incompressible flow models. Samet
NASA Astrophysics Data System (ADS)
Polyanskii, Peter V.; Felde, Christina V.; Konovchuk, Alexey V.; Oleksyuk, Maxim V.
2015-11-01
Recording nonlinearity is conventionally considered as the source of noise in holographic imaging. Important exclusion from this general statement is nonlinear holographic associative memory, where the quadratic recording nonlinearity causes true brightness rendering and the possibility for associative coupling and reconstructing optical signals of arbitrary complexity which are stored at the same carrier without interference. In this paper we discuss the role of nonlinearities of an amplitude response of a hologram of the orders higher than the quadratic one in implementing the second-ordered holographic associative memory. We show that higher-order nonlinearities are also involved in implementing this type of memory. This conclusion may be of importance for interpretation of biological/human memory also. The highlight of our study is the conclusion that reconstruction of the complex conjugate heteroassociative response is provided directly, viz. by the set of specified by us pseudogratings, rather than by the mechanism of sequential diffractions.
Ilić, Milica; Flockerzi, Dietrich; Seidel-Morgenstern, Andreas
2010-04-01
A competitive adsorption isotherm model is derived for binary mixtures of components characterized by single component isotherms which are second-order truncations of higher order equilibrium models suggested by multi-layer theory and statistical thermodynamics. The competitive isotherms are determined using the ideal adsorbed solution (IAS) theory which, in case of complex single component isotherms, does not generate explicit expressions to calculated equilibrium loadings and causes time consuming iterations in simulations of adsorption processes. The explicit model derived in this work is based on an analysis of the roots of a cubic polynomial resulting from the set of IAS equations. The suggested thermodynamically consistent and widely applicable competitive isotherm model can be recommended as a flexible tool for efficient simulations of fixed-bed adsorber dynamics.
Second-order corrections to the wave function at the origin in muonic hydrogen and pionium
Ivanov, Vladimir G.; Korzinin, Evgeny Yu.; Karshenboim, Savely G.
2009-07-15
Nonrelativistic second-order corrections to the wave function at the origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at the origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects, and the hyperfine splitting. The results are obtained for the 1s and 2s states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of {pi}{sup +} and {pi}{sup -}. Applications to the hyperfine structure and the Lamb shift in muonic hydrogen are also considered.
Pavlovian conditioning of sexual arousal: first- and second-order effects.
Zamble, E; Hadad, G M; Mitchell, J B; Cutmore, T R
1985-10-01
Despite the likely importance of Pavlovian conditioning in sexual behavior, previous evidence of reliable or sizeable effects is very sparse. This report includes four experiments in the conditioning of sexual arousal in the males of a mammalian species, namely, the rat. In each case the unconditioned response (UR) was unconsummated arousal after exposure to a female. There was evidence of a substantial conditioned effect, as shown by decreases in the time to complete copulation during postconditioning conditioned stimulus (CS) tests. It is also possible to establish a second-order conditioned response (CR), which retains its strength even after extinction of the first-order response. These results confirm the power of Pavlovian contingencies in sexual responding and provide implications for conditioning theory and applied work.
First and second order operator splitting methods for the phase field crystal equation
Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub
2015-10-15
In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods.
Optical flow based deformable volume registration using a novel second-order regularization prior
NASA Astrophysics Data System (ADS)
Grbić, Saša; Urschler, Martin; Pock, Thomas; Bischof, Horst
2010-03-01
Nonlinear image registration is an initial step for a large number of medical image analysis applications. Optical flow based intensity registration is often used for dealing with intra-modality applications involving motion differences. In this work we present an energy functional which uses a novel, second-order regularization prior of the displacement field. Compared to other methods our scheme is robust to non-Gaussian noise and does not penalize locally affine deformation fields in homogeneous areas. We propose an efficient and stable numerical scheme to find the minimizer of the presented energy. We implemented our algorithm using modern consumer graphics processing units and thereby increased the execution performance dramatically. We further show experimental evaluations on clinical CT thorax data sets at different breathing states and on dynamic 4D CT cardiac data sets.
Observed galaxy number counts on the lightcone up to second order: II. Derivation
Bertacca, Daniele; Maartens, Roy; Clarkson, Chris E-mail: roy.maartens@gmail.com
2014-11-01
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a general gauge, and applies to all dark energy models (including interacting dark energy) and to metric theories of modified gravity. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.
Zhou, Yun Pollak, Eli; Miret-Artés, Salvador
2014-01-14
A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.
NASA Astrophysics Data System (ADS)
Bologna, Mauro
2010-09-01
This paper addresses the problem of finding an asymptotic solution for first- and second-order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of the paper is to go beyond the Tauberian theorem in the case of integral-differential equations which are widely used by the scientific community. The results are applied to the convolute form of the Lindblad equation setting generic conditions on the kernel in such a way as to generate a positive definite density matrix, and show that the structure of the eigenvalues of the correspondent Liouvillian operator plays a crucial role in determining the positivity of the density matrix.
Bioethics as a second-order discipline: who is not a bioethicist?
Kopelman, Loretta M
2006-12-01
A dispute exists about whether bioethics should become a new discipline with its own methods, competency standards, duties, honored texts, and core curriculum. Unique expertise is a necessary condition for disciplines. Using the current literature, different views about the sort of expertise that might be unique to bioethicists are critically examined to determine if there is an expertise that might meet this requirement. Candidates include analyses of expertise based in "philosophical ethics," "casuistry," "atheoretical or situation ethics," "conventionalist relativism," "institutional guidance," "regulatory guidance and compliance," "political advocacy," "functionalism," and "principlism." None succeed in identifying a unique area of expertise for successful bioethicists that could serve as a basis for making it a new discipline. Rather expertise in bioethics is rooted in many professions, disciplines and fields and best understood as a second-order discipline.
Syndrome evaluation in traditional Chinese medicine using second-order latent variable model.
Li, Yang; Yi, Danhui; Zhang, Huiyun; Qin, Yichen
2012-03-30
The syndrome is one of the most important concepts and ingredients in the theoretical and clinical research of traditional Chinese medicine (TCM). TCM doctors believe that all diseases are caused by an imbalance in the patient's body, which is called syndrome. All the therapies and formulas in TCM are decided according to the patients' syndrome situation. To quantitatively evaluate the level of syndrome, many statistical methodologies have been discussed in recent years. In this article, we introduce a second-order latent variable model to evaluate the level of patients' syndrome with many clinical symptoms. An objective evaluation score can be easily derived by the proposed model, with a high speed of convergence and without joint-distribution assumption. We illustrate the application of this model by an analysis of premenstrual disorder syndrome of liver-qi invasion syndrome evaluation research.
Vector and tensor contributions to the curvature perturbation at second order
NASA Astrophysics Data System (ADS)
Carrilho, Pedro; Malik, Karim A.
2016-02-01
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part of the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.
Second-order schedules with fixed-ratio components: variation of component size.
Lee, J K; Gollub, L R
1971-05-01
Key pecking by pigeons was reinforced with food under second-order schedules with fixed-ratio units. A constant total number of key pecks was required for reinforcement under each condition, but the size and, inversely, number of fixed-ratio components were varied. The total response requirement of 256 pecks was divided into fixed-ratio units of 128, 64, 32, 8, and 2 responses. A brief stimulus, which always preceded food reinforcement, was presented upon completion of each fixed-ratio unit. Under most conditions, the pattern of within-unit responding was typical of that under simple fixed-ratio schedules. Overall response rate was an inverted U-shaped function of component size. That is, response rates were highest under moderate sized units (fixed ratio 128 and 64). This relationship is consistent with previous determinations of rate as a function of fixed-ratio value for simple fixed-ratio schedules.
Second-Order Modeling of Low-Reynolds-Number Turbulence Near Walls
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Mansour, N. N.
1989-01-01
This paper presents a set of second-order closure models for low-Reynolds-number turbulence near the wall. Existing closure models for the Reynolds-stress equations were modified to show proper near-wall behavior. A dissipation-rate equation for the turbulent kinetic energy is also reformulated. The proposed models satisfy realizability and will not produce unphysical behavior. Fully developed channel flows are used for model testing. The equations are solved for the mean velocity, the Reynolds stresses, and the dissipation rate of the turbulent kinetic energy. The calculations are compared with both direct numerical simulations and with measurements. It is shown that the present models perform well in predicting the behavior of the turbulence near a wall. Significant improvements over previous models in predicting the components of the Reynolds stress tensor are obtained in the present models.
NASA Astrophysics Data System (ADS)
Ito, Kazuma; Sato, Yasuaki; Takasu, Ryosuke; Mase, Nobuyuki; Kawata, Yoshimasa; Tasaka, Shigeru; Sugita, Atsushi
2014-01-01
In this manuscript, we describe the current manuscript describes the second-order nonlinear optical susceptibility of guest-host polymers possessing chromophores with strongly electron-accepting tricyanofuran (TCF). Chromophores substituted with different numbers of hydroxyl groups were prepared. Our experimental results demonstrated that the guest-host polymers exhibited nonlinear optical susceptibilities simply upon annealing at temperatures higher than the glass transition point of the host polymers even in the absence of applied external DC electric fields. Nonelectrical poling behaviors were only available for the materials possessing hydroxyl-group-functionalized chromophores. The results indicate that chemisorption of the hydroxyl groups on the substrate led to the orientation order of the guest chromophores. The orientation order of the chromophores was reproduced well by the model of poled polymers in previous studies.
An optimal PID controller via LQR for standard second order plus time delay systems.
Srivastava, Saurabh; Misra, Anuraag; Thakur, S K; Pandit, V S
2016-01-01
An improved tuning methodology of PID controller for standard second order plus time delay systems (SOPTD) is developed using the approach of Linear Quadratic Regulator (LQR) and pole placement technique to obtain the desired performance measures. The pole placement method together with LQR is ingeniously used for SOPTD systems where the time delay part is handled in the controller output equation instead of characteristic equation. The effectiveness of the proposed methodology has been demonstrated via simulation of stable open loop oscillatory, over damped, critical damped and unstable open loop systems. Results show improved closed loop time response over the existing LQR based PI/PID tuning methods with less control effort. The effect of non-dominant pole on the stability and robustness of the controller has also been discussed.
Photoassociation of a cold-atom-molecule pair. II. Second-order perturbation approach
Lepers, M.; Vexiau, R.; Bouloufa, N.; Dulieu, O.; Kokoouline, V.
2011-04-15
The electrostatic interaction between an excited atom and a diatomic ground-state molecule in an arbitrary rovibrational level at large mutual separations is investigated with a general second-order perturbation theory, in the perspective of modeling the photoassociation between cold atoms and molecules. We find that the combination of quadrupole-quadrupole and van der Waals interactions competes with the rotational energy of the dimer, limiting the range of validity of the perturbative approach to distances larger than 100 Bohr radii. Numerical results are given for the long-range interaction between Cs and Cs{sub 2}, showing that the photoassociation is probably efficient for any Cs{sub 2} rotational energy.
Kim, T; Pasciak, J E; Vassilevski, P S
2004-09-20
In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
NASA Technical Reports Server (NTRS)
Wickens, C.; Gill, R.; Kramer, A.; Ross, W.; Donchin, E.
1981-01-01
Three experiments are described in which tracking difficulty is varied in the presence of a covert tone discrimination task. Event related brain potentials (ERPs) elicited by the tones are employed as an index of the resource demands of tracking. The ERP measure reflected the control order variation, and this variable was thereby assumed to compete for perceptual/central processing resources. A fine-grained analysis of the results suggested that the primary demands of second order tracking involve the central processing operations of maintaining a more complex internal model of the dynamic system, rather than the perceptual demands of higher derivative perception. Experiment 3 varied tracking bandwidth in random input tracking, and the ERP was unaffected. Bandwidth was then inferred to compete for response-related processing resources that are independent of the ERP.
A First and Second Order Moment Approach to Probabilistic Control Synthesis
NASA Technical Reports Server (NTRS)
Crespo, Luis G.; Kenny, Sean P.
2005-01-01
This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.
Further development and testing of a second-order bulk boundary layer model. Master's thesis
Krasner, R.D.
1993-05-03
A one-layer bulk boundary layer model is developed. The model predicts the mixed layer values of the potential temperature, mixing ratio, and u- and v-momentum. The model also predicts the depth of the boundary layer and the vertically integrated turbulence kinetic energy (TKE). The TKE is determined using a second-order closure that relates the rate of dissipation to the TKE. The fractional area covered by rising motion sigma and the entrainment rate (E) are diagnostically determined. The model is used to study the clear convective boundary layer (CBL) using data from the Wangara, Australia boundary layer experiment. The Wangara data is also used as an observation base to validate model results. A further study is accomplished by simulating the planetary boundary layer (PBL) over an ocean surface. This study is designed to find the steady-state solutions of the prognostic variable.
Treatment of Second-Order Structures of Proteins Using Oxygen Radio Frequency Plasma
NASA Astrophysics Data System (ADS)
Hayashi, Nobuya; Nakahigashi, Akari; Liu, Hao; Goto, Masaaki
2010-08-01
Decomposition characteristics of second-order structures of proteins are determined using an oxygen radio frequency (RF) plasma sterilizer in order to prevent infectious proteins from contaminating medical equipment in hospitals. The removal of casein protein as a test protein with a concentration of 50 mg/cm2 on the plane substrate requires approximately 8 h when singlet atomic oxygen is irradiated. The peak intensity of Fourier transform infrared spectroscopy (FTIR) spectra of the β-sheet structures decreases at approximately the same rate as those of the α-helix and first-order structures of proteins. Active oxygen has a sufficient oxidation energy to dissociate hydrogen bonds within the β-sheet structure.
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
Hermant, Audrey
2010-02-15
This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points.
Salgado, Ivan; Chairez, Isaac; Camacho, Oscar; Yañez, Cornelio
2014-07-01
Designing a proportional derivative (PD) controller has as main problem, to obtain the derivative of the output error signal when it is contaminated with high frequency noises. To overcome this disadvantage, the supertwisting algorithm (STA) is applied in closed-loop with a PD structure for multi-input multi-output (MIMO) second order nonlinear systems. The stability conditions were analyzed in terms of a strict non-smooth Lyapunov function and the solution of Riccati equations. A set of numerical test was designed to show the advantages of implementing PD controllers that used STA as a robust exact differentiator. The first numerical example showed the stabilization of an inverted pendulum. The second example was designed to solve the tracking problem of a two-link robot manipulator.
Willow, Soohaeng Yoo; Zhang, Jinmei; Valeev, Edward F.; Hirata, So
2014-01-21
A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H{sub 2}O, CH{sub 4}, and C{sub 6}H{sub 6} within a few mE{sub h} after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.
Determination of Second-Order Nonlinear Optical Susceptibility of GaN Films on Sapphire
NASA Astrophysics Data System (ADS)
Fujita, Takashi; Hasegawa, Tatsuo; Haraguchi, Masanobu; Okamoto, Toshihiro; Fukui, Masuo; Nakamura, Syuji
2000-05-01
The second-order nonlinear susceptibilities of GaN films on sapphire were determined by the Maker fringe technique. In deriving the second-harmonic intensity, the bound wave propagating from the GaN-air interface to the GaN-sapphire interface and that propagating in the opposite direction were taken into account. We obtained |χ(2)zxx|=14.7±0.2 pm/V, |χ(2)xzx|=14.4±0.2 pm/V and |χ(2)zzz|=29.7±0.7 pm/V for the GaN film with a thickness of 2.55 μm using fundamental light with a wavelength of 1.064 μm.
Distributed impulsive group consensus in second-order multi-agent systems under directed topology
NASA Astrophysics Data System (ADS)
Liu, Jun; Zhou, Jin
2015-05-01
This paper investigates the impulsive group consensus problems of second-order multi-agent systems under directed network topology with acyclic partition. Two distributed impulsive sampled-data protocols are presented to realise group consensus for both cases with leaders and leaderless, and then some simple yet generic criteria on convergence for such algorithms are established. It is shown that, for the case with leaderless, a feature of the present protocols is to give an explicit expression of group consensus states in terms of the initial values of the agents, which allows us to develop a simple approach yielding the desired group or cluster consensus. While for the case of virtual leaders, a pinning-like tracking technique is effectively designed to regulate all the agents access to the virtual leaders respectively for the purpose of practical control strategy. Finally, simulation results are presented to illustrate the effectiveness of the theoretical analysis.
Second Order Catalytic Quasispecies Yields Discontinuous Mean Fitness at Error Threshold
NASA Astrophysics Data System (ADS)
Wagner, Nathaniel; Tannenbaum, Emmanuel; Ashkenasy, Gonen
2010-05-01
The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that second order mechanisms lead to a discontinuity in the mean fitness of the population at the error threshold. This is in contrast to the behavior of the first order, autocatalytic replication mechanism considered in the standard quasispecies model. This suggests that quasispecies models with higher order replication mechanisms produce discontinuities in the mean fitness, and hence the viable population fraction as well, at the error threshold, while lower order replication mechanisms yield a continuous mean fitness function. We discuss potential implications for understanding replication in the RNA world and in virology.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, P.; Tiberio, E.
2000-06-01
This work is concerned with the development of an analytical method for estimating the macroscopic behavior of heterogeneous elastic systems subjected to finite deformations. The objective is to generate variational estimates for the effective or homogenized stored-energy function of hyperelastic composites, which will be accomplished by means of a suitable generalization of the "second-order procedure" of Ponte Castañeda (Ponte Castañeda, P., 1996. J. Mech. Phys. Solids 44, 827-862). The key idea in this method is the introduction of an optimally chosen "linear thermoelastic comparison composite," which can then be used to convert available homogenization estimates for linear systems directly into new estimates for nonlinear composites. To illustrate the use of the method, an application is given for carbon-black filled elastomers and estimates analogous to the well-known Hashin-Shtrikman and self-consistent estimates for linear-elastic composites are generated.
Second-order estimates for nonlinear isotropic composites with spherical pores and rigid particles
NASA Astrophysics Data System (ADS)
Idiart, Martín; Ponte Castañeda, Pedro
2005-02-01
The 'second-order' nonlinear homogenization method (Ponte Castañeda, J. Mech. Phys. Solids 50 (2002) 737-757) is used to generate estimates of the Hashin-Shtrikman-type for the effective behavior of viscoplastic materials with isotropically distributed spherical pores or rigid particles. In the limiting case of an ideally plastic matrix with a dilute concentration of pores, the resulting estimates were found to exhibit a linear dependence on the porosity when the material is subjected to axisymmetric shear, but this dependence becomes singular for simple shear. In the process of this work, an alternative prescription for certain reference tensors used in the method is proposed, and shown to lead to more consistent estimates for the effective behavior than the earlier prescription. To cite this article: M. Idiart, P. Ponte Castañeda, C. R. Mecanique 333 (2005).
Possible second-order phase transition in strongly coupled unquenched planar four-dimensional QED
Oliensis, J. ); Johnson, P.W. )
1990-07-15
We study chiral-symmetry breaking in four-dimensional QED with {ital N} fermion species using truncated Schwinger-Dyson equations, and taking vacuum-polarization effects into account via a momentum-dependent gauge coupling. These effects transmute the infinite-order phase transition found previously for the case of a fixed gauge coupling into a second-order phase transition. For large {ital N}, the phase transition may not exist, as it is determined primarily by the physics at the cutoff. We also carry out a preliminary renormalization-group analysis of the theory near the critical coupling: the results are compatible with the existence of a nontrivial continuum limit for the planar theory at the critical value, with an effectively dimensionless fermion field.
Second-order quantized Hamilton dynamics coupled to classical heat bath
Heatwole, Eric M.; Prezhdo, Oleg V.
2005-06-15
Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.
NASA Astrophysics Data System (ADS)
Saker, S. H.; O'Regan, Donal
2011-01-01
In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation (p(t)([y(t)+r(t)y(τ(t))]Δ)γ)Δ+f(t,y(θ(t))=0,t∈[t0,∞)T, on a time scale T, where |f(t,u)|⩾q(t)|uγ|, r, p and q are real valued rd-continuous positive functions defined on T, γ⩾1 is the quotient of odd positive integers. Our results improve existence results in the literature in the sense that our results do not require pΔ(t)⩾0, and ∫t0∞θγ(s)q(s)[1-r(θ(s))]γΔs=∞. Some examples are given to illustrate the main results.
NASA Astrophysics Data System (ADS)
Saravanan, M.; Senthil, A.; Rajasekar, S. Abraham
2016-09-01
Good optical quality, potential second order nonlinear optical crystal L-asparaginium picrate (LASP) was grown by the slow cooling method. The solubility and metastable zone width of LASP specimen was studied. The LASP crystal belongs to monoclinic crystal system with noncentrosymmetric space group P21. UV-Visible-NIR transmittance spectrum determines the optical band gap of LASP. Excellence of the grown crystal is ascertained by the etching studies. Laser Damage Threshold and Photoluminescence studies designate that the grown crystal contains less imperfection. The mechanical behaviour of LASP sample was investigated at different temperatures. The piezoelectric nature, Photoconductive nature and the relative Second Harmonic Generation (for various particle sizes) of the material were also studied. Birefringence and ocular (optical) homogeneity of the crystal were assessed using modified channel spectrum method.
A fast converging robust controller using adaptive second order sliding mode.
Mondal, Sanjoy; Mahanta, Chitralekha
2012-11-01
This paper proposes an adaptive second order sliding mode (SOSM) controller with a nonlinear sliding surface. The nonlinear sliding surface consists of a gain matrix having a variable damping ratio. Initially the sliding surface uses a low value of damping ratio to get a quick system response. As the closed loop system approaches the desired reference, the value of the damping ratio gets increased with an aim to reducing the overshoot and the settling time. The time derivative of the control signal is used to design the controller. The actual control input obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used by the proposed controller eliminates the need of prior knowledge about the upper bound of system uncertainties. Simulation results demonstrate the effectiveness of the proposed control strategy.
Fast full waveform inversion with source encoding and second-order optimization methods
NASA Astrophysics Data System (ADS)
Castellanos, Clara; Métivier, Ludovic; Operto, Stéphane; Brossier, Romain; Virieux, Jean
2015-02-01
Full waveform inversion (FWI) of 3-D data sets has recently been possible thanks to the development of high performance computing. However, FWI remains a computationally intensive task when high frequencies are injected in the inversion or more complex wave physics (viscoelastic) is accounted for. The highest computational cost results from the numerical solution of the wave equation for each seismic source. To reduce the computational burden, one well-known technique is to employ a random linear combination of the sources, rather that using each source independently. This technique, known as source encoding, has shown to successfully reduce the computational cost when applied to real data. Up to now, the inversion is normally carried out using gradient descent algorithms. With the idea of achieving a fast and robust frequency-domain FWI, we assess the performance of the random source encoding method when it is interfaced with second-order optimization methods (quasi-Newton l-BFGS, truncated Newton). Because of the additional seismic modelings required to compute the Newton descent direction, it is not clear beforehand if truncated Newton methods can indeed further reduce the computational cost compared to gradient algorithms. We design precise stopping criteria of iterations to fairly assess the computational cost and the speed-up provided by the source encoding method for each optimization method. We perform experiment on synthetic and real data sets. In both cases, we confirm that combining source encoding with second-order optimization methods reduces the computational cost compared to the case where source encoding is interfaced with gradient descent algorithms. For the synthetic data set, inspired from the geology of Gulf of Mexico, we show that the quasi-Newton l-BFGS algorithm requires the lowest computational cost. For the real data set application on the Valhall data, we show that the truncated Newton methods provide the most robust direction of descent.
The nature of letter crowding as revealed by first- and second-order classification images
Nandy, Anirvan S.; Tjan, Bosco S.
2009-01-01
Visual crowding refers to the marked inability to identify an otherwise perfectly identifiable object when it is flanked by other objects. Crowding places a significant limit on form vision in the visual periphery; its mechanism is, however, unknown. Building on the method of signal-clamped classification images (Tjan & Nandy, 2006), we developed a series of first- and second-order classification-image techniques to investigate the nature of crowding without presupposing any model of crowding. Using an “o” versus “x” letter-identification task, we found that (1) crowding significantly reduced the contrast of first-order classification images, although it did not alter the shape of the classification images; (2) response errors during crowding were strongly correlated with the spatial structures of the flankers that resembled those of the erroneously perceived targets; (3) crowding had no systematic effect on intrinsic spatial uncertainty of an observer nor did it suppress feature detection; and (4) analysis of the second-order classification images revealed that crowding reduced the amount of valid features used by the visual system and, at the same time, increased the amount of invalid features used. Our findings strongly support the feature-mislocalization or source-confusion hypothesis as one of the proximal contributors of crowding. Our data also agree with the inappropriate feature-integration account with the requirement that feature integration be a competitive process. However, the feature-masking account and a front-end version of the spatial attention account of crowding are not supported by our data. PMID:18217820
The nature of letter crowding as revealed by first- and second-order classification images.
Nandy, Anirvan S; Tjan, Bosco S
2007-01-01
Visual crowding refers to the marked inability to identify an otherwise perfectly identifiable object when it is flanked by other objects. Crowding places a significant limit on form vision in the visual periphery; its mechanism is, however, unknown. Building on the method of signal-clamped classification images (Tjan & Nandy, 2006), we developed a series of first- and second-order classification-image techniques to investigate the nature of crowding without presupposing any model of crowding. Using an "o" versus "x" letter-identification task, we found that (1) crowding significantly reduced the contrast of first-order classification images, although it did not alter the shape of the classification images; (2) response errors during crowding were strongly correlated with the spatial structures of the flankers that resembled those of the erroneously perceived targets; (3) crowding had no systematic effect on intrinsic spatial uncertainty of an observer nor did it suppress feature detection; and (4) analysis of the second-order classification images revealed that crowding reduced the amount of valid features used by the visual system and, at the same time, increased the amount of invalid features used. Our findings strongly support the feature-mislocalization or source-confusion hypothesis as one of the proximal contributors of crowding. Our data also agree with the inappropriate feature-integration account with the requirement that feature integration be a competitive process. However, the feature-masking account and a front-end version of the spatial attention account of crowding are not supported by our data. PMID:18217820
A Generic Length-scale Equation For Second-order Turbulence Models of Oceanic Boundary Layers
NASA Astrophysics Data System (ADS)
Umlauf, L.; Burchard, H.
A generic transport equation for a generalized length-scale in second-order turbulence closure models for geophysical boundary layers is suggested. This variable consists of the products of powers of the turbulent kinetic energy, k, and the integral length-scale, l. The new approach generalizes traditional second-order models used in geophysical boundary layer modelling, e.g. the Mellor-Yamada model and the k- model, which, however, can be recovered as special cases. It is demonstrated how this new model can be calibrated with measurements in some typical geophysical boundary layer flows. As an example, the generic model is applied to the uppermost oceanic boundary layer directly influenced by the effects of breaking surface waves. Recent measurements show that in this layer the classical law of the wall is invalid, since there turbulence is dominated by turbulent transport of TKE from above, and not by shear-production. A widely accepted approach to describe the wave-affected layer with a one-equation turbulence model was suggested by Craig and Banner (1994). Here, some deficien- cies of their solutions are pointed out and a generalization of their ideas for the case of two-equation models is suggested. Direct comparison with very recently obtained measurements of the dissipation rate, , in the wave-affected boundary layer with com- puted results clearly demonstrate that only the generic two-equation model yields cor- rect predictions for the profiles of and the turbulent length scale, l. Also, the pre- dicted velocity profiles in the wave-affected layer, important e.g. for the interpretation of surface drifter experiments, are reproduced correctly only by the generic model. Implementation and computational costs of the generic model are comparable with traditonal two-equation models.
Hospital diversification: evaluating alternatives.
Hammer, L
1987-05-01
The appropriateness of diversification as a growth strategy for hospitals is discussed, and planning for diversification is described. Because new forms of health-care delivery are now in direct competition with hospitals, many hospitals are confronting environmental pressures and preparing for future survival through diversification. To explore the potential risks and benefits of diversification, the hospital must identify opportunities for new business ventures. Diversification can be "related," through an expansion of the primary product line (health care), or "unrelated," into areas not directly associated with health care. The hospital must establish specific criteria for evaluating each diversification alternative, and the two or three most attractive options should be analyzed further through a financial feasibility study. The hospital should also seek legal advice to determine the implications of diversification for maintenance of tax status, antitrust limitations, and applicability of certificate of need. Although diversification may not be appropriate for every institution, hospitals should consider it as a strategy for increasing their revenue base, confronting environmental pressures, and securing future survival. PMID:3300300
Hospital diversification: evaluating alternatives.
Hammer, L
1987-05-01
The appropriateness of diversification as a growth strategy for hospitals is discussed, and planning for diversification is described. Because new forms of health-care delivery are now in direct competition with hospitals, many hospitals are confronting environmental pressures and preparing for future survival through diversification. To explore the potential risks and benefits of diversification, the hospital must identify opportunities for new business ventures. Diversification can be "related," through an expansion of the primary product line (health care), or "unrelated," into areas not directly associated with health care. The hospital must establish specific criteria for evaluating each diversification alternative, and the two or three most attractive options should be analyzed further through a financial feasibility study. The hospital should also seek legal advice to determine the implications of diversification for maintenance of tax status, antitrust limitations, and applicability of certificate of need. Although diversification may not be appropriate for every institution, hospitals should consider it as a strategy for increasing their revenue base, confronting environmental pressures, and securing future survival.
Windhorst, U; Kokkoroyiannis, T; Laouris, Y; Meyer-Lohmann, J
1994-03-01
Spinal recurrent inhibition via Renshaw cells and proprioceptive feedback via skeletal muscle and muscle spindle afferents have been hypothesized to constitute a compound feedback system [Windhorst (1989) Afferent Control of Posture and Locomotion; Windhorst (1993) Robots and Biological Systems--Towards a New Bionics]. To assess their detailed functions, it is necessary to know their dynamic characteristics. Previously we have extensively described the properties of signal transmission from motor axons to Renshaw cells using random motor axon stimulation and data analysis methods based thereupon. Using the same methods, we here compare these properties, in the cat, with those between motor axons and group Ia muscle spindle afferents in terms of frequency responses and nonlinear features. The frequency responses depend on the mean rate (carrier rate) of activation of motor axons and on the strength of coupling between motor units and spindles. In general, they are those of a second-order low-pass system with a cut-off at fairly low frequencies. This contrasts with the dynamics of motor axon-Renshaw cell couplings which are those of a much broader band-pass with its peak in the range of c. 2-15 Hz [Christakos (1987) Neuroscience 23, 613-623]. The second-order non-linearities in motor unit-muscle spindle signal lines are much more diverse than those in motor axon-Renshaw cell couplings. Although the average strength of response declines with mean stimulus rate in both subsystems, there is no systematic relationship between the amount of non-linearity and the average response in the former, whilst there is in the latter. The qualitative appearance of motor unit-muscle spindle non-linearities was complicated as was the average response to motor unit twitches. Thus, whilst Renshaw cells appear to dynamically reflect motor output rather faithfully, muscle spindles seem to signal local muscle fibre length changes and their dynamics. This would be consistent with the
NASA Astrophysics Data System (ADS)
Šprlák, Michal; Novák, Pavel
2016-10-01
New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.
NASA Astrophysics Data System (ADS)
Dzida, Marzena; Kaczmarczyk, Aleksandra
2012-04-01
Second-order thermodynamic derivative properties, such as isobaric thermal molar expansions, isothermal and adiabatic molar compressibilities, and isochoric molar heat capacities of (ethanol, decan-1-ol, 2-methyl-2-butanol) + heptane mixtures at pressures up to 100 MPa and in the temperature range from 293.15 K to 318.15 K were derived from experimental speed-of-sound u( T, p), density ρ( T, p = 0.1 MPa), and isobaric heat-capacity C p ( T, p = 0.1 MPa) data using appropriate thermodynamic relations. Excess values for the given properties were calculated according to the criterion of thermodynamic ideality of a mixture (Douhéret et al., Chem. Phys. Chem. 2, 148 (2001)), i.e., assuming that the chemical potential of component i in the ideal liquid mixture is equal to the chemical potential of component i in the mixture of perfect gases. The deviations from ideality for the mixtures under test have been explained in terms of the self-association of alcohols in solution which produces a strong departure from random mixing, the change in the non-specific interactions during mixing, and the packing effects.
NASA Astrophysics Data System (ADS)
Lei, T.; Engelbrecht, K.; Nielsen, K. K.; Neves Bez, H.; Bahl, C. R. H.
2016-09-01
Magnetocaloric materials (MCM) with a first order phase transition (FOPT) usually exhibit a large, although sharp, isothermal entropy change near their Curie temperature, compared to materials with a second order phase transition (SOPT). Experimental results of applying FOPT materials in recent magnetocaloric refrigerators (MCR) demonstrated the great potential for these materials, but a thorough study on the impact of the moderate adiabatic temperature change and strong temperature dependence of the magnetocaloric effect (MCE) is lacking. Besides, comparing active magnetic regenerators (AMR) using FOPT and SOPT materials is also of fundamental interest. We present modeling results of multi-layer AMRs using FOPT and SOPT materials based on a 1D numerical model. First the impact of isothermal entropy change, adiabatic temperature change and shape factor describing the temperature dependence of the MCE are quantified and analyzed by using artificially built magnetocaloric properties. Then, based on measured magnetocaloric properties of La(Fe,Mn,Si)13H y and Gd, an investigation on how to layer typical FOPT and SOPT materials with different temperature spans is carried out. Moreover, the sensitivity of variation in Curie temperature distribution for both groups of AMRs is investigated. Finally, a concept of mixing FOPT and SOPT materials is studied for improving the stability of layered AMRs with existing materials.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
NASA Technical Reports Server (NTRS)
Miller, Ronald H.; Winske, Dan; Gary, S. P.
1992-01-01
A second-order theory for electrostatic instabilities driven by counterstreaming ion beams is developed which describes momentum coupling and heating of the plasma via wave-particle interactions. Exchange rates between the waves and particles are derived, which are suitable for the fluid equations simulating microscopic effects on macroscopic scales. Using a fully kinetic simulation, the electrostatic ion cyclotron instability due to counterstreaming H(+) beams has been simulated. A power spectrum from the kinetic simulation is used to evaluate second-order exchange rates. The calculated heating and momentum loss from second-order theory is compared to the numerical simulation.
Second-order Wagner theory for two-dimensional water-entry problems at small deadrise angles
NASA Astrophysics Data System (ADS)
Oliver, J. M.
The theory of Wagner from 1932 for the normal symmetric impact of a two-dimensional body of small deadrise angle on a half-space of ideal and incompressible liquid is extended to derive the second-order corrections for the locations of the higher-pressure jet-root regions and for the upward force on the impactor using a systematic matched-asymptotic analysis. The second-order predictions for the upward force on an entering wedge and parabola are compared with numerical and experimental data, respectively, and it is concluded that a significant improvement in the predictive capability of Wagner's theory is afforded by proceeding to second order.
Cournane, S; Sheehy, N; Cooke, J
2014-06-01
Benford's law is an empirical observation which predicts the expected frequency of digits in naturally occurring datasets spanning multiple orders of magnitude, with the law having been most successfully applied as an audit tool in accountancy. This study investigated the sensitivity of the technique in identifying system output changes using simulated changes in interventional radiology Dose-Area-Product (DAP) data, with any deviations from Benford's distribution identified using z-statistics. The radiation output for interventional radiology X-ray equipment is monitored annually during quality control testing; however, for a considerable portion of the year an increased output of the system, potentially caused by engineering adjustments or spontaneous system faults may go unnoticed, leading to a potential increase in the radiation dose to patients. In normal operation recorded examination radiation outputs vary over multiple orders of magnitude rendering the application of normal statistics ineffective for detecting systematic changes in the output. In this work, the annual DAP datasets complied with Benford's first order law for first, second and combinations of the first and second digits. Further, a continuous 'rolling' second order technique was devised for trending simulated changes over shorter timescales. This distribution analysis, the first employment of the method for radiation output trending, detected significant changes simulated on the original data, proving the technique useful in this case. The potential is demonstrated for implementation of this novel analysis for monitoring and identifying change in suitable datasets for the purpose of system process control.
Construction of Second-Order TVD Schemes for Nonhomogeneous Hyperbolic Conservation Laws
NASA Astrophysics Data System (ADS)
Gascón, Ll.; Corberán, J. M.
2001-09-01
Many of the problems of approximating numerically solutions to nonhomogeneous hyperbolic conservation laws appear to arise from an inability to balance the source and flux terms at steady states. In this paper we present a technique based on the transformation of the nonhomogeneous problem to homogeneous form through the definition of a new flux formed by the physical flux and the primitive of the source term. This change preserves the mentioned balance directly and suggests a way to apply well-known schemes to nonhomogeneous conservation laws. However, the application of the numerical methods described for homogeneous conservation laws is not immediate and a new formalization of the classic schemes is required. Particularly, for such cases we extend the explicit, second-order, total variation diminishing schemes of Harten [11]. Numerical test cases in the context of the quasi-one-dimensional flow validate the current schemes, although these schemes are more general and can also be applied to solve other hyperbolic conservation laws with source terms.
An efficient second-order accurate and continuous interpolation for block-adaptive grids
NASA Astrophysics Data System (ADS)
Borovikov, Dmitry; Sokolov, Igor V.; Tóth, Gábor
2015-09-01
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of the resolution changes, which allows us to employ efficient and simple linear interpolation in the majority of the computational domain. The algorithm is well suited for massively parallel computations. Our interpolation algorithm allows extracting jump-free interpolated data distribution along lines and surfaces within the computational domain. This capability is important for various applications, including kinetic particles tracking in three dimensional vector fields, visualization (i.e. surface extraction) and extracting variables along one-dimensional curves such as field lines, streamlines and satellite trajectories, etc. Particular examples are models for acceleration of solar energetic particles (SEPs) along magnetic field-lines. As such models are sensitive to sharp gradients and discontinuities the capability to interpolate the data from the AMR grid to be passed to the SEP model without producing false gradients numerically becomes crucial. We provide a complete description of the algorithm and make the code publicly available as a Fortran 90 library.
Time-dependent Models for Blazar Emission with the Second-order Fermi Acceleration
NASA Astrophysics Data System (ADS)
Asano, Katsuaki; Takahara, Fumio; Kusunose, Masaaki; Toma, Kenji; Kakuwa, Jun
2014-01-01
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. The hard electron spectrum predicted by the Fermi-II process agrees with the hard photon spectrum of 1ES 1101-232. For other blazars that show softer spectra, the Fermi-II model requires radial evolution of the electron injection rate and/or diffusion coefficient in the outflow. Such evolutions can yield a curved electron spectrum, which can reproduce the synchrotron spectrum of Mrk 421 from the radio to the X-ray regime. The photon spectrum in the GeV energy range of Mrk 421 is hard to fit with a synchrotron self-Compton model. However, if we introduce an external radio photon field with a luminosity of 4.9 × 1038 erg s-1, GeV photons are successfully produced via inverse Compton scattering. 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.
Time-dependent models for blazar emission with the second-order Fermi acceleration
Asano, Katsuaki; Takahara, Fumio; Toma, Kenji; Kusunose, Masaaki; Kakuwa, Jun
2014-01-01
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. The hard electron spectrum predicted by the Fermi-II process agrees with the hard photon spectrum of 1ES 1101–232. For other blazars that show softer spectra, the Fermi-II model requires radial evolution of the electron injection rate and/or diffusion coefficient in the outflow. Such evolutions can yield a curved electron spectrum, which can reproduce the synchrotron spectrum of Mrk 421 from the radio to the X-ray regime. The photon spectrum in the GeV energy range of Mrk 421 is hard to fit with a synchrotron self-Compton model. However, if we introduce an external radio photon field with a luminosity of 4.9 × 10{sup 38} erg s{sup –1}, GeV photons are successfully produced via inverse Compton scattering. 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.
Boots for Achilles: progesterone's reduction of cholesterol is a second-order adaptation.
Amir, Dorsa; Fessler, Daniel M T
2013-06-01
Progesterone and cholesterol are both vital to pregnancy. Among other functions, progesterone downregulates inflammatory responses, allowing for maternal immune tolerance of the fetal allograft. Cholesterol a key component of cell membranes, is important in intracellular transport, cell signaling, nerve conduction, and metabolism Despite the importance of each substance in pregnancy, one exercises an antagonistic effect on the other, as periods of peak progesterone correspond with reductions in cholesterol availability, a consequence of progesterone's negative effects on cholesterol biosynthesis. This arrangement is understandable in light of the threat posed by pathogens early in pregnancy. Progesterone-induced immunomodulation entails increased vulnerability to infection, an acute problem in the first trimester, when fetal development is highly susceptible to insult. Many pathogens rely on cholesterol for cell entry, egress, and replication. Progesterone's antagonistic effects on cholesterol thus partially compensate for the costs entailed by progesterone-induced immunomodulation. Among pathogens to which the host's vulnerability is increased by progesterone's effects, approximately 90% utilize cholesterol, and this is notably true of pathogens that pose a risk during pregnancy. In addition to having a number of possible clinical applications, our approach highlights the potential importance of second-order adaptations, themselves a consequence of the lack of teleology in evolutionary processes. PMID:23909226
Consensus for second-order multi-agent systems with position sampled data
NASA Astrophysics Data System (ADS)
Wang, Rusheng; Gao, Lixin; Chen, Wenhai; Dai, Dameng
2016-10-01
In this paper, the consensus problem with position sampled data for second-order multi-agent systems is investigated. The interaction topology among the agents is depicted by a directed graph. The full-order and reduced-order observers with position sampled data are proposed, by which two kinds of sampled data-based consensus protocols are constructed. With the provided sampled protocols, the consensus convergence analysis of a continuous-time multi-agent system is equivalently transformed into that of a discrete-time system. Then, by using matrix theory and a sampled control analysis method, some sufficient and necessary consensus conditions based on the coupling parameters, spectrum of the Laplacian matrix and sampling period are obtained. While the sampling period tends to zero, our established necessary and sufficient conditions are degenerated to the continuous-time protocol case, which are consistent with the existing result for the continuous-time case. Finally, the effectiveness of our established results is illustrated by a simple simulation example. Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13F030005) and the National Natural Science Foundation of China (Grant No. 61501331).
NASA Astrophysics Data System (ADS)
Guardia, M.; Kaloshin, V.; Zhang, J.
2016-11-01
In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko (Sov Phys JETP 27:851-857, 1968) and studied by Treschev (Physica D 116(1-2):21-43, 1998; J Nonlinear Sci 12(1):27-58, 2002), Piftankin (Nonlinearity (19):2617-2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3-108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.
A second-order two-scale homogenization procedure using macrolevel discretization
NASA Astrophysics Data System (ADS)
Lesičar, Tomislav; Tonković, Zdenko; Sorić, Jurica
2014-08-01
The present study deals with a second-order two-scale computational homogenization procedure for modeling deformation responses of heterogeneous materials at small strains. The macro to micro transition and the application of generalized periodic boundary conditions on the representative volume element (RVE) at the microlevel are investigated. The structure at macroscale level is discretized by the two dimensional triangular finite elements, while the quadrilateral finite element is used for the discretization of the RVE. The finite element formulations and the new proposed multiscale scheme have been implemented into the finite element software ABAQUS using user subroutines derived. Due to the continuity transition, an additional integral condition on microlevel fluctuation field has to be imposed, as expected. The integration has been performed using various numerical integration techniques and the results obtained are compared in a few examples. It is concluded that only trapezoidal rule gives a physically based deformed shape of the RVE. Finally, the efficiency and accuracy of the proposed multiscale homogenization approach are demonstrated by the modeling of a shear layer problem, usually used as a benchmark in multiscale analyses.
Investigating the Dimits Shift using the Second-order Cumulant Expansion Statistical Closure
NASA Astrophysics Data System (ADS)
St-Onge, D. A.; Krommes, J. A.
2015-11-01
The Dimits shift is the nonlinear upshift of the critical temperature gradient that signals the onset of collisionless ion-temperature-gradient-driven turbulence. This phenomenon is caused by the shearing away of turbulent streamers in the radial direction by poloidal zonal flows (ZFs). While the effect is witnessed in both gyrokinetic and gyrofluid simulations, there exists no analytical model that satisfactorily describes the mechanics through which it operates. In this work, a new model is developed by applying the second-order cumulant expansion closure to a simplified set of gyrofluid equations. In particular, we calculate the threshold for the zonostrophic instability of a two-field model, generalizing the work of Parker and Krommes on the modified Hasegawa-Mima equation, and assess whether the Reynolds-stress-generated ZFs can be destabilized in the model, thus indicating a Dimits shift. This work was supported by an NSERC PGS-D scholarship, as well as by U.S. DOE contract DE-AC02-09CH11466.
Second-order schedules of token reinforcement with pigeons: implications for unit price.
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). The token-production and exchange-production ratios were manipulated systematically across conditions. Response rates varied inversely with the token-production ratio at each exchange-production ratio. Response rates also varied inversely with the exchange-production ratio at each token-production ratio, particularly at the higher token-production ratios. At higher token-production and exchange-production ratios, response rates increased in token-production segments closer to exchange periods and food. Some conditions were conducted in a closed economy, in which the pigeons earned all their daily ration of food within the session. Relative to comparable open-economy conditions, response rates in the closed economy were less affected by changes in token-production ratio, resulting in higher levels of food intake and body weight. Some of the results are consistent with the economic concept of unit price, a cost-benefit ratio comprised of responses per unit of food delivery, but most are well accounted for by a consideration of the number of responses required to produce exchange periods, without regard to the amount of reinforcement available during those exchange periods. PMID:16602378
NASA Astrophysics Data System (ADS)
Ge, Hao
2015-01-01
A stochastic process is an essential tool for the investigation of the physical and life sciences at nanoscale. In the first-order stochastic processes widely used in chemistry and biology, only the flux of mass rather than that of heat can be well defined. Here we investigate the two macroscopic fluxes in second-order stochastic processes driven by position-dependent forces and temperature gradient. We prove that the thermodynamic equilibrium defined through the vanishing of macroscopic fluxes is equivalent to that defined via time reversibility at mesoscopic scale. In the small noise limit, we find that the entropy production rate, which has previously been defined by the mesoscopic irreversible fluxes on the phase space, matches the classic macroscopic expression as the sum of the products of macroscopic fluxes and their associated thermodynamic forces. Further we show that the two pairs of forces and fluxes in such a limit follow a linear phenomenonical relation and the associated scalar coefficients always satisfy the reciprocal relation for both transient and steady states. The scalar coefficient is proportional to the square of local temperature divided by the local frictional coefficient and originated from the second moment of velocity distribution along each dimension. This result suggests the very close connection between the Soret effect (thermal diffusion) and Dufour effect at nanoscale even far from equilibrium.
Kolmogorov constants for the second-order structure function and the energy spectrum.
Ni, Rui; Xia, Ke-Qing
2013-02-01
We examine the behavior of the Kolmogorov constants C(2), C(k), and C(k1), which are, respectively, the prefactors of the second-order longitudinal structure function and the three-dimensional and one-dimensional longitudinal energy spectrum in the inertial range. We show that their ratios, C(2)/C(k1) and C(k)/C(k1), exhibit clear dependence on the microscale Reynolds number R(λ), implying that they cannot all be independent of R(λ). In particular, it is found that (C(k1)/C(2)-0.25)=1.95R(λ)(-0.68). The study further reveals that the widely used relation C(2)=4.02C(k1) holds only asymptotically when R(λ)>/~10(5). It is also found that C(2) has much stronger R(λ) dependence than either C(k) or C(k1) if the latter indeed has a systematic dependence on R(λ). We further show that the varying dependence on R(λ) of these three numbers can be attributed to the difference of the inertial range in real- and wave-number space, with the inertial range in real-space known to be much shorter than that in wave-number space.
NASA Astrophysics Data System (ADS)
Guardia, M.; Kaloshin, V.; Zhang, J.
2016-07-01
In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko (Sov Phys JETP 27:851-857, 1968) and studied by Treschev (Physica D 116(1-2):21-43, 1998; J Nonlinear Sci 12(1):27-58, 2002), Piftankin (Nonlinearity (19):2617-2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3-108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.
Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald; Werner, Hans-Joachim
2013-03-14
We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.
Byrd, L D; Marr, M J
1969-09-01
Key-pecking behavior in the pigeon was maintained under second-order schedules in which food was presented after a variable number of 2-min fixed-interval components were completed. When either the same stimulus (Exp. I) or different stimuli (Exp. II) appeared on the key during consecutive components, and a stimulus that was occasionally paired with food was presented briefly at completion of each component, (1) patterns of positively accelerated responding were maintained during the components, and, (2) mean response rates were generally as high during the initial components of a sequence as during the later components. In both experiments, when the food-paired stimulus was omitted and either no stimulus or a stimulus never paired with food was presented at completion of each component, mean rates of responding increased, but patterns of positively accelerated responding were not maintained during individual components. When a food-paired stimulus was not presented at completion of the components, mean response rates in Exp. I were low during the initial components of a sequence and gradually increased during subsequent components; in Exp. II mean response rates were variable, and pauses and abrupt changes in response rates were typical.
Quan, Runai; Zhai, Yiwei; Wang, Mengmeng; Hou, Feiyan; Wang, Shaofeng; Xiang, Xiao; Liu, Tao; Zhang, Shougang; Dong, Ruifang
2016-01-01
Based on the second-order quantum interference between frequency entangled photons that are generated by parametric down conversion, a quantum strategic algorithm for synchronizing two spatially separated clocks has been recently presented. In the reference frame of a Hong-Ou-Mandel (HOM) interferometer, photon correlations are used to define simultaneous events. Once the HOM interferometer is balanced by use of an adjustable optical delay in one arm, arrival times of simulta- neously generated photons are recorded by each clock. The clock offset is determined by correlation measurement of the recorded arrival times. Utilizing this algorithm, we demonstrate a proof-of-principle experiment for synchronizing two clocks separated by 4 km fiber link. A minimum timing stability of 0.44 ps at averaging time of 16000 s is achieved with an absolute time accuracy of 73.2 ps. The timing stability is verified to be limited by the correlation measurement device and ideally can be better than 10 fs. Such results shine a light to the application of quantum clock synchronization in the real high-accuracy timing system. PMID:27452276
Quan, Runai; Zhai, Yiwei; Wang, Mengmeng; Hou, Feiyan; Wang, Shaofeng; Xiang, Xiao; Liu, Tao; Zhang, Shougang; Dong, Ruifang
2016-01-01
Based on the second-order quantum interference between frequency entangled photons that are generated by parametric down conversion, a quantum strategic algorithm for synchronizing two spatially separated clocks has been recently presented. In the reference frame of a Hong-Ou-Mandel (HOM) interferometer, photon correlations are used to define simultaneous events. Once the HOM interferometer is balanced by use of an adjustable optical delay in one arm, arrival times of simulta- neously generated photons are recorded by each clock. The clock offset is determined by correlation measurement of the recorded arrival times. Utilizing this algorithm, we demonstrate a proof-of-principle experiment for synchronizing two clocks separated by 4 km fiber link. A minimum timing stability of 0.44 ps at averaging time of 16000 s is achieved with an absolute time accuracy of 73.2 ps. The timing stability is verified to be limited by the correlation measurement device and ideally can be better than 10 fs. Such results shine a light to the application of quantum clock synchronization in the real high-accuracy timing system. PMID:27452276
Second-order splitting schemes for a class of reactive systems
NASA Astrophysics Data System (ADS)
Ren, Zhuyin; Pope, Stephen B.
2008-09-01
We consider the numerical time integration of a class of reaction-transport systems that are described by a set of ordinary differential equations for primary variables. In the governing equations, the terms involved may require the knowledge of secondary variables, which are functions of the primary variables. Specifically, we consider the case where, given the primary variables, the evaluation of the secondary variables is computationally expensive. To solve this class of reaction-transport equations, we develop and demonstrate several computationally efficient splitting schemes, wherein the portions of the governing equations containing chemical reaction terms are separated from those parts containing the transport terms. A computationally efficient solution to the transport sub-step is achieved through the use of linearization or predictor-corrector methods. The splitting schemes are applied to the reactive flow in a continuously stirred tank reactor (CSTR) with the Davis-Skodjie reaction model, to the CO+H oxidation in a CSTR with detailed chemical kinetics, and to a reaction-diffusion system with an extension of the Oregonator model of the Belousov-Zhabotinsky reaction. As demonstrated in the test problems, the proposed splitting schemes, which yield efficient solutions to the transport sub-step, achieve second-order accuracy in time.
Simultaneous first- and second-order percolation transitions in interdependent networks
NASA Astrophysics Data System (ADS)
Zhou, Dong; Bashan, Amir; Cohen, Reuven; Berezin, Yehiel; Shnerb, Nadav; Havlin, Shlomo
2014-07-01
In a system of interdependent networks, an initial failure of nodes invokes a cascade of iterative failures that may lead to a total collapse of the whole system in the form of an abrupt first-order transition. When the fraction of initial failed nodes 1-p reaches criticality p =pc, the abrupt collapse occurs by spontaneous cascading failures. At this stage, the giant component decreases slowly in a plateau form and the number of iterations in the cascade τ diverges. The origin of this plateau and its increasing with the size of the system have been unclear. Here we find that, simultaneously with the abrupt first-order transition, a spontaneous second-order percolation occurs during the cascade of iterative failures. This sheds light on the origin of the plateau and how its length scales with the size of the system. Understanding the critical nature of the dynamical process of cascading failures may be useful for designing strategies for preventing and mitigating catastrophic collapses.
Compensated second-order recoupling: application to third spin assisted recoupling†
Giffard, Mathilde; Hediger, Sabine; Lewandowski, Józef R.; Bardet, Michel; Simorre, Jean-Pierre; Griffin, Robert G.; De Paëpe, Gaël
2015-01-01
We consider the effect of phase shifts in the context of second-order recoupling techniques in solid-state NMR. Notably we highlight conditions leading to significant improvements for the Third Spin Assisted Recoupling (TSAR) mechanism and demonstrate the benefits of resulting techniques for detecting long-distance transfer in biomolecular systems. The modified pulse sequences of PAR and PAIN-CP, Phase-Shifted Proton Assisted Recoupling (AH-PS-PAR) and Phase-Shifted Proton-Assisted Insensitive Nuclei Cross Polarization (ABH-PS-PAIN-CP), still rely on cross terms between heteronuclear dipolar couplings involving assisting protons that mediate zero-quantum polarization transfer between low-γ nuclei (13C–13C, 15N–15N, 15N–13C polarization transfer). Using Average Hamiltonian Theory we show that phase inversion compensates off-resonance contributions and yields improved polarization transfer as well as substantial broadening of the matching conditions. PS-TSAR greatly improves on the standard TSAR based methods because it alleviates their sensitivity to precise RF settings which significantly enhances robustness of the experiments. We demonstrate these new methods on a 19.6 kDa protein (U–[15N, 13C]-YajG) at high magnetic fields (up to 900 MHz 1H frequency) and fast sample spinning (up to 65 kHz MAS frequency). PMID:22513727
Li, Lebao; Sun, Lingling; Zhang, Shengzhou
2016-05-01
A new mean deviation coupling synchronization control strategy is developed for multiple motor control systems, which can guarantee the synchronization performance of multiple motor control systems and reduce complexity of the control structure with the increasing number of motors. The mean deviation coupling synchronization control architecture combining second-order adaptive sliding mode control (SOASMC) approach is proposed, which can improve synchronization control precision of multiple motor control systems and make speed tracking errors, mean speed errors of each motor and speed synchronization errors converge to zero rapidly. The proposed control scheme is robustness to parameter variations and random external disturbances and can alleviate the chattering phenomena. Moreover, an adaptive law is employed to estimate the unknown bound of uncertainty, which is obtained in the sense of Lyapunov stability theorem to minimize the control effort. Performance comparisons with master-slave control, relative coupling control, ring coupling control, conventional PI control and SMC are investigated on a four-motor synchronization control system. Extensive comparative results are given to shown the good performance of the proposed control scheme. PMID:26899554
Gravitational-wave implications for structure formation: A second-order approach
NASA Astrophysics Data System (ADS)
Pazouli, Despoina; Tsagas, Christos G.
2016-03-01
Gravitational waves are propagating undulations in the spacetime fabric, which interact very weakly with their environment. In cosmology, gravitational-wave distortions are produced by most of the inflationary scenarios and their anticipated detection should open a new window to the early Universe. Motivated by the relative lack of studies on the potential implications of gravitational radiation for the large-scale structure of the Universe, we consider its coupling to density perturbations during the postrecombination era. We do so by assuming an Einstein-de Sitter background cosmology and by employing a second-order perturbation study. At this perturbative level and on superhorizon scales, we find that gravitational radiation adds a distinct and faster growing mode to the standard linear solution for the density contrast. Given the expected weakness of cosmological gravitational waves, however, the effect of the new mode is currently subdominant and it could start becoming noticeable only in the far future. Nevertheless, this still raises the intriguing possibility that the late-time evolution of large-scale density perturbations may be dictated by the long-range (the Weyl), rather than the local (the Ricci) component of the gravitational field.
NASA Astrophysics Data System (ADS)
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
On the second-order asymptotics for entanglement-assisted communication
NASA Astrophysics Data System (ADS)
Datta, Nilanjana; Tomamichel, Marco; Wilde, Mark M.
2016-06-01
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms of the quantum mutual information and does not increase in the presence of a noiseless quantum feedback channel from receiver to sender. In this work, we investigate second-order asymptotics of the entanglement-assisted classical communication task. That is, we consider how quickly the rates of entanglement-assisted codes converge to the entanglement-assisted classical capacity of a channel as a function of the number of channel uses and the error tolerance. We define a quantum generalization of the mutual information variance of a channel in the entanglement-assisted setting. For covariant channels, we show that this quantity is equal to the channel dispersion and thus completely characterize the convergence toward the entanglement-assisted classical capacity when the number of channel uses increases. Our results also apply to entanglement-assisted quantum communication, due to the equivalence between entanglement-assisted classical and quantum communication established by the teleportation and super-dense coding protocols.
Time reversibility and nonequilibrium thermodynamics of second-order stochastic processes
NASA Astrophysics Data System (ADS)
Ge, Hao
2014-02-01
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time reversibility over the phase space is equivalent to the antisymmetry of spatial flux and the symmetry of velocity flux. Then we show that the condition of time reversibility alone cannot always guarantee the Maxwell-Boltzmann distribution. Comparing the two conditions together, we find that the frictional force naturally emerges as the unique odd term of the total force at thermodynamic equilibrium, and is followed by the Einstein relation. The two conditions respectively correspond to two previously reported different entropy production rates. In the case where the external force is only position dependent, the two entropy production rates become one. We prove that such an entropy production rate can be decomposed into two non-negative terms, expressed respectively by the conditional mean and variance of the thermodynamic force associated with the irreversible velocity flux at any given spatial coordinate. In the small inertia limit, the former term becomes the entropy production rate of the corresponding overdamped dynamics, while the anomalous entropy production rate originates from the latter term. Furthermore, regarding the connection between the first law and second law, we find that in the steady state of such a limit, the anomalous entropy production rate is also the leading order of the Boltzmann-factor weighted difference between the spatial heat dissipation densities of the underdamped and overdamped dynamics, while their unweighted difference always tends to vanish.
Effect of carbazole as a donor moiety on the second-order nonlinearity of organic molecules
NASA Astrophysics Data System (ADS)
Meshulam, Guilia; Berkovic, Garry; Kotler, Zvi; Ben-Asuly, Amos; Mazor, Royi; Shapiro, Lev; Khodorkovsky, Vladimir
1999-10-01
The second order nonlinearity of conjugated organic molecules involving, 1,3 indandione derivatives as an acceptor moiety has been studied. Varying the donor from dialkylamino to the chemically similar substituent, N- carbazolyl resulted in a drastic reduction of electric field induced second harmonic (beta) values. For some molecules, even a small negative value of (beta) was received. Quantum chemical calculations indicate that the decrease occurs as a result of two overlapping transitions, which contribute to (beta) with opposite signs. The charge transfer band gives a positive (beta) zzz along the molecular long axis, while a transition essentially within the carbazole moiety provides a negative (beta zzz contribution to (beta EFISH. Thus, these molecules must be described with a 2D model as opposed to the 'classical' model of 1D nonlinear optical chromophores. The prediction of the 2D model was verified experimentally by using a combination of two methods, EFISH and Hyper-Rayleigh Scattering, which probe different combination of the (beta) tensor elements.
Second-order small-disturbance solutions for hypersonic flow over power-law bodies
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1975-01-01
Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.
NASA Astrophysics Data System (ADS)
Pointon, T. D.
2008-10-01
A second-order, exact charge-conserving algorithm for accumulating charge and current on the spatial grid for electromagnetic particle-in-cell (EM-PIC) simulation in bounded geometry is presented. The algorithm supports standard EM-PIC exterior boundary conditions and complex internal conductors on non-uniform grids. Boundary surfaces are handled by smoothly transitioning from second to first-order weighting within half a cell of the boundary. When a particle is exactly on the boundary surface (either about to be killed, or just created), the weighting is fully first-order. This means that particle creation and particle/surface interaction models developed for first-order weighting do not need to be modified. An additional feature is the use of an energy-conserving interpolation scheme from the electric field on the grid to the particles. Results show that high-density, cold plasmas with ωΔt˜1, and Δx/λ≫1, can be modeled with reasonable accuracy and good energy conservation. This opens up a significant new capability for explicit simulation of high-density plasmas in high-power devices.
On the effective behavior of nonlinear inelastic composites: II. A second-order procedure
NASA Astrophysics Data System (ADS)
Lahellec, Noël; Suquet, Pierre
2007-09-01
A new method for determining the overall behavior of composite materials comprising nonlinear viscoelastic and elasto-viscoplastic constituents is presented. Part I of this work showed that upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In part I of this paper the nonlinearity was handled using a variational (or secant) technique. In this second part of the study, a proper modification of the second-order procedure of Ponte Castañeda is proposed and leads to replacing, at each time-step, the actual nonlinear viscoelastic composite by a linear viscoelastic one. The linearized problem is even further simplified by using an "effective internal variable" in each individual phase. The resulting predictions are in good agreement with exact results and improve on the predictions of the secant model proposed in part I of this paper.
NASA Astrophysics Data System (ADS)
Lahellec, N.; Mazerolle, F.; Michel, J. C.
2004-01-01
This paper deals with some theoretical and experimental aspects of the behavior of periodic hyperelastic composites. We focus here on composites consisting of an elastomeric matrix periodically reinforced by long fibers. The paper is composed of three parts. The first part deals with the theoretical aspects of compressible behavior. The second-order theory of Ponte Castañeda (J. Mech. Phys. Solids 44 (1996) 827) is considered and extended to periodic microstructures. Comparisons with results obtained by the finite element method show that the composite behavior predicted by the present model is much more accurate for compressible than for incompressible materials. The second part deals with the extension of the method to incompressible behavior. A mixed formulation (displacement-pressure) is used which improves the accuracy of the estimate given by the model. The third part presents experimental results. The composite tested is made of a rubber matrix reinforced by steel wires. Firstly, the matrix behavior is identified with a tensile test and a shear test carried out on homogeneous samples. Secondly, the composite is tested under shearing. The experimentally measured homogenized stress is then compared with the predictions of the model.
The second-order procedure: exact vs approximate results for isotropic, two-phase composites
NASA Astrophysics Data System (ADS)
Nebozhyn, M. V.; Castañeda, P. Ponte
1999-10-01
Estimates for the effective behavior of statistically isotropic, two-phase, nonlinear elastic (or viscous) composites were given by Ponte Castañeda (1996; J. Mech. Phys. Solids44, 827), making use of the 'second-order procedure', also introduced in that reference. The actual computation of these estimates took advantage of a simplifying hypothesis consisting of taking the average strain deviators in the phases to be proportional to the macroscopic strain deviator. In this paper, a more general analysis is presented that shows that while the 'proportional strain' hypothesis does hold for some special cases, it does not in general. In fact, the average strain deviators in the phases are found to be only co-axial with the macroscopic strain deviator. On the other hand, the proportional strain hypothesis, together with an approximate form of the relevant P tensor, is found to lead to fairly small errors, relative to the exact solution of the problem. The largest errors, which occur for large phase contrast and nonlinearity, are less than about two percent. Because of this, and given the significant simplifications achieved, the use of the proportional strain hypothesis and of the approximate form of the P tensor are recommended. Certainly, these approximations are much more accurate than the isotropic-type approximations that have been used in the past in the context of other homogenization procedures.
Second-order estimates for the large-deformation response of particle-reinforced rubbers
NASA Astrophysics Data System (ADS)
Lopez-Pamies, Oscar; Ponte Castañeda, Pedro
2003-01-01
This paper presents the application of a recently proposed 'second-order' homogenization method (J. Mech. Phys. Solids 50 (2002) 737-757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of 'generalized' secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin-Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389-1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).
Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals
NASA Astrophysics Data System (ADS)
Liu, Yi; Ponte Castañeda, Pedro
2004-02-01
A recently developed "second-order" homogenization procedure (Ponte Castañeda (J. Mech. Phys. Solids 50 (2002a, b) 737, 759)) is extended to viscoplastic polycrystals and applied to compute the effective response of a certain special class of isotropic polycrystals. The method itself reduces to a simple expression requiring the computation of the averages of the stress field and the covariances of its fluctuations over the various grain orientations in an optimally selected "linear comparison polycrystal". Therefore, the method not only allows the determination of the effective behavior of the polycrystal, but as a byproduct also yields information on the heterogeneity of the stress and strain-rate fields within the polycrystal. An application is given for a model 2-dimensional, isotropic polycrystal with power-law behavior for the constituent grains. The resulting predictions for the effective behavior are found to satisfy sharp bounds available from the literature and to be consistent with the results of recent numerical simulations. The associated averages and fluctuations of the stresses and strain rates are found to depend strongly on the strain-rate sensitivity (i.e., nonlinearity) and grain anisotropy. In particular, the stress and strain-rate fluctuations were found to grow and become strongly anisotropic with increasing values of the nonlinearity and grain anisotropy parameters.
Pachori, Ram Bilas; Patidar, Shivnarayan
2014-02-01
Epilepsy is a neurological disorder which is characterized by transient and unexpected electrical disturbance of the brain. The electroencephalogram (EEG) is a commonly used signal for detection of epileptic seizures. This paper presents a new method for classification of ictal and seizure-free EEG signals. The proposed method is based on the empirical mode decomposition (EMD) and the second-order difference plot (SODP). The EMD method decomposes an EEG signal into a set of symmetric and band-limited signals termed as intrinsic mode functions (IMFs). The SODP of IMFs provides elliptical structure. The 95% confidence ellipse area measured from the SODP of IMFs has been used as a feature in order to discriminate seizure-free EEG signals from the epileptic seizure EEG signals. The feature space obtained from the ellipse area parameters of two IMFs has been used for classification of ictal and seizure-free EEG signals using the artificial neural network (ANN) classifier. It has been shown that the feature space formed using ellipse area parameters of first and second IMFs has given good classification performance. Experimental results on EEG database available by the University of Bonn, Germany, are included to illustrate the effectiveness of the proposed method.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1991-01-01
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
NASA Astrophysics Data System (ADS)
Quan, Runai; Zhai, Yiwei; Wang, Mengmeng; Hou, Feiyan; Wang, Shaofeng; Xiang, Xiao; Liu, Tao; Zhang, Shougang; Dong, Ruifang
2016-07-01
Based on the second-order quantum interference between frequency entangled photons that are generated by parametric down conversion, a quantum strategic algorithm for synchronizing two spatially separated clocks has been recently presented. In the reference frame of a Hong-Ou-Mandel (HOM) interferometer, photon correlations are used to define simultaneous events. Once the HOM interferometer is balanced by use of an adjustable optical delay in one arm, arrival times of simulta- neously generated photons are recorded by each clock. The clock offset is determined by correlation measurement of the recorded arrival times. Utilizing this algorithm, we demonstrate a proof-of-principle experiment for synchronizing two clocks separated by 4 km fiber link. A minimum timing stability of 0.44 ps at averaging time of 16000 s is achieved with an absolute time accuracy of 73.2 ps. The timing stability is verified to be limited by the correlation measurement device and ideally can be better than 10 fs. Such results shine a light to the application of quantum clock synchronization in the real high-accuracy timing system.
NASA Astrophysics Data System (ADS)
Casanova, David; Rhee, Young Min; Head-Gordon, Martin
2008-04-01
Scaled opposite spin (SOS) second order perturbative corrections to single excitation configuration interaction (CIS) are extended to correctly treat quasidegeneracies between excited states. Two viable methods, termed as SOS-CIS(D0) and SOS-CIS(D1), are defined, implemented, and tested. Each involves one empirical parameter (plus a second for the SOS-MP2 ground state), has computational cost that scales with the fourth power of molecule size, and has storage requirements that are cubic, with only quantities of the rank of single excitations produced and stored during iterations. Tests on a set of low-lying adiabatic valence excitation energies and vertical Rydberg excitations of organic and inorganic molecules show that the empirical parameter can be acceptably transferred from the corresponding nondegenerate perturbation theories without any further fitting. Further tests on higher excited states show that the new methods correctly perform for surface crossings for which nondegenerate approaches fail. Numerical results show that SOS-CIS(D0) appears to treat Rydberg excitations in a more balanced way than SOS-CIS(D1) and is, therefore, likely to be the preferred approach. It should be useful for exploring excited state geometries, transition structures, and conical intersections for states of medium to large organic molecules that are dominated by single excitations.
Estimating Sea Ice Parameters from Multi-Look SAR Images Using - and Second-Order Variograms
NASA Astrophysics Data System (ADS)
Wang, Xiaojian; Li, Yu; Zhao, Quanhua
2016-06-01
The spatial structures revealed in SAR intensity imagery provide essential information characterizing the natural variation processes of sea ice. This paper proposes a new method to extract the spatial structures of sea ice based on two spatial stochastic models. One is a multi-Gamma model, which characterizes continuous variations corresponding to ice-free area or the background. The other is a Poisson line mosaic model, which characterizes the regional variations of sea ice with different types. The linear combination of the two models builds the mixture model to represent spatial structures of sea ice within SAR intensity imagery. To estimate different sea ice parameters, such as its concentration, scale etc. We define two kinds of geostatistic metrics, theoretical first- and second-order variograms. Their experimental alternatives can be calculated from the SAR intensity imagery directly, then the parameters of the mixture model are estimated through fitting the theoretical variograms to the experimental ones, and by comparing the estimated parameters to the egg code, it is verified that the estimated parameters can indicate sea ice structure information showing in the egg code. The proposed method is applied to simulated images and Radarsat-1 images. The results of the experiments show that the proposed method can estimate the sea ice concentration and floe size accurately and stably within SAR testing images.
Li, Lebao; Sun, Lingling; Zhang, Shengzhou
2016-05-01
A new mean deviation coupling synchronization control strategy is developed for multiple motor control systems, which can guarantee the synchronization performance of multiple motor control systems and reduce complexity of the control structure with the increasing number of motors. The mean deviation coupling synchronization control architecture combining second-order adaptive sliding mode control (SOASMC) approach is proposed, which can improve synchronization control precision of multiple motor control systems and make speed tracking errors, mean speed errors of each motor and speed synchronization errors converge to zero rapidly. The proposed control scheme is robustness to parameter variations and random external disturbances and can alleviate the chattering phenomena. Moreover, an adaptive law is employed to estimate the unknown bound of uncertainty, which is obtained in the sense of Lyapunov stability theorem to minimize the control effort. Performance comparisons with master-slave control, relative coupling control, ring coupling control, conventional PI control and SMC are investigated on a four-motor synchronization control system. Extensive comparative results are given to shown the good performance of the proposed control scheme.
A second-order Godunov method for wave problems in coupled solid-water-gas systems
Tang, H.S.; Sotiropoulos, F.
1999-05-20
Wave problems in solid-water-gas systems with distinct phase interfaces are commonly encountered in practice, such as in water entry of a recovered body, reservoir-dam interaction during earthquakes, and spallation of steel plates caused by blast waves. Here, the authors present a second-order Godunov method for computing unsteady, one-dimensional wave problems with a fracture and cavitation in coupled solid-water-gas systems. The method employs a hydro-elasto-plastic body, the Tait equation, and the ideal gas law for solid, water, and gaseous phases, respectively, and models both fractures and cavities as vacuum zones with distinct borders. The numerical approach utilizes a Lagrangian formulation in conjunction with local solid-water-gas-vacuum Riemann problems, which have unique solutions and can be solved efficiently. The various phases are treated in a unified manner and no supplementary interface conditions are necessary for tracking material boundaries. Calculations are carried out for Riemann problems, wave propagation and reflection in a water-rock-air system, and spallation and cavitation in an explosion-steel-water-gas system. It is shown that the Godunov method has high resolution for shocks and phase interfaces, clearly resolves elastic and plastic waves, and successfully describes onset and propagation of fracture and cavitation zones.
Naito, Mika; Seki, Yoshimi
2009-01-01
To investigate the relation between cognitive and affective social understanding, Japanese 4- to 8-year-olds received tasks of first- and second-order false beliefs and prosocial and self-presentational display rules. From 6 to 8 years, children comprehended display rules, as well as second-order false belief, using social pressures justifications decreasingly and motivational justifications with embedded perspectives increasingly with age. Although not related to either type of display across ages, second-order tasks were associated with both types of display tasks only at 8 years when examined in each age group. Results suggest that children base their second-order theory of mind and display rules understanding on distinct reasoning until middle childhood, during which time the originally distinct aspects of social understanding are integrated. PMID:19120423
NASA Technical Reports Server (NTRS)
Ha Minh, H.; Viegas, J. R.; Rubesin, M. W.; Spalart, P.; Vandromme, D. D.
1989-01-01
The turbulent boundary layer under a freestream whose velocity varies sinusoidally in time around a zero mean is computed using two second order turbulence closure models. The time or phase dependent behavior of the Reynolds stresses are analyzed and results are compared to those of a previous SPALART-BALDWIN direct simulation. Comparisons show that the second order modeling is quite satisfactory for almost all phase angles, except in the relaminarization period where the computations lead to a relatively high wall shear stress.
Do we care about the distance to the CMB? Clarifying the impact of second-order lensing
Bonvin, Camille; Clarkson, Chris; Durrer, Ruth; Maartens, Roy; Umeh, Obinna E-mail: chris.clarkson@gmail.com E-mail: roy.maartens@gmail.com
2015-06-01
It has recently been shown that second-order corrections to the background distance-redshift relation can build up significantly at large redshifts, due to an aggregation of gravitational lensing events. This shifts the expectation value of the distance to the CMB by 1%. In this paper we show that this shift is already properly accounted for in standard CMB analyses. We clarify the role that the area distance to the CMB plays in the presence of second-order lensing corrections.
NASA Astrophysics Data System (ADS)
Wang, Yuqing; Peng, Zhenming
2016-06-01
As the extension of time-bandwidth product (TBP) in the fractional domain, the generalized time-bandwidth product (GTBP) provides a rotation-independent measure of compactness. A new fractional S transform (FrST) is proposed to avoid missing the physical meaning of the fractional time-frequency plane. FrST is based on the GTBP criterion and the time-frequency rotation property of fractional Fourier transform (FrFT). In addition, we introduce the normalized second-order central moment (NSOCM) calculation method to determine the optimal order. The optimal order searching process can be converted into the NSOCM calculation. Compared with TBP search algorithms, the NSOCM approach has higher computational efficiency. The qualitative advantage of the NSOCM approach in the optimal order selection is demonstrated by a series of model tests. The optimal FrST based on NSOCM (OFrST) can produce more compact time-frequency support than the S transform. The real seismic data spectral decomposition results show that the proposed algorithm can obtain single-frequency visualization with better time-frequency concentration, thereby enhancing the precision of reservoir prediction.
Grabowski, Ireneusz Śmiga, Szymon; Buksztel, Adam; Fabiano, Eduardo; Teale, Andrew M.; Sala, Fabio Della
2014-07-14
The performance of correlated optimized effective potential (OEP) functionals based on the spin-resolved second-order correlation energy is analysed. The relative importance of singly- and doubly- excited contributions as well as the effect of scaling the same- and opposite- spin components is investigated in detail comparing OEP results with Kohn–Sham (KS) quantities determined via an inversion procedure using accurate ab initio electronic densities. Special attention is dedicated in particular to the recently proposed scaled-opposite–spin OEP functional [I. Grabowski, E. Fabiano, and F. Della Sala, Phys. Rev. B 87, 075103 (2013)] which is the most advantageous from a computational point of view. We find that for high accuracy, a careful, system dependent, selection of the scaling coefficient is required. We analyse several size-extensive approaches for this selection. Finally, we find that a composite approach, named OEP2-SOSh, based on a post-SCF rescaling of the correlation energy can yield high accuracy for many properties, being comparable with the most accurate OEP procedures previously reported in the literature but at substantially reduced computational effort.
Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
NASA Astrophysics Data System (ADS)
del Campo, A.; Kibble, T. W. B.; Zurek, W. H.
2013-10-01
When a second-order phase transition is crossed at a finite rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: it obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental testing of defect formation theories.
Explicitly correlated atomic orbital basis second order Møller-Plesset theory.
Hollman, David S; Wilke, Jeremiah J; Schaefer, Henry F
2013-02-14
The scope of problems treatable by ab initio wavefunction methods has expanded greatly through the application of local approximations. In particular, atomic orbital (AO) based wavefunction methods have emerged as powerful techniques for exploiting sparsity and have been applied to biomolecules as large as 1707 atoms [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012)]. Correlated wavefunction methods, however, converge notoriously slowly to the basis set limit and, excepting the use of large basis sets, will suffer from a severe basis set incompleteness error (BSIE). The use of larger basis sets is prohibitively expensive for AO basis methods since, for example, second-order Møller-Plesset perturbation theory (MP2) scales linearly with the number of atoms, but still scales as O(N(5)) in the number of functions per atom. Explicitly correlated F12 methods have been shown to drastically reduce BSIE for even modestly sized basis sets. In this work, we therefore explore an atomic orbital based formulation of explicitly correlated MP2-F12 theory. We present working equations for the new method, which produce results identical to the widely used molecular orbital (MO) version of MP2-F12 without resorting to a delocalized MO basis. We conclude with a discussion of several possible approaches to a priori screening of contraction terms in our method and the prospects for a linear scaling implementation of AO-MP2-F12. The discussion includes concrete examples involving noble gas dimers and linear alkane chains.
Rhee, Young Min; Head-Gordon, Martin
2007-02-01
Two modifications of the perturbative doubles correction to configuration interaction with single substitutions (CIS(D)) are suggested, which are excited state analogs of ground state scaled second order Moeller-Plesset (MP2) methods. The first approach employs two parameters to scale the two spin components of the direct term of CIS(D), starting from the two-parameter spin-component scaled (SCS) MP2 ground state, and is termed SCS-CIS(D). An efficient resolution-of-the-identity (RI) implementation of this approach is described. The second approach employs a single parameter to scale only the opposite-spin direct term of CIS(D), starting from the one-parameter scaled opposite spin (SOS) MP2 ground state, and is called SOS-CIS(D). By utilizing auxiliary basis expansions and a Laplace transform, a fourth order algorithm for SOS-CIS(D) is described and implemented. The parameters describing SCS-CIS(D) and SOS-CIS(D) are optimized based on a training set including valence excitations of various organic molecules and Rydberg transitions of water and ammonia, and they significantly improve upon CIS(D) itself. The accuracy of the two methods is found to be comparable. This arises from a strong correlation between the same-spin and opposite-spin portions of the excitation energy terms. The methods are successfully applied to the zincbacteriochlorin-bacteriochlorin charge transfer transition, for which time-dependent density functional theory, with presently available exchange-correlation functionals, is known to fail. The methods are also successfully applied to describe various electronic transitions outside of the training set. The efficiency of SOS-CIS(D) and the auxiliary basis implementation of CIS(D) and SCS-CIS(D) are confirmed with a series of timing tests.
The making of an Alfvenic fluctuation: The resolution of a second-order analysis
NASA Technical Reports Server (NTRS)
Vasquez, Bernard J.; Hollweg, Joseph V.
1995-01-01
Ulysses observations of the high speed polar streams show that they are largely occupied by very large amplitude Alfvenic fluctuations accompanied by many rotational discontinuities. These fluctuations have a nearly constant magnetic intensity or amplitude, and the magnetic field direction per wave cycle sweeps only through a limited arc, much as a car wiperblade would do. Barnes and Hollweg (JGR, 79, 2302, 1974) suggested that this unusual waveform could arise from an obliquely propagating and linearly polarized Alfven wave of finite amplitude. From a second-order analysis, they showed that the existence of a particular solution with a constant amplitude but could not resolve the outcome of the homogeneous solution which consisted of fast waves. They suggested that Landau damping of these fast waves may be needed to get the observed waveform. We present a 1 1/2 D hybrid simulation which is fully nonlinear and correctly describes the ion kinetics for an initially monochromatic and linearly polarized Alfven wave propagating obliquely to the background magnetic field. The wave has a large amplitude and a wavelength so long that it can be considered dispersionless for simulation times. At early times, the second harmonic in density and in magnetic field transverse to the initial wave magnetic field are generated and have more power than other harmonics. Steepening is observed with a weak fast shock emerging, but no rotational discontinuity is left behind, and instead a constant amplitude and an arc-shaped waveform is made. The compressional component which develops after the shocks have dissipated is to zeroth order better described as a pure acoustic wave than as a fast wave. This might be explained by the relaxing of the Alfven wave to a state where its ponderomotive force vanishes so that the compressional component can travel almost independently of it.
Second order Method for Solving 3D Elasticity Equations with Complex Interfaces
Wang, Bao; Xia, Kelin; Wei, Guo-Wei
2015-01-01
Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422