Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D.; Head-Gordon, Martin
2004-08-02
A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Moller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite spin second order energy (SOS-MP2) yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the 5th order computational steps associated with MP2 theory, even without exploiting any spatial locality. A 4th order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.
Vilkas, M J; Ishikawa, Y; Trabert, E
2007-03-27
Relativistic multireference many-body perturbation theory calculations have been performed on Xe{sup 43+}-Xe{sup 39+} ions, resulting in energy levels, electric dipole transition probabilities, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, frequency-dependent Breit correction and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.
A localized basis that allows fast and accurate second order Moller-Plesset calculations
Subotnik, Joseph E.; Head-Gordon, Martin
2004-10-27
We present a method for computing a basis of localized orthonormal orbitals (both occupied and virtual), in whose representation the Fock matrix is extremely diagonal-dominant. The existence of these orbitals is shown empirically to be sufficient for achieving highly accurate MP@ energies, calculated according to Kapuy's method. This method (which we abbreviate KMP2), which involves a different partitioning of the n-electron Hamiltonian, scales at most quadratically with potential for linearity in the number of electrons. As such, we believe the KMP2 algorithm presented here could be the basis of a viable approach to local correlation calculations.
Intrinsic ambiguity in second order viscosity parameters in relativistic hydrodynamics
Nakayama, Yu
2012-01-01
We show that relativistic hydrodynamics in Minkowski space-time has intrinsic ambiguity in second order viscosity parameters in the Landau-Lifshitz frame. This stems from the possibility of improvements of energy-momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly non-conformal hydrodynamic theories can be hiddenly conformal invariant.
Relativistic quantum transport coefficients for second-order viscous hydrodynamics
Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw; Strickland, Michael
2015-01-01
We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of boost-invariant and transversally homogeneous longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of massive 0+1d Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation in relaxation-time approximation.
On the relative importance of second-order terms in relativistic dissipative fluid dynamics
Molnár, E; Denicol, G S; Rischke, D H
2013-01-01
In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scatt...
A covering second-order Lagrangian for the relativistic top without forces
Matsyuk, Roman
2012-01-01
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
Ten-no, Seiichiro; Yamaki, Daisuke
2012-10-07
We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Lévy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansätze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Møller-Plesset perturbation theory.
Derivation of second-order relativistic hydrodynamics for reactive multi-component systems
Kikuchi, Yuta; Kunihiro, Teiji
2015-01-01
We derive the second-order hydrodynamic equation for reactive multi-component systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation laws during the collision process. Our derivation is based on the renormalization group (RG) method, in which the Boltzmann equation is solved in an organized perturbation method as faithfully as possible and possible secular terms are resummed away by a suitable setting of the initial value of the distribution function. The microscopic formulae of the relaxation times and the lengths are explicitly given as well as those of the transport coefficients for the reactive multi-component system. The resultant hydrodynamic equation with these formulae has nice properties that it satisfies the positivity of the entropy production rate and the Onsager's reciprocal theorem, which ensure the validity of our derivation.
Hwang, J.; Noh, H.
2004-01-01
The dynamic world model and its linear perturbations were first studied in Einstein's gravity. In the system without pressure the relativistic equations coincide exactly with the later known ones in Newton's gravity. Here we prove that, except for the gravitational wave contribution, even to the second-order perturbations, equations for the relativistic irrotational zero-pressure fluid in a flat Friedmann background coincide exactly with the previously known Newtonian equations. Thus, to the ...
Luo,Y.; Tepikian, S.; Fischer, W.; Robert-Demolaize, G.; Trbojevic, D.
2009-01-02
Based on the contributions of the chromatic sextupole families to the half-integer resonance driving terms, we discuss how to sort the chromatic sextupoles in the arcs of the Relativistic Heavy Ion Collider (RHIC) to easily and effectively correct the second order chromaticities. We propose a method with 4 knobs corresponding to 4 pairs of chromatic sextupole families to online correct the second order chromaticities. Numerical simulation justifies this method, showing that this method reduces the unbalance in the correction strengths of sextupole families and avoids the reversal of sextupole polarities. Therefore, this method yields larger dynamic apertures for the proposed RHIC 2009 100GeV polarized proton run lattices.
Amano, Takanobu
2016-01-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small sca...
Amano, Takanobu
2016-11-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.
Olejniczak, Malgorzata; Gomes, Andre Severo Pereira
2016-01-01
We report an implementation of the nuclear magnetic resonance (NMR) shielding ($\\sigma$), isotope-independent indirect spin-spin coupling ($K$) and the magnetizability ($\\xi$) tensors in the frozen density embedding (FDE) scheme using the four-component (4c) relativistic Dirac--Coulomb (DC) Hamiltonian and the non-collinear spin density functional theory (SDFT). The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXH$\\cdots$OH$_2$ complexes (X = Se, Te, Po) and compared with the supermolecular calculations and with the approach based on the integration of the magnetically induced current density vector. A comparison with the approximate Zeroth-Order Regular Approximation (ZORA) Hamiltonian indicates non-negligible differences in $\\sigma$ and $K$ in the HPoH$\\cdots$OH$_2$ complex, and calls for a thourou...
Kobayashi, Masato; Imamura, Yutaka; Nakai, Hiromi
2007-08-21
A new scheme for obtaining the approximate correlation energy in the divide-and-conquer (DC) method of Yang [Phys. Rev. Lett. 66, 1438 (1991)] is presented. In this method, the correlation energy of the total system is evaluated by summing up subsystem contributions, which are calculated from subsystem orbitals based on a scheme for partitioning the correlation energy. We applied this method to the second-order Moller-Plesset perturbation theory (MP2), which we call DC-MP2. Numerical assessment revealed that this scheme provides a reliable correlation energy with significantly less computational cost than the conventional MP2 calculation.
Mehrabi Pari, Sharareh; Taghavi Shahri, Fatemeh; Javidan, Kurosh
2016-10-01
The nuclear suppression factor RAA and elliptic flow ν2 are calculated by considering the effects of shear viscosity to the entropy density ratio η/s, using the viscose hydrodynamics at the first- and second-orders of approximation and considering temperature dependent coupling αs(T). It is shown that the second-order viscose hydrodynamics (varying shear viscosity to entropy ratio) with averaged value of 4πη/s = 1.5 ± 0.1 gives the best results of RAA and ν2 in comparison to the experimental data.
Nakano, Masahiko; Seino, Junji; Nakai, Hiromi
2017-05-01
We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.
Bates, Jefferson E.; Shiozaki, Toru [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States)
2015-01-28
We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of the Dirac equation that takes into account spin–orbit and other relativistic effects self-consistently. Orbitals are optimized using a trust-region quasi-Newton method with Hessian updates so that energies are minimized with respect to rotations among electronic orbitals and maximized with respect to rotations between electronic and positronic orbitals. Utilizing density fitting and parallel computation, we demonstrate that Dirac–Coulomb CASSCF calculations can be routinely performed on systems with 100 atoms and a few heavy-elements. The convergence behavior and wall times for octachloridodirhenate(III) and a tungsten methylidene complex are presented. In addition, the excitation energies of octachloridodirhenate(III) are reported using a state-averaged variant.
Bates, Jefferson E.; Shiozaki, Toru
2015-01-01
We develop an efficient algorithm for four-component complete active space self-consistent field (CASSCF) methods on the basis of the Dirac equation that takes into account spin-orbit and other relativistic effects self-consistently. Orbitals are optimized using a trust-region quasi-Newton method with Hessian updates so that energies are minimized with respect to rotations among electronic orbitals and maximized with respect to rotations between electronic and positronic orbitals. Utilizing density fitting and parallel computation, we demonstrate that Dirac-Coulomb CASSCF calculations can be routinely performed on systems with 100 atoms and a few heavy-elements. The convergence behavior and wall times for octachloridodirhenate(III) and a tungsten methylidene complex are presented. In addition, the excitation energies of octachloridodirhenate(III) are reported using a state-averaged variant.
Chen, Lizhu; Cui, Fenping; Wu, Yuanfang
2016-01-01
We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant ($C_6/C_2$) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on $C_6/C_2$ of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract $C_6/C_2$ with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of $C_6/C_2$ is observed in central collisions using the UrQMD model. We find if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.
Chen, Lizhu; Li, Zhiming; Cui, Fenping; Wu, Yuanfang
2017-01-01
We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant (C6 /C2) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on C6 /C2 of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract C6 /C2 with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of C6 /C2 is observed in central collisions using the UrQMD model. We find that if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.
Wang, L. M.; Li, Chun; Yan, Z.-C.; Drake, G. W. F.
2017-03-01
Isotope shifts and total transition frequencies are calculated for the 2 2S-3 2S transition of the lithium isotopes 6Li, 7Li, 8Li, 9Li, and the halo nucleus 11Li. The accuracy is improved for previously calculated relativistic and quantum electrodynamic corrections, and in particular a disagreement for the Bethe logarithm is resolved for the ground 2S state. Our previous result is confirmed for the 2 2P state. We use the pseudostate expansion method to perform the sum over virtual intermediate states. Results for the second-order relativistic recoil term of order α2(μ/M ) 2 Ry are shown to make a significant contribution relative to the theoretical uncertainty, but because of accidental cancellations the final result for the isotope shift is nearly unchanged. However, the spin-orbit term makes an unexpectedly large contribution to the splitting isotope shift (SIS) for the 2 1/2 2P -2 3/2 2P fine structure, increasing the theoretical value for the 6Li-7Li isotopes to 0.556 31 (7 )±0.001 MHz. A comparison is made with high-precision measurements and other calculations for the SIS and for the total 2 2S-3 2S transition frequency.
Johnny Espin
2015-06-01
Full Text Available It is known, though not commonly, that one can describe fermions using a second order in derivatives Lagrangian instead of the first order Dirac one. In this description the propagator is scalar, and the complexity is shifted to the vertex, which contains a derivative operator. In this paper we rewrite the Lagrangian of the fermionic sector of the Standard Model in such second order form. The new Lagrangian is extremely compact, and is obtained from the usual first order Lagrangian by integrating out all primed (or dotted 2-component spinors. It thus contains just half of the 2-component spinors that appear in the usual Lagrangian, which suggests a new perspective on unification. We sketch a natural in this framework SU(2×SU(4⊂SO(9 unified theory.
Espin, Johnny
2015-01-01
It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then integrating out the spinors of one chirality ($e.g.$ primed or dotted). The resulting new Lagrangian is second-order in derivatives, and contains two-component spinors of only one chirality. The new second-order formulation simplifies the fermion Feynman rules of the theory considerably, $e.g.$ the propagator becomes a multiple of an identity matrix in the field space. The aim of this thesis is to work out the details of this formulation for theories such as Quantum Electrodynamics, and the Standard Model of elementary particles. After having developed the tools necessary to establish the second-order formalism as an equivalent approach to spinor field theories, we proceed with some important consistency checks that the new formulation is required to pass, namely the presence...
Second Order Darboux Displacements
Samsonov, B F; Negro, J; Nieto, L M
2003-01-01
The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived.
Kim, Inkoo; Lee, Yoon Sup, E-mail: yslee@kaist.edu [Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701 (Korea, Republic of)
2014-10-28
We report the formulation and implementation of KRCASPT2, a two-component multi-configurational second-order perturbation theory based on Kramers restricted complete active space self-consistent field (KRCASSCF) reference function, in the framework of the spin-orbit relativistic effective core potential. The zeroth-order Hamiltonian is defined as the sum of nondiagonal one-electron operators with generalized two-component Fock matrix elements as scalar factors. The Kramers symmetry within the zeroth-order Hamiltonian is maintained via the use of a state-averaged density, allowing a consistent treatment of degenerate states. The explicit expressions are derived for the matrix elements of the zeroth-order Hamiltonian as well as for the perturbation vector. The use of a fully variational reference function and nondiagonal operators in relativistic multi-configurational perturbation theory is reported for the first time. A series of initial calculations are performed on the ionization potential and excitation energies of the atoms of the 6p-block; the results display a significant improvement over those from KRCASSCF, showing a closer agreement with experimental results. Accurate atomic properties of the superheavy elements of the 7p-block are also presented, and the electronic structures of the low-lying excited states are compared with those of their lighter homologues.
Kim, Inkoo; Lee, Yoon Sup
2014-10-28
We report the formulation and implementation of KRCASPT2, a two-component multi-configurational second-order perturbation theory based on Kramers restricted complete active space self-consistent field (KRCASSCF) reference function, in the framework of the spin-orbit relativistic effective core potential. The zeroth-order Hamiltonian is defined as the sum of nondiagonal one-electron operators with generalized two-component Fock matrix elements as scalar factors. The Kramers symmetry within the zeroth-order Hamiltonian is maintained via the use of a state-averaged density, allowing a consistent treatment of degenerate states. The explicit expressions are derived for the matrix elements of the zeroth-order Hamiltonian as well as for the perturbation vector. The use of a fully variational reference function and nondiagonal operators in relativistic multi-configurational perturbation theory is reported for the first time. A series of initial calculations are performed on the ionization potential and excitation energies of the atoms of the 6p-block; the results display a significant improvement over those from KRCASSCF, showing a closer agreement with experimental results. Accurate atomic properties of the superheavy elements of the 7p-block are also presented, and the electronic structures of the low-lying excited states are compared with those of their lighter homologues.
Kullie, Ossama [Institute de Chimie de Strasbourg, CNRS et Universite de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg (France); Saue, Trond, E-mail: trond.saue@isamc.ups-tlse.fr [Laboratoire de Chimie et Physique Quantique (UMR 5626), CNRS/Universite de Toulouse 3 (Paul Sabatier), 118 route de Narbonne, 31062 Toulouse (France)
2012-02-20
Highlights: Black-Right-Pointing-Pointer First implementation of 4-component relativistic long-range MP2/short-range DFT. Black-Right-Pointing-Pointer First complete study of spectroscopic constants of the rare gas dimers He{sub 2}-Uuo{sub 2}. Black-Right-Pointing-Pointer MP2-srLDA has a performance similar to pure MP2, but the overbinding of MP2 can be tuned by the range-separation parameter. - Abstract: We report the implementation of long-range second-order Moller-Plesset perturbation theory coupled with short-range density functional theory (MP2-srDFT) based on the 4-component relativistic Dirac-Coulomb Hamiltonian. The range separation of the two-electron interaction is based on the error function, such that the long-range interaction, to be handled by wave function theory, corresponds to the potential of finite electrons with a Gaussian charge distribution. We argue that the interelectronic distance associated with the range-separation parameter should accordingly be determined from a Gaussian rather than a hard-sphere model. As a first application of our relativistic MP2-srDFT implementation we calculate spectroscopic constants of the complete series of homoatomic rare gas dimers, from helium to the superheavy element 118 and with bonding dominated by dispersion forces. We find that the MP2-srDFT method is less sensitive to the basis set quality than pure MP2, but for the heavier rare gas dimers the computational cost is approximately the same as for pure MP2 if one seeks convergence with respect to both basis set and number of correlated electrons. The inclusion of a short-range DFT contribution allows to dampen the tendency of pure MP2 to overbind the heavier dimers, but it is difficult to find an optimal range-separation parameter for the whole series of diatomics. Interestingly, MP2-srLDA shows better performance than MP2-srPBE for the selected molecules.
Quantization of Second Order Fermions
Angeles, Rene; Napsuciale, Mauro, E-mail: rene@fisica.ugto.mx, E-mail: mauro@fisica.ugto.mx [Departamento de Fisica, Universidad de Guanajuato, Lomas del Bosque 103, Fraccionamiento Lomas del Campestre, Leon Guanajuato, 37150 (Mexico)
2011-04-01
We review how second order equations for fields arise just by using projectors over Poincare invariant subspaces. We focus in the case of fields describing massive spin 1/2 particles, we propose a particular second order Lagrangian and present preliminary results in its quantization.
Doser, Bernd; Lambrecht, Daniel S; Kussmann, Jörg; Ochsenfeld, Christian
2009-02-14
A Laplace-transformed second-order Moller-Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the atomic orbital (AO)-MP2 energy are preselected using the so-called multipole-based integral estimates (MBIE) introduced earlier by us [J. Chem. Phys. 123, 184102 (2005)]. Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AO-MP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the calculation of intermolecular interaction energies for the S22 test set. The efficiency and accuracy of our AO-MP2 method is demonstrated for linear alkanes, stacked DNA base pairs, and carbon nanotubes: e.g., for DNA systems the crossover toward conventional MP2 schemes occurs between one and two base pairs. In this way, it is for the first time possible to compute wave function-based correlation energies for systems containing more than 1000 atoms with 10 000 basis functions as illustrated for a 16 base pair DNA system on a single-core computer, where no empirical restrictions are introduced and numerical accuracy is fully preserved.
Second-Order Footsteps Illusions
Akiyoshi Kitaoka
2015-12-01
Full Text Available 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.
Second order pedagogy as an example of second order cybernetics
Anne B. Reinertsen
2012-07-01
Full Text Available This article is about seeing/creating/trying out an idea of pedagogy and pedagogical/ educational research in/as/with self-reflexive, circular and diffractive perspectives and about using second order cybernetics as thinking tool. It is a move away from traditional hypothesis driven activities and a move towards data driven pedagogies and research: Teachers, teacher researchers and researchers simultaneously producing and theorizing our practices and ourselves. Deleuzian becomings- eventually becomings with data - theory - theodata is pivotal. It is a move towards a Derridean bricolage. A different science of pedagogy operating as a circular science of self-reflexivity and diffraction in search of quality again and again and again: Theopractical becomings and inspiractionresearch.
Second-order gravitational self-force
Pound, Adam
2012-01-01
Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The motion is found to be geodesic in a certain locally defined regular geometry satisfying Einstein's equation at second order. I provide a practical scheme for numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.
Source of second order chromaticity in RHIC
Luo, Y.; Gu, X.; Fischer, W.; Trbojevic, D.
2011-01-01
In this note we will answer the following questions: (1) what is the source of second order chromaticities in RHIC? (2) what is the dependence of second order chromaticity on the on-momentum {beta}-beat? (3) what is the dependence of second order chromaticity on {beta}* at IP6 and IP8? To answer these questions, we use the perturbation theory to numerically calculate the contributions of each quadrupole and sextupole to the first, second, and third order chromaticities.
Second-order logic and set theory
J. Väänänen
2015-01-01
Both second-order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved. We take it upon ourselves in this paper to compare the two approaches, second-order logic on one hand and set theory on
Second-Order Gravitational Self-Force
Pound, Adam
2015-01-01
In order to extract physical parameters from the waveform of an extreme-mass-ratio binary, one requires a second-order-accurate description of the motion of the smaller of the two objects in the binary. Using a method of matched asymptotic expansions, I derive the second-order equation of motion of a small, nearly spherical and non-rotating compact object in an arbitrary vacuum spacetime. I find that the motion is geodesic in a certain locally defined effective metric satisfying the vacuum Einstein equation through second order, and I outline a method of numerically determining this effective metric.
Forbidden second order optical nonlinearity of graphene
Cheng, J L; Sipe, J E
2016-01-01
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllablity of these responses by tuning the chemical potential, where the interband optical transitions play a dominant role.
Second-Order Science of Interdisciplinary Research
Alrøe, Hugo Fjelsted; Noe, Egon
2014-01-01
require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where...... there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory...... of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem...
Second-Order Science of Interdisciplinary Research
Alrøe, Hugo Fjelsted; Noe, Egon
2014-01-01
require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where...... there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory...... of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem...
Degenerate second order mean field games systems
Tonon, Daniela; Cardaliaguet, Pierre; Graber, Philip,; Poretta, Alessio
2014-01-01
Parallel session; International audience; We consider degenerate second order mean field games systems with a local coupling. The starting point is the idea that mean field games systems can be understood as an optimality condition for optimal control of PDEs. Developing this strategy for the degenerate second order case, we discuss the existence and uniqueness of a weak solution as well as its stability (vanishing viscosity limit). Speaker: Daniela TONON
Systemic Design for Second-Order Effects
Evan Barba
2017-04-01
Full Text Available Second-order effects refer to changes within a system that are the result of changes made somewhere else in the system (the first-order effects. Second-order effects can occur at different spatial, temporal, or organizational scales from the original interventions, and are difficult to control. Some organizational theorists suggest that careful management of feedback processes can facilitate controlled change from one organizational configuration to another. Recognizing that skill in managing feedback processes is a core competency of design suggests that design skills are potentially useful tools in achieving organizational change. This paper describes a case study in which a co-design methodology was used to control the second-order effects resulting from a classroom intervention to create organizational change. This approach is then theorized as the Instigator Systems approach.
Beyond Special Relativity at second order
Carmona, J M; Relancio, J J
2016-01-01
The study of generic, non-linear, deformations of Special Relativity parametrized by a high-energy scale $M$, which was carried out at first order in $M$ in Phys.Rev. D86, 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 $\\kappa$-Poincar\\'e, the most commonly used example in the literature, is reproduced as a particular case of the generic framework exposed here.
Second Order Mode Selective Phase-Matching
Lassen, Mikael Østergaard; Delaubert, Vincent; Bachor, Hans. A-
2006-01-01
We exploit second order (χ(2)) nonlinear optical phase matching for the selection of individual high order transverse modes. The ratio between the generated components can be adjusted continuously via changes in the phase-matching condition. ©2007 Optical Society of America...
Nonlinear second order elliptic equations involving measures
Marcus, Moshe
2013-01-01
This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data,especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.
Second order perturbation theory for embedded eigenvalues
Faupin, Jeremy; Møller, Jacob Schach; Skibsted, Erik
2011-01-01
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum...
Forte, G; March, N H; Pucci, R
2014-01-01
The Hartree-Fock (HF) method, supplemented by low-order Moller-Plesset (MP2) perturbation theory, has been utilized to predict the nuclear geometry, assuming planarity, of a low-lying isomer of the free space cluster BOSi$_2$. The planar structure found at equilibrium geometry is shown to be stable against small amplitude molecular vibrations. Finally, some brief comments are made on the possible relevance of the above free-space cluster geometry to the known B-O defects which limit the improvement of minority carrier lifetime in a form of p-type silicon.
On Second Order Degree of Graphs
Gabriela ARAUJO-PARDO; Camino BALBUENA; Mika OLSEN; Pilar VALENCIA
2012-01-01
Given a vertex v of a graph G the second order degree of v denoted as d2 (v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.
Pole Assignment for Second-Order Systems
CHU, E. K.
2002-01-01
This paper contains some results for pole assignment problems for the second-order system M ẍ(t)+D ẋ(t)+K x (t)=B u (t) . Specifically, Algorithm 0 constructs feedback matrices F1 and F2 such that the closed-loop quadratic pencil Pc( λ)= λ2M+ λ ( D+ BF2)+( K+ BF1) has a desired set of eigenvalues and the associated eigenvectors are well-conditioned. The method is a modification of the SVD-based method proposed by Juang and Maghami [1, 2] which is a second-order adaptation of the well-known robust eigenvalue assignment method by Kautsky et al. [3] for first-order systems. Robustness is achieved by minimising some not-so-well-known condition numbers of the eigenvalues of the closed-loop second-order pencil. We next consider the partial pole assignment problem. In 1997, Datta, Elhay and Ram proposed three biorthogonality relations for eigenvectors of symmetric definite quadratic pencils [4]. One of these relations was used to derive an explicit solution to the partial pole assignment problem by state feedback for the related single-input symmetric definite second-order control system. The solution shed new light on the stabilisation and control of large flexible space structures, for which only one small subset of the spectrum needs to be reassigned while retaining the complementary part of the spectrum. In this paper, the method has been generalised for multi-input and non-symmetric quadratic pencils. Finally, we discuss briefly the output feedback pole assignment problem.
Mode matching in second order susceptibility metamaterials
Héron, Sébastien; Haïdar, Riad
2016-01-01
We present an effective model for a subwavelength periodically patterned metallic layer, its cavities being filled with a nonlinear dielectric material, which accounts for both the linear and second order behavior. The effective non linear susceptibility for the homogenized layer is driven by the nonlinearity of the dielectric material and by the geometrical parameters, thus leading to much higher susceptibility than existing materials. This leads to a huge enhancement of non linear processes when used together with resonances. Furthermore, multiple resonances are taking place in the metallic cavities, and we investigate the mode matching situations for frequency conversion processes and show how it enhances further their efficiency.
Anomalous transport in second order hydrodynamics
Megías, Eugenio; Valle, Manuel
2016-11-01
We study the non-dissipative transport effects appearing at second order in the hydrodynamic expansion for a non-interacting gas of chiral fermions by using the partition function formalism. We discuss some features of the corresponding constitutive relations, derive the explicit expressions for the conductivities and compare with existing results in the literature. Talk given by E. Megías at the 4th International Conference on New Frontiers in Physics (ICNFP 2015), 23-30 August 2015, Kolymbari, Crete, Greece.
Magnetic fields from second-order interactions
Osano, Bob
2014-01-01
It is well known that when two types of perturbations interact in cosmological perturbation theory, the interaction may lead to the generation of a third type. In this article we discuss the generation of magnetic fields from such interactions. We determine conditions under which the interaction of a first-order magnetic field with a first-order scalar-or vector-, or tensor-perturbations would lead to the generation of second order magnetic field. The analysis is done in a covariant-index-free approach, but could be done in the standard covariant indexed-approach.
Optimizing second-order differential equation systems
Tamas Hajba
2011-03-01
Full Text Available In this article we study some continuous versions of the Fletcher-Reeves iteration for minimization described by a system of second-order differential equations. This problem has been studied in earlier papers [19, 20] under the assumption that the minimizing function is strongly convex. Now instead of the strong convexity, only the convexity of the minimizing function will be required. We will use the Tikhonov regularization [28, 29] to obtain the minimal norm solution as the asymptotically stable limit point of the trajectories.
Forecast Bias Correction: A Second Order Method
Crowell, Sean
2010-01-01
The difference between a model forecast and actual observations is called forecast bias. This bias is due to either incomplete model assumptions and/or poorly known parameter values and initial/boundary conditions. In this paper we discuss a method for estimating corrections to parameters and initial conditions that would account for the forecast bias. A set of simple experiments with the logistic ordinary differential equation is performed using an iterative version of a first order version of our method to compare with the second order version of the method.
Magnetic fields from second-order interactions
Osano, Bob
2014-01-01
It is well known that when two types of perturbations interact in cosmological perturbation theory, the interaction may lead to the generation of a third type. In this article we discuss the generation of magnetic fields from such interactions. We determine conditions under which the interaction of a first-order magnetic field with a first-order scalar-or vector-, or tensor-perturbations would lead to the generation of second order magnetic field. The analysis is done in a covariant-index-fre...
Second-Order Eikonal Corrections for A(e,e'p)
Van Overmeire, B.; Ryckebusch, J.
2007-01-01
The first-order eikonal approximation is frequently adopted in interpreting the results of $A(e,e'p)$ measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to $A(e,e'p)$ which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of ...
Full-sky lensing shear at second order
Bernardeau, Francis; Vernizzi, Filippo
2009-01-01
We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the infinitesimal cross-section of light bundle in the optical limit, and maps galaxy intrinsic shapes into their angular images. The calculation is done in the Poisson gauge without a specific matter content, including vector and tensor perturbations generated at second order and taking account of the inhomogeneities of a fixed redshift source plane. Our final result is expressed in terms of spin-2 operators on the sphere and is valid on the full sky. Beside the well known lens-lens and Born corrections that dominate on small angular scales, we find new non-linear couplings. These are a purely general relativistic intrinsic contribution, a coupling between the gravitational potential at the source with the lens, couplings between the time delay with the lens, couplings between two ...
Second-order impartiality and public sphere
Sládeček Michal
2016-01-01
Full Text Available In the first part of the text the distinction between first- and second-order impartiality, along with Brian Barry’s thorough elaboration of their characteristics and the differences between them, is examined. While the former impartiality is related to non-favoring fellow-persons in everyday occasions, the latter is manifested in the institutional structure of society and its political and public morality. In the second part of the article, the concept of public impartiality is introduced through analysis of two examples. In the first example, a Caledonian Club with its exclusive membership is considered as a form of association which is partial, but nevertheless morally acceptable. In the second example, the so-called Heinz dilemma has been reconsidered and the author points to some flaws in Barry’s interpretation, arguing that Heinz’s right of giving advantage to his wife’s life over property rights can be recognized through mitigating circum-stances, and this partiality can be appreciated in the public sphere. Thus, public impartiality imposes limits to the restrictiveness and rigidity of political impartiality implied in second-order morality. [Projekat Ministarstva nauke Republike Srbije, br. 179049
Nonlocal diffusion second order partial differential equations
Benedetti, I.; Loi, N. V.; Malaguti, L.; Taddei, V.
2017-02-01
The paper deals with a second order integro-partial differential equation in Rn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.
Oscillation theory for second order dynamic equations
Agarwal, Ravi P; O''Regan, Donal
2003-01-01
The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal. Many books deal exclusively with the oscillation of solutions of differential equations, but most of these books appeal only to researchers who already know the subject. In an effort to bring Oscillation Theory to a new and broader audience, the authors present a compact, but thorough, understanding of Oscillation Theory for second order differential equations. They include several examples throughout the text not only to illustrate the theory, but also to provide new direction.
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
Pathwise definition of second order SDEs
Quer-Sardanyons, Lluis
2010-01-01
In this article, a class of second order differential equations on [0,1], driven by a general H\\"older continuous function and with multiplicative noise, is considered. We first show how to solve this equation in a pathwise manner, thanks to Young integration techniques. We then study the differentiability of the solution with respect to the driving process and consider the case where the equation is driven by a fractional Brownian motion, with two aims in mind: show that the solution we have produced coincides with the one which would be obtained with Malliavin calculus tools, and prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure.
Second-order temporal modulation transfer functions.
Lorenzi, C; Soares, C; Vonner, T
2001-08-01
Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181
OPTIMAL CONTROL ALGORITHMS FOR SECOND ORDER SYSTEMS
Danilo Pelusi
2013-01-01
Full Text Available Proportional Integral Derivative (PID controllers are widely used in industrial processes for their simplicity and robustness. The main application problems are the tuning of PID parameters to obtain good settling time, rise time and overshoot. The challenge is to improve the timing parameters to achieve optimal control performances. Remarkable findings are obtained through the use of Artificial Intelligence techniques as Fuzzy Logic, Genetic Algorithms and Neural Networks. The combination of these theories can give good results in terms of settling time, rise time and overshoot. In this study, suitable controllers able of improving timing performance of second order plants are proposed. The results show that the PID controller has good overshoot values and shows optimal robustness. The genetic-fuzzy controller gives a good value of settling time and a very good overshoot value. The neural-fuzzy controller gives the best timing parameters improving the control performances of the others two approaches. Further improvements are achieved designing a real-time optimization algorithm which works on a genetic-neuro-fuzzy controller.
Kouranbaeva, Shinar; Shkoller, Steve
1999-01-01
This paper presents a geometric-variational approach to continuous and discrete {\\it second-order} field theories following the methodology of \\cite{MPS}. Staying entirely in the Lagrangian framework and letting $Y$ denote the configuration fiber bundle, we show that both the multisymplectic structure on $J^3Y$ as well as the Noether theorem arise from the first variation of the action function. We generalize the multisymplectic form formula derived for first order field theories in \\cite{MPS...
Second-order perturbation theory: Problems on large scales
Pound, Adam
2015-11-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.
Second-order perturbation theory: problems on large scales
Pound, Adam
2015-01-01
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 timescales. 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 ef...
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Second order singular pertubative theory for gravitational lenses
Alard, C
2016-01-01
The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second order expansion is considered as a small correction to the first order expansion. Using this approach it is demonstrated that the second order expansion is reducible to a first order expansion via a re-definition of the first order pertubative fields. Even if in practice the second order correction is small the reducibility of the second order expansion to the first order expansion indicates a degeneracy problem. In general this degeneracy is hard to break. A useful and simple second order approximation is the thin source approximation which offers a direct estimation of the correction. The practical application of the corrections derived in this paper are illustrated by using an elliptical NFW lens model. The second order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude ...
Second order logic, set theory and foundations of mathematics
Väänänen, J.A.; Dybjer, P; Lindström, S; Palmgren, E; Sundholm, G
2012-01-01
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the po
Second order logic, set theory and foundations of mathematics
Väänänen, J.A.; Dybjer, P; Lindström, S; Palmgren, E; Sundholm, G
2012-01-01
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the
Superposition rules and second-order Riccati equations
Cariñena, J F
2010-01-01
The concept of superposition rule for second-order differential equations is stated and conditions ensuring the existence of such superposition rules are analysed. In this way, second-order differential equations become formally included within the theory of Lie systems. The theory is illustrated by analysing the properties of a family of second-order differential equations with applications to Physics and we obtain a superposition rule common for all its members. Finally, time-dependent superposition rules for second-order differential equations are defined and we derive a particular instance for a family of second-order Riccati equations by means of the theory of quasi-Lie schemes.
Second order gauge invariant measure of a tidally deformed black hole
Ahmadi, Nahid
2012-01-01
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 \\cite{Vega+Poisson}, 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 general expression for this observable, which accomodates tidal perturbations, is also presented.
Second order gauge invariant measure of a tidally deformed black hole
Ahmadi, Nahid, E-mail: nahmadi@ut.ac.ir [Department of Physics, University of Tehran, Kargar Avenue North, Tehran 14395-547 (Iran, Islamic Republic of)
2012-08-01
In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.
Second-order sensitivity of eigenpairs in multiple parameter structures
Su-huan CHEN; Rui GUO; Guang-wei MENG
2009-01-01
This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms, and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed. With these formulations, the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation, and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs. A numerical example is given to demonstrate application and accuracy of the proposed method.
Homoclinic orbits of second-order nonlinear difference equations
Haiping Shi
2015-06-01
Full Text Available We establish existence criteria for homoclinic orbits of second-order nonlinear difference equations by using the critical point theory in combination with periodic approximations.
Analysis of Second-Order Effect in Frame
毕继红; 丛蓉; 张利华
2004-01-01
The second-order effect is the interaction between the vertical load and the deformation in a vertically forced element. In order to deduce a more brief but practical method, which has considered the second-order effect in a sway frame, some factors which affect the second-order deformation in a sway frame should be generalized based on a more accurate method. Nonlinear finite element is adopted in this paper, and according to this theory, a program, which can calculate the inner force and the deformation of the sway frame considering the second-order effects is coded.
THE SECOND-ORDER OPTIMALITY CONDITIONS FOR VARIABLE PROGRAMMING
Yanping Wang; Chuanlong Wang
2008-01-01
We study in this paper the continuity of the objective function for variable program-ming. In particular, we study the second-order optimality conditions for unconstrained and constrained variable programming. Some new second-order sufficient and necessary conditions are obtained.
SOME OSCILLATION CRITERIA FOR SECOND-ORDER DELAY DYNAMIC EQUATIONS
Raegan Higgins
2010-09-01
Full Text Available We investigate the oscillation of second-order delay dynamicequations. Our results extend and improve known results foroscillation of second-order differential equations that have beenestablished by extsc{Erbe} [Canad. Math. Bull. extbf{16} (1973, 49--56]. We apply results from the theory of upper and lower solutions and give some examples to illustrate the main results.
Recursive belief manipulation and second-order false-beliefs
Braüner, Torben; Blackburn, Patrick Rowan; Polyanskaya, Irina
2016-01-01
The literature on first-order false-belief is extensive, but less is known about the second-order case. The ability to handle second-order false-beliefs correctly seems to mark a cognitively significant step, but what is its status? Is it an example of *complexity only* development, or does it in...
The second-order decomposition model of nonlinear irregular waves
Yang, Zhi Wen; Bingham, Harry B.; Li, Jin Xuan;
2013-01-01
into the first- and the second-order super-harmonic as well as the second-order sub-harmonic components by transferring them into an identical Fourier frequency-space and using a Newton-Raphson iteration method. In order to evaluate the present model, a variety of monochromatic waves and the second...
Differential invariants of second-order ordinary differential equations
Rosado Maria, Maria Eugenia
2011-01-01
The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.
Inhomogeneous spatial point processes with hidden second-order stationarity
Hahn, Ute; Jensen, Eva B. Vedel
correlation function g(u, v) is a function of u −˘ v, where −˘ is a generalized subtraction operator. For the reweighted second-order stationary processes, the subtraction operator is simply u −˘ v = u − v. The processes in the extended class are called hidden second-order stationary because, in many cases......Modelling of inhomogeneous spatial point patterns is a challenging research area with numerous applications in diverse areas of science. In recent years, the focus has mainly been on the class of reweighted second-order stationary point processes that is characterized by the mathematically...... attractive property of a translation invariant pair correlation function. Motivated by examples where this model class is not adequate, we extend the class of reweighted second-order stationary processes. The extended class consists of hidden second-order stationary point processes for which the pair...
Ram Verma
2016-02-01
Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions.
Second-order gravitational self-force -- a quick summary
Pound, Adam
2013-01-01
In order to extract physical parameters from the waveform of an extreme-mass-ratio binary, one requires a second-order--accurate description of the motion of the smaller of the two objects in the binary. Using a method of matched asymptotic expansions, I derive the second-order equation of motion of a small, nearly spherical and non-rotating compact object in an arbitrary vacuum spacetime. I find that the motion is geodesic in a certain locally defined effective metric satisfying the vacuum Einstein equation through second order, and I outline a method of numerically calculating this effective metric.
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.
INTRUSION DETECTION BASED ON THE SECOND-ORDER STOCHASTIC MODEL
无
2007-01-01
This paper presents a new method based on a second-order stochastic model for computer intrusion detection. The results show that the performance of the second-order stochastic model is better than that of a first-order stochastic model. In this study, different window sizes are also used to test the performance of the model. The detection results show that the second-order stochastic model is not so sensitive to the window size, comparing with the first-order stochastic model and other previous researches. The detection result of window sizes 6 and 10 is the same.
Second order guiding-center Vlasov–Maxwell equations
Madsen, Jens
2010-01-01
Second order gyrogauge invariant guiding-center coordinates with strong E×B-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 E×B-flows and finite-Larmor-radius effects are mutually important....
CMB Anisotropies at Second-Order II: Analytical Approach
Bartolo, N; Riotto, Antonio; Bartolo, Nicola; Matarrese, Sabino; Riotto, Antonio
2007-01-01
We provide an analytical approach to the second-order Cosmic Microwave Background (CMB) anisotropies generated by the non-linear dynamics taking place at last scattering. We study the acoustic oscillations of the photon-baryon fluid in the tight coupling limit and we extend at second-order the Meszaros effect.We allow for a generic set of initial conditions due to primordial non-Gaussianity and we compute all the additional contributions arising at recombination. Our results are useful to provide the full second-order radiation transfer function at all scales necessary for establishing the level of non-Gaussianity in the CMB.
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.
Axion as a Cold Dark Matter Candidate: Proof to Second order
Noh, Hyerim; Hwang, Jai-chan
2013-01-01
We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale. The proof is made in the axion-comoving gauge. For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size. Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order. We also show that the axion fluid does not generate the rotational (vector-type) perturbation even to the second order. Thus, in the case of axion fluid, we have the relativistic/Newtonian correspondence to the second order, even considering the rotational perturbation. Our analysis is made in the presence of the cosmological constant, and can be easily extended to the realistic situation including other components of fluids and fields.
Second-order equation of motion for electromagnetic radiation back-reaction
Matolcsi, T.; Fülöp, T.; Weiner, M.
2017-09-01
We take the viewpoint that the physically acceptable solutions of the Lorentz-Dirac equation for radiation back-reaction are actually determined by a second-order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second-order equation of motion exactly in the non-relativistic regime via each of these three methods, leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.
Algebroid Solutions of Second Order Complex Differential Equations
Lingyun Gao
2014-01-01
Full Text Available Using value distribution theory and maximum modulus principle, the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that our results are sharp.
OSCILLATION THEOREMS FOR SECOND ORDER QUASILINEAR PERTURBED DIFFERENTIAL EQUATIONS
无
2001-01-01
New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results.
Variational principles for multisymplectic second-order classical field theories
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Variational principles for multisymplectic second-order classical field theories
Román Roy, Narciso; Prieto Martínez, Pedro Daniel
2015-01-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework. Peer Reviewed
Dirichlet problem for a second order singular differential equation
Wenshu Zhou
2006-12-01
Full Text Available This article concerns the existence of positive solutions to the Dirichlet problem for a second order singular differential equation. To prove existence, we use the classical method of elliptic regularization.
Abnormal Waves Modelled as Second-order Conditional Waves
Jensen, Jørgen Juncher
2005-01-01
The paper presents results for the expected second order short-crested wave conditional of a given wave crest at a specific point in time and space. The analysis is based on the second order Sharma and Dean shallow water wave theory. Numerical results showing the importance of the spectral density......, the water depth and the directional spreading on the conditional mean wave profile are presented. Application of conditional waves to model and explain abnormal waves, e.g. the well-known New Year Wave measured at the Draupner platform January 1st 1995, is discussed. Whereas the wave profile can be modelled...... quite well by the second order conditional wave including directional spreading and finite water depth the probability to encounter such a wave is still, however, extremely rare. The use of the second order conditional wave as initial condition to a fully non-linear three-dimensional analysis...
BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION
无
2006-01-01
The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order impulsive differential equation.
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.
Some remarks on a second order evolution equation
Mohammed Aassila
1998-07-01
Full Text Available We prove the strong asymptotic stability of solutions to a second order evolution equation when the LaSalle's invariance principle cannot be applied due to the lack of monotonicity and compactness.
ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION
无
2009-01-01
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
Simulation of transient viscoelastic flow with second order time integration
Rasmussen, Henrik Koblitz; Hassager, Ole
1995-01-01
The Lagrangian Integral Method (LIM) for the simulation of time-dependent flow of viscoelastic fluids is extended to second order accuracy in the time integration. The method is tested on the established sphere in a cylinder benchmark problem.......The Lagrangian Integral Method (LIM) for the simulation of time-dependent flow of viscoelastic fluids is extended to second order accuracy in the time integration. The method is tested on the established sphere in a cylinder benchmark problem....
Geometric second order field equations for general tensor gauge fields
de Medeiros, Paul; Hull, Christopher M.
2003-05-01
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.
Geometric Second Order Field Equations for General Tensor Gauge Fields
De Medeiros, P
2003-01-01
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.
First integrals and stability of second-order differential equations
Xu Xue-Jun; Mei Feng-Xiang
2006-01-01
The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserved quantity of the mechanical system or a part of the system is obtained by using the Noether theory. It is possible that the conserved quantity becomes a Liapunov function and the stability of the system is proved by the Liapunov theorem.
Second-order hyperbolic Fuchsian systems. General theory
Beyer, Florian; LeFloch, Philippe G.
2010-01-01
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a class of equations in which hyperbolicity is not assumed and we construct asymptotic solutions of arbitrary order. Second, for the proposed class of second-order hyperbolic Fuchsian systems, we establish the existence of solutions with prescribed asymptotic beh...
Second-Order Model Reduction Based on Gramians
Cong Teng
2012-01-01
Full Text Available Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds on error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.
Costate estimation for dynamic systems of the second order
无
2009-01-01
The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.
Costate estimation for dynamic systems of the second order
WEN Hao; JIN DongPing; HU HaiYan
2009-01-01
The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear mapping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conversion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.
Second-Order Type Isomorphisms Through Game Semantics
De Lataillade, Joachim
2007-01-01
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\\mu$-calculus, which can be seen as an extension of system F to classical logic, and for which we deﬁne a categorical framework: control hyperdoctrines. Our game model of λ$\\mu$-calculus is based on polymorphic arenas (closely related to Hughes' hyperforests) which evolve during the play (following the ideas of Murawski-Ong). We show that type isomorphisms coincide with the "equality" on arenas associated with types. Finally we deduce the equational characterization of type isomorphisms from this equality. We also recover from the same model Roberto Di Cosmo's characterization of type isomorphisms for system F. This approach leads to a geometrical comprehension on the question of second order type isomorphisms, which can be easily extended to some other polymorphic calculi inc...
Second-Order Risk Constraints in Decision Analysis
Love Ekenberg
2014-01-01
Full Text Available Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities are associated with distributions over them (second-order representations have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.
Second-order hyperbolic Fuchsian systems. I. General theory
Beyer, Florian
2010-01-01
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a class of equations in which hyperbolicity is not assumed and we construct asymptotic solutions of arbitrary order. Second, for the proposed class of second-order hyperbolic Fuchsian systems, we establish the existence of solutions with prescribed asymptotic behavior on the singularity. Our proof is based on a new scheme which is also suitable to design numerical approximations. Furthermore, as shown in a follow-up paper, the second-order Fuchsian framework is appropriate to handle Einstein's field equations for Gowdy symmetric spacetimes and allows us to recover (and slightly generalize) earlier results by Rendall and collaborators, while providing a direct approach leading to accurate numerical solutions. The proposed framework is also robust enough to encompass matter models ...
The second-order Klein-Gordon field equation
Gomes, D.; E. Capelas De Oliveira
2004-01-01
We introduce and discuss the generalized Klein-Gordon second-order partial differential equation in the Robertson-Walker space-time, using the Casimir second-order invariant operator written in hyperspherical coordinates. The de Sitter and anti-de Sitter space-times are recovered by means of a convenient choice of the parameter associated to the space-time curvature. As an application, we discuss a few properties of the solutions. We also discuss the case where we have positive frequency expo...
Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
Ioffe, M V; Nishnianidze, D N
2016-01-01
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 itertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest - constant - ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Second-order relative exponent of isotropic turbulence
无
2011-01-01
Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter.Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function),we have studied the relative scaling using the ESS method.It is found that the relative EES scaling exponent S_2 is greater than the real or theoretical inertial range scaling exponentξ_2,which is attributed to an evident bump in the ESS range.
Second-order nonlinear silicon-organic hybrid waveguides.
Alloatti, L; Korn, D; Weimann, C; Koos, C; Freude, W; Leuthold, J
2012-08-27
We describe a concept for second-order nonlinear optical processes in silicon photonics. A silicon-organic hybrid (SOH) double slot waveguide is dispersion-engineered for mode phase-matching (MPM). The proposed waveguide enables highly efficient nonlinear processes in the mid-IR range. With a cladding nonlinearity of χ(2) = 230 pm/V and 20 dBm pump power at a CW wavelength of 1550 nm, we predict a gain of 14.7 dB/cm for a 3100 nm signal. The suggested structure enables for the first time efficient second-order nonlinear optical mixing in silicon photonics with standard technology.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
Alloatti, L., E-mail: alloatti@mit.edu; Kieninger, C.; Lauermann, M.; Köhnle, K. [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Froelich, A.; Wegener, M. [Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), 76021 Karlsruhe (Germany); Frenzel, T. [Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Freude, W. [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute for Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen (Germany); Leuthold, J.; Koos, C., E-mail: christian.koos@kit.edu [Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe (Germany); Institute for Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen (Germany)
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.
PID control of second-order systems with hysteresis
Jayawardhana, Bayu; Logemann, Hartmut; Ryan, Eugene P.
2008-01-01
The efficacy of proportional, integral and derivative (PID) control for set point regulation and disturbance rejection is investigated in a context of second-order systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the
Monadic Second Order Logic on Tree-like Structures
Walukiewicz, Igor
2002-01-01
of monadic second-order logic (MSOL) over tree-like structures. Using this characterisation it is proved that MSOL theory of a tree-like structure is effectively reducible to that of the original structure. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree...
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 variational equations for N-body simulations
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 Backward Stochastic Differential Equations with Quadratic Growth
Dylan, Possamai
2012-01-01
We prove the existence and uniqueness of a solution for one-dimensionnal second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2010), with a bounded terminal condition and a generator which is continuous with quadratic growth in z. We also prove a Feyman-Kac formula and a probabilistic representation for fully nonlinear PDEs in this setting.
Generalized Second-Order Partial Derivatives of 1/r
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…
Oscillation Theorems for Nonlinear Second Order Elliptic Equations
2007-01-01
Some oscillation theorems are given for the nonlinear second order elliptic equation N ∑i,j=1 Di[aij(x)Ψ(y)||(△)y||p-2Djy]+c(x)f(y)=0. The results are extensions of modified Riccati techniques and include recent results of Usami.
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes; Wainwright, John
2013-08-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a cosmological constant Λ >0 have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if Λ >0 but logarithmic if Λ =0 and K0 the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (K=Λ =0) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
Accurate estimates of solutions of second order recursions
Mattheij, R.M.M.
1975-01-01
Two important types of two dimensional matrix-vector and second order scalar recursions are studied. Both types possess two kinds of solutions (to be called forward and backward dominant solutions). For the directions of these solutions sharp estimates are derived, from which the solutions themselve
RANDOM SINGULAR INTEGRAL OF RANDOM PROCESS WITH SECOND ORDER MOMENT
Wang Chuanrong
2005-01-01
This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Hα(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.
Forward and Backward Second-Order Pavlovian Conditioning in Honeybees
Hussaini, Syed Abid; Komischke, Bernhard; Menzel, Randolf; Lachnit, Harald
2007-01-01
Second-order conditioning (SOC) is the association of a neutral stimulus with another stimulus that had previously been combined with an unconditioned stimulus (US). We used classical conditioning of the proboscis extension response (PER) in honeybees ("Apis mellifera") with odors (CS) and sugar (US). Previous SOC experiments in bees were…
Second-order phase transitions of pure substances
Schaftenaar, H.P.C.
2009-01-01
In this report we are dealing with the thermodynamic theory of second-order phase transitions or continuous transitions of unary systems. The first classification of these phase transitions is due to Ehrenfest (1933), based on chemical potentials. First-order transitions are changes in which the der
Stability of second-order recurrences modulo pr
Lawrence Somer
2000-01-01
Full Text Available The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p-stable if the set of residue frequencies of the sequence reduced modulo pr is eventually constant as a function of r. The authors identify and characterize the stability of second-order recurrences modulo odd primes.
Focal decompositions for linear differential equations of the second order
L. Birbrair
2003-01-01
two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.
Self-triggered rendezvous of gossiping second-order agents
De Persis, Claudio; Frasca, Paolo; Hendrickx, Julien M.
2013-01-01
A recent paper by some of the authors introduced several self-triggered coordination algorithms for first-order continuous-time systems. The extension of these algorithms to second-order agents is relevant in many practical applications but presents some challenges that are tackled in this contribut
Oscillatory Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations
Yong Xiang LI
2005-01-01
In this paper the existence results of oscillatory periodic solutions are obtained for a second order ordinary differential equation -u"(t) = f(t, u(t)), where f: R2 → R is a continuous odd function and is 2π-periodic in t. The discussion is based on the fixed point index theory in cones.
Periodic and Subharmonic Solutions for Second Order -Laplacian Difference Equations
Xia Liu; Yuanbiao Zhang; Bo Zheng; Haiping Shi
2011-11-01
In this paper, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to second order -Laplacian difference equations are obtained by using the critical point theory. The proof is based on the Linking theorem in combination with variational technique.
Modeling Ability Differentiation in the Second-Order Factor Model
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,…
Modeling ability differentiation in the second-order factor model
Molenaar, D.; Dolan, C.V.; van der Maas, H.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
Specificity of brain reactions to second-order visual stimuli.
Babenko, Vitaly V; Ermakov, Pavel N
2015-01-01
The second-order visual mechanisms perform the operation of integrating the spatially distributed local visual information. Their organization is traditionally considered within the framework of the filter-rectify-filter model. These are the second-order filters that provide the ability to detect texture gradients. However, the question of the mechanisms' selectivity to the modulation dimension remains open. The aim of this investigation is to answer the above question by using visual evoked potentials (VEPs). Stimuli were textures consisting of staggered Gabor patches. The base texture was nonmodulated (NM). Three other textures represented the base texture which was sinusoidally modulated in different dimensions: contrast, orientation, or spatial frequency. EEG was recorded with 20 electrodes. VEPs of 500 ms duration were obtained for each of the four textures. After that, VEP to the NM texture was subtracted from VEP to each modulated texture. As a result, three different waves (d-waves) were obtained for each electrode site. Each d-wave was then averaged across all the 48 observers. The revealed d-waves have a latency of about 200 ms and, in our opinion, reflect the second-order filters reactivation through the feedback connection. The d-waves for different modulation dimensions were compared with each other in time, amplitude, topography, and localization of the sources of activity that causes the d-wave (with sLORETA). We proceeded from the assumption that the d-wave (its first component) represents functioning of the second-order visual mechanisms and activity changes at the following processing stages. It was found that the d-waves for different modulation dimensions significantly differ in all parameters. The obtained results indicate that the spatial modulations of different texture parameters caused specific changes in the brain activity, which could be evidence supporting the specificity of the second-order visual mechanisms to modulation dimension.
Describing failure in geomaterials using second-order work approach
François Nicot
2015-04-01
Full Text Available Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work, involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.
Second order optical nonlinearity in silicon by symmetry breaking
Cazzanelli, Massimo, E-mail: massimo.cazzanelli@unitn.it [Laboratorio IdEA, Dipartimento di Fisica, Università di Trento, via Sommarive, 14 Povo (Trento) (Italy); Schilling, Joerg, E-mail: joerg.schilling@physik.uni-halle.de [Centre for Innovation Competence SiLi-nano, Martin-Luther-University Halle-Wittenberg, Karl-Freiherr-von-Fritsch Str. 3, 06120 Halle (Germany)
2016-03-15
Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.
PERFORMANCE ANALYSIS OF SECOND-ORDER STATISTICS FOR CYCLOSTATIONARY SIGNALS
姜鸣; 陈进
2002-01-01
The second-order statistics for cyclostationary signals were introduced, and their performance were discussed. It especially researched the time lag characteristic of the cyclic autocorrelation function and spectral correlation characteristic of spectral correlation density function. It was pointed out that those functions can be available to extract the time-vary information of the kind of non-stationary signals. Using the relations of time lag-cyclic frequency and frequency-cyclic frequency independently, vibration signals of a rolling element bearing measured on test bed were analyzed. The results indicate that the second-order cyclostationary statistics might provide a powerful tool for the feature extracting and fault diagnosis of rolling element bearing.
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 envelope equation of graphene electrons
Luo, Ji
2014-10-01
A treatment of graphene's electronic states based on the tight-binding method is presented. Like Dirac equation, this treatment uses envelope functions to eliminate crystal potential. Besides, a density-functional-theory Kohn-Sham (KS) orbital of an isolated carbon atom is employed. By locally expanding envelope functions into second-order polynomials and by involving up to third-nearest atoms in calculating orbital integrals, the second-order envelope equation is obtained. This equation does not contain any experimental data except graphene's crystal structure, and its coefficients are determined through several kinds of integrals of the carbon KS orbital. As an improvement, it leads to more accurate energy dispersion than Dirac equation including the triangular warping effect and asymmetry for electrons and holes, and gives the Fermi velocity which is in good agreement with the experimental value.
Bioethics as public discourse and second-order discipline.
Kopelman, Loretta M
2009-06-01
Bioethics is best viewed as both a second-order discipline and also part of public discourse. Since their goals differ, some bioethical activities are more usefully viewed as advancing public discourse than academic disciplines. For example, the "Universal Declaration on Bioethics and Human Rights" sponsored by the United Nations Educational, Scientific, and Cultural Organization seeks to promote ethical guidance on bioethical issues. From the vantage of philosophical ethics, it fails to rank or specify its stated principles, justify controversial principles, clarify key terms, or say what is meant by calling potentially conflicting norms "foundational." From the vantage of improving the public discourse about bioethical problems and seeking ethical solutions in the public arena, however, this document may have an important role. The goals and relations between bioethics as a second-order discipline and public discourse are explored.
Second order ancillary: A differential view from continuity
Fraser, Ailana M; Staicu, Ana-Maria; 10.3150/10-BEJ248
2010-01-01
Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic ancillary contour is given explicitly as the plug-in estimate of the vector quantile function. The derivation uses a Taylor expansion of the full quantile function, and the linear term gives a tangent to the observed ancillary contour. For the scalar parameter case, there is a vector field that integrates to give the ancillary contours, but for the vector case, there are multiple vector fields and the Frobenius conditions for mutual consistency may not hold. We demonstrate, however, that the conditions hold in a restricted way and that this verifies the second order ancillary contours in moderate deviations. The methodology can generate an appropriate exact ancillary when such exists or an approximate ancillary for the numerical or Monte Carlo calculation of $p$-values and confid...
Second-Order Assortative Mixing in Social Networks
Zhou, Shi; Cox, Ingemar; Hansen, Lars Kai
2017-01-01
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node’s importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node...... degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes...... themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same...
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.
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.
Second order elastic metrics on the shape space of curves
Bauer, Martin; Bruveris, Martins; Harms, Philipp
2015-01-01
problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover......Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value......, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects....
Modulation masking produced by second-order modulators
Füllgrabe, Christian; Moore, Brian C.J.; Demany, Laurent;
2005-01-01
Recent studies suggest that an auditory nonlinearity converts second-order sinusoidal amplitude modulation (SAM) (i.e., modulation of SAM depth) into a first-order SAM component, which contributes to the perception of second-order SAM. However, conversion may also occur in other ways......-carrier modulation frequency, phase relationship between the probe and masker modulator, and probe modulation depth. In experiment 1, the carrier was a 5-kHz sinusoid presented either alone or within a notched-noise masker in order to restrict off-frequency listening. In experiment 2, the carrier was a white noise....... The data obtained in both carrier conditions are consistent with the existence of a modulation distortion component. However, the phase yielding poorest detection performance varied across experimental conditions between 0° and 180°, confirming that, in addition to nonlinear mechanisms, cochlear filtering...
Finite differencing second order systems describing black hole spacetimes
Calabrese, G
2005-01-01
Keeping Einstein's equations in second order form can be appealing for computational efficiency, because of the reduced number of variables and constraints. Stability issues emerge, however, which are not present in first order formulations. We show that a standard discretization of the second order ``shifted'' wave equation leads to an unstable semi-discrete scheme if the shift parameter is too large. This implies that discretizations obtained using integrators such as Runge-Kutta, Crank-Nicholson, leap-frog are unstable for any fixed value of the Courant factor. We argue that this situation arises in numerical relativity, particularly in simulations of spacetimes containing black holes, and discuss several ways of circumventing this problem. We find that the first order reduction in time based on ``ADM'' type variables is very effective.
High T{sub c} superconducting second-order gradiometer
Kittel, A.; Kouznetsov, K.A.; McDermott, R.; Oh, B.; Clarke, J. [Department of Physics, University of , California (United States)]|[Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720 (United States)
1998-10-01
A planar, second-order gradiometer was fabricated from single-layer YBa{sub 2}Cu{sub 3}O{sub 7{minus}x} films. The gradiometer consists of a symmetric flux transformer with an overall length of 80 mm inductively coupled to a directly coupled magnetometer, and has a baseline of 31 mm. The mutual inductance between the flux transformer and the magnetometer is adjusted mechanically to reduce the response to a uniform magnetic field applied perpendicularly to the plane of the gradiometer to typically 50 ppm. From an independent measurement, the residual first-order gradient response was determined to be at most 1.4{percent} relative to the second-order gradient response. {copyright} {ital 1998 American Institute of Physics.}
Second-order variational equations for N-body simulations
Rein, Hanno
2016-01-01
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 impro...
First- and second-order statistics of optical near fields.
Apostol, Adela; Dogariu, Aristide
2004-02-01
The statistical properties of the intensity in close proximity to highly scattering, randomly inhomogeneous media are investigated. Whereas the intensity probability density function obeys the same law irrespective of the distance z from the interface, the second-order intensity correlation length changes for distances smaller than the wavelength. Contrary to predictions of the conventional coherence theory, the corresponding field correlation length can be smaller than the wavelength of light.
A modified multi-reference second order perturbation theory
无
2010-01-01
A new scheme with extended model space is proposed to improve the calculation of multi-reference second order perturbation theory (MRPT2). The new scheme preserves the concise code structure of the original program, and avoids intruder states in constructions of the potential energy surface, which is confirmed by a series of comparable calculations. The new MRPT2 program is an available tool for the research of molecular excited states and electronic spectrum.
MAXIMUM PRINCIPLES FOR SECOND-ORDER PARABOLIC EQUATIONS
Antonio Vitolo
2004-01-01
This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of infinite cylindrical and non-cylindrical domains.
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
The Existence of Homoclinic Solutions for Second Order Hamiltonian System
Jie Gao
2011-10-01
Full Text Available The research of homoclinic orbits for Hamiltonian system is a classical problem, it has valuable applications in celestial mechanics, plasma physis, and biological engineering. For example, homoclinic orbits rupture can yield chaos lead to more complex dynamics behaviour. This paper studies the existence of homoclinic solutions for a class of second order Hamiltonian system, we will prove this system exists at least one nontrivial homoclinic solution.
Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems
Shi Xia LUAN; An Min MAO
2005-01-01
In this paper, we develop the local linking theorem given by Li and Willem by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems (H) ü + A (t)U+▽V(t,u)=0,u∈RN,t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.
ANALYTIC INVARIANT CURVES OF A NONLINEAR SECOND ORDER DIFFERENCE EQUATION
Wang Wusheng
2009-01-01
This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S1 and the case on S1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.
Subharmonic solutions for nonautonomous second-order Hamiltonian systems
Mohsen Timoumi
2012-10-01
Full Text Available In this article, we prove the existence of subharmonic solutions for the non-autonomous second-order Hamiltonian system $ddot{u}(t+V'(t,u(t=0$. Also we study the minimality of their periods, when the nonlinearity $V'(t,x$ grows faster than $|x|^{alpha}$, $alphain[0,1[$ at infinity. The proof is based on the Least Action Principle and the Saddle Point Theorem.
Second order perturbations of a Schwarzschild black hole
1995-01-01
We study the even-parity $\\ell=2$ perturbations of a Schwarzschild black hole to second order. The Einstein equations can be reduced to a single linear wave equation with a potential and a source term. The source term is quadratic in terms of the first order perturbations. This provides a formalism to address the validity of many first order calculations of interest in astrophysics.
Gravitational waves from global second order phase transitions
Jr, John T. Giblin [Department of Physics, Kenyon College, 201 North College Rd, Gambier, OH 43022 (United States); Price, Larry R.; Siemens, Xavier; Vlcek, Brian, E-mail: giblinj@kenyon.edu, E-mail: larryp@caltech.edu, E-mail: siemens@gravity.phys.uwm.edu, E-mail: bvlcek@uwm.edu [Center for Gravitation and Cosmology, Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201 (United States)
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.
Non-Liouvillian solutions for second order linear ODEs
Chan, L; Cheb-Terrab,E. S.
2004-01-01
There exist sound literature and algorithms for computing Liouvillian solutions for the important problem of linear ODEs with rational coefficients. Taking as sample the 363 second order equations of that type found in Kamke's book, for instance, 51 % of them admit Liouvillian solutions and so are solvable using Kovacic's algorithm. On the other hand, special function solutions not admitting Liouvillian form appear frequently in mathematical physics, but there are not so general algorithms fo...
Gravitational radiation reaction and second order perturbation theory
Detweiler, Steven
2011-01-01
A point particle of small mass m moves in free fall through a background vacuum spacetime metric g0_ab and creates a first-order metric perturbation h^1ret_ab that diverges at the particle. Elementary expressions are known for the singular m/r part of h^1ret_ab and its tidal distortion determined by the Riemann tensor in a neighborhood of m. Subtracting this singular part h^1S_ab from h^1ret_ab leaves a regular remainder h^1R_ab. The self-force on the particle from its own gravitational field adjusts the world line at O(m) to be a geodesic of g0_ab+h^1R_ab. The generalization of this description to second-order perturbations is developed and results in a wave equation governing the second-order h^2ret_ab with a source that that has an O(m^2) contribution from the stress-energy tensor of m added to a term nonlinear in h^1ret_ab. Second-order self-force effects are described as well.
Nonlinear Second-Order Multivalued Boundary Value Problems
Leszek Gasiński; Nikolaos S Papageorgiou
2003-08-01
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector -Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operatory theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.
THE MIXED PROBLEM FOR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER
Guochun Wen
2005-01-01
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order.
Second Order Sliding Mode Control of the Coupled Tanks System
Fayiz Abu Khadra
2015-01-01
Full Text Available Four classes of second order sliding mode controllers (2-SMC have been successfully applied to regulate the liquid level in the second tank of a coupled tanks system. The robustness of these classes of 2-SMC is investigated and their performances are compared with a first order controller to show the merits of these controllers. The effectiveness of these controllers is verified through computer simulations. Comparison between the controllers is based on the time domain performance measures such as rise time, settling time, and the integral absolute error. Results showed that controllers are able to regulate the liquid level with small differences in their performance.
Adaptive second-order sliding mode control with uncertainty compensation
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.
Detection of a diffusive cloak via second-order statistics
Koirala, Milan
2016-01-01
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.
A framework for second-order parton showers
Li, Hai Tao
2016-01-01
A framework is presented for including second-order perturbative corrections to the radiation patterns of parton showers. The formalism allows to combine O(alphaS^2)-corrected iterated 2->3 kernels for "ordered" gluon emissions with tree-level 2->4 kernels for "unordered" ones. The combined Sudakov evolution kernel is thus accurate to O(alphaS^2). As a first step towards a full-fledged implementation of these ideas, we develop an explicit implementation of 2->4 shower branchings in this letter.
Slowly rotating scalar field wormholes: the second order approximation
Kashargin, P E
2008-01-01
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 non-rotating one, and the NEC violation in the rotating wormhole spacetime is weaker than that in the non-rotating one.
Periodic and Boundary Value Problems for Second Order Differential Equations
Nikolaos S Papageorgiou; Francesca Papalini
2001-02-01
In this paper we study second order scalar differential equations with Sturm–Liouville and periodic boundary conditions. The vector field (, , ) is Caratheodory and in some instances the continuity condition on or is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.
Maximal regularity of second order delay equations in Banach spaces
无
2010-01-01
We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu’t + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).
Second order kinetic Kohn-Sham lattice model
Solorzano, Sergio; Herrmann, Hans
2016-01-01
In this work we introduce a new semi-implicit second order correction scheme to the kinetic Kohn-Sham lattice model. The new 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.
Langevin dynamics of financial systems: A second-order analysis
Canessa, E.
2001-07-01
We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat Cq, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that Cq can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point.
Product closure of some second-order modal logics
Zvesper, Jonathan
2010-01-01
Product update is an operation on models introduced into epistemic logic in order to represent a broad class of informational events. If adding modalities representing product update to a language does not alter its expressive power then we say that the language is "closed for product update." The basic modal language is known to be closed for product update. We establish that monadic second order logic is closed for product update (Theorem 5). Our technique is to pass via an intermediate language with what we call "action nominals." We obtain as corollaries that propositionally quantified modal logic is closed for product update, as is the modal mu-calculus.
Nonchaotic random behaviour in the second order autonomous system
Xu Yun; Zhang Jian-Xia; Xu Xia; Zhou Hong
2007-01-01
Evidence is presented for the nonchaotic random behaviour in a second-order autonomous deterministic system. This behaviour is different from chaos and strange nonchaotic attractor. The nonchaotic random behaviour is very sensitive to the initial conditions. Slight difference of the initial conditions will generate wholly different phase trajectories. This random behaviour has a transient random nature and is very similar to the coin-throwing case in the classical theory of probability. The existence of the nonchaotic random behaviour not only can be derived from the theoretical analysis, but also is proved by the results of the simulated experiments in this paper.
Finite dimensional thermo-mechanical systems and second order constraints
Cendra, Hernán; Amaya, Maximiliano Palacios
2016-01-01
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example by using, essentially, the Newton's law and the First Law of Thermodynamics only. We show that such equations are similar to those defining certain mechanical systems with higher order constraints. Moreover, we show that all of the given examples can be described in a variational formalism in terms of second order constrained systems.
On the Monadic Second-Order Transduction Hierarchy
Blumensath, Achim
2010-01-01
We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder C <= K :iff C is a subset of tau(K) for some transduction tau. If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type omega + 3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of all trees of height n, for each n in N, of all paths, of all trees, and of all grids.
Fluid/Gravity Correspondence, Second Order Transport and Gravitational Anomaly
Megias, Eugenio
2013-01-01
We study the transport properties of a relativistic fluid affected by chiral and gauge-gravitational anomalies. The computation is performed in the framework of the fluid/gravity correspondence for a 5 dim holographic model with Chern-Simons terms in the action. We find new anomalous and non anomalous transport coefficients, as well as new contributions to the existing ones coming from the mixed gauge-gravitational anomaly. Consequences for the shear waves dispersion relation are analyzed.
Strong Orbital Interaction in pi-pi Stacking System
Fu, Xiao-Xiao; Zhang, Rui-Qin
2016-01-01
A simple prototypical model of aromatic pi-pi stacking system -- benzene sandwich dimer is investigated by ab initio calculations based on second-order Moller-Plesset perturbation theory (MP2) and Minnesota hybrid functional M06-2X.
Bludsky, O.; Bak, Keld L.; JORGENSEN, P
1995-01-01
The quartic force field and the cubic dipole moment surface are calculated for trans-2,3-dideuteriooxirane at the self-consistent field and the second order Moller-Plesset levels of theory using a triple zeta plus two polarization functions basis set. Contact transformation theory is used to dete...... for frequencies. (C) 1995 American Institute of Physics....
Adaptive suboptimal second-order sliding mode control for microgrids
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.
A-posteriori error estimation for second order mechanical systems
Thomas Ruiner; J(ǒ)rg Fehr; Bernard Haasdonk; Peter Eberhard
2012-01-01
One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies degrees of freedom.As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important.In this work,an a-posteriori error estimator for linear first order systems is extended for error estimation of mechanical second order systems.Due to the special second order structure of mechanical systems,an improvement of the a-posteriori error estimator is achieved· A major advantage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique.Therefore,it can be used for moment-matching based,Gramian matrices based or modal based model reduction techniques.The capability of the proposed technique is demonstrated by the a-posteriori error estimation of a mechanical system,and a sensitivity analysis of the parameters involved in the error estimation process is conducted.
Second-order relational manipulations affect both humans and monkeys.
Christoph D Dahl
Full Text Available Recognition and individuation of conspecifics by their face is essential for primate social cognition. This ability is driven by a mechanism that integrates the appearance of facial features with subtle variations in their configuration (i.e., second-order relational properties into a holistic representation. So far, there is little evidence of whether our evolutionary ancestors show sensitivity to featural spatial relations and hence holistic processing of faces as shown in humans. Here, we directly compared macaques with humans in their sensitivity to configurally altered faces in upright and inverted orientations using a habituation paradigm and eye tracking technologies. In addition, we tested for differences in processing of conspecific faces (human faces for humans, macaque faces for macaques and non-conspecific faces, addressing aspects of perceptual expertise. In both species, we found sensitivity to second-order relational properties for conspecific (expert faces, when presented in upright, not in inverted, orientation. This shows that macaques possess the requirements for holistic processing, and thus show similar face processing to that of humans.
Asymptotic analysis of perturbed dust cosmologies to second order
Uggla, Claes
2013-01-01
Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a positive cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if the cosmological constant is positive but logarithmic if it is zero and and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if the cosmological constant is positive the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic ...
SECOND-ORDER CYBERNETICS, SEMIOTICS AND THE ART
Niculae V. Mihaita
2011-04-01
Full Text Available We take into consideration the concept of second order cybernetics and Pierce‘s approach of semiotics fundamentals. I am also an observer, experimenter and mental interpreter of metasigns given to the audience by Eugene Ionesco‘s absurd theatre. The interpreting of signs meaning is determinate by the context. From Semiotics ‗point of view, the objects I‘m studying (The Love Poem Lucifer or Evening Star, the short play Foursome and the most known, The Chairs gives me a lot of information about differences or NOT between actors, positive and negative interactions and become knowledge when I see them as signs. Second order cybernetics brings to the semiotics the idea of closure of structural coupling, interpretation and language [Soren, Cybersemiotics, 2008]. Them, the objects chosen are, for EXPERIMENTER, the YOYO in figure 1, and signifies the OBJECT of recursion. Boje [Boje, David, 2005] redefines antenarrative communication more holistically as an enactive phenomenon, and makes connections between varieties of disciplines in order to find out how antenarratives help us understand communication in the world. Instead of the finite event of producing an artifact, betting is a process and an end in itself, through which the practitioners might gain self-awareness. By synthesizing enactive-thinking in virtual space and the practice of communicating we appeal for valuable insights into the creative mind, challenging scholars and practitioners alike. Drawing contributions as above ideograms are useful for practicing cyberneticians, statisticians, researchers and academics, Informational Statistics applications [Mihaita, 2010] explores the ways in which liberal arts writers seek to involve, create and engage with new and diverse audiences from beginners encountering and participating in the work unexpectedly, to professionals from other disciplines and members of particular communities. Taking into consideration the Second-order Cybernetics
Feature Scaling via Second-Order Cone Programming
Zhizheng Liang
2016-01-01
Full Text Available Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP. Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods.
Second order higher-derivative corrections in Double Field Theory
Lescano, Eric
2016-01-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives ${\\cal O} (\\alpha'{}^2)$ for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS
无
2002-01-01
This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = P(t)x(t) + Q(t)x(g2(t)), where P, Q,g: [t0, ∞) → R+ =[0, ∞) are given real valued functions such that g(t) t, limt-∞g(t) = ∞. It is proved here that when 0 ≤ m := lim inft-∞ Q(t)P(g(t)) ≤ 1/4 all solutions of this equation oscillate if the condition limn sup Q(t)P(g(t)) ＞is satisfied. It should be emphasized that the condition (*) can not be improved in some sense.
Measurement of the second-order coherence of pseudothermal light
Kuusela, Tom A.
2017-04-01
We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.
Generalised equilibrium of cosmological fluids in second-order thermodynamics
Zimdahl, W; Le Denmat, G; Zimdahl, Winfried
1999-01-01
Combining the second-order entropy flow vector of the causal Israel-Stewart theory with the conformal Killing-vector property of $u_{i}/T$, where $u_{i}$ is the four-velocity of the medium and T its equilibrium temperature, we investigate generalized equilibrium states for cosmological fluids with nonconserved particle number. We calculate the corresponding equilibrium particle production rate and show that this quantity is reduced compared with the results of the previously studied first-order theory. Generalized equilibrium for massive particles turns out to be compatible with a dependence of the Robertson-Walker metric and may be regarded as a realization of so-called K-matter.
Nonoscillation for second order sublinear dynamic equations on time scales
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, 0researchers. 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 higher-derivative corrections in Double Field Theory
Lescano, Eric; Marqués, Diego
2017-06-01
HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives O({α}^' 2}) for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected Chern-Simons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.
Isochronous bifurcations in second-order delay differential equations
Andrea Bel
2014-07-01
Full Text Available In this article we consider a special type of second-order delay differential equations. More precisely, we take an equation of a conservative mechanical system in one dimension with an added term that is a function of the difference between the value of the position at time $t$ minus the position at the delayed time $t-\\tau$. For this system, we show that, under certain conditions of non-degeneration and of convergence of the periodic solutions obtained by the Homotopy Analysis Method, bifurcation branches appearing in a neighbourhood of Hopf bifurcation due to the delay are isochronous; i.e., all the emerging cycles have the same frequency.
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.
Second-Order Accurate Projective Integrators for Multiscale Problems
Lee, S L; Gear, C W
2005-05-27
We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution accuracy comparable to those obtained by implicit integrators. If the stiff differential equations are not directly available, our formulations and stability analysis are general enough to allow the combined outer-inner projective integrators to be applied to black-box legacy codes or perform a coarse-grained time integration of microscopic systems to evolve macroscopic behavior, for example.
Second order Gyrokinetic theory for Particle-In-Cell codes
Tronko, Natalia; Sonnendruecker, Eric
2016-01-01
The main idea of Gyrokinetic dynamical reduction consists in systematical removing of fastest scale of motion (the gyro motion) from plasma's dynamics, resulting in a considerable model simplification and gain of computing time. Gyrokinetic Maxwell-Vlasov system is broadly implemented in nowadays numerical experiments for modeling strongly magnetized plasma (both laboratory and astrophysical). Different versions of reduced set of equations exist depending on the construction of the Gyrokinetic reduction procedure and approximations assumed while their derivation. The purpose of this paper is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the Modern Gyrokinetic theory derivation and the model currently implemented in global electromagnetic Particle in Cell code ORB5. Strictly necessary information about the Modern Gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from the first pri...
Second order semiclassics with self-generated magnetic fields
Erdös, Laszlo; Fournais, Søren; Solovej, Jan Philip
2012-01-01
We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field $B$. We also add the field energy $\\beta \\int B^2$ and we minimize over all magnetic fields. The parameter $\\beta......$ effectively determines the strength of the field. We consider the weak field regime with $\\beta h^{2}\\ge {const}>0$, where $h$ is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order...... in the companion paper \\cite{EFS3} to prove the second order Scott correction to the ground state energy of large atoms and molecules....
"H"-shape second order NLO polymers: synthesis and characterization.
Li, Zhong'an; Hu, Pan; Yu, Gui; Zhang, Wei; Jiang, Zuoquan; Liu, Yunqi; Ye, Cheng; Qin, Jingui; Li, Zhen
2009-02-28
In this work, two "H"-shape and one "AB"-type second order nonlinear optical (NLO) polymers were prepared for the first time. The linkage positions of chromophores in the "H"-shape polymers were shoulder-to-shoulder, in which the chromophore moieties were part of the polymeric backbone. The subtle structure could be easily modified by the introduction of different isolation groups, to adjust the property of the resultant polymers. All the polymers exhibited good film-forming ability and thermal stability. The second harmonic generation (SHG) experiments demonstrated that the two "H"-shape polymers (P1 and P2) exhibited large SHG coefficients of d(33) values (up to 90 pm V(-1)), and P2 even demonstrated relatively good long-term temporal stability.
Second-order hyperbolic Fuchsian systems and applications
Beyer, Florian
2010-01-01
We introduce a new class of singular partial differential equations, referred to as the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First, we establish a general existence theory of solutions with asymptotic behavior prescribed on the singularity, which relies on a new approximation scheme, suitable also for numerical purposes. Second, this theory is applied to the (vacuum) Einstein equations for Gowdy spacetimes, and allows us to recover, by more direct arguments, well-posedness results established earlier by Rendall and collaborators. Another main contribution in this paper is the proposed approximation scheme, which we refer to as the Fuchsian numerical algorithm and is shown to provide highly accurate numerical approximations to the singular initial value problem. For the class of Gowdy spacetimes, the numerical experiments presented here show the interest and efficiency of the proposed method and demonstrate t...
Second order closure for stratified convection: bulk region and overshooting
Biferale, L; Sbragaglia, M; Scagliarini, A; Toschi, F; Tripiccione, R
2011-01-01
The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density -or both- develop highly non-linear mean profiles due to the interactions between the turbulent boundary layer and the unmixed -stable- flow above/below it. We present a second order closure able to cope simultaneously with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art 2D numerical simulations in a convective and stratified belt for values of the Rayleigh number, up to Ra = 10^9. Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient.
Second order closure modeling of turbulent buoyant wall plumes
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.
Fractional integration associated with second order divergence operators on Rn
DENG; Donggao(
2003-01-01
［1］McIntosh, A., Operators which have an H∞-calculus, Miniconference on Operator Theory and Partial Differential Equations (Proceedings of the Centre for Mathematical Analysis, ANU), 1986, 14: 210.［2］Stein, E. M., Singular Integral and Differentiability Properties of Functions, Princeton: Princeton Univ. Press,1970.［3］Auscher, P., Tchamitchian, P., Square Root Problem for Divergence Operators and Related Topics, Astérisque,vol. 249, 1998.［4］Auscher, P., Coulhon, T., Tchamitchian, P., Absence de principe du maximum pour certaines équations paraboliques complexes, Coll. Math., 1996, 171: 87.［5］Auscher, P., Hofmann, S., Lacey, M., The solution of Kato's conjectures, C. R. Acad. Sci. Paris Sr. I Math.,2001, 332: 601.［6］Davies, E. B., Uniformly elliptic operators with measurable coefficients, J. Funct. Anal., 1995, 132: 141.［7］Liskevich, V., Vogt, H., On Lp-spectrum and essential spectra of second order elliptic operators, Proc. London Math. Soc., 2000, 80: 590.［8］Duong, X. T., McIntosh, A., Singular integral operators with non-smooth kernels on irregular domains, Rev.Mat. Iberoamericana, 1999, 15: 233.［9］Lions, J. L., Espaces d'interpolation et domaines de puissances fractionnaires, J. Math. Soc. Japan, 1962, 14:233.［10］Auscher, P., McIntosh, A., Nahmod, A., The square root problem of Kato in one dimension, and first order elliptic systems, Indiana Univ. Math. J., 1997, 46: 659.［11］Deng, D. G., Hah, Y. S., Theory of Hp Spaces (in Chinese), Beijing: Peking Univ. Press, 1992.Vector subdivision schemes in (Lp(Rs))r(1 ≤ p ≤∞) spacesLI Song(李松)［12］Auscher,P.,Tchamitchian,P.,Square roots of elliptic second order divergence operators on strongly Lipschitz domain:L2 theory ,to appear in Journal d' Analyse Mathematique.
Second order anisotropy contribution in perpendicular magnetic tunnel junctions.
Timopheev, A A; Sousa, R; Chshiev, M; Nguyen, H T; Dieny, B
2016-06-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form -K2cos(4)θ must be added to the conventional uniaxial -K1cos(2)θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated -K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from "easy-axis" to "easy-cone" regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface.
Second order gyrokinetic theory for particle-in-cell codes
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.
Second order evolution equations which describe pseudospherical surfaces
Catalano Ferraioli, D.; de Oliveira Silva, L. A.
2016-06-01
Second order evolution differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K = - 1, and can be seen as the compatibility condition of an associated sl (2 , R) -valued linear problem, also referred to as a zero curvature representation. Under the assumption that the linear problem is defined by 1-forms ωi =fi1 dx +fi2 dt, i = 1 , 2 , 3, with fij depending on (x , t , z ,z1 ,z2) and such that f21 = η, η ∈ R, we give a complete and explicit classification of equations of the form zt = A (x , t , z) z2 + B (x , t , z ,z1) . According to the classification, these equations are subdivided in three main classes (referred to as Types I-III) together with the corresponding linear problems. Explicit examples of differential equations of each type are determined by choosing certain arbitrary differentiable functions. Svinolupov-Sokolov equations admitting higher weakly nonlinear symmetries, Boltzmann equation and reaction-diffusion equations like Murray equation are some known examples of such equations. Other explicit examples are presented, as well.
Second order semiclassics with self-generated magnetic fields
Erdos, Laszlo; Solovej, Jan Philip
2011-01-01
We consider the semiclassical asymptotics of the sum of negative eigenvalues of the three-dimensional Pauli operator with an external potential and a self-generated magnetic field $B$. We also add the field energy $\\beta \\int B^2$ and we minimize over all magnetic fields. The parameter $\\beta$ effectively determines the strength of the field. We consider the weak field regime with $\\beta h^{2}\\ge {const}>0$, where $h$ is the semiclassical parameter. For smooth potentials we prove that the semiclassical asymptotics of the total energy is given by the non-magnetic Weyl term to leading order with an error bound that is smaller by a factor $h^{1+\\e}$, i.e. the subleading term vanishes. However, for potentials with a Coulomb singularity the subleading term does not vanish due to the non-semiclassical effect of the singularity. Combined with a multiscale technique, this refined estimate is used in the companion paper \\cite{EFS3} to prove the second order Scott correction to the ground state energy of large atoms an...
Riccati-parameter solutions of nonlinear second-order ODEs
Reyes, M A [Instituto de Fisica, Universidad de Guanajuato, Leon, Guanajuato (Mexico); Rosu, H C [PotosIInstitute of Science and Technology, Apdo Postal 3-74 Tangamanga, 78231 San Luis PotosI (Mexico)], E-mail: hcr@ipicyt.edu.mx
2008-07-18
It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure.
Holographic dark matter and dark energy with second order invariants
Aviles, Alejandro; Luongo, Orlando; Quevedo, Hernando
2011-01-01
The main goal of modern cosmology remains to summon up a self consistent policy, able to explain, in the framework of the Einstein's theory, the cosmic speed up and the presence of Dark Matter in the Universe. Accordingly to the Holographic principle, which postulates the existence of a minimal size of a physical region, we argue, in this paper, that if this size exists for the Universe and it is accrued from the independent geometrical second order invariants, it would be possible to ensure a surprising source for Dark Matter and a viable candidate for explaining the late acceleration of the Universe. Along the work, we develop low redshift tests, such as Supernovae Ia and kinematical analysis complied by the use of Cosmography and we compare the outcomes with higher redshift tests, such as CMB peak and anisotropy of the cosmic power spectrum. All the upshots are in agreement with the chance that our overture would be undertaken to be an unified one, being able as well to explain both the Dark Matter and Dar...
On computing first and second order derivative spectra
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.
Correction of the second-order degree of coherence measurement
Congcong Li; Xiangdong Chen; Shen Li; Fangwen Sun
2016-01-01
The measurement of the second-order degree of coherence [g(2)(τ)] is one of the important methods used to study the dynamical evolution of photon-matter interaction systems.Here,we use a nitrogen-vacancy center in a diamond to compare the measurement of g(2)(τ) with two methods.One is the prototype measurement process with a tunable delay.The other is a start-stop process based on the time-to-amplitude conversion (TAC) and multichannel analyzer (MCA) system,which is usually applied to achieve efficient measurements.The divergence in the measurement results is observed when the delay time is comparable with the mean interval time between two neighboring detected photons.Moreover,a correction function is presented to correct the results from the TAC-MCA system to the genuine g(2)(τ).Such a correction method will provide a way to study the dynamics in photonic systems for quantum information techniques.
Fuzzy Random Walkers with Second Order Bounds: An Asymmetric Analysis
Georgios Drakopoulos
2017-03-01
Full Text Available Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph analysis must rely on non-deterministic design principles. One such principle is Random Walker, which is based on a virtual entity and selects either edges or, like in this case, vertices of a fuzzy graph to visit. This allows the estimation of global graph properties through a long sequence of local decisions, making it a viable strategy candidate for graph processing software relying on native graph databases such as Neo4j. As a concrete example, Chebyshev Walktrap, a heuristic fuzzy community discovery algorithm relying on second order statistics and on the teleportation of the Random Walker, is proposed and its performance, expressed in terms of community coherence and number of vertex visits, is compared to the previously proposed algorithms of Markov Walktrap, Fuzzy Walktrap, and Fuzzy Newman–Girvan. In order to facilitate this comparison, a metric based on the asymmetric metrics of Tversky index and Kullback–Leibler divergence is used.
Second-order spatial correlation in the far-field: Comparing entangled and classical light sources
Zhang, Erfeng; Liu, Weitao; Lin, Huizu; Chen, Pingxing
2016-02-01
We consider second-order spatial correlation with entangled and classical light in the far-field. The quantum theory of second-order spatial correlation is analyzed, and the role of photon statistics and detection mode in the second-order spatial correlation are discussed. Meanwhile, the difference of second-order spatial correlation with entangled and classical light sources is deduced.
Controllability of Second-Order Equations in L2(Ω
Hugo Leiva
2010-01-01
Full Text Available We present a simple proof of the interior approximate controllability for the following broad class of second-order equations in the Hilbert space L2(Ω: ÿ+Ay=1ωu(t, t∈(0,τ], y(0=y0, ẏ(0=y1, where Ω is a domain in RN(N≥1, y0,y1∈L2(Ω, ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to L2(0,τ;L2(Ω, and A:D(A⊂L2(Ω→L2(Ω is an unbounded linear operator with the following spectral decomposition: Az=∑j=1∞λj∑k=1γj〈z,ϕj,k〉ϕj,k, with the eigenvalues λj given by the following formula: λj=j2mπ2m, j=1,2,3,… and m≥1 is a fixed integer number, multiplicity γj is equal to the dimension of the corresponding eigenspace, and {ϕj,k} is a complete orthonormal set of eigenvectors (eigenfunctions of A. Specifically, we prove the following statement: if for an open nonempty set ω⊂Ω the restrictions ϕj,kω=ϕj,k|ω of ϕj,k to ω are linearly independent functions on ω, then for all τ≥2/πm-1 the system is approximately controllable on [0,τ]. As an application, we prove the controllability of the 1D wave equation.
Second order multidimensional sign-preserving remapping for ALE methods
Hill, Ryan N [Los Alamos National Laboratory; Szmelter, J. [LOUGHBOROUGH UNIV.
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
Fluid/Gravity Correspondence, Second Order Transport and Gravitational Anomaly***
Megías, Eugenio; Pena-Benitez, Francisco
2014-03-01
We study the transport properties of a relativistic fluid affected by chiral and gauge-gravitational anomalies. The computation is performed in the framework of the fluid/gravity correspondence for a 5 dim holographic model with Chern-Simons terms in the action. We find new anomalous and non anomalous transport coefficients, as well as new contributions to the existing ones coming from the mixed gauge-gravitational anomaly. Consequences for the shear waves dispersion relation are analyzed. Talk given by E. Megías at the International Nuclear Physics Conference INPC 2013, 2-7 June 2013, Firenze, Italy.Supported by Plan Nacional de Altas Energías (FPA2009-07908, FPA2011-25948), Spanish MICINN Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042), Comunidad de Madrid HEP-HACOS S2009/ESP-1473, Spanish MINECO's Centro de Excelencia Severo Ochoa Program (SEV-2012-0234, SEV-2012-0249), and the Juan de la Cierva Program.
Marozzi, Giovanni
2014-01-01
We present the generalization of previously published results, about the perturbed redshift and the luminosity-redshift relation up to second order in perturbation theory, for the case of the Poisson gauge with anisotropic stress. The results are therefore valid for general dark energy models and (most) modify gravity models. We use an innovative approach based on the recently proposed "geodesic light-cone" gauge. We then compare our finding with other results, which recently appeared in the literature, for the particular case of vanishing anisotropic stress. To arrive at a common accepted expression for the non-linear and relativistic corrections to the redshift and distance-redshift relation is of fundamental importance in view of future cosmological surveys. Thanks to these surveys the Universe will be further probed with high precision and at very different scales, where non-linear and relativistic effects can play a key role.
Solutions of relativistic radial quasipotential equations
Minh, V.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1985-11-01
A systematic approach to the investigation of relativistic radial quasipotential equations is developed. The quasipotential equations can be interpreted either as linear equations in finite differences of fourth and second orders, respectively, or as differential equations of infinite order.
Andrei Perjan
2009-07-01
Full Text Available We study the behavior of solutions to perturbed second order abstract evolution equations in Hilbert spaces, when the small parameter, multiplying the second order time derivative, converges to zero.
Existential Second Order Logic Expression With Horn First Order for Max Clique (Decision Version)
Manyem, Prabhu
2010-01-01
We will show that the maximum clique problem (decision version) can be expressed in existential second order (ESO) logic, where the first order part is a Horn formula in second-order quantified predicates.
Gauge-invariant perturbations at second order: multiple scalar fields on large scales
Malik, K A
2005-01-01
We derive the governing equations for multiple scalar fields minimally coupled to gravity in a flat Friedmann-Robertson-Walker (FRW) background spacetime on large scales. We include scalar perturbations up to second order and write the equations in terms of physically transparent gauge-invariant variables at first and second order. This allows us to write the perturbed Klein-Gordon equation at second order solely in terms of the field fluctuations on flat slices at first and second order.
Xuewen Mu
2015-01-01
quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.
Second-order spatial correlation in the far-field: Comparing entangled and classical light sources
Zhang, Erfeng, E-mail: efzhang@163.com; Liu, Weitao; Lin, Huizu; Chen, Pingxing
2016-02-15
Highlights: • Second-order spatial correlation with entangled and classical light in the far-field is investigated. • The role of photon statistics and detection mode in the second-order spatial correlation are discussed. • The difference of second-order spatial correlation with entangled and classical light sources is deduced. - Abstract: We consider second-order spatial correlation with entangled and classical light in the far-field. The quantum theory of second-order spatial correlation is analyzed, and the role of photon statistics and detection mode in the second-order spatial correlation are discussed. Meanwhile, the difference of second-order spatial correlation with entangled and classical light sources is deduced.
A relativistic correction to semiclassical charmonium
Weiss, J.
1995-09-01
It is shown that the relativistic linear potentials, introduced by the author within the particle à la Wheeler-Feynman direct-interaction (AAD) theory, applied to the semiclassically quantized charmonium, yield energy spectrum comparable to that of some known models. Using the expansion of the relativistic linear AAD potentials in powers ofc -1, the charmonium spectrum, given as a rule by Bohr-Sommerfeld quantization of circular orbits, is extended up to the second order of relativistic corrections.
The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas
TIAN Chu-Shun; ZHANG Chi; LU Quan-Kang
2001-01-01
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.
Xuewen Mu; Yaling Zhang
2015-01-01
An alternating direction method is proposed for convex quadratic second-order cone programming problems with bounded constraints. In the algorithm, the primal problem is equivalent to a separate structure convex quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is ...
Second-order projection from the posterior lateral line in the early zebrafish brain.
Ghysen Alain; Brajon Carole; Fame Ryann M
2006-01-01
Abstract Background Mechanosensory information gathered by hair cells of the fish lateral-line system is collected by sensory neurons and sent to the ipsilateral hindbrain. The information is then conveyed to other brain structures through a second-order projection. In the adult, part of the second-order projection extends to the contralateral hindbrain, while another part connects to a midbrain structure, the torus semicircularis. Results In this paper we examine the second-order projection ...
Rafiq, Arif [Department of Mathematics, COMSATS Institute of Information Technology, Islamabad (Pakistan)], E-mail: arafiq@comsats.edu.pk; Ahmed, Munshoor [Department of Mathematics, COMSATS Institute of Information Technology, Islamabad (Pakistan)], E-mail: ahmed.manshoor@gmail.com; Hussain, Sifat [CASPAM, Bahauddin Zakariya University, Multan (Pakistan)], E-mail: siffat2002@gmail.com
2008-07-21
Homotopy perturbation method is used to solve specific second order ordinary differential equations and tested for different examples. The results obtained demonstrate efficiency of the proposed method.
Linear matrix inequalities for analysis and control of linear vector second-order systems
Adegas, Fabiano D. [Aalborg Univ. (Denmark); Stoustrup, Jakob [Aalborg Univ. (Denmark)
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.
Temporal response properties to second-order visual stimuli in the LGN of cats
XU PengJing; YE Xiang; ZHOU Yifeng
2007-01-01
Visual stimuli occurring naturally are rich in instances of objects delineated from the backgrounds only by differences in luminance, which is called first-order stimuli, as well as those defined by differences of contrast or texture, referred to as second-order stimuli.The neuronal mechanism for processing second-order stimuli is still unclear.In this study, we compared the responses of cat LGN (lateral geniculate nucleus) cells to second-order stimuli at five temporal frequencies to their responses to first-order stimuli.Our results showed that most LGN cells can be evoked by second-order stimuli, and their firing rates to second-order stimuli decreased relative to first-order stimuli as temporal frequency increased from 0.5 to 8 Hz; moreover the ratio of a nonlinear to linear factor had a higher value in the responses to second-order stimuli than to first-order stimuli.We also found that the responses of Y-cells to second-order stimuli were significantly higher than the responses of X-cells, suggesting the Y-cells have a more important role in the processing of second-order stimuli.All these results reveal that first-order and second-order signals might be processed in separate 'streams' of the visual system.
Almost Regularity Conditions of Spectral Problems for a Second Order Equation
Yu.A. Mamedov; H.I. Ahmadov
2004-01-01
The asymptotic distributions are exactly solved for linearly independent solutions considering problem of the second order and for the coefficients of asymptotic distribution the recurrent formulas are obtained. Further, using obtained recurrent formulas the necessary and sufficient conditions for almost regularity of spectral problem for the equation of the second order is proved.
Plasmon ruler with gold nanorod dimers: utilizing the second-order resonance
Le, Anton T; Dubrovina, Natalia; Lupu, Anatole; Fedyanin, Andrey A
2014-01-01
The idea of utilizing the second-order plasmon resonance of the gold nanorod {\\pi}-dimers for plasmon rulers is introduced. We report on a qualitatively different dependence of the plasmon resonance shift on the interparticle distance for the first- and second-order longitudinal modes, extending the working range of plasmon rulers up to the distance values of 400 nm.
Combined First and Second Order Total Variation Inpainting using Split Bregman
Konstantinos Papafitsoros
2013-07-01
Full Text Available In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.
Second-order polarization-mode dispersion in photonic crystal fibers
Larsen, T; Bjarklev, Anders Overgaard; Peterson, A
2003-01-01
We report the first experimental measurements of second-order polarization-mode dispersion in two successive 900 meter pulls of a silica photonic crystal fiber.......We report the first experimental measurements of second-order polarization-mode dispersion in two successive 900 meter pulls of a silica photonic crystal fiber....
Closed orbits and limit cycles of second-order autonomous Birkhoff systems
陈向炜
2003-01-01
In this paper,the existence of periodic orbits and the non-existence of limit cycles for the second-order autonomous Birkhoff system are studied.Further the existence of algebraic limit cycles for a generalized second-order autonomous Birkhoff system is studied.
Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems
Yu, Wenwu; Chen, Guanrong; Cao, Ming
2010-01-01
This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic vel
Synthesis of Imidazole Derivatives for Their Second-order Nonlinear Optics
无
2003-01-01
The design and the synthesis of two conjugated donor-acceptor imidazole derivatives(1, 2) were carried out for second-order nonlinear optics. The thermal properties, the transparency and second-order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity-transparency-thermal stability trade-off is achieved for them.
Non-differentiable second-order mixed symmetric duality with cone constraints
Shiv Kumar Gupta
2012-10-01
Full Text Available A pair of mixed non-differentiable second-order symmetric dual programmesover cones is considered. Weak, strong and converse duality theorems are establishedunder second-order (F, convexity/pseudo-convexity assumptions. Special cases arealso discussed to show that this paper extends some known results in the literature.
An unconstrained optimization method using nonmonotone second order Goldstein's line search
Wen-yu; SUN; Qun-yan; ZHOU
2007-01-01
In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed. By using the negative curvature information from the Hessian,the sequence generated is shown to converge to a stationary point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency of our new method.
Second Order perturbation Theory: A covariant approach involving a barotropic equation of state
Osano, Bob
2015-01-01
We first revisit the motivations for developing techniques to study Second-Order effects, before presenting the formalism. We study second-order tensor perturbations about FLRW with dust on the one hand, and with a general barotropic equation of state on the other. Solutions to the wave equations are presented.
Second-Order Integrals for Systems in E2 Involving Spin
İsmet Yurduşen
2015-01-01
Full Text Available In two-dimensional Euclidean plane, existence of second-order integrals of motion is investigated for integrable Hamiltonian systems involving spin (e.g., those systems describing interaction between two particles with spin 0 and spin 1/2 and it has been shown that no nontrivial second-order integrals of motion exist for such systems.
Combined First and Second Order Total Variation Inpainting using Split Bregman
Papafitsoros, Konstantinos
2013-07-12
In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman) in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.
Assessing Stability and Change in a Second-Order Confirmatory Factor Model of Meaning in Life.
Krause, Neal; Hayward, R David
2014-04-01
Research indicates that meaning in life is an important correlate of health and well-being. However, relatively little is known about the way a sense of meaning may change over time. The purpose of this study is to explore two ways of assessing change in meaning within a second-order confirmatory factor analysis framework. First, tests are conducted to see if the first and second-order factor loadings and measurement error terms are invariant over time. Second, a largely overlooked technique is used to assess change and stability in meaning at the second-order level. Findings from a nationwide survey reveal that the first and second-order factor loadings are invariant of time. Moreover, the second-order measurement error terms, but not the first-order measurement error terms, are invariant, as well. The results further reveal that standard ways of assessing stability mask significant change in meaning that is due largely to regression to the mean.
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 bounce back boundary condition for the lattice Boltzmann fluid simulation
Kim, In Chan [Kunsan National Univ., Kunsan (Korea, Republic of)
2000-01-01
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.
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.
On the Linearization of Second-Order Differential and Difference Equations
Vladimir Dorodnitsyn
2006-08-01
Full Text Available This article complements recent results of the papers [J. Math. Phys. 41 (2000, 480; 45 (2004, 336] on the symmetry classification of second-order ordinary difference equations and meshes, as well as the Lagrangian formalism and Noether-type integration technique. It turned out that there exist nonlinear superposition principles for solutions of special second-order ordinary difference equations which possess Lie group symmetries. This superposition springs from the linearization of second-order ordinary difference equations by means of non-point transformations which act simultaneously on equations and meshes. These transformations become some sort of contact transformations in the continuous limit.
Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects
Cheng, J. L.; Vermeulen, N.; Sipe, J. E.
2017-01-01
We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference frequency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response. PMID:28262762
Separation and extension of cover inequalities for second-order conic knapsack constraints with GUBs
Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David
We consider the second-order conic equivalent of the classic knapsack polytope where the variables are subject to generalized upper bound constraints. We describe and compare a number of separation and extension algorithms which make use of the extra structure implied by the generalized upper bound...... constraints in order to strengthen the second-order conic equivalent of the classic cover cuts. We show that determining whether a cover can be extended with a variable is NP-hard. Computational experiments are performed comparing the proposed separation and extension algorithms. These experiments show...... that applying these extended cover cuts can greatly improve solution time of second-order cone programs....
Conditional Second Order Short-crested Water Waves Applied to Extreme Wave Episodes
Jensen, Jørgen Juncher
2005-01-01
A derivation of the mean second order short-crested wave pattern and associated wave kinematics, conditional on a given magnitude of the wave crest, is presented. The analysis is based on the second order Sharma and Dean finite water wave theory. A comparison with a measured extreme wave profile......, the Draupner New Year Wave, shows a good agreement in the mean, indicating that this second order wave can be a good identifier of the shape and occurrence of extreme wave events. A discussion on its use as an initial condition for a fully non-linear three-dimensional surface wave analysis is given....
MERGING AND SPLITTING SECOND-ORDER SELF-SIMILAR PROCESSES (TRAFFICS)
无
2000-01-01
Recent traffic measurements in corporate LANs, Variable-Bit-Rate (VBR) video sources, ISDN control channels, and other communication systems, have indicated traffic behavior of self-similar nature, which has implications for design, control and analysis of high-speed networks. Merging and splitting are two basic networking operations. This paper gave the necessary and sufficient conditions for that merging of second-order self-similar traffic streams also results in a second-order self-similar stream. It shows that splitting traffic streams of the second-order self-similar stream are still self-similar streams by the independent splitting operation.
Reina, Borja
2014-01-01
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 presen...
A SECOND ORDER DIFFERENCE SCHEME WITH NONUNIFORM MESHES FOR NONLINEAR PARABOLIC SYSTEM
WAN Zhengsu; CHEN Guangnan
2003-01-01
In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spacestep and timestep.
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Balashov, Maxim V.; Repovš, Dušan,
2011-01-01
We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
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.
Adaptive-Gain Second-Order Sliding Mode Control of Attitude Tracking of Flexible Spacecraft
Chutiphon Pukdeboon
2014-01-01
finite-time second-order sliding mode control algorithms are presented to solve this problem. For the first controller, a novel second-order sliding mode control scheme is developed to achieve high-precision tracking performance. For the second control law, an adaptive-gain second-order sliding mode control algorithm combing an adaptive law with second-order sliding mode control strategy is designed to relax the requirement of prior knowledge of the bound of the system uncertainties. The rigorous proofs show that the proposed controllers provide finite-time convergence of the attitude and angular velocity tracking errors. Numerical simulations on attitude tracking control are presented to demonstrate the performance of the developed controllers.
EXISTENCE FOR SECOND-ORDER FOUR-POINT BOUNDARY VALUE PROBLEM AT RESONANCE
无
2006-01-01
This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance. The main methods depend on the technique of the upper and lower solutions and the coincidence degree theory.
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL DIFFERENTIAL SYSTEM WITH DELAY
无
2010-01-01
This paper is concerned with the existence of solution to nonlinear second order neutral differential equations with infinite delay in a Banach space. Sufficient conditions for the existence of solution are obtained by a Schaefer fixed point theorem.
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION
无
2012-01-01
In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
无
2010-01-01
This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.
Shi Ping LU; Wei Gao GE
2005-01-01
By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
Yinying KONG; Daochun SUN
2013-01-01
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients,which perfect the solution theory of such equations.
Loads on a 3D body due to second order waves and a current
Skourup, Jesper; Cheung, K. F.; Bingham, Harry B.
2000-01-01
Non-linear loads on a fixed body due to waves and a current are investigated. Potential theory is used to describe the flow, and a three-dimensional (3D) boundary element method (BEM), combined with a time-stepping procedure, is used to solve the problem. The exact free-surface boundary conditions...... are expanded about the still-water level by Taylor series so that the solution is evaluated on a time-invariant geometry. A formulation correct to second order in the wave steepness and to first order in the current speed is used. Numerical results are obtained for the first-order and the second......-order oscillatory forces and for the second-order mean force on a fixed vertical circular cylinder in waves and a current. The second-order oscillatory forces on the body in waves and current are new results, while the remaining force components are verified by comparison with established numerical and analytical...
Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Dong-Lun Wu
2015-06-01
Full Text Available We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Renlong Zhou
2014-01-01
Full Text Available We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obtained. We also described the second harmonic conversion efficiencies in the second order nonlinear optical process with the spectra. Moreover, the electric field distributions of fundamental frequency above the gold film region are calculated. The light propagation through the holes results in the enhancement of the second order nonlinearity including second harmonic generation as well as the sum (difference frequency generation.
Second order perturbations of rotating bodies in equilibrium; the exterior vacuum problem
MacCallum, M A H; Vera, R; Callum, Malcolm A. H. Mac; Mars, Marc; Vera, Raul
2005-01-01
We study the exterior vacuum problem for first and second order stationary and axially symmetric perturbations of static bodies. The boundary conditions and their compatibility for the existence of an asymptotically flat exterior solution are discussed.
Second-order symmetric Lorentzian manifolds II: structure and global properties
Blanco, O F; Senovilla, J M M
2011-01-01
We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.
Second-order symmetric Lorentzian manifolds II: structure and global properties
Blanco, O F; Sanchez, M [Departamento de GeometrIa y TopologIa, Facultad de Ciencias, Universidad de Granada Campus Fuentenueva s/n, 18071 Granada (Spain); Senovilla, J M M, E-mail: oihane@ugr.es, E-mail: sanchezm@ugr.es, E-mail: josemm.senovilla@ehu.es [Fisica Teorica, Universidad del PaIs Vasco, Apartado 644, 48080 Bilbao (Spain)
2011-09-22
We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.
Second-Order Feed-Forward Renderingfor Specular and Glossy Reflections.
Wang, Lili; Xie, Naiwen; Ke, Wei; Popescu, Voicu
2014-09-01
The feed-forward pipeline based on projection followed by rasterization handles the rays that leave the eye efficiently: these first-order rays are modeled with a simple camera that projects geometry to screen. Second-order rays however, as, for example, those resulting from specular reflections, are challenging for the feed-forward approach. We propose an extension of the feed-forward pipeline to handle second-order rays resulting from specular and glossy reflections. The coherence of second-order rays is leveraged through clustering, the geometry reflected by a cluster is approximated with a depth image, and the color samples captured by the second-order rays of a cluster are computed by intersection with the depth image. We achieve quality specular and glossy reflections at interactive rates in fully dynamic scenes.
Periodic Solutions for Some Second-order Differential System with p(t)-Laplacian
WANG Qi; LU Di-cheng; MA Qi; DAI Jin
2015-01-01
In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.
Second order QCD corrections to inclusive semileptonic b \\to Xc l \\bar \
Biswas, Sandip
2009-01-01
We extend previous computations of the second order QCD corrections to semileptonic b \\to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \\to c \\tau \\bar \
Study on hydrodynmic lubrication with second-order thed (Ⅰ)——Basic equations
2001-01-01
First, the basic equations for solving one dimensional lubrication problem are derivedfrom the full second-order fluid constitutive equations. Then, the Reynolds’ boundary conditionsare introduced to solve the problems of a journal bearing and the solution with Reynolds boundarycondition for the second-order fluid is given to compare with the solution with Sommerfeld bound-ary condition. Finally, the equations for the slider and journal bearing lubrication are presented.
The statistical nature of the second order corrections to the thermal SZE
2004-01-01
This paper shows that the accepted expressions for the second order corrections in the parameter $z$ to the thermal Sunyaev-Zel'dovich effect can be accurately reproduced by a simple convolution integral approach. This representation allows to separate the second order SZE corrections into two type of components. One associated to a single line broadening, directly related to the even derivative terms present in the distortion intensity curve, while the other is related to a frequency shift, ...
Improved Nonlinear Model of a Second-Order Charge-Pump Pll
Gillespie, Diarmaid; Kennedy, Michael Peter; Kolumbán, Géza
An improved model of a second-order Charge-Pump Phase-Locked Loop (CP-PLL) is proposed. An event-driven second-order CP-PLL o-model is further developed from that described by Hedayat [1]. This model is made practical by taking account of VCO overload. Transient simulations are shown which illustrate the nature of phase-locking.
Lagrange-Noether method for solving second-order differential equations
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
A new Lie systems approach to second-order Riccati equations
Cariñena, J F; Sardón, C
2011-01-01
This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre transforms. This result allows us to construct new superposition rules for studying second-order Riccati equations and to reduce their integration to solving (first-order) Riccati equations.
El-Morshedy, Hassan A
2010-01-01
New global attractivity criteria are obtained for the second order difference equation \\[ x_{n+1}=cx_{n}+f(x_{n}-x_{n-1}),\\quad n=1, 2, ... \\] via a Lyapunov-like method. Some of these results are sharp and support recent related conjectures. Also, a necessary and sufficient condition for the oscillation of this equation is obtained using comparison with a second order linear difference equation with positive coefficients.
Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales
YANG Jia-shan
2013-01-01
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article.By using the generalized Riccati technique,integral averaging technique and the time scales theory,some new sufficient conditions for oscillation of the equation are proposed.These results generalize and extend many known results for second order dynamic equations.Some examples are given to illustrate the main results of this article.
Explicit One-Step P-Stable Methods for Second Order Periodic Initial Value Problems
Qinghong Li; Yongzhong Song
2006-01-01
In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.
Dynamical Consensus Algorithm for Second-Order Multi-Agent Systems Subjected to Communication Delay
LIU Cheng-Lin; LIU Fei
2013-01-01
To solve the dynamical consensus problem of second-order multi-agent systems with communication delay,delay-dependent compensations are added into the normal asynchronously-coupled consensus algorithm so as to make the agents achieve a dynamical consensus.Based on frequency-domain analysis,sufficient conditions are gained for second-order multi-agent systems with communication delay under leaderless and leader-following consensus algorithms respectively.Simulation illustrates the correctness of the results.
Comments on the present state of second-order closure models for incompressible flows
Speziale, Charles G.
1992-01-01
Second-order closure models account for history and nonlocal effects of the mean velocity gradients on the Reynolds stress tensor. Turbulent flows involving body forces or curvature, Reynolds stress relaxational effects, and counter-gradient transport are usually better described. The topics are presented in viewgraph form and include: (1) the Reynolds stress transport equation; (2) issues in second-order closure modeling; and (3) near wall models.
Initial-boundary value problems for second order systems of partial differential equations
Kreiss, Heinz-Otto; Ortiz, Omar E.; Petersson, N. Anders
2010-01-01
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger firs...
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.
Second-order model for free surface convection and interface reconstruction
Kim, Seong O.; Hwang, Young Dong; Kim, Young In; Chang, Moon Hee
1997-03-01
To improve the numerical analysis of free surface convection and its reconstruction, both first- and second-order algorithms are developed based on the volume of fraction method. Through the rearrangement of the surface cell and resetting of volume fraction, 16 possible cases of distribution of volume fraction in a cell block can be reduced to a single case. The methodology applied to the second-order model is to define the second-order linear curve having both face slopes as near to horizontal as possible while satisfying the cell`s defined volume fraction. The second-order method is compared with the FLAIR method and the first-order method through the simulation of the convection for various sizes of circular liquid shapes and solitary waves. For the small curvature of a free surface, e.g. circles with a large diameter, the linear method such as the FLAIR method and the first-order method shows relatively good predictions. However, for large curvature configurations, e.g. circles with a relatively small diameter or solitary waves, the linear approach shows large distortion of free surface. On the contrary, the second-order model always shows powerful prediction capabilities of free surface convection. Therefore, it is recommended that for the reconstruction and convection of free surface geometry with a large curvature, the second-order model should be used. (author). 21 refs., 1 tab., 21 figs.
Refined OPLS All-Atom Force Field for Saturated Phosphatidylcholine Bilayers at Full Hydration
Maciejewski, A.; Pasenkiewicz-Gierula, M.; Cramariuc, O.
2014-01-01
. In the present study, we determined the parameters for torsion angles in the phosphatidylcholine and glycerol moieties and in the acyl chains, as well the partial atomic charges. In these calculations, we used three methods: (1) Hartree-Fock (HF), (2) second order Moller-Plesset perturbation theory (MP2), and (3...... one was found to be able to satisfactorily reproduce experimental data for the lipid bilayer. The successful DPPC model was obtained from MP2 calculations in an implicit polar environment (PCM)....
Forte, G; March, N H; Pucci, R
2013-01-01
After some introductory comments relating to antiferromagnetism of crystalline O_2, and brief remarks on the geometry of ozone, Hartree-Fock (HF) theory plus second-order Moller-Plesset (MP2) corrections are used to predict the nuclear structure of low-lying isomers of free-space O_n clusters, for n=6, 8, and 12. The equilibrium nuclear-nuclear potential energy is also discussed in relation to the number n of oxygen atoms in the cluster.
Lazur, V. Yu.; Myhalyna, S. I.; Reity, O. K.
The problem of interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. The interaction is considered as a second-order effect of quantum electrodynamics in the coordinate representation. It is shown that a consistent account for the natural condition of the interaction symmetry with respect to both electrons leads to an additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator known previously. The generalized Breit-Pauli operator and the operator of electric dipole-dipole interaction of two quasimolecular electrons located at an arbitrary distance from each other are obtained. Modern methods of accounting for the relativistic and correlative effects in the problem of ion-atom interactions are discussed.
New Developments in Relativistic Viscous Hydrodynamics
Romatschke, Paul
2009-01-01
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized second law of thermodynamics, kinetic theory, and a complete second-order gradient expansion are reviewed. The resulting fluid dynamic equations are shown to be consistent for all these derivations, when properly accounting for the respective region of appl...
Second-Order Born Effect in Single Ionization of Argon by Electron Impact
WANG Yang; ZHOU Ya-Jun; JIAO Li-Guang
2012-01-01
We extend the standard distorted wave Born approximation (DWBA) to include the second-order Born amplitude in order to describe the multiple interactions between a projectile and an atomic target. Both the first- and second-order DWBA models are used to calculate triply differential cross sections (TDCS) of coplanar (e,2e) on atomic argon with the scattered electron energy fixed at 500 eV, the scattering angle at 6° and the ejected electron energies at 37, 74 and 205 eV. Overall agreements with experimental measurements have been obtained in shape, and the second-order DWBA model improves the calculations as expected, especially for recoil peak of TDCS.%We extend the standard distorted wave Born approximation (DWBA ) to include the second-order Born amplitude in order to describe the multiple interactions between a projectile and an atomic target.Both the first- and secondorder DWBA models are used to calculate triply differential cross sections (TDCS) of coplanar (e,2e) on atomic argon with the scattered electron energy fixed at 500eV,the scattering angle at 6° and the ejected electron energies at 37,74 and 205 e V.Overall agreements with experimental measurements have been obtained in shape,and the second-order DWBA model improves the calculations as expected,especially for recoil peak of TDCS.
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.
Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
Nakano, Hiroyuki
2007-01-01
We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\\sim 10%$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of ...
Second-order projection from the posterior lateral line in the early zebrafish brain
Ghysen Alain
2006-11-01
Full Text Available Abstract Background Mechanosensory information gathered by hair cells of the fish lateral-line system is collected by sensory neurons and sent to the ipsilateral hindbrain. The information is then conveyed to other brain structures through a second-order projection. In the adult, part of the second-order projection extends to the contralateral hindbrain, while another part connects to a midbrain structure, the torus semicircularis. Results In this paper we examine the second-order projection from the posterior lateral-line system in late embryonic/early larval zebrafish. At four days after fertilization the synaptic field of the sensory neurons can be accurately targeted, allowing a very reproducible labeling of second-order neurons. We show that second-order projections are highly stereotyped, that they vary according to rhombomeric identity, and that they are almost completely lateralized. We also show that the projections extend not only to the contralateral hindbrain and torus semicircularis but to many other brain centers as well, including gaze- and posture-controlling nuclei in the midbrain, and presumptive thalamic nuclei. Conclusion We propose that the extensive connectivity observed in early brain development reveals a basic scaffold common to most vertebrates, from which different subsets are later reinforced in various vertebrate groups. The large repertoire of projection targets provides a promising system to study the genetic encoding of this differential projection capacity.
Theoretical study of second-order hyperpolarizability for nitrogen radical cation
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.
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.
Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence
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.
Ambiguities in second-order cosmological perturbations for non-canonical scalar fields
Appignani, Corrado; Shankaranarayanan, S
2010-01-01
Over the last few years, it was realised that non-canonical scalar fields can lead to the accelerated expansion in the early universe. The primordial spectrum in these scenarios not only shows near scale-invariance consistent with CMB observations,but also large primordial non-Gaussianity. Second-order perturbation theory is the primary theoretical tool to investigate such non-Gaussianity. However, it is still uncertain which quantities are gauge-invariant at second-order and their physical understanding therefore remains unclear. As an attempt to understand second order quantities, we consider a general non-canonical scalar field, minimally coupled to gravity, on the unperturbed FRW background where metric fluctuations are neglected a priori. In this simplified set-up, we show that there arise ambiguities in the expressions of physically relevant quantities, such as the effective speeds of the perturbations. Further, the stress tensor and energy density display a potential instability which is not present at...
On Second Order Gauge Invariant Perturbations in Multi-Field Inflationary Models
Rigopoulos, G I
2002-01-01
In a recent letter [1] Acquaviva et. al presented results from a second order calculation for a single field inflationary model. In this paper we elaborate on their approach. We present equations for the second order superhorizon perturbations of a generic multi field model. We utilise a change of coordinates in field space - first presented in [2] and given a more geometrical flavour here - to separate isocurvature and adiabatic perturbations and construct gauge invariant variables related to them to second order. Explicit relations are given for two scalar fields on a flat field manifold although the results can be generalised to curved field manifolds and an arbitrary number of fields. This is an outline of a possible procedure to study nonlinear and nongaussian effects during multifield inflation. For a more detailed discussion we refer to a future publication [12].
Stability-Controllable Second-Order Difference Scheme for Convection Term
无
1998-01-01
A new finite difference scheme-SCSD scheme has been propsed based on CD( Central Difference) scheme and SUD(Second-order Upwind Difference)scheme.Its basic feature is controllable convective stability and always second-order accuracy(Stability-Controllable Second-order Difference),It has been proven that this Scheme is convective-Stable if the grid Peclet number|PΔ|≤2/β（0≤β≤1).The advantage of this new scheme has been discussed based on the modified wavenumber analysis by using Fourier transform.This scheme has been applied to the 2-D incompressible convective-diffusive equation and 2-D compressible Euler equation,and corresponding finite difference equations have been derived.Numerical examples of 1-D Burgers equation and 2-D transport equation have been presented to show its good accuracy and controllable convective stability.
Second-order perturbation theory for the single-impurity Anderson model of a BCS superconductor
Alastalo, Ari T.
2017-09-01
This paper presents a conserving approximation for a single magnetic impurity embedded in a BCS superconductor according to the Anderson model. The calculation generalizes the second-order selfenergy theory of a normal metal host into a superconducting medium. Within the second-order theory, both spin and pairing fluctuations contribute to the selfenergy. The second-order theory removes the unphysical spontaneous symmetry breaking of the Hartree-Fock approximation but results in a doubling of the bound-state spectrum within the energy gap. The HF bound states may be recovered in the small-U limit as the average of the two separate bound states. For increasing U, the novel pronounced low-energy bound states tend towards the center of the gap while the other bound states approach the gap edge and their spectral weights vanish.
The second-order interference of two independent single-mode He-Ne lasers
Liu, Jianbin; Bai, Bin; Wang, Wentao; Chen, Hui; Zhou, Yu; Li, Fu-Li; Xu, Zhuo
2014-01-01
The second-order spatial and temporal interference patterns with two independent single-mode He-Ne lasers are observed in a Hong-Ou-Mandel interferometer. Two-photon interference in Feynman's path integral theory is employed to interpret the experimental results. The conditions to observe the second-order interference pattern with two independent single-mode continuous wave lasers are discussed. It is concluded that two-photon interference exists for not only identical photons, but also photons with different spectrums if the detection system can not distinguish them in principle. The second-order temporal beating with two independent lasers can be employed to measure the coherence time and frequency of one laser if the properties of the other laser were known.
New second order Mumford-Shah model based on Γ-convergence approximation for image processing
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.
α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problens
张寄洲; 陶有山
2001-01-01
In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
Constructing set-valued fundamental diagrams from jamiton solutions in second order traffic models
Seibold, Benjamin
2013-09-01
Fundamental diagrams of vehicular traiic ow are generally multivalued in the congested ow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traiic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traiic phases. © American Institute of Mathematical Sciences.
Nonsingularity in second-order cone programming via the smoothing metric projector
无
2010-01-01
Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke’s generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition.
Stabilization and PID tuning algorithms for second-order unstable processes with time-delays.
Seer, Qiu Han; Nandong, Jobrun
2017-03-01
Open-loop unstable systems with time-delays are often encountered in process industry, which are often more difficult to control than stable processes. In this paper, the stabilization by PID controller of second-order unstable processes, which can be represented as second-order deadtime with an unstable pole (SODUP) and second-order deadtime with two unstable poles (SODTUP), is performed via the necessary and sufficient criteria of Routh-Hurwitz stability analysis. The stability analysis provides improved understanding on the existence of a stabilizing range of each PID parameter. Three simple PID tuning algorithms are proposed to provide desired closed-loop performance-robustness within the stable regions of controller parameters obtained via the stability analysis. The proposed PID controllers show improved performance over those derived via some existing methods.
Mean-value second-order uncertainty analysis method: application to water quality modelling
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.
Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
Rutwig Campoamor-Stursberg
2016-03-01
Full Text Available A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.
Perceived timing of first- and second-order changes in vision and hearing.
Arrighi, Roberto; Alais, David; Burr, David
2005-10-01
Simultaneous changes in visual stimulus attributes (such as motion or color) are often perceived to occur at different times, a fact usually attributed to differences in neural processing times of those attributes. However, other studies suggest that perceptual misalignments are not due to stimulus attributes, but to the type of change, first- or second-order. To test whether this idea generalizes across modalities, we studied perceptual synchrony of acoustic and of audiovisual cross-modal stimuli, which varied in a first- or second-order fashion. First-order changes were abrupt changes in tone intensity or frequency (auditory), or spatial position (visual), while second-order changes were an inversion of the direction of change, such as a turning point when a rising tone starts falling or a translating visual blob reverses. For both pure acoustic and cross-modal stimuli, first-order changes were systematically perceived before second-order changes. However, when both changes were first-order, or both were second-order, little or no difference in perceptual delay was found between them, regardless of attribute or modality. This shows that the type of attribute change, as well as latency differences, is a strong determinant of subjective temporal alignments. We also performed an analysis of reaction times (RTs) to the first- and second-order attribute changes used in these temporal alignment experiments. RT differences between these stimuli did not correspond with our temporal alignment data, suggesting that subjective alignments cannot be accounted for by a simple latency-based explanation.
A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme
B. A. Jacobs
2015-01-01
Full Text Available A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.
Loads on a 3D body due to second order waves and a current
Skourup, Jesper; Cheung, K. F.; Bingham, Harry B.;
2000-01-01
Non-linear loads on a fixed body due to waves and a current are investigated. Potential theory is used to describe the flow, and a three-dimensional (3D) boundary element method (BEM), combined with a time-stepping procedure, is used to solve the problem. The exact free-surface boundary conditions......-order oscillatory forces and for the second-order mean force on a fixed vertical circular cylinder in waves and a current. The second-order oscillatory forces on the body in waves and current are new results, while the remaining force components are verified by comparison with established numerical and analytical...
Existence of solutions for second-order differential inclusions involving proximal normal cones
Bernicot, Frederic
2010-01-01
In this work, we prove global existence of solutions for second order differential problems in a general framework. More precisely, we consider second order differential inclusions involving proximal normal cone to a set-valued map. This set-valued map is supposed to take admissible values (so in particular uniformly prox-regular values, which may be non-smooth and non-convex). Moreover we require the solution to satisfy an impact law, appearing in the description of mechanical systems with inelastic shocks.
Second-order explicit finite-difference methods for transient-flow analysis
Chaudhry, M. H.; Hussaini, M. Y.
1983-01-01
Three second-order accurate numerical methods - MacCormack's method, Lambda scheme and Gabutti scheme - are introduced to solve the quasi-linear, hyperbolic partial differential equations describing transient flows in closed conduits. The details of these methods and the treatment of boundary conditions are presented and the results computed by using these methods for a typical piping system are compared. It is shown that for the same accuracy, second-order methods require considerably lesser number of computational nodes and computer time as compared to those required by the first-order methods.
Blazek, Martin; Hartmann, Sébastien; Molitor, Andreas; Elsaesser, Wolfgang
2011-09-01
We present joint investigations of relative intensity noise (RIN) and second-order coherence properties of amplified spontaneous emission (ASE) generated by a superluminescent diode. We introduce a generalized intensity noise description for ASE sources that contains the shot noise contribution but also accounts for first- and second-order coherence properties reflecting the process of light generation. We find excellent agreement between pump-current-dependent RIN values and this new description, with the perspective of particular interesting consequences for the realization of low-noise broadband emitters.
Tahavori, Maryamsadat; Shaker, Hamid Reza
A method for model reduction of dynamical systems with the second order structure is proposed in this paper. The proposed technique preserves the second order structure of the system, and also preserves the stability of the original systems. The method uses the controllability and observability...... gramians within the time interval to build the appropriate Petrov-Galerkin projection for dynamical systems within the time interval of interest. The bound on approximation error is also derived. The numerical results are compared with the counterparts from other techniques. The results confirm...
Rotational Symmetry and Absolute Sign of Second-Order Susceptibility of α-Quartz
吕荣; 王鸿飞
2003-01-01
We investigate the rotational symmetry and absolute sign of the effective second-order susceptibility of the righthanded z-cut α-quartz crystal in different crystal orientations through the second-harmonic-generation phase interference between standard and reference of thin α-quartz plates. The Ds rotational symmetry of the z-cut α-quartz crystal shows 6 alternating sign sections of the second-order susceptibility in the 360° rotation, which leads to two distinctive interference patterns between the reference and standard second harmonic field. From this information, the sign of the interference pattern in the second harmonic phase measurement could be readily derived.
The statistical nature of the second order corrections to the thermal SZE
Sandoval-Villalbazo, A
2004-01-01
This paper shows that the accepted expressions for the second order corrections in the parameter $z$ to the thermal Sunyaev-Zel'dovich effect can be accurately reproduced by a simple convolution integral approach. This representation allows to separate the second order SZE corrections into two type of components. One associated to a single line broadening, directly related to the even derivative terms present in the distortion intensity curve, while the other is related to a frequency shift, which is in turn related to the first derivative term.
Imaging in scattering media via the second-order correlation of light field
Gong, Wenlin; Shen, Xia; Han, Shensheng
2009-01-01
Imaging with the second-order correlation of two light fields is a method to image an object by two-photon interference involving a joint detection of two photons at distant space-time points. We demonstrate for the first time that an image with high quality can still be obtained in the scattering media by applying the second-order correlation of illuminating light field. The scattering effect on the visibility of images is analyzed both theoretically and experimentally. Potential applications and the methods to further improve the visibility of the images in scattering media are also discussed.
On the conservation of second-order cosmological perturbations in a scalar field dominated universe
Vernizzi, F
2005-01-01
We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on the uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform and comoving curvature perturbations at second-order in a scalar field dominated universe are conserved.
Yavor, M.I. [Institute for Analytical Instrumentation RAS, 190103 St. Petersburg (Russian Federation)], E-mail: mikhail.yavor@gmail.com; Belov, V.D.; Pomozov, T.V. [Institute for Analytical Instrumentation RAS, 190103 St. Petersburg (Russian Federation)
2008-12-15
A new way of correcting the second-order angular aberration in sector field and polar-toroidal electron energy analyzers with object and image located outside the field is proposed. Correction is performed by biasing the optic axis electrostatic potential inside the analyzer with respect to the potential of surrounding field-free space. The strength of the correcting aberration concentrated in the fringing field regions of the analyzer is calculated with the aid of the fringing field integral method. The described correction allows achieving second-order focusing and thus increasing the energy resolving power in sector field analyzers, in particular used for angle resolved energy measurements.
Yang, Xiaofeng; Han, Daozhi
2017-02-01
In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank-Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.
Primordial magnetic fields from second-order cosmological perturbations:Tight coupling approximation
Maeda, Satoshi; Kobayashi, Tsutomu; Shiromizu, Tetsuya
2008-01-01
We explore the possibility of generating large-scale magnetic fields from second-order cosmological perturbations during the pre-recombination era. The key process for this is Thomson scattering between the photons and the charged particles within the cosmic plasma. To tame the multi-component interacting fluid system, we employ the tight coupling approximation. It is shown that the source term for the magnetic field is given by the product of the first order perturbations and so the intrinsically second-order quantities do not contribute to magnetogenesis. The magnetic fields generated by this process are estimated to be \\sim 10^{-26},Gauss on the horizon scale.
Second-order corrections to mean-field evolution of weakly interacting Bosons, II
Grillakis, M; Margetis, D
2010-01-01
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state.
The first- and second-order temporal interference between thermal and laser light
Liu, Jianbin; Chen, Hui; Zhou, Yu; Li, Fu-li; Xu, Zhuo
2014-01-01
The first- and second-order temporal interference between two independent thermal and laser light beams is discussed by employing the superposition principle in Feynman's path integral theory. It is concluded that the first-order temporal interference pattern can not be observed by superposing thermal and laser light, while the second-order temporal interference pattern can be observed in the same condition. These predictions are experimentally verified by employing pseudothermal light to simulate thermal light. The conclusions and method in the paper can be generalized to any order interference of light or massive particles, which is helpful to understand the physics of interference.
Stable Second-Order Nonlinear Optical Materials Based on Interpenetrating Polymer Networks
1994-03-17
0IJUN93 to 31MAY94 4. 1I1Lk ANDLSUBI1ILIE D. ?-UNUING NUMBERS •’• Stable Second-Order Nonlinear Optical Materials Based On C:N00014-90-J-1148...release and sale; its distribution is unlimited. I Stable Second-Order Nonlinear Optical Materials Based On Interpenetrating Polymer Networks S... Optical Materials Based On Interpenetrating Polymer Networks by S. Marturunkakul, J. I. Chen, L. Li, X. L. Jiang, R. J. Jeng, S. K. Sengupta, J. Kumar
Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales
Guangrong Zhang
2010-01-01
Full Text Available We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations [r(t(zΔ(tγ]Δ+q1(txα(τ1(t+q2(txβ(τ2(t=0 on a time scale 𝕋, where z(t=x(t+p(tx(τ0(t, 0<α<γ<β. Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.
Measurement of the second-order coherence function for metallic nanolasers
Hayenga, William E; Hodaei, Hossein; Reimer, Christian; Morandotti, Roberto; Likamwa, Patrick; Khajavikhan, Mercedeh
2016-01-01
Due to the high spontaneous emission coupled into the resonance mode in metallic nanolasers, there has been a debate concerning the coherence properties of this family of light sources. The second-order coherence function can unambiguously determine the nature of a given radiation. In this paper, an approach to measure the second-order coherence function for broad linewidth sources in the near-infrared telecommunication band is established based on a modified Hanbury Brown and Twiss configuration. Using this set-up, it is shown that metallic coaxial and disk-shaped nanolasers with InGaAsP multiple quantum well gain systems are indeed capable of generating coherent radiation.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
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.
On q-Difference Riccati Equations and Second-Order Linear q-Difference Equations
Zhi-Bo Huang
2013-01-01
Full Text Available We consider q-difference Riccati equations and second-order linear q-difference equations in the complex plane. We present some basic properties, such as the transformations between these two equations, the representations and the value distribution of meromorphic solutions of q-difference Riccati equations, and the q-Casorati determinant of meromorphic solutions of second-order linear q-difference equations. In particular, we find that the meromorphic solutions of these two equations are concerned with the q-Gamma function when q∈ℂ such that 0<|q|<1. Some examples are also listed to illustrate our results.
Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming
Shaohua Pan
2013-01-01
Full Text Available This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP, specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.
A second-order projection method for variable-density flows
Bell, John B.; Marcus, Daniel L.
1992-08-01
The second-order projection method presented for variable-density, incompressible flows is based on a second-order, fractional-step scheme in which diffusion-convection terms are advanced without enforcing the compressibility condition. The resulting, intermediate velocity field is then projected onto the space of discretely divergence-free vector fields. Attention is given to the form taken by the method in the cases of finite-amplitude density variation; simplifications for a Boussinesq approximation are given, in conjunction with numerical results validating the method's convergence properties.
Guermond, Jean-Luc
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Motion de-blurring by second-order intensity-correlated imaging
Zunwang Bo; Wenlin Gong; Shensheng Han
2016-01-01
For a Hanbury Brown and Twiss system,the influence of relative motion between the object and the detection plane on the resolution of second-order intensity-correlated imaging is investigated.The analytical results,which are backed up by experiments,demonstrate that the amplitude and mode of the object's motion have no effect on the second-order intensity-correlated imaging and that high-resolution imaging can be always achieved by using a phase-retrieval method from the diffraction patterns.The use of motion de-blurring imaging for this approach is also discussed.
Second order asymptotics for Brownian motion among a heavy tailed Poissonian potential
Fukushima, Ryoki
2010-01-01
We consider the Feynman-Kac functional associated with a Brownian motion among a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by Pastur~(1977) and the first order term of the moment asymptotics was determined. In this paper, both moment and almost sure asymptotics are determined up to the second order. As an application, we also derive the second order asymptotics of the integrated density of states of the corresponding random Schr\\"{o}dinger operator.
Contributions to the second order dielectric response of an electron liquid
Bachlechner, Martina E.; Miesenboeck, Helga M.; Macke, Wilhelm
1988-06-01
The dielectric response function χ of a uniform electron gas is investigated up to the second order of the Coulomb interaction with different methods. When examining all polarisation diagrams with two interaction lines, it is confirmed that previous work in the Green's function formalism does not contain all second order processes and the importance of the corrections is pointed out. It is further shown, how the evaluation of χ with Green's function can be greatly simplified when taking into account the symmetry of the expressions.
Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model
Van Koten, Brian
2012-01-01
We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys.
Orbital angular momentum of the laser beam and the second order intensity moments
无
2000-01-01
From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre_Gaussian beam,but in any beam with an angular_dependent structure. By calculating the second order intensity moments of the beam the relation between the orbital angular momentum and the second order moments 〈xθy〉, 〈yθx〉 is given. As an example the orbital angular momentum of the general astigmatic Gaussian beam is studied.
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.
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation
Kollmann, Robert
2013-01-01
This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the ‘pruning’ scheme of Kim, Kim, Schaumburg and Sims (2008). By contrast to particle filters, no stochastic simulations are needed for the filter here--the present method is thus much faster. In Monte Carlo e...
VAGO method for the solution of elliptic second-order boundary value problems
Vabishchevich, Nikolay P
2010-01-01
Mathematical physics problems are often formulated using differential oprators of vector analysis - invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural to employ similar operator formulations for grid problems, too. The VAGO (Vector Analysis Grid Operators) method is based on such a methodology. In this paper the vector analysis difference operators are constructed using the Delaunay triangulation and the Voronoi diagrams. Further the VAGO method is used to solve approximately boundary value problems for the general elliptic equation of second order. In the convection-diffusion-reaction equation the diffusion coefficient is a symmetric tensor of second order.
Orbital angular momentum of the laser beam and the second order intensity moments
高春清[1; 魏光辉[2; HorstWeber[3
2000-01-01
From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre-Gaussian beam, but in any beam with an angular-dependent structure. By calculating the second order intensity moments of the beam the relation between the orbital angular momentum and the second order moments 〈xθy〉, 〈yθx〉 is given. As an example the orbital angular momentum of the general astigmatic Gaussian beam is studied.
Analysis of general second-order fluid flow in double cylinder rheometer
黄军旗; 何光渝; 刘慈群
1997-01-01
The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the analytical solution of which the derivative order is 1/2 is derived with the analytical solution and the reliability of Laplace numerical inversion based on Crump algorithm for the problem is verified, then the characteristics of second-order fluid flow in the rheometer by using Crump method is analyzed. The results indicate that the more obvious the viscoelastic properties of fluid are, the more sensitive the dependence of velocity and stress on fractional derivative order is.
A new implementation of the second-order polarization propagator approximation (SOPPA)
Packer, Martin J.; Dalskov, Erik K.; Enevoldsen, Thomas
1996-01-01
We present a new implementation of the second-order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear transfor......We present a new implementation of the second-order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear...
The analysis of second-order sloshing resonance in a 3-D tank
张洪生; 吴鹏飞; 刘文白
2014-01-01
Based on the potential theory and perturbation techniques, the problem of second-order sloshing in a three-dimensional tank in combination with surge and sway motions is analyzed. When excitation is applied in both horizontal directions, the second-order resonance can occur when the sum frequency or the difference frequency of any two excitation components is equal to one of the natural frequencies. The resonance can also occur when the sum or difference frequency of one of the excitation frequencies and one of the natural frequencies is equal to another natural frequency.
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…
INTEGRAL AVERAGING TECHNIQUE FOR OSCILLATION OF ELLIPTIC EQUATIONS OF SECOND ORDER
徐志庭; 贾保国; 马东魁
2003-01-01
The elliptic differential equations of second order n∑i,j=1 Di[Aij(x,y)Djy] +P(x,y) +Q(x,y, (△)y) == e(x), x ∈Ω.will be considered in an exterior domain Ω (∩) Rn, n ≥ 2. Some oscillation criteria are given by integral averaging technique.
Da Lio, Francesca; 10.1137/S0363012904440897
2010-01-01
In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation.
Enhancement of linear and second-order hyperpolarizabilities in wedge-shaped nanostructures
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.
Subharmonic solutions for non-autonomous second-order sublinear Hamiltonian systems with p-Laplacian
Zhiyong Wang
2011-10-01
Full Text Available In this article, we study the existence of subharmonic solutions to the non-autonomous second-order sublinear Hamiltonian systems with p-Laplacian. Introducing some kinds of control functions, infinitely many subharmonic solutions are obtained by using the minimax methods in critical point theory. We point out that our results are new even in the case p=2.
Jiun-Wei Horng
2012-01-01
Full Text Available A configuration for realizing low input and high output impedances current-mode multifunction filters using multiple output second-generation current conveyors (MOCCIIs is presented. From the proposed circuit configuration, first-order allpass, highpass, lowpass and second-order allpass, notch, bandpass filters can be obtained. The simulation results confirm the theoretical analysis.
On the Robustness of Hysteretic Second-Order Systems with PID : iISS approach
Ouyang, Ruiyue; Jayawardhana, Bayu; Andrieu, Vincent
2012-01-01
In this paper, we study the robustness property of a second-order linear plant controlled by a proportional, integral and derivative (PID) controller with a hysteretic actuator. The hysteretic actuator is modeled by a Duhem model that exhibits clockwise (CW) input-output (I/O) dynamics (such as the
Huang, Jie; Cao, Ming; Zhou, Ning
2016-01-01
This paper investigates the formation control problem of multiple mobile agents with second-order nonlinear dynamics in complex environments containing multiple obstacles. By employing the null-space-based behavioral (NSB) control architecture, a novel fast terminal sliding mode based adaptive contr
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
Full Text Available We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
A Probabilistic Approach to Second Order Variational Inequalities with Bilateral Constraints
Mrinal K Ghosh; K S Mallikarjuna Rao
2003-11-01
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to this solution. As an application, we study a stochastic game with stopping times and show the existence of a saddle point equilibrium.
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numer
Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Functional Differential Equations
张全信; 高丽; 王少英
2012-01-01
This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation. Our results generalize and improve some known theorems.
Second-order asymptotics in level crossing for differences of renewal processes
Kroese, D.P.; Kallenberg, W.C.M.
1992-01-01
We consider level crossing for the difference of independent renewal processes. Second-order expansions for the distribution function of the crossing time of level n are found, as n - oo. As a by-product several other results on the difference process are found. The expected minimum of the differenc
Validity of the Quality of School Life Scale: A Primary and Second-Order Factor Analysis.
Johnson, William L.; Johnson, Annabel M.
1993-01-01
Primary and second-order principal components analyses were performed on the Quality of School Life Scale (QSL), a measure of elementary school climate, for responses of 141 fourth through sixth graders. Findings suggest three general factors, but item composition of subscales differs somewhat from that proposed by the QSL's developers. (SLD)
A Primary- and Second-Order Component Analysis of the Organizational Identification Questionnaire.
Johnson, William L.; Johnson, Annabel M.; Heimberg, Felix
1999-01-01
Examined the factor structure of the Organizational Identification Questionnaire (G. Cheney, 1982), widely used to assess organizational identification. Analysis of results from 369 social-service employers yields four first-order and two second-order components. Contains 33 references. (SLD)
Deleuze, M.S.; Pickup, B.T.; Wilton, D.J.
2000-04-05
The authors present the theory of the electron propagator perturbed by an external electric field and show how it can be used to calculate a variety of one-electron linear response properties that are accurate through second order in electron correlation. Some illustrative calculations are discussed.
Second-order magnetic critical points at finite magnetic fields: Revisiting Arrott plots
Bustingorry, S.; Pomiro, F.; Aurelio, G.; Curiale, J.
2016-06-01
The so-called Arrott plot, which consists in plotting H /M against M2, with H the applied magnetic field and M the magnetization, is used to extract valuable information in second-order magnetic phase transitions. Besides, it is widely accepted that a negative slope in the Arrott plot is indicative of a first-order magnetic transition. This is known as the Banerjee criterion. In consequence, the zero-field transition temperature T* is reported as the characteristic first-order transition temperature. By carefully analyzing the mean-field Landau model used for studying first-order magnetic transitions, we show in this work that T* corresponds in fact to a triple point where three first-order lines meet. More importantly, this analysis reveals the existence of two symmetrical second-order critical points at finite magnetic field (Tc,±Hc) . We then show that a modified Arrott plot can be used to obtain information about these second-order critical points. To support this idea we analyze experimental data on La2 /3Ca1 /3MnO3 and discuss an estimate for the location of the triple point and the second-order critical points.
Generation of non-classical optical fields by a beam splitter with second-order nonlinearity
Prakash, Hari
2016-01-01
We propose quantum-mechanical model of a beam splitter with second-order nonlinearity and show that non-classical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output fundamental and second harmonic modes when we mix coherent light beams via such a nonlinear beam splitter.
Breil, J; Maire, P-H; Nicolai, P; Schurtz, G [CELIA, Universite Bordeaux I, CNRS, CEA, 351 cours de la Liberation, 33405 Talence (France)], E-mail: breil@celia.u-bordeaux1.fr
2008-05-15
In laser produced plasmas large self-generated magnetic fields have been measured. The classical formulas by Braginskii predict that magnetic fields induce a reduction of the magnitude of the heat flux and its rotation through the Righi-Leduc effect. In this paper a second order tensorial diffusion method used to correctly solve the Righi-Leduc effect in multidimensional code is presented.
Modelling Distributed Shape Priors by Gibbs Random Fields of Second Order
Flach, Boris
2011-01-01
We analyse the potential of Gibbs Random Fields for shape prior modelling. We show that the expressive power of second order GRFs is already sufficient to express simple shapes and spatial relations between them simultaneously. This allows to model and recognise complex shapes as spatial compositions of simpler parts.
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)
Do Children with Autism Perceive Second-Order Relational Features? The Case of the Thatcher Illusion
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…
Comparison of Several Modes in Simple ARC Second-Order Filter
A. I. Rybin
1994-07-01
Full Text Available In this paper the popular, multiple-feedback, ARC single opamp, highpass second-order filter is proposed in several types of modes, namely voltage, current and hybrid ones. These modes are studied and compared in detail. Computer experimental results are given supporting the theory.
Spatio-temporal second-order quantum correlations of surface plasmon polaritons
Berthel, Martin; Drezet, Aurélien
2016-01-01
We present an experimental methodology to observe spatio-temporal second-order quantum coherence of surface plasmon polaritons which are emitted by nitrogen vacancy color centers attached at the apex of an optical tip. The approach relies on leakage radiation microscopy in the Fourier space and we use this approach to test wave-particle duality for surface plasmon polaritons.
m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE
无
2012-01-01
In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION ON TIME SCALES
无
2011-01-01
In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.
FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES
无
2012-01-01
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
Journee, Henricus Louis; Postma, Alida Annechien; Sun, Mingui; Staal, Michiel J.
2008-01-01
Introduction: Conventional linear signal processing techniques are not always suitable for the detection of tremor bursts in clinical practice due to inevitable noise from electromyographic (EMG) bursts. This study introduces (1) a non-linear analysis technique based on a running second order moment
Multiple periodic solutions for a class of second-order nonlinear neutral delay equations
2006-01-01
Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .
Direct measurement of second-order coupling in a waveguide lattice
Keil, Robert; Heilmann, René; Gräfe, Markus; Weihs, Gregor; Szameit, Alexander
2015-01-01
We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes.
Semantic Characterisations of Second-Order Computability over the Real Numbers
Korovina, Margarita V.; Kudinov, Oleg V.
2001-01-01
We propose semantic characterisations of second-order computability over the reals based on σ-definability theory. Notions of computability for operators and real-valued functionals defined on the class of continuous functions are introduced via domain theory. We consider the reals with and witho...
A smart nonstandard finite difference scheme for second order nonlinear boundary value problems
Erdogan, Utku; Ozis, Turgut
2011-01-01
A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed.
Social Referencing and Second Order Effects in Ten-Month-Old Infants.
Feinman, Saul; Lewis, Michael
One pathway through which second order effects proceed is "social referencing," a process in which the individual utilizes another's interpretation when appraising a situation. This phenomenon is well identified in adults and older children. While it had not been studied in infancy, there are good indications that the necessary cognitive…
Multidimensional first and second order symmetric strang splitting for hyperbolic systems
Kucharik, Milan [Los Alamos National Laboratory; Wendroff, Burton [Los Alamos National Laboratory
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.
Independence of First- and Second-Order Memories in Newborn Rabbits
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…
Relative boundedness and compactness theory for second-order differential operators
Don B. Hinton
1997-01-01
Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.
Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems
Adegas, Fabiano Daher; Stoustrup, Jakob
2015-01-01
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...
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sármány, D.; Botchev, M.A.; Vegt, van der J.J.W.
2012-01-01
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\\mathrm{curl})$-conf
Boundary-value problems for first and second order functional differential inclusions
Shihuang Hong
2003-03-01
Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
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…
Quantization effects on synchronized motion of teams of mobile agents with second-order dynamics
Liu, Hui; Cao, Ming; De Persis, Claudio
2012-01-01
For a team of mobile agents governed by second-order dynamics, this paper studies how different quantizers affect the performances of consensus-type schemes to achieve synchronized collective motion. It is shown that when different types of quantizers are used for the exchange of relative position a
Huabin Chen
2011-01-01
Full Text Available By establishing two Lemmas, the exponential stability and the asymptotical stability for mild solution to the second-order neutral stochastic partial differential equations with infinite delay are obtained, respectively. Our results can generalize and improve some existing ones. Finally, an illustrative example is given to show the effectiveness of the obtained results.
无
2010-01-01
This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and involves first order derivatives. The main tool used in this paper is a fixed point index theory in a cone.
Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance
Ruijter, M.J.; Oosterlee, C.W.
2016-01-01
We develop a Fourier method to solve quite general backward stochastic differential equa-tions (BSDEs) with second-order accuracy. The underlying forward stochastic differential equation (FSDE) is approximated by different Taylor schemes, such as the Euler, Milstein, and Order2.0 weak Taylor schemes
QUALITATIVE ANALYSIS FOR A CLASS OF SECOND-ORDER NONLINEAR SYSTEM WITH DELAY
彭奇林
2001-01-01
The second-order nonlinear system with delaybeing considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov's second method. The conclusion in the literatures are generalized.
Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Kurths, Juergen; Kurths, Jürgen
This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a
Optimized Second-Order Dynamical Systems and Their RLC Circuit Models with PWL Controlled Sources
J. Brzobohaty
2004-09-01
Full Text Available Complementary active RLC circuit models with a voltage-controlledvoltage source (VCVS and a current-controlled current source (CCCSfor the second-order autonomous dynamical system realization areproposed. The main advantage of these equivalent circuits is the simplerelation between the state model parameters and their correspondingcircuit parameters, which leads also to simple design formulas.
An algorithm for computing a standard form for second-order linear q-difference equations
Hendriks, Peter
1997-01-01
In this article an algorithm is presented for computing a standard form for second order linear q-difference equations. This standard form is useful for determining the q-difference Galois group and the set of Liouvillian solutions of a given equation. (C) 1997 Elsevier Science B.V.
THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS
无
2010-01-01
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
N. Daoudi-Merzagui
2012-01-01
Full Text Available We discuss the existence of subharmonic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions are provided enable us to obtain infinitely many distinct subharmonic solutions. Our approach is based on a variational method, in particular the saddle point theorem.
Stabilization for a class of second-order switched systems with saturation constrains
SONG Yang; GU Yu-qi; FEI Min-rui
2009-01-01
This paper proposes a global stabilization method for a class of planar switched systems with input saturation constrains by using a state feedback and switching strategy.This method is proved to be effective by analyzing the characteristics of the trajectory of second-order linear systems with input saturation.
A Second-Order Method for the Electromagnetic Scattering from a Large Cavity
Yingxi Wang; Kui Du; Weiwei Sun
2008-01-01
In this paper, we study the electromagnetic scattering from a two dimensional large rectangular open cavity embedded in an infinite ground plane, which is modelled by Helmholtz equations. By introducing nonlocal transparent boundary conditions, the problem in the open cavity is reduced to a bounded domain problem. A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases, respectively. A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper-singular integral operator on the aperture and the Helmholtz in the cavity, respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers. A fast algorithm for the second-order approximation is pro-posed for solving the cavity model with layered media. Numerical results show the second-order accuracy and efficiency of the fast algorithm. More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.
Electronic anisotropy between open shell atoms in first and second order perturbation theory
Groenenboom, G.C.; Chu, X.; Krems, R.V.
2007-01-01
The interaction between two atoms in states with nonzero electronic orbital angular momenta is anisotropic and can be represented by a spherical tensor expansion. The authors derive expressions for the first order (electrostatic) and second order (dispersion and induction) anisotropic interaction co
Branson, T P; Vasilevich, D V
1998-01-01
Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying Tr Qe^{-tD}, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.
Existence Theorems for Nonlinear Boundary Value Problems for Second Order Differential Inclusions
Kandilakis, Dimitrios A.; Papageorgiou, Nikolaos S.
1996-11-01
In this paper we consider a nonlinear two-point boundary value problem for second order differential inclusions. Using the Leray-Schauder principle and its multivalued analog due to Dugundji-Granas, we prove existence theorems for convex and nonconvex problems. Our results are quite general and incorporate as special cases several classes of problems which are of interest in the literature.
Time domain reflectometry waveform analysis with second order bounded mean oscillation
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...
Recent Existence Results for Second-Order Singular Periodic Differential Equations
Nieto JuanJ
2009-01-01
Full Text Available We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed point theorem in cones, and Schauder's fixed point theorem are used in the proof. The results shed some light on the differences between a strong singularity and a weak singularity.
Dai Qiuyi; Christopher C. Tisdell
2009-01-01
This article considers the Dirichlet problem of homogeneous and inhomoge-neous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the ex-istence of multiple positive solutions for inhomogeneous systems axe obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
Ishii, H.; Lions, P. L.
We investigate comparison and existence results for viscosity solutions of fully nonlinear, second-order, elliptic, possibly degenerate equations. These results complement those recently obtained by R. Jensen and H. Ishii. We consider various boundary conditions like for instance Dirichlet and Neumann conditions. We also apply these methods and results to quasilinear Monge-Ampère equations. Finally, we also address regularity questions.
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
An approach for second order control with finite time convergence for electro-hydraulic drives
Schmidt, Lasse; Andersen, Torben Ole; Pedersen, Henrik C.
2013-01-01
Being a second order sliding algorithm, the super twisting algorithm is highly attractive for application in control of hydraulic drives and mechanical systems in general, as it utilizes only the control error while driving the control error as well as its derivative to zero for properly chosen a...
Second-order wave kinematics conditional on a given wave crest
Jensen, Jørgen Juncher
1996-01-01
-Gaussian contributions. As an application, the mean wave elevation and the associated wave kinematics are determined for a Stokes second-order wave theory. The results are compared to the linear (Gaussian) predictions and the effect of the non-linearities is quantified both for the wave profile and the horizontal wave...
Chen, X.; Cui, W.; Jensen, Jørgen Juncher
2003-01-01
The theory and typical numerical results of a second order nonlinear hydroelastic analysis of floating bodies are presented in a series of papers in which only nonlinearity in fluids is considered. Under the assumption of linear fluid, the hydroelastic analysis methods of nonlinear structure are ...
Oscillation theory for a pair of second order dynamic equations with a singular interface
Pallav Kumar Baruah
2008-03-01
Full Text Available In this paper we consider a pair of second order dynamic equations defined on the time scale $I = [a,c]cup [sigma(c,b]$. We impose matching interface conditions at the singular interface $c$. We prove a theorem regarding the relationship between the number of eigenvalues and zeros of the corresponding eigenfunctions.
Shanying Zhu
2009-01-01
This paper deals with the existence of positive solutions to the singular second-order periodic boundary value problem, We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
Asymptotic behavior and stability of second order neutral delay differential equations
Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd
2014-01-01
We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed
Second-order fully discretized projection method for incompressible Navier-Stokes equations
Daniel X. Guo
2016-03-01
Full Text Available A second-order fully discretized projection method for the incompressible Navier-Stokes equations is proposed. It is an explicit method for updating the pressure field. No extra conditions of immediate velocity fields are needed. The stability and convergence are investigated.
A second-order boundary-fitted projection method for free-surface flow computations
Yang, B.; Prosperetti, A.
2006-01-01
This paper describes a new approach to the high-fidelity simulation of axisymmetric free-surface flows. A boundary-fitted grid is coupled with a new projection method for the solution of the Navier–Stokes equations with second-order accuracy in space and time. Two variants of this new method are dev
Second-order fully discretized projection method for incompressible Navier-Stokes equations
Daniel X. Guo
2016-01-01
A second-order fully discretized projection method for the incompressible Navier-Stokes equations is proposed. It is an explicit method for updating the pressure field. No extra conditions of immediate velocity fields are needed. The stability and convergence are investigated.
Model reduction of second-order network systems using graph clustering
Cheng, Xiaodong; Scherpen, Jacquelien M.A.; Kawano, Yu
2016-01-01
A general framework is proposed for structure-preserving model reduction of a second-order network system. The method is based on graph clustering, and a recursive algorithm is proposed to find an appropriate clustering. Behaviors of nodes are interpreted by transfer functions, and the similarities
Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems
Ke WANG
2011-01-01
Based on the theory of semi-global C1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng
2016-12-01
In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we first propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite-element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML. Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: (1) for an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; (2) unlike the M-PML with high-order damping profile, the M-PML with second-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; (3) in an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with second-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.
Deffayet, C; Esposito-Farèse, G
2009-01-01
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.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation
Petersson, N A; Sjogreen, B
2012-03-26
Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the
Parallel Computation of Air Pollution Using a Second-Order Closure Model
Pai, Prasad Prabhakar
1991-02-01
Rational analysis, prediction and policy making of air pollution problems depend on our understanding of the individual processes that govern the atmospheric system. In the past, computational constraints have prohibited the incorporation of detailed physics of many individual processes in air pollution models. This has resulted in poor model performance for realistic situations. Recent advances in computing capabilities make it possible to develop air pollution models which capture the essential physics of the individual processes. The present study uses a three -dimensional second-order closure diffusion model to simulate dispersion from ground level and elevated point sources in convective (daytime) boundary layers. The model uses mean and turbulence variables simulated with a one-dimensional second-order closure fluid dynamic model. The calculated mean profiles of wind and temperature are found to be in good agreement with the observed Day 33 Wangara data, whereas the calculated vertical profiles of turbulence variables agree well with those estimated from other numerical models and laboratory experiments. The three-dimensional second -order closure diffusion model can capture the plume behavior in daytime atmospheric boundary layer remarkably well in comparison with laboratory data. We also compare the second -order closure diffusion model with the commonly used K -diffusion model for the same meteorological conditions. In order to reduce the computational requirements for second -order closure models, we propose a parallel algorithm of a time-splitting finite element method for the numerical solution of the governing equations. The parallel time -splitting finite element method substantially reduces the model wallclock or turnaround time by exploiting the vector and parallel capabilities of modern supercomputers. The plethora of supercomputers in the market today made it important for us to study the key issue of algorithm "portability". In view of this, we
Arun Kumar Tripathy
2014-03-01
Full Text Available In this paper, a new class of second order (Φ,ρ-univex and second order (Φ,ρ-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain.
Second-order perturbation theory: The problem of infinite mode coupling
Miller, Jeremy; Wardell, Barry; Pound, Adam
2016-11-01
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in Pound [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
Second-order perturbation theory: the problem of infinite mode coupling
Miller, Jeremy; Pound, Adam
2016-01-01
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method
M. Mechee
2013-01-01
Full Text Available Runge-Kutta-Nyström (RKN method is adapted for solving the special second order delay differential equations (DDEs. The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.
Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input
Pedro R. Acosta
2013-01-01
Full Text Available This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.
On Application of Second Order Sliding Mode Control to Electro-Hydraulic Systems
Schmidt, Lasse; Andersen, Torben Ole; Pedersen, Henrik C.
2014-01-01
This paper discusses the application of second order mode controls to hydraulic valve-cylinder drives with a special focus on the limitations resulting from nonlinear dynamic effects in flow control valves. Second order sliding mode algorithms appear highly attractive in the successive...... implementation of sliding mode control, achieving continuous control inputs, while maintaining the main properties of sliding modes. Under certain model assumptions, some of these controllers may even be applied as output feedback controllers. However, intrinsic nonlinear dynamic effects of hydraulic valves...... sliding algorithm known as the super twisting controller is considered for output feedback control and compared with conventional first order sliding mode control. The controllers under consideration are applied for position tracking control of a hydraulic valve-cylinder drive exhibiting strong variations...
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
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.
{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics
Hubbard, S.F.; Petschek, R.G.; Singer, K.D. [Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics] [and others
1997-10-01
We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light for which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.
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.
Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator.
Doron, A; Tamir, I; Mitra, S; Zeltzer, G; Ovadia, M; Shahar, D
2016-02-05
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.
Improved LSB-matching Steganography for Preserving Second-order Statistics
Guangjie Liu
2010-10-01
Full Text Available In the paper, for enhancing the security of the traditional LSB matching, two improved LSB-matching methods are proposed. In the steganograhical procedure, the Markov chain distance based on the second-order statistics is chosen as the security metric to control the modification directions of ±1 embedding. The first method is based on stochastic modification, which directly determines the modification directions by the empirical Markov transition matrix of a cover image and the pseudorandom number generated by a pseudorandom number generator. The second one is based on genetic algorithm, which is used to find the optimum matching vector to make the security metric as small as possible. Experiments show the proposed algorithms outperform LSB matching and LSB replacement in a sense of the firstorder and second-order security metrics. And the adjacent calibrated COM-HCF steganalytical tests also show that the two algorithms are more secure than the traditional ones.
Corrected second-order slip boundary condition for fluid flows in nanochannels.
Zhang, Hongwu; Zhang, Zhongqiang; Zheng, Yonggang; Ye, Hongfei
2010-06-01
A corrected second-order slip boundary condition is proposed to solve the Navier-Stokes equations for fluid flows confined in parallel-plate nanochannels. Compared with the classical second-order slip boundary condition proposed by Beskok and Karniadakis, the corrected slip boundary condition is not only dependent on the Knudsen number and the tangential momentum accommodation coefficient, but also dependent on the relative position of the slip surface in the Knudsen layer. For the fluid flows in slip-flow regime with the Knudsen number less than 0.3, Couette cell is investigated using molecular-dynamics simulations to verify Newtonian flow behaviors by examining the constitutive relationship between shear stress and strain rate. By comparing the velocity profiles of Poiseuille flows predicted from the Navier-Stokes equations with the corrected slip boundary condition with that from molecular-dynamics simulations, it is found that the flow behaviors in our models can be effectively captured.
Dynamic Analysis of Kineto-Elastic Beam System with Second-order Effect
LU Nian-li; LUO Bing; XIA Yong-jun
2009-01-01
Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis, three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system, dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane, the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.
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.
Gauge-invariant perturbations at second order in two-field inflation
Tzavara, Eleftheria; Tent, Bartjan van, E-mail: Eleftheria.Tzavara@th.u-psud.fr, E-mail: Bartjan.Van-Tent@th.u-psud.fr [Laboratoire de Physique Théorique, Université Paris-Sud 11 and CNRS, Bâtiment 210, 91405 Orsay Cedex (France)
2012-08-01
We study the second-order gauge-invariant adiabatic and isocurvature perturbations in terms of the scalar fields present during inflation, along with the related fully non-linear space gradient of these quantities. We discuss the relation with other perturbation quantities defined in the literature. We also construct the exact cubic action of the second-order perturbations (beyond any slow-roll or super-horizon approximations and including tensor perturbations), both in the uniform energy-density gauge and the flat gauge in order to settle various gauge-related issues. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale.
Gauge-invariant perturbations at second order in two-field inflation
Tzavara, Eleftheria
2011-01-01
We study the second-order gauge-invariant adiabatic and isocurvature perturbations in terms of the scalar fields present during inflation, along with the related fully non-linear space gradient of these quantities. We discuss the relation with other perturbation quantities defined in the literature. We also construct the exact cubic action of the second-order perturbations (beyond any slow-roll or super-horizon approximations and including tensor perturbations), both in the uniform energy density gauge and the flat gauge in order to settle various gauge-related issues. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale.
Second-order nonlinear susceptibility in quantum dot structure under applied electric field
Abdullah, M.; Noori, Farah T. Mohammed; Al-Khursan, Amin H.
2015-06-01
A model for quantum dot (QD) subbands, when the dots are in the form of quantum disks, under applied electric field was stated. Then, subbands of dots with different disk radii and heights were calculated under applied field. The competition between the shift due to confinement by field and the size was shown for subbands. Second-order nonlinear susceptibility in quantum dots (QDs) was derived using density matrix theory which is, then, simulated using the calculated subbands. Both interband (IB) and intersubband (ISB) transitions were discussed. High second-order susceptibility in QDs was predicted. The results show a reduction in the susceptibility with the applied field while the peak wavelength was mainly relates to energy difference between subbands. A good match between theory and laboratory experiments was observed. Laboratory experiments at terahertz region might be possible using valence intersubband which is important in many device applications.
Two parametric approaches for eigenstructure assignment in second-order linear systems
Guangren DUAN
2003-01-01
This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus nurnerically simple and reliable; the second one utilizes the right factorization of the system, and allows the dosed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches.
Vein Texture Extraction Using the Multiscale Second-Order Differential Model
Xiong Xinyan
2013-07-01
Full Text Available In order to analyze the back of hand vein pattern rapidly and effectively, a novel approach based on multi-scale second-order differential model is proposed to extract the vein texture from vein samples directly, which is made up of two section: one is the foundation of local second-order differential model of vein texture(VLSDM, the other is texture extraction based on the multi-scale VLSDM. This paper analyzes the vein extraction using the multi-scale VLSDM and handles the filter response using the method of multi-scale analyzed noise filtered. This new algorithm has achieved good results for the vein texture, which is fuzzy, uneven distributed and cross-adhesion. Additionally this method keeps the original form of local shape and achieves orientation and scale information of the vein texture. The experiment result getting from this new method has also compared with another method and shown its outstanding performance.
Sustainable institutionalized punishment requires elimination of second-order free-riders.
Perc, Matjaž
2012-01-01
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.
Chelladurai CALLINS CHRISTIYANA
2013-12-01
Full Text Available This work proposes a new method called Center Symmetric Local Binary Pattern Grey Level Co-occurrence Matrix (CSLBPGLCM for the purpose of extracting second order statistical texture features in ultrasound kidney images. These features are then feed into ultrasound kidney images retrieval system for the point of medical applications. This new GLCM matrix combines the benefit of CSLBP and conventional GLCM. The main intention of this CSLBPGLCM is to reduce the number of grey levels in an image by not simply accumulating the grey levels but incorporating another statistical texture feature in it. The proposed approach is cautiously evaluated in ultrasound kidney images retrieval system and has been compared with conventional GLCM. It is experimentally proved that the proposed method increases the retrieval efficiency, accuracy and reduces the time complexity of ultrasound kidney images retrieval system by means of second order statistical texture features.
Vrkoč Ivo
2001-01-01
Full Text Available The notions of lower and upper functions of the second order differential equations take their beginning from the classical work by C. Scorza-Dragoni and have been investigated till now because they play an important role in the theory of nonlinear boundary value problems. Most of them define lower and upper functions as solutions of the corresponding second order differential inequalities. The aim of this paper is to compare two more general approaches. One is due to Rachůnková and Tvrdý (Nonlinear systems of differential inequalities and solvability of certain boundary value problems (J. of Inequal. & Appl. (to appear who defined the lower and upper functions of the given equation as solutions of associated systems of two differential inequalities with solutions possibly not absolutely continuous. The second belongs to Fabry and Habets (Nonlinear Analysis, TMA 10 (1986, 985–1007 and requires the monotonicity of certain integro-differential expressions.
Second-order accurate finite volume method for well-driven flows
Dotlić, Milan; Pokorni, Boris; Pušić, Milenko; Dimkić, Milan
2013-01-01
We consider a finite volume method for a well-driven fluid flow in a porous medium. Due to the singularity of the well, modeling in the near-well region with standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. Local grid refinement can help, but it comes at computational cost. In this article we propose two methods to address well singularity. In the first method the flux through well faces is corrected using a logarithmic function, in a way related to the Peaceman correction. Coupling this correction with a second-order accurate two-point scheme gives a greatly improved total well flux, but the resulting scheme is still not even first order accurate on coarse grids. In the second method fluxes in the near-well region are corrected by representing the hydraulic head as a sum of a logarithmic and a linear function. This scheme is second-order accurate.
Essaïdi, Zacaria; Krupka, Oksana; Iliopoulos, Konstantinos; Champigny, Emilie; Sahraoui, Bouchta; Sallé, Marc; Gindre, Denis
2013-01-01
The second-order nonlinear optical properties of photocross-linkable coumarin-based copolymers were investigated using the optical second harmonic generation (SHG) with the Maker fringes technique. High quality and transparent spin-deposited thin films of various methacrylic copolymers containing 4-methylcoumarin pendant chromophores were prepared and the coumarin units were ordered and oriented by the corona poling technique. Nonlinear optical investigations were performed using a picosecond Q-switched Nd:YAG laser working at the fundamental wavelength (λ = 1064 nm) and the second order nonlinear optical susceptibilities of the functionalized polymers were determined. The samples were irradiated using two wavelengths (λ = 254 nm and λ > 300 nm) promoting the reversible photo-induced dimerisation of coumarin moieties within the film. The latter is shown to have a significant impact on the nonlinear optical response of the corresponding material. A large SHG response of photocross-linkable coumarin-based copolymers is obtained.
Asymptotic solutions of forced nonlinear second order differential equations and their extensions
Angelo B. Mingarelli
2007-03-01
Full Text Available Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.
Second-Order Resonant Interaction of Ring Current Protons with Whistler-Mode Waves
XIAO Fu-Liang; CHEN Liang-Xu; HE Hui-Yong; ZHOU Qing-Hua
2008-01-01
We present a study on the second-order resonant interaction between the ring current protons with Whistler-mode waves propagating near the quasi electrostatic limit following the previous second-order resonant theory.The diffusion coefficients are proportional to the electric field amplitude E,much greater than those for the regular first-order resonance.which are proportional to the electric field amplitudes square E2.Numerical calculations for the pitch angle scattering are performed for typical energies of protons Ek=50ke V and 100ke V at locations L=2 and L=3.5.The timescale for the loss process of protons by the Whistler waves is found to approach one hour,comparable to that by the EMIC waves,suggesting that Whistler waves may also contribute significantly to the ring current decay under appropriate conditions.
Electronic structure, first and second order physical properties of MPS4: a theoretical study
Dahame Tahar
2016-06-01
Full Text Available We have calculated the electronic structure and physical properties of metal thiophosphate compounds InPS4 and AlPS 4by means of pseudopotential density functional theory (DFT coupled with the modern theory of polarization. The targeted physical properties are ﬁrst and second order optical properties as well as elastic, piezoelectric and electro-optic coefﬁcients. Furthermore, population analysis is presented in order to evaluate the covalent-ionic character of the constituent bonds. The calculated elastic constants, refractive indices and second order optical coefﬁcients of InPS4 are in good agreement with experimental values. With the absence of any theoretical or experimental physical properties of AlPS4, we predict that this compound has high piezoelectric coefﬁcients with d14 = − 73.82 pm/V, d25 = − 10.96 pm/V and d36 = 28.19 pm/V.
无
2009-01-01
DFT B3LYP/LANL2DZ method was employed to calculate electron properties and the second-order nonlinear optical(NLO) respond of platinum(Ⅱ) complexes which have been synthesized by Weinstein group.4,7-diphenyl-1,10-phenanthroline shows the ability to push electron in these complexes.Metal Pt plays a balancing charge role.Comparing complex 1b-6b with complex a,the βvec value of complex 1b-5b is larger than one of complex a,while the βvec value of complex 6b is smaller than one of com-plex a.In these seven complexes,the βvec values of complexes increase with decreasing of the energy difference between HOMO and LUMO.Moreover,the electron transfers from deeper layer occupied orbitals to empty orbitals have a distinct contribution to second-order NLO coefficient.
Sahoo, Tapas; Pollak, Eli [Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot (Israel)
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.
Conditional Short-crested second order waves in shallow water and with superimposed current
Jensen, Jørgen Juncher
2004-01-01
For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes' wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean...... wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected second order short-crested wave riding on a uniform current is given. The analysis is based on the second order Sharma and Dean shallow water wave theory and the direction...... of the main wind direction can make any direction with the current. Numerical results showing the importance of the water depth, the directional spreading and the current on the conditional mean wave profile and the associated wave kinematics are presented. A discussion of the use of the conditional wave...
Direct method for second-order sensitivity analysis of modal assurance criterion
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.
Scaled Group Consensus in Multiagent Systems With First/Second-Order Continuous Dynamics.
Yu, Junyan; Shi, Yang
2017-08-29
We investigate scaled group consensus problems of multiagent systems with first/second-order linear continuous dynamics. For a complex network consisting of two subnetworks with different physical quantities or task distributions, it is concerned with this case that the agents' states in one subnetwork converge to a consistent value asymptotically, while the states in the other subnetwork approach another value with a ratio of the former. For the case of the information exchange being directed, novel consensus protocols are designed for both first-order and second-order dynamics to solve the scaled group consensus problems. By utilizing algebra theory, graph theory, and Lyapunov stability theory, several necessary and sufficient conditions are established to guarantee the agents' states reaching the scaled group consensus asymptotically. Finally, several simulation results are presented to demonstrate the effectiveness of the theoretical results.
Pandey, Arun Kumar
2016-01-01
We study the collective behaviour of a chiral plasma, for the first and second order conformal hydrodynamics. We have shown that in the early Universe, when the Universe was in thermal equilibrium and there was an asymmetry in the number densities of right and left handed particles, few modes grow exponentially for the values of wave number $k \\leq \\xi^B$. However, by using conformal first order hydro, we have shown that in a quasi-equilibrium state of the chiral plasma, waves moving parallel or perpendicular to the background magnetic field, get split into two modes similar to the fast and slow hydrodynamic modes in the standard plasma. However, for the second order conformal hydrodynamics, dispersion relation has a series of terms proportional to different powers of $k$. These terms are in accordance with the results obtained using ADS/CFT correspondence.
Sustainable institutionalized punishment requires elimination of second-order free-riders
Perc, Matjaz
2012-01-01
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 defector...
Sustainable institutionalized punishment requires elimination of second-order free-riders
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 Nonlinear Optical Properties of a Series of Benzothiazole Derivatives
LIU,Xiao-Juan; LENG,Wei-Nan; FENG,Ji-Kang; REN,Ai-Min; ZHOU,Xin
2003-01-01
The second- order nonlinear optical ( NLO ) properties of a series of benzothiazole derivatives were studied by use of the ZINDO-SOS method. These chromphores are formed by a donor-π-bridge-acceptor system, based on a nitro group connected with benzothiazole as the acceptor and a hydroxyl-functional amino group as the donor. For the purpose of comparison, we also designed molecules in which nitrobenzene is an acceptor. The calculation results indicate that benzothiazole derivatives exhibit larger second-order polarizabilities than nitrobenzene derivatives. In order to clarify the origin of the NLO response of these chromophores, their electron properties were investigated as well. The benzothiazole derivatives are good candidates for application in electro-optical device due to their high optical nonlinearities, good thermla and photonic stability.
A Novel OFDM Receiver with Optimum Second Order Polynomial Nyquist Windowing
SONG Rong-fang; AI Si; LEUNG Shu-hung
2006-01-01
This paper proposes a new receive scheme and a class of time domain second order polynomial Nyquist window functions, and applies them to Orthogonal Frequency-Division Multiplexing( OFDM) systems in order to reduce Inter-Carrier Interference (ICI) induced by frequency offset. This paper also analyzes the Signal to ICI plus Noise Ratio (SINR)and Bit Error Rate (BER) performances of the receiver. Additionally, this paper proposes a method to select optimum window parameters to maximize the SINR of the receiver thus providing an adaptive receiving capability. Our results show that the proposed method enables the use of unity roll-off factor, provides better SINR and BER than conventional receive methods whose roll-off factors are generally less than one. The new second order polynomial window is shown to provide better performance than raised cosine and "better than" Nyquist window.
Conditional Short-crested second order waves in shallow water and with superimposed current
Jensen, Jørgen Juncher
2004-01-01
wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected second order short-crested wave riding on a uniform current is given. The analysis is based on the second order Sharma and Dean shallow water wave theory and the direction......For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes' wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean...... waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy...
Enhancement of second-order nonlinear-optical signals by optical stimulation
Goodman, Aaron J
2015-01-01
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 >10^4 relative to the spontaneous signal. The stimulation enhancement is greatest in situations where spontaneous signals are the weakest - such as low laser pow...
Second-Order Wave Diffraction Around 3-D Bodies by A Time-Domain Method
柏威; 滕斌
2001-01-01
A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.
Performance of third-order ghost imaging with second-order intensity correlation
Bin Cao; Chunxi Zhang; Pan Ou
2011-01-01
@@ The third-order ghost imaging with the second-order intensity correlation is theoretically and experimentally demonstrated.The resolution and visibility of the reconstructed image are discussed,and the relationship between resolution and visibility is analyzed.The theoretical results show that a tradeoff exists between the visibility and resolution of the reconstructed image; the better the image resolution,the worse the image visibility.%The third-order ghost imaging with the second-order intensity correlation is theoretically and experimentally demonstrated. The resolution and visibility of the reconstructed image are discussed, and the relationship between resolution and visibility is analyzed. The theoretical results show that a tradeoff exists between the visibility and resolution of the reconstructed image; the better the image resolution, the worse the image visibility. Numerical simulations are carried out to verify this theory, and a ghost imaging experiment is conducted to validate our calculations. The experimental results agree with the theoretical predictions.
The collision of boosted black holes second order close limit calculations
Gleiser, R J; Price, R; Pullin, J; Gleiser, Reinaldo; Nicasio, Oscar; Price, Richard; Pullin, Jorge
1999-01-01
We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent appli...
Sanchez, David Garcia; Musy, Marjorie; Bourges, Bernard
2012-01-01
Sensitivity analysis plays an important role in the understanding of complex models. It helps to identify influence of input parameters in relation to the outputs. It can be also a tool to understand the behavior of the model and then can help in its development stage. This study aims to analyze and illustrate the potential usefulness of combining first and second-order sensitivity analysis, applied to a building energy model (ESP-r). Through the example of a collective building, a sensitivity analysis is performed using the method of elementary effects (also known as Morris method), including an analysis of interactions between the input parameters (second order analysis). Importance of higher-order analysis to better support the results of first order analysis, highlighted especially in such complex model. Several aspects are tackled to implement efficiently the multi-order sensitivity analysis: interval size of the variables, management of non-linearity, usefulness of various outputs.
Second order effect of binary sources on characteristics of queue and loss rate
Sheng, Hong-Dah; Li, San-Qi
1994-02-01
A wideband source in high speed networks is typically represented by a binary random process. In this paper we characterize the second-order properties of each binary source by a multi-state MMPP. A comprehensive numerical study is carried out to identify the individual effect of the source second-order dynamics on the queue length and loss rate. The results can be used to verify the validity of the two-state Markov chain binary source assumption which is commonly made within the framework of input rate control and bandwidth allocation in high speed networks. The concept of input power spectrum is then developed as a unified source characterization for multimedia traffic queueing analyses.
Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs
K. S. Mahomed
2012-01-01
Full Text Available Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique.
Temporal second-order coherence function for displaced-squeezed thermal states
Alexanian, Moorad
2015-01-01
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 the dynamical generation at time $t$ of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time $\\tau \\geq 0$ apart. The generation of the Gaussian state by the parametric amplifier ensures that the temporal second-order coherence function depends only on $\\tau$, via $\\tau/t$, for given Gaussian state parameters, Gaussian state preparation time $t$, and average number $\\bar{n}$ of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in $\\tau/t$ rather than an exponential one as is the case for general, displaced-squeezed thermal states.
The monadic second-order logic of graphs XVI : Canonical graph
decompositions
Courcelle, Bruno
2005-01-01
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic Se...
Second-order Born approximation for the ionization of molecules by electron and positron impact
Dal Cappello, C. [Universite Paul Verlaine-Metz, Laboratoire de Physique Moleculaire et des Collisions, Institut Jean Barriol (FR2843), 1 Boulevard Arago, F-57078 Metz Cedex 3 (France); Rezkallah, Z.; Houamer, S. [Laboratoire de Physique Quantique et Systemes Dynamiques, Departement de Physique, Faculte des Sciences Universite Ferhat Abbas, Setif 19000 (Algeria); Charpentier, I. [Universite Paul Verlaine-Metz, Laboratoire de Physique et Mecanique des Materiaux UMR 7554, Ile du Saulcy, F-57045 Metz Cedex 1 (France); Hervieux, P. A. [Institut de Physique et Chimie des Materiaux de Strasbourg, 23 Rue du Loess, BP 43, F-67034 Strasbourg Cedex 2 (France); Ruiz-Lopez, M. F. [Nancy-University, Equipe de Chimie et Biochimie Theoriques, UMR CNRS-UHP 7565, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Dey, R. [Max-Planck Institut fuer Plasmaphysik, Boltzmannstr. 2, D-85748 Garching (Germany); Roy, A. C. [School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur Math 711202, West Bengal (India)
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.
Monotone methods for solving a boundary value problem of second order discrete system
Wang Yuan-Ming
1999-01-01
Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.
Second Order Sliding Mode-Based Output Feedback Tracking Control for Uncertain Robot Manipulators
Van, Mien; Hee-Jun Kang; Young-Soo Suh
2013-01-01
In this paper, a robust output feedback tracking control scheme for motion control of uncertain robot manipulators without joint velocity measurement based on a second-order sliding mode (SOSM) observer is presented. Two second‐order sliding mode observers with finite time convergence are developed for velocity estimation and uncertainty identification, respectively. The first SOSM observer is used to estimate the state vector in finite time without filtration. However, for uncertainty identi...
Homotopy perturbation method for Ozone decomposition of the second order in aqueous solutions
Ayati Z.
2015-05-01
Full Text Available In this article the problem of mass transfer of ozone of the second order from a gaseous phase into an aqueous phase has been studied. Homotopy perturbation method is employed to derive an analytical approximation to the solutions of the system of differential equations governing on the problem. Some parametric studies have been included. The effects of the temperature and hydroxyl ion reaction order to the solutions are illustrated by some plots
Solvability of a class of second-order quasilinear boundary value problems
Qing-liu YAO
2009-01-01
The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution ff the integration of the limit growth function has an appropriate value.
Second-order asymptotics in level crossing for differences of renewal processes
Kroese, D. P.; Kallenberg, W.C.M.
1992-01-01
We consider level crossing for the difference of independent renewal processes. Second-order expansions for the distribution function of the crossing time of level n are found, as n - oo. As a by-product several other results on the difference process are found. The expected minimum of the difference process appears to play an important role in the analysis. This makes this problem essentially harder than the level crossing for the sum process which was studied earlier.
Ben-Aryeh, Y
2006-01-01
The possibility of measuring the second order correlation function of the gravitational waves detectors' currents or photonumbers, and the observation of the gravitational signals by using a spectrum analyzer is discussed. The method is based on complicated data processing and is expected to be efficient for coherent periodic gravitational waves. It is suggested as an alternative method to the conventional one which is used now in the gravitational waves observatories.
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.
Finite-time consensus for leader-following second-order multi-agent system
Sun, Fenglan; Guan, Zhi-Hong
2013-04-01
The finite-time consensus problems of second-order multi-agent system under fixed and switching network topologies are studied in this article. Based on the graph theory, LaSalle's invariance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. The leader-following finite-time consensus is analysed in detail. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
CRITICAL DAMPING OF THE SECOND-ORDER PENDULUM-LIKE SYSTEMS
李鑫滨; 黄永念; 杨莹; 黄琳
2005-01-01
First, the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed. Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations. As a result, sufficient conditions for estimating the critical damp are established, which improves the work by Leonov et al.
First Versus Second Order Latent Growth Curve Models: Some Insights From Latent State-Trait Theory
Geiser, Christian; Keller, Brian; Lockhart, Ginger
2013-01-01
First order latent growth curve models (FGMs) estimate change based on a single observed variable and are widely used in longitudinal research. Despite significant advantages, second order latent growth curve models (SGMs), which use multiple indicators, are rarely used in practice, and not all aspects of these models are widely understood. In this article, our goal is to contribute to a deeper understanding of theoretical and practical differences between FGMs and SGMs. We define the latent ...
Flow of a Second Order Fluid Between Two Infinite Porous Rotating Disks
H. G. Sharma
1983-07-01
Full Text Available The flow of an incompressible second-order fluid between two infinite porous rotating disks has been studied with the assumption that the rate of injuction of the fluid at one disc is equal to the rate of suction at the other. The velocity components have been expressed in terms of three dimensionless functions, which in turn are obtained in ascending powers of the Reynold number (taken to be small, defined in terms of the angular velocities of the disks.
Second order pseudo-maximum likelihood estimation and conditional variance misspecification
Lejeune, Bernard
1997-01-01
In this paper, we study the behavior of second order pseudo-maximum likelihood estimators under conditional variance misspecification. We determine sufficient and essentially necessary conditions for such a estimator to be, regardless of the conditional variance (mis)specification, consistent for the mean parameters when the conditional mean is correctly specified. These conditions implie that, even if mean and variance parameters vary independently, standard PML2 estimators are generally not...
Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
2016-01-01
Differentiators play an important role in (continuous) feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used...
Boundedness of the Solutions of a Second Order nonlinear Differential System
LIUBing-wen; ZHONGYi-lin; PENGLe-qun
2003-01-01
In this paper,author obtain sufficient condition for the boundedness of solutions of the second order nonlinear differential system dx/dt=y-ψ(x),dy/dt=-yf(x)-g(x).(E)The result can be applied to the Liénard-type system.which substantially extends and imporves some impotant results associated with the same problems in the literatures[1-10]et al.
A Compositional Query Algebra for Second-Order Logic and Uncertain Databases
Koch, Christoph
2008-01-01
World-set algebra is a variable-free query language for uncertain databases. It constitutes the core of the query language implemented in MayBMS, an uncertain database system. This paper shows that world-set algebra captures exactly second-order logic over finite structures, or equivalently, the polynomial hierarchy. The proofs also imply that world-set algebra is closed under composition, a previously open problem.
metaXCMS: Second-Order Analysis of Untargeted Metabolomics Data
Tautenhahn, Ralf; Patti, Gary J.; Kalisiak, Ewa; Miyamoto, Takashi; Schmidt, Manuela; Lo, Fang Yin; McBee, Joshua; Nitin S Baliga; Siuzdak, Gary
2010-01-01
Mass spectrometry-based untargeted metabolomics often results in the observation of hundreds to thousands of features that are differentially regulated between sample classes. A major challenge in interpreting the data is distinguishing metabolites that are causally associated with the phenotype of interest from those that are unrelated but altered in downstream pathways as an effect. To facilitate this distinction, here we describe new software called metaXCMS for performing second-order (“m...
On the second-order temperature jump coefficient of a dilute gas
Radtke, Gregg A; Takata, Shigeru; Aoki, Kazuo
2012-01-01
We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.
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:YVO4 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.
A Second-order Fluid Queue with Subordinator Input and Markov-modulated Linear Output
Jin-zhi Li
2009-01-01
We consider an infinite capacity second-order fluid queue with subordinator input and Markov-modulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differ-ential equation (SDE). Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level's convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property.
Refinement of approximated solution of nonlinear differential equation of second order
Zhidkov, E.P.; Sidorova, O.V.
1982-01-01
The boundary problem for nonlinear differential equation of the second order is considered. The problem is assumed to have a unique solution, stable over the right part. It was proved that if the step of the net is small, then the corresponding difference value problem has a unique solution, stable over the right part. Expansion over degrees of discrediting step for approximate solutions is established. The expansion allows one to apply the Richardson type extrapolation. Efficiency of extrapolation is illustrated by numerical example.
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.
FU, Wei; FENG, Ji-Kang; YU, Kun-Qian; REN, Ai-Min; CUI, Meng
2000-01-01
On the basis of Z1NDO methods, according to the sum-overstates (SOS) expression, the progran for the calculation of the second-order nonlinear optical susceptibilities βuk and βμ ofmolecules was devised, and the structures and nonlinear optical properties of unsymmetric bis (phenylethynyl) benzene series derivatives were studied. The influence of the molecular conjugated chain lengths, the donor and the acceptor on βμwas examined.
CHEN Fang-qi; TIAN Rui-lan; CHEN Yu-shu
2006-01-01
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
ZHU Zhi-Chao; LI Zhong-An; LI Qian-Qian; ZENG Qi; LI Zhen; YE Cheng; QIN Jin-Gui
2007-01-01
A novel hyperbranched polymer (3) was prepared by copolymerization of tri-aldehyde moieties with azo chromophores having two active methelene groups, from "A2+B3" approach based on simple Kneovenagel reaction.For comparison, its analogue linear polymer (5) was also synthesized. The two polymers are soluble in common organic solvents, and exhibit good thermal stability. Interestingly, the hyperbranched polymer demonstrates dramatically enhanced second-order nonlinear optical property with comparison to its linear analogue.
Electron-Helium Scattering in a Bichromatic Laser Field in the Second-Order Born Approximation
ZHOU Bin; LI Shu-Min
2009-01-01
@@ The elastic scattering of electrons in atomic helium assisted by a bichromatic laser field is investigated in the second order Born approximation. The target atom is approximated by a simple screening potential. The dependence of the differential cross section on the relative phase between the two laser components is calculated, and compared with the recent results of first order Born approximation [Sun J F, Liang M C and Zhu Z L 2007Chin. Phys. Lett. 24 2572].