Visualization of second order tensor fields and matrix data
NASA Technical Reports Server (NTRS)
Delmarcelle, Thierry; Hesselink, Lambertus
1992-01-01
We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.
Deffayet, C.; Deser, S.; Esposito-Farese, G.
2009-09-15
We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.
Spacetime encodings. III. Second order Killing tensors
Brink, Jeandrew
2010-01-15
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action
NASA Astrophysics Data System (ADS)
Bettoni, Dario; Liberati, Stefano
2013-10-01
The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and properties are worth analyzing along the experience accumulated in the latter context. Here, we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for scalar-tensor theories a là Brans-Dicke. We identify the most general transformation preserving second-order field equations and discuss the issue of viable frames for this kind of theory, in particular, the possibility to cast the action in the so-called Einstein frame. Interestingly, we find that only for a subset of the Horndeski Lagrangian such a frame exists. Finally, we investigate the transformation properties of such frames under field redefinitions and frame transformations and their reciprocal relationship.
NASA Astrophysics Data System (ADS)
Šprlák, Michal; Novák, Pavel
2016-10-01
New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.
Constraints on general second-order scalar-tensor models from gravitational Cherenkov radiation
Kimura, Rampei; Yamamoto, Kazuhiro E-mail: kazuhiro@hiroshima-u.ac.jp
2012-07-01
We demonstrate that the general second-order scalar-tensor theories, which have attracted attention as possible modified gravity models to explain the late time cosmic acceleration, could be strongly constrained from the argument of the gravitational Cherenkov radiation. To this end, we consider the purely kinetic coupled gravity and the extended galileon model on a cosmological background. In these models, the propagation speed of tensor mode could be less than the speed of light, which puts very strong constraints from the gravitational Cherenkov radiation.
NASA Astrophysics Data System (ADS)
Zumalacárregui, Miguel; García-Bellido, Juan
2014-03-01
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector), and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second-order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although second-order in the Einstein frame, generic disformally coupled theories are described by higher-order equations of motion in the Jordan frame. This apparent contradiction is solved by the use of a hidden constraint: the contraction of the metric equations with a Jacobian eigentensor provides a constraint relation for the higher field derivatives, which allows one to express the dynamical equations in a second-order form. This signals a loophole in Horndeski's theorem and allows one to enlarge the set of scalar-tensor theories which are Ostrogradski stable. The transformed Gauss-Bonnet terms are also discussed for the simplest conformal and disformal relations.
Vector and tensor contributions to the curvature perturbation at second order
NASA Astrophysics Data System (ADS)
Carrilho, Pedro; Malik, Karim A.
2016-02-01
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part of the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.
Slowly rotating scalar field wormholes: The second order approximation
Kashargin, P. E.; Sushkov, S. V.
2008-09-15
We discuss rotating wormholes in general relativity with a scalar field with negative kinetic energy. To solve the problem, we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole's throat and the velocity of light. We construct the rotating wormhole solution in the second-order approximation with respect to the small parameter. The analysis shows that the asymptotical mass of the rotating wormhole is greater than that of the nonrotating one, and the null energy condition violation in the rotating wormhole spacetime is weaker than that in the nonrotating one.
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien
2012-02-01
In this short note we explain how to use the linear equations of motion to simplify the third-order action for the cosmological fluctuations. No field redefinition is needed in this exact procedure which considerably limits the range of independent cubic operators, and hence of possible shapes of the primordial bispectrum. We demonstrate this in the context of the most general single-field scalar-tensor theory with second-order equations of motion, whose third-order action has been calculated recently in arXiv:1107.2642 and 1107.3917. In particular, we show that the three cubic operators initially pointed out in these works as new compared to k-inflation can actually be expressed in terms of standard k-inflationary operators.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
In Part I of this work, an improved "second-order" homogenization theory was developed. This new theory makes use of generalized secant moduli that are intermediate between the standard secant and tangent moduli of the nonlinear phases, and that depend not only on the averages, or first-moments of the fields in the phases, but also on the second-moments of the field fluctuations, or phase covariance tensors. In this article, the theory, which is known to be exact to second-order in the heterogeneity contrast, is applied to the special cases of rigidly reinforced and porous materials. These are cases corresponding to infinite contrast where fairly explicit analytical expressions of the Hashin-Shtrikman and self-consistent-type may be generated for nonlinear composites. The results show that the new theory improves on the earlier theory (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) in at least two ways. First, the new theory satisfies rigorous bounds, even near the percolation limit, where field fluctuations become important, and the earlier second-order theory had been found to fail. Second, the new theory predicts fully compressible behavior for porous materials with an incompressible matrix phase, where the earlier theory had also been found to fail. In addition, the new estimates are found to be in better agreement with numerical simulations available from the literature.
Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass.
Rodríguez, Francisco J; Wang, Fu X; Canfield, Brian K; Cattaneo, Stefano; Kauranen, Martti
2007-07-01
We use two-beam second-harmonic generation to perform a quantitative tensor analysis of the effective dipolar surface nonlinearity and the separable multipolar bulk nonlinearity for BK7 glass. The most straightforward, self-consistent interpretation of the results is obtained when the effective surface response is assumed to have approximate Kleinman symmetry and the bulk contribution is dominated by magnetic, rather than quadrupole, effects.
NASA Astrophysics Data System (ADS)
Delgado Acosta, E. G.; Banda Guzmán, V. M.; Kirchbach, M.
2015-03-01
We propose a general method for the description of arbitrary single spin- j states transforming according to ( j, 0) ⊕ (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz tensors for bosons, and tensor-spinors for fermions, and by means of second-order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂2 j order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz tensor (tensor-spinor) representation spaces hosting one sole ( j, 0) ⊕ (0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin- j sector of interest from the rest, while preserving the separate Lorentz and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are of second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0) ⊕ (0, 3/2) is comfortably described by a second-order Lagrangian in the basis of the totally anti-symmetric Lorentz tensor-spinor of second rank, Ψ [ μν]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) ⊕ (0, 3/2) as part of Ψ [ μν] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross-section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.
Zhang, Jin; Peng, Qianrong; Xu, Longquan; Yang, Min; Wu, Aijing; Ye, Shizhu
2014-11-01
Using dropline separation, tangent skimming, and triangulation to estimate the area of an overlapping chromatographic peak might contribute to a large deviation. It is easy, however, to eliminate these errors caused by geometric segmentation using three-way data analysis (second-order tensor decomposition) algorithms. This method of chromatographic analysis has many advantages: automation, anti-interference, high accuracy in the resolution of overlapping chrom- atographic peaks. It even makes the final goal of analytical chemistry achievable without the aid of complicated separation procedures. The core of this method is the process of utilizing useful information and building models through chemometric algorithms. Three-way chromatographic data set can be divided into trilinear dataset and nontrilinear dataset, correspondingly, three-way data analysis (second-order tensor decomposition) algorithms can be divided into trilinear algorithms and nontrilinear algorithms. In this paper, three-way calibration used in liquid chromatography for complex chemical systems in the last decade is reviewed, and focused on sample pretreatment, auxiliary algorithms, the combination and comparison of correction algorithms. PMID:25764649
NASA Astrophysics Data System (ADS)
Sei, Masaki; Nagayama, Kohei; Kajikawa, Kotaro; Ishii, Hisao; Seki, Kazuhiko; Kondo, Katsumi; Matsumoto, Yoshiyasu; Ouchi, Yukio
1998-04-01
We demonstrated full determination of second-order nonlinear susceptibility of a 4‧-n-octyl-4-cyanobiphenyl (8CB) liquid crystal (LC) monolayer adsorbed on a second-harmonic (SH) active polyimide (PI) substrate. In order to separate the SH signal of the LC film from that of the PI film, we adopted an interferometry technique of second-harmonic generation (SHG) using an ultra-thin film local oscillator. We have found a variety of phases in the components of susceptibility: those of χzii and χizi are almost the same but the phase of χzzz differs by 80° from the other two. The phases of the components of the surface susceptibility tensor are not always identical. This fact indicates that the surface SH response is more complicated than what we expected.
The Topology of Symmetric Tensor Fields
NASA Technical Reports Server (NTRS)
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Tensor gauge condition and tensor field decomposition
NASA Astrophysics Data System (ADS)
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castañeda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work.
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.
Loibl, Stefan; Schütz, Martin
2014-07-14
In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation.
Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker.
Yang, Jun; Sha, Kan; Gan, Woon-Seng; Tian, Jing
2005-04-01
The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer.
Modeling of finite-amplitude sound beams: second order fields generated by a parametric loudspeaker.
Yang, Jun; Sha, Kan; Gan, Woon-Seng; Tian, Jing
2005-04-01
The nonlinear interaction of sound waves in air has been applied to sound reproduction for audio applications. A directional audible sound can be generated by amplitude-modulating the ultrasound carrier with an audio signal, then transmitting it from a parametric loudspeaker. This brings the need of a computationally efficient model to describe the propagation of finite-amplitude sound beams for the system design and optimization. A quasilinear analytical solution capable of fast numerical evaluation is presented for the second-order fields of the sum-, difference-frequency and second harmonic components. It is based on a virtual-complex-source approach, wherein the source field is treated as an aggregation of a set of complex virtual sources located in complex distance, then the corresponding fundamental sound field is reduced to the computation of sums of simple functions by exploiting the integrability of Gaussian functions. By this result, the five-dimensional integral expressions for the second-order sound fields are simplified to one-dimensional integrals. Furthermore, a substantial analytical reduction to sums of single integrals also is derived for an arbitrary source distribution when the basis functions are expressible as a sum of products of trigonometric functions. The validity of the proposed method is confirmed by a comparison of numerical results with experimental data previously published for the rectangular ultrasonic transducer. PMID:16060510
Visualization of 3-D tensor fields
NASA Technical Reports Server (NTRS)
Hesselink, L.
1996-01-01
Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.
First and second order operator splitting methods for the phase field crystal equation
Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub
2015-10-15
In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods.
NASA Astrophysics Data System (ADS)
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals
NASA Astrophysics Data System (ADS)
Liu, Yi; Ponte Castañeda, Pedro
2004-02-01
A recently developed "second-order" homogenization procedure (Ponte Castañeda (J. Mech. Phys. Solids 50 (2002a, b) 737, 759)) is extended to viscoplastic polycrystals and applied to compute the effective response of a certain special class of isotropic polycrystals. The method itself reduces to a simple expression requiring the computation of the averages of the stress field and the covariances of its fluctuations over the various grain orientations in an optimally selected "linear comparison polycrystal". Therefore, the method not only allows the determination of the effective behavior of the polycrystal, but as a byproduct also yields information on the heterogeneity of the stress and strain-rate fields within the polycrystal. An application is given for a model 2-dimensional, isotropic polycrystal with power-law behavior for the constituent grains. The resulting predictions for the effective behavior are found to satisfy sharp bounds available from the literature and to be consistent with the results of recent numerical simulations. The associated averages and fluctuations of the stresses and strain rates are found to depend strongly on the strain-rate sensitivity (i.e., nonlinearity) and grain anisotropy. In particular, the stress and strain-rate fluctuations were found to grow and become strongly anisotropic with increasing values of the nonlinearity and grain anisotropy parameters.
NASA Astrophysics Data System (ADS)
Idiart, M. I.; Moulinec, H.; Ponte Castañeda, P.; Suquet, P.
2006-05-01
This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417-1423], while the theoretical estimates follow from the so-called "second-order" procedure [Ponte Castañeda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. J. Mech. Phys. Solids 50, 737-757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding "second-order" estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the "second-order" estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the "second-order" method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites.
NASA Astrophysics Data System (ADS)
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris
2016-05-01
We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
NASA Astrophysics Data System (ADS)
Banda Guzmán, V. M.; Kirchbach, M.
2016-09-01
A boson of spin j≥ 1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second-order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly D^{(j,0)oplus (0,j)} representation specific second-order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum-independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank 2 j.
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Visualization of 2-D and 3-D Tensor Fields
NASA Technical Reports Server (NTRS)
Hesselink, Lambertus
1997-01-01
In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyper-streamlines about these points give rise to tri-sector or wedge points. These singularities and their connecting hyper-streamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find , analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.
Visualization of 2-D and 3-D Tensor Fields
NASA Technical Reports Server (NTRS)
Hesselink, Lambertus
1995-01-01
In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyperstreamlines about these points give rise to trisector or wedge points. These singularities and their connecting hyperstreamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find, analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.
Covariant second-order perturbations in generalized two-field inflation
Tzavara, Eleftheria; Tent, Bartjan van; Mizuno, Shuntaro E-mail: Shuntaro.Mizuno@apc.univ-paris7.fr
2014-07-01
We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a possibly non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general class of models that allows for well-defined adiabatic and entropic sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation.
Long-wavelength properties of phase-field-crystal models with second-order dynamics
NASA Astrophysics Data System (ADS)
Heinonen, V.; Achim, C. V.; Ala-Nissila, T.
2016-05-01
The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.
NASA Astrophysics Data System (ADS)
Dias, F.; Assumpcao, M.
2012-12-01
The knowledge of stress field is fundamental not only to understand driving forces and plate deformation as also it helps in the study of intraplate seismicity. In Brazil, we find reverse, strike-slip and normal mechanisms that indicates a variable stress field. The stress field has been mainly obtained using focal mechanism results and a few breakout data and in-situ measurements. However the stress field is still poorly known in Brazil. Recent earthquake focal mechanisms were determinate using P-wave modeling of seismogram stacks of several teleseismic stations ( > 30°) grouped according to distance and azimuth and first motion polarities. Every record was visually inspected and those with a good signal/noise ratio (SNR) were grouped in latitude-longitude windows of ten degrees and stacked. We usually consider groups with at least two stations, but, in sometimes a good record of single station with different azimuth was also used to constrain the focal depth. The P, pP, sP wavetrains of the stacked signals were modelled using the hudson96 program of Herrman seismology package (Herrman, 2002). We also determinate moment tensor of same events in the central region. The major difficulty is to determinate focal mechanism of low magnitudes events (< 4.0 mb) using distants seismograph stations. The central region shows a purely compressional pattern which are predicted by regional theoretical models (Richardson & Coblentz, 1996 and the TD0 model of Lithgow& Bertelloni, 2004). Meanwhile in the Amazonic region we find a SHmax from E-W to SE-NW probably caused by Caribbean and South American plates interaction (Meijer, 1995). In NE region, the compression rotates following the coast line which indicates an important component regional present in stress field spreading effects due to the continental/oceanic crustal (Assumpção, 1998) and cases of stress caused by sedimentary load in Amazon Fan in agreement local theoretical models (Watts et al., 2009). We determinate the
Wang, Shiwei; Zhao, Lisha; Zhang, Xiaolong; Shi, Zuosen; Cui, Zhanchen; Yang, Yanqiang
2009-08-15
This work focused on the development of a novel method for molecular level assembly and processing of inorganic-organic hybrid second-order nonlinear optical (SONLO) multilayer films. Aromatic diazo group linked silicon sol was first synthesized and used as a polycation. This oligomer was assembled into inorganic-organic hybrid SONLO multilayer films by electric-field-induced layer-by-layer assembly technique with a low molecular weight chromophore molecule as an anion. After UV irradiation, the electrostatic interaction between layers converted to covalent bonds. Large second-harmonic generation signal of the assembled film was observed, which confirmed that the chromophore in the film had a high degree of molecular orientation as assembled under the electric field. As the cross-linked structure and silicon oxygen meshwork in the films, the resulting inorganic-organic hybrid multilayer films displayed good thermal and chemical stability, and excellent NLO properties. PMID:19433327
NASA Technical Reports Server (NTRS)
Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)
1999-01-01
Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Xuelei; Li, Wuqun
2014-08-01
Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms (Born/single scattering approximation) are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation (heterogeneous) medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps: firstly, to handle the forward scattering by taking into account the second-order Born approximation, which is related to generalized Radon transform (GRT) about quadratic scattering potential; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation () of background media up to 10 %, and its inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the perturbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a transmission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.
Curvature tensors unified field equations on SEXn
NASA Astrophysics Data System (ADS)
Chung, Kyung Tae; Lee, Il Young
1988-09-01
We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.
Fast stray field computation on tensor grids.
Exl, L; Auzinger, W; Bance, S; Gusenbauer, M; Reichel, F; Schrefl, T
2012-04-01
A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N(4/3) for N computational cells used and with N(2/3) (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.
Fast stray field computation on tensor grids
Exl, L.; Auzinger, W.; Bance, S.; Gusenbauer, M.; Reichel, F.; Schrefl, T.
2012-01-01
A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N4/3 for N computational cells used and with N2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples. PMID:24910469
Lazur, V. Yu.; Myhalyna, S. I.; Reity, O. K.
2010-06-15
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 consistent account of the natural condition of the interaction symmetry with respect to both electrons leads to the additional contribution to the relativistic interaction of the two quasimolecular electrons compared with both the standard Breit operator and the generalized Breit operator obtained previously [O. N. Gadomskii, Usp. Fiz. Nauk 170, 1145 (2000) [Phys. Usp. 43, 1071 (2000)
Visualization of Tensor Fields Using Superquadric Glyphs
Ennis, Daniel B.; Kindlman, Gordon; Rodriguez, Ignacio; Helm, Patrick A.; McVeigh, Elliot R.
2007-01-01
The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (λi, sorted eigenvalues), λ1 = λ2 = λ3 (spherical), λ1 < λ2 = λ3 (oblate), λ1 > λ2 = λ3 (prolate), and λ1 > λ2 > λ3 (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids. PMID:15690516
NASA Astrophysics Data System (ADS)
Wang, Xinjie; Vanderbilt, David
2007-03-01
We present a perturbative treatment of the response properties of insulating crystals under a dc bias field, and use this to study the effects of such bias fields on the Born effective charge tensor and dielectric tensor of insulators. We start out by expanding a variational field-dependent total-energy functional with respect to the electric field within the framework of density-functional perturbation theory. The second-order term in the expansion of the total energy is then minimized with respect to the first-order wave functions, from which the Born effective charge tensor and dielectric tensor are easily computed. We demonstrate an implementation of the method and perform illustrative calculations for the III-V semiconductors AlAs and GaAs under finite bias field.
Moussa, Jonathan E.
2014-01-07
The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and it scales as O(n{sup 5}) operations and O(n{sup 3}) memory for n electrons. We derive a new algorithm that reduces its scaling to O(n{sup 3}) operations and O(n{sup 2}) memory using controlled approximations and a new self-consistent field that approximates Brueckner coupled-cluster doubles theory with RPA+SOSEX, referred to as Brueckner RPA theory. The algorithm comparably reduces the scaling of second-order Møller-Plesset perturbation theory with smaller cost prefactors than RPA+SOSEX. Within a semiempirical model, we study H{sub 2} dissociation to test accuracy and H{sub n} rings to verify scaling.
NASA Technical Reports Server (NTRS)
Landahl, M.; Loefgren, P.
1973-01-01
A second-order theory for supersonic flow past slender bodies is presented. Through the introduction of characteristic coordinates as independent variables and the expansion procedure proposed by Lin and Oswatitsch, a uniformly valid solution is obtained for the whole flow field in the axisymmetric case and for far field in the general three-dimensional case. For distances far from the body the theory is an extension of Whitham's first-order solution and for the domain close to the body it is a modification of Van Dyke's second-order solution in the axisymmetric case. From the theory useful formulas relating flow deflections to the Whitham F-function are derived, which permits one to determine the sonic boom strength from wind tunnel measurements fairly close to the body.
Bates, Jefferson E.; Shiozaki, Toru
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.
Second-Order Algebraic Theories
NASA Astrophysics Data System (ADS)
Fiore, Marcelo; Mahmoud, Ola
Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
Numazaki, Kazuya; Imai, Hiromitsu; Morinaga, Atsuo
2010-03-15
The second-order Zeeman effect of the sodium clock transition in a weak magnetic field of less than 50 {mu}T was measured as the scalar Aharonov-Bohm phase by two-photon stimulated Raman atom interferometry. The ac Stark effect of the Raman pulse was canceled out by adopting an appropriate intensity ratio of two photons in the Raman pulse. The Ramsey fringes for the pulse separation of 7 ms were obtained with a phase uncertainty of {pi}/200 rad. The nondispersive feature of the scalar Aharonov-Bohm phase was clearly demonstrated through 18 fringes with constant amplitude. The Breit-Rabi formula of the sodium clock transition was verified to be {Delta}{nu}=(0.222{+-}0.003)x10{sup 12}xB{sup 1.998{+-}0.004} in a magnetic field of less than 50 {mu}T.
The Topology of Three-Dimensional Symmetric Tensor Fields
NASA Technical Reports Server (NTRS)
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
Second-Order Footsteps Illusions.
Kitaoka, Akiyoshi; Anstis, Stuart
2015-12-01
In the "footsteps illusion", light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures-even though luminance-based neural motion detectors are blind to such edges. PMID:27551366
K-inflationary power spectra at second order
Martin, Jérôme; Vennin, Vincent; Ringeval, Christophe E-mail: christophe.ringeval@uclouvain.be
2013-06-01
Within the class of inflationary models, k-inflation represents the most general single field framework that can be associated with an effective quadratic action for the curvature perturbations and a varying speed of sound. The incoming flow of high-precision cosmological data, such as those from the Planck satellite and small scale Cosmic Microwave Background (CMB) experiments, calls for greater accuracy in the inflationary predictions. In this work, we calculate for the first time the next-to-next-to-leading order scalar and tensor primordial power spectra in k-inflation needed in order to obtain robust constraints on the inflationary theory. The method used is the uniform approximation together with a second order expansion in the Hubble and sound flow functions. Our result is checked in various limits in which it reduces to already known situations.
Tensor classification of structure in smoothed particle hydrodynamics density fields
NASA Astrophysics Data System (ADS)
Forgan, Duncan; Bonnell, Ian; Lucas, William; Rice, Ken
2016-04-01
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a `by eye' search. We present tensor classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that tensor classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tessellation of the density field, as required by some classification algorithms. As examples, we show that tensor classification using the tidal tensor and the velocity shear tensor successfully identifies filaments, shells and sheet structures in giant molecular cloud simulations, as well as spiral arms in discs. The relationship between structures identified using different tensors illustrates how different forces compete and co-operate to produce the observed density field. We therefore advocate the use of multiple tensors to classify structure in SPH simulations, to shed light on the interplay of multiple physical processes.
Degeneracy-aware interpolation of 3D diffusion tensor fields
NASA Astrophysics Data System (ADS)
Bi, Chongke; Takahashi, Shigeo; Fujishiro, Issei
2012-01-01
Visual analysis of 3D diffusion tensor fields has become an important topic especially in medical imaging for understanding microscopic structures and physical properties of biological tissues. However, it is still difficult to continuously track the underlying features from discrete tensor samples, due to the absence of appropriate interpolation schemes in the sense that we are able to handle possible degeneracy while fully respecting the smooth transition of tensor anisotropic features. This is because the degeneracy may cause rotational inconsistency of tensor anisotropy. This paper presents such an approach to interpolating 3D diffusion tensor fields. The primary idea behind our approach is to resolve the possible degeneracy through optimizing the rotational transformation between a pair of neighboring tensors by analyzing their associated eigenstructure, while the degeneracy can be identified by applying a minimum spanning tree-based clustering algorithm to the original tensor samples. Comparisons with existing interpolation schemes will be provided to demonstrate the advantages of our scheme, together with several results of tracking white matter fiber bundles in a human brain.
Calculating Second-Order Effects in MOSFET's
NASA Technical Reports Server (NTRS)
Benumof, Reuben; Zoutendyk, John A.; Coss, James R.
1990-01-01
Collection of mathematical models includes second-order effects in n-channel, enhancement-mode, metal-oxide-semiconductor field-effect transistors (MOSFET's). When dimensions of circuit elements relatively large, effects neglected safely. However, as very-large-scale integration of microelectronic circuits leads to MOSFET's shorter or narrower than 2 micrometer, effects become significant in design and operation. Such computer programs as widely-used "Simulation Program With Integrated Circuit Emphasis, Version 2" (SPICE 2) include many of these effects. In second-order models of n-channel, enhancement-mode MOSFET, first-order gate-depletion region diminished by triangular-cross-section deletions on end and augmented by circular-wedge-cross-section bulges on sides.
Kubo Formulas for Second-Order Hydrodynamic Coefficients
Moore, Guy D.; Sohrabi, Kiyoumars A.
2011-03-25
At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity {eta} and on five additional ''second-order'' hydrodynamical coefficients {tau}{sub {Pi}}, {kappa}, {lambda}{sub 1}, {lambda}{sub 2}, and {lambda}{sub 3}. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient {lambda}{sub 3} can be evaluated directly by Euclidean means and does not in general vanish.
Cascaded second-order contribution to the third-order nonlinear susceptibility
NASA Astrophysics Data System (ADS)
Kolleck, Christian
2004-05-01
Cascading of second-order nonlinear effects leads to an effective third-order nonlinearity. In addition to the macroscopic electric field at the intermediate frequencies another term has to be taken into account which is due to the locality of the intermediate polarization sources. Combining the correction terms at the three intermediate frequencies gives rise to a third-order susceptibility tensor, which exhibits the same symmetry properties as an intrinsic susceptibility. This particularly applies to the contributions from the rectified and the second-harmonic fields to the degenerate susceptibility.
Total angular momentum waves for scalar, vector, and tensor fields
NASA Astrophysics Data System (ADS)
Dai, Liang; Kamionkowski, Marc; Jeong, Donghui
2012-12-01
Most calculations in cosmological perturbation theory, including those dealing with the inflationary generation of perturbations, their time evolution, and their observational consequences, decompose those perturbations into plane waves (Fourier modes). However, for some calculations, particularly those involving observations performed on a spherical sky, a decomposition into waves of fixed total angular momentum (TAM) may be more appropriate. Here we introduce TAM waves—solutions of fixed total angular momentum to the Helmholtz equation—for three-dimensional scalar, vector, and tensor fields. The vector TAM waves of given total angular momentum can be decomposed further into a set of three basis functions of fixed orbital angular momentum, a set of fixed helicity, or a basis consisting of a longitudinal (L) and two transverse (E and B) TAM waves. The symmetric traceless rank-2 tensor TAM waves can be similarly decomposed into a basis of fixed orbital angular momentum or fixed helicity, or a basis that consists of a longitudinal (L), two vector (VE and VB, of opposite parity), and two tensor (TE and TB, of opposite parity) waves. We show how all of the vector and tensor TAM waves can be obtained by applying derivative operators to scalar TAM waves. This operator approach then allows one to decompose a vector field into three covariant scalar fields for the L, E, and B components and symmetric-traceless-tensor fields into five covariant scalar fields for the L, VE, VB, TE, and TB components. We provide projections of the vector and tensor TAM waves onto vector and tensor spherical harmonics. We provide calculational detail to facilitate the assimilation of this formalism into cosmological calculations. As an example, we calculate the power spectra of the deflection angle for gravitational lensing by density perturbations and by gravitational waves. We comment on an alternative approach to cosmic microwave background fluctuations based on TAM waves. An
Can Torsion BE Treated as Just another Tensor Field?
NASA Astrophysics Data System (ADS)
Nester, James M.; Wang, Chih-Hung
Many alternative gravity theories use an independent connection which leads to torsion in addition to curvature. Some have argued that there is no physical need to use such connections, that one can always use the Levi-Civita connection and just treat torsion as another tensor field. We explore this issue here in the context of the Poincaré Gauge theory of gravity, which is usually formulated in terms of an affine connection for a Riemann-Cartan geometry (torsion and curvature). We compare the equations obtained by taking as the independent dynamical variables: (i) the orthonormal coframe and the connection and (ii) the orthonormal coframe and the torsion (contortion), and we also consider the coupling to a source. From this analysis we conclude that, at least for this class of theories, torsion should not be considered as just another tensor field.
NASA Astrophysics Data System (ADS)
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z <0 and rises like zα, α >0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
An Analysis of Second-Order Autoshaping
ERIC Educational Resources Information Center
Ward-Robinson, Jasper
2004-01-01
Three mechanisms can explain second-order conditioning: (1) The second-order conditioned stimulus (CS2) could activate a representation of the first-order conditioned stimulus (CS1), thereby provoking the conditioned response (CR); The CS2 could enter into an excitatory association with either (2) the representation governing the CR, or (3) with a…
Second order guiding-center Vlasov-Maxwell equations
Madsen, Jens
2010-08-15
Second order gyrogauge invariant guiding-center coordinates with strong ExB-flow are derived using the Lie transformation method. The corresponding Poisson bracket structure and equations of motion are obtained. From a variational principle the explicit Vlasov-Maxwell equations are derived including second order terms. The second order contributions contain the lowest order finite-Larmor-radius corrections to the electromagnetic field. Therefore, the model is capable of describing situations where strong ExB-flows and finite-Larmor-radius effects are mutually important.
Second-order corrected Hadamard formulas
NASA Astrophysics Data System (ADS)
Epele, L. N.; Fanchiotti, H.; Canal, C. A. García
1985-08-01
The second-order correction to the Hadamard formulas for the Green's function, harmonic measures, and period matrix of a two-dimensional domain is obtained in the context of the domain-variational theory.
NASA Astrophysics Data System (ADS)
Nguyen Lan, Tran; Chalupský, Jakub; Yanai, Takeshi
2015-07-01
The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin-orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin-orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled-perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas-Kroll-Hess picture change of Zeeman operators are given in detail.
Chen, Zhenhua; Chen, Xun; Ying, Fuming; Gu, Junjing; Zhang, Huaiyu; Wu, Wei
2014-10-01
Using the formulas and techniques developed in Papers I and II of this series, the recently developed second-order perturbation theory based on a valence bond self-consistent field reference function (VBPT2) has been extended by using the internally contracted correction wave function. This ansatz strongly reduces the size of the interaction space compared to the uncontracted wave function and thus improves the capability of the VBPT2 method dramatically. Test calculations show that internally contracted VBPT2 using only a small number of reference valence bond functions, can give results as accuracy as the VBPT2 method and other more sophisticated methods such as full configuration interaction and multireference configuration interaction. PMID:25296795
NASA Astrophysics Data System (ADS)
Harding, Michael E.; Vázquez, Juana; Stanton, John F.; Diezemann, Gregor; Gauss, Jürgen
2011-06-01
For a small set of linear and non-linear molecules, a detailed comparison of two different procedures for predicting vibrationally averaged molecular properties, i.e., second-order vibrational perturbation theory (VPT2) and a variational approach, is carried out. Results for vibrational corrections to dipole and quadrupole moments, nuclear quadrupole moments, static electric-dipole polarizabilities, NMR chemical shielding tensors, nuclear spin-rotation tensors, magnetizabilities, and rotational g-tensors are reported.
When scalar field is kinetically coupled to the Einstein tensor
Gao, Changjun
2010-06-01
We explore the cosmic evolution of a scalar field with the kinetic term coupled to the Einstein tensor. We find that, in the absence of other matter sources or in the presence of only pressureless matter, the scalar behaves as pressureless matter and the sound speed of the scalar is vanishing. These properties enable the scalar field to be a candidate of cold dark matter. By also considering the scalar potential, we find the scalar field may play the role of both dark matter and dark energy. In this case, the equation of state of the scalar can cross the phantom divide, but this can lead to the sound speed becoming superluminal as it crosses the divide, and so is physically forbidden. Finally, if the kinetic term is coupled to more than one Einstein tensor, we find the equation of state is always approximately equal to -1 whether the potential is flat or not, and so the scalar may also be a candidate for the inflaton.
Selfishness as second-order altruism.
Eldakar, Omar Tonsi; Wilson, David Sloan
2008-05-13
Selfishness is seldom considered a group-beneficial strategy. In the typical evolutionary formulation, altruism benefits the group, selfishness undermines altruism, and the purpose of the model is to identify mechanisms, such as kinship or reciprocity, that enable altruism to evolve. Recent models have explored punishment as an important mechanism favoring the evolution of altruism, but punishment can be costly to the punisher, making it a form of second-order altruism. This model identifies a strategy called "selfish punisher" that involves behaving selfishly in first-order interactions and altruistically in second-order interactions by punishing other selfish individuals. Selfish punishers cause selfishness to be a self-limiting strategy, enabling altruists to coexist in a stable equilibrium. This polymorphism can be regarded as a division of labor, or mutualism, in which the benefits obtained by first-order selfishness help to "pay" for second-order altruism. PMID:18448681
Second-order (2 +1 ) -dimensional anisotropic hydrodynamics
NASA Astrophysics Data System (ADS)
Bazow, Dennis; Heinz, Ulrich; Strickland, Michael
2014-11-01
We present a complete formulation of second-order (2 +1 ) -dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.
Second-order reconstruction of the inflationary potential
NASA Technical Reports Server (NTRS)
Liddle, Andrew R.; Turner, Michael S.
1994-01-01
To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.
Second-Order Conditioning in "Drosophila"
ERIC Educational Resources Information Center
Tabone, Christopher J.; de Belle, J. Steven
2011-01-01
Associative conditioning in "Drosophila melanogaster" has been well documented for several decades. However, most studies report only simple associations of conditioned stimuli (CS, e.g., odor) with unconditioned stimuli (US, e.g., electric shock) to measure learning or establish memory. Here we describe a straightforward second-order conditioning…
Nine Practices of Second Order Schools
ERIC Educational Resources Information Center
Brown, Bill; Tucker, Patrick; Williams, Thomas L.
2012-01-01
Many schools are in some stage of implementing differentiated instruction, with some already in what Carol Tomlinson describes in "The Differentiated School" as "second order change," where the entire school practices differentiation. In high-performing schools, differentiation has proved to be an effective instructional strategy; in classroom…
NASA Astrophysics Data System (ADS)
Kim, Inkoo; Lee, Yoon Sup
2014-10-01
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.
Beyond special relativity at second order
NASA Astrophysics Data System (ADS)
Carmona, J. M.; Cortés, J. L.; Relancio, J. J.
2016-10-01
The study of generic, nonlinear, deformations of special relativity parametrized by a high-energy scale M , which was carried out at first order in 1 /M in J. M. Carmona, J. L. Cortés, and F. Mercati, Phys. Rev. D 86, 084032 (2012), is extended to second order. This can be done systematically through a ("generalized") change of variables from momentum variables that transform linearly. We discuss the different perspectives on the meaning of the change of variables, obtain the coefficients of modified composition laws and Lorentz transformations at second order, and work out how κ -Poincaré, the most commonly used example in the literature, is reproduced as a particular case of the generic framework exposed here.
The Poisson equation at second order in relativistic cosmology
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A. E-mail: Adam.Christopherson@nottingham.ac.uk
2013-08-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field.
Remarks on the second-order Seiberg-Witten maps
Trampetic, Josip; Wohlgenannt, Michael
2007-12-15
In this brief report, we discuss the Seiberg-Witten maps up to the second order in the noncommutative parameter {theta}. They add to the recently published solutions in [A. Alboteanu, T. Ohl, and R. Rueckl, Phys. Rev. D 76, 105018 (2007).]. Expressions for the vector, fermion, and Higgs fields are given explicitly.
Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît
2014-05-13
The linear [χ((1))] and second-order nonlinear [χ((2))] optical susceptibilities of the 2-methyl-4-nitroaniline (MNA) crystal are calculated within the local field theory, which consists of first computing the molecular properties, accounting for the dressing effects of the surroundings, and then taking into account the local field effects. Several aspects of these calculations are tackled with the aim of monitoring the convergence of the χ((1)) and χ((2)) predictions with respect to experiment by accounting for the effects of (i) the dressing field within successive approximations, of (ii) the first-order ZPVA corrections, and of (iii) the geometry. With respect to the reference CCSD-based results, besides double hybrid functionals, the most reliable exchange-correlation functionals are LC-BLYP for the static χ((1)) and CAM-B3LYP (and M05-2X, to a lesser extent) for the dynamic χ((1)) but they strongly underestimate χ((2)). Double hybrids perform better for χ((2)) but not necessarily for χ((1)), and, moreover, their performances are much similar to MP2, which is known to slightly overestimate β, with respect to high-level coupled-clusters calculations and, therefore, χ((2)). Other XC functionals with less HF exchange perform poorly with overestimations/underestimations of χ((1))/χ((2)), whereas the HF method leads to underestimations of both. The first-order ZPVA corrections, estimated at the B3LYP level, are usually small but not negligible. Indeed, after ZPVA corrections, the molecular polarizabilities and first hyperpolarizabilities increase by 2% and 5%, respectively, whereas their impact is magnified on the macroscopic responses with enhancements of χ((1)) by up to 5% and of χ((2)) by as much as 10%-12% at λ = 1064 nm. The geometry plays also a key role in view of predicting accurate susceptibilities, particularly for push-pull π-conjugated compounds such as MNA. So, the geometry optimized using periodic boundary conditions is characterized
Flavour fields in steady state: stress tensor and free energy
NASA Astrophysics Data System (ADS)
Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan
2016-02-01
The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the stress tensor of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1-background, for d = 2, 4, and is related to conformal anomaly. For the special case of d = 2, the universal factor has a striking resemblance to the well-known heat current formula in (1 + 1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d = 6.
Second-order coherence of supercontinuum light.
Genty, Goëry; Surakka, Minna; Turunen, Jari; Friberg, Ari T
2010-09-15
We analyze the coherence properties of supercontinuum generated in photonic crystal fibers by applying the second-order coherence theory of nonstationary light. Using an ensemble of simulated realizations, we construct two-frequency cross-spectral density and two-time mutual coherence functions. This allows us to introduce measures of temporal and spectral coherence. We show that, in the long-pulse regime, supercontinuum light can be decomposed into a sum of coherent and quasi-stationary contributions. Our approach and findings are also applicable in the short-pulse regime. PMID:20847777
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C. H.
1993-01-01
This report presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design.
First- and second-order Poisson spots
NASA Astrophysics Data System (ADS)
Kelly, William R.; Shirley, Eric L.; Migdall, Alan L.; Polyakov, Sergey V.; Hendrix, Kurt
2009-08-01
Although Thomas Young is generally given credit for being the first to provide evidence against Newton's corpuscular theory of light, it was Augustin Fresnel who first stated the modern theory of diffraction. We review the history surrounding Fresnel's 1818 paper and the role of the Poisson spot in the associated controversy. We next discuss the boundary-diffraction-wave approach to calculating diffraction effects and show how it can reduce the complexity of calculating diffraction patterns. We briefly discuss a generalization of this approach that reduces the dimensionality of integrals needed to calculate the complete diffraction pattern of any order diffraction effect. We repeat earlier demonstrations of the conventional Poisson spot and discuss an experimental setup for demonstrating an analogous phenomenon that we call a "second-order Poisson spot." Several features of the diffraction pattern can be explained simply by considering the path lengths of singly and doubly bent paths and distinguishing between first- and second-order diffraction effects related to such paths, respectively.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI.
Yang, Feng; Zhu, Yue-Min; Magnin, Isabelle E; Luo, Jian-Hua; Croisille, Pierre; Kingsley, Peter B
2012-02-01
Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensor's symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations. PMID:22154961
Matyjasek, Jerzy; Tryniecki, Dariusz
2009-04-15
The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed. It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients a{sub 3} and a{sub 4}. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tensor even in the closest vicinity of the event horizon. The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed.
Computational Harmonic Analysis for Tensor Fields on the Two-Sphere
NASA Astrophysics Data System (ADS)
Kostelec, Peter J.; Maslen, David K.; Healy, Dennis M.; Rockmore, Daniel N.
2000-08-01
In this paper we describe algorithms for the numerical computation of Fourier transforms of tensor fields on the two-sphere, S2. These algorithms reduce the computation of an expansion on tensor spherical harmonics to expansions in scalar spherical harmonics, and hence can take advantage of recent improvements in the efficiency of computation of scalar spherical harmonic transforms.
Deformable Registration of Feature-Endowed Point Sets Based on Tensor Fields
Wassermann, Demian; Ross, James; Washko, George; Wells, William M.; San Jose-Estepar, Raul
2014-01-01
The main contribution of this work is a framework to register anatomical structures characterized as a point set where each point has an associated symmetric matrix. These matrices can represent problem-dependent characteristics of the registered structure. For example, in airways, matrices can represent the orientation and thickness of the structure. Our framework relies on a dense tensor field representation which we implement sparsely as a kernel mixture of tensor fields. We equip the space of tensor fields with a norm that serves as a similarity measure. To calculate the optimal transformation between two structures we minimize this measure using an analytical gradient for the similarity measure and the deformation field, which we restrict to be a diffeomorphism. We illustrate the value of our tensor field model by comparing our results with scalar and vector field based models. Finally, we evaluate our registration algorithm on synthetic data sets and validate our approach on manually annotated airway trees. PMID:25473253
Cosmology of Modified (but second order) Gravity
NASA Astrophysics Data System (ADS)
Koivisto, Tomi S.
2010-01-01
This is a brief review of applications of extended gravity theories to cosmology, in particular to the dark energy problem. Generically extensions of gravity action involve higher derivative terms, which can result in ghosts and instabilities. We consider three ways to circumvent this: Chern-Simons terms, first order variational principle and nonlocality. We consider some recent cosmological applications within these three classes of modified gravity models avoiding introduction of extra degrees of freedom. The viable parameter space can be very efficiently bounded by taking into account cosmological constraints from all epochs in addition to bounds from Solar system tests and stability considerations. We make some new remarks concerning so called algebraic scalar-tensor theories, biscalar reformulation of nonlocal actions involving the inverse d'Alembertian, and a possible covariant formulation holographic cosmology with nonperturbative gravity.
Overconnections and the energy-tensors of gauge and gravitational fields
NASA Astrophysics Data System (ADS)
Canarutto, Daniel
2016-08-01
A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational fields, and shares the main properties of the energy-tensor of a matter field in the jet space formulation of Lagrangian field theory, in particular with regards to symmetries of the Poincaré-Cartan form. Accordingly, the joint energy-tensor for interacting matter and gauge fields turns out to be a natural geometric object, whose definition needs no auxiliary structures. Various topics related to energy-tensors, symmetries and the Einstein equations in a theory with interacting matter, gauge and gravitational fields can be viewed under a clarifying light. Finally, the symmetry determined by the "Komar superpotential" is expressed as a symmetry of the gravitational Poincaré-Cartan form.
Spectral expansions of homogeneous and isotropic tensor-valued random fields
NASA Astrophysics Data System (ADS)
Malyarenko, Anatoliy; Ostoja-Starzewski, Martin
2016-06-01
We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space {E^3} and in the space {S^2(E^3)} of symmetric rank 2 tensors over {E^3}. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.
First- and second-order charged particle optics
Brown, K.L.; Servranckx, R.V.
1984-07-01
Since the invention of the alternating gradient principle there has been a rapid evolution of the mathematics and physics techniques applicable to charged particle optics. In this publication we derive a differential equation and a matrix algebra formalism valid to second-order to present the basic principles governing the design of charged particle beam transport systems. A notation first introduced by John Streib is used to convey the essential principles dictating the design of such beam transport systems. For example the momentum dispersion, the momentum resolution, and all second-order aberrations are expressed as simple integrals of the first-order trajectories (matrix elements) and of the magnetic field parameters (multipole components) characterizing the system. 16 references, 30 figures.
Approximate stress-energy tensor of the massless spin-1/2 field in Schwarzschild spacetime
Matyjasek, Jerzy
2005-01-15
The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in good agreement with the numerical calculations. The backreaction of the quantized field upon the spacetime metric is briefly discussed.
Conservation laws and stress-energy-momentum tensors for systems with background fields
Gratus, Jonathan; Obukhov, Yuri N.; Tucker, Robin W.
2012-10-15
This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.
Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field
NASA Astrophysics Data System (ADS)
Yazadjiev, Stoytcho S.; Doneva, Daniela D.; Popchev, Dimitar
2016-04-01
In the scalar-tensor theories with a massive scalar field, the coupling constants, and the coupling functions in general, which are observationally allowed, can differ significantly from those in the massless case. This fact naturally implies that the scalar-tensor neutron stars with a massive scalar field can have rather different structure and properties in comparison with their counterparts in the massless case and in general relativity. In the present paper, we study slowly rotating neutron stars in scalar-tensor theories with a massive gravitational scalar. Two examples of scalar-tensor theories are examined—the first example is the massive Brans-Dicke theory and the second one is a massive scalar-tensor theory indistinguishable from general relativity in the weak-field limit. In the latter case, we study the effect of the scalar field mass on the spontaneous scalarization of neutron stars. Our numerical results show that the inclusion of a mass term for the scalar field indeed changes the picture drastically compared to the massless case. It turns out that mass, radius, and moment of inertia for neutron stars in massive scalar-tensor theories can differ drastically from the pure general relativistic solutions if sufficiently large masses of the scalar field are considered.
Characterization of Tricoordinate Boron Chemical Shift Tensors: Definitive High-Field
Bryce, David L.; Wasylishen, Roderick E.; Gee, Myrlene
2001-01-01
Despite the large known chemical shift (CS) range for boron and the large number of 11B NMR studies of glasses, no boron CS tensors have been characterized to date. We report the application of solid-state NMR techniques at moderate (9.4 T) and high (17.63 T) applied magnetic field strengths to the characterization of the boron CS tensors in trimesitylborane (BMes3) and triphenyl borate (B(OPh)3). The boron CS tensor of the former compound exhibits a remarkably large span,? 121 1 ppm, which encompasses the known range of isotropic chemical shifts for tricoordinate boron compounds. Conversely, the effect of the boron CS tensor on the 11B NMR spectra of B(OPh)3 is difficult to observe and quantify even at field strengths as high
NASA Astrophysics Data System (ADS)
Moore, R. L.; Thompson, M. C.; Robbins, T. S.
1990-03-01
An analysis is presented to calculate scalar permittivity and tensor permeability for ferrite materials from waveguide transmission cavity data. A correct measurement of the permittivity of ferrites and other high dielectric constant materials, requires an extension of current techniques to a second-order perturbational analysis. This second-order correction offsets an apparent frequency dependent dielectric behavior measured during a multimode cavity measurement. The analysis implies that dimensions of ferrite samples to be used in various waveguides (X-Ka bands) must be reduced to a near 0.015-in. cross-sections to eliminate a coupling of permittivity and permeability measurements.
Entanglement in a second-order quantum phase transition
Vidal, Julien; Palacios, Guillaume; Mosseri, Remy
2004-02-01
We consider a system of mutually interacting spins 1/2 embedded in a transverse magnetic field which undergoes a second-order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusplike singularity appears at the critical point {lambda}{sub c} in the thermodynamical limit. We also show that there exists a value {lambda}{sub 0}{>=}{lambda}{sub c} above which the ground state is not spin squeezed despite a nonvanishing concurrence.
Vacuum stress-energy tensor of a massive scalar field in a wormhole spacetime
Bezerra, V. B.; Bezerra de Mello, E. R.; Khusnutdinov, N. R.; Sushkov, S. V.
2010-04-15
The vacuum average value of the stress-energy tensor of a massive scalar field with nonminimal coupling {xi} to the curvature on the short-throat flat-space wormhole background is calculated. The final analysis is made numerically. It was shown that the energy-momentum tensor does not violate the null energy condition near the throat. Therefore, the vacuum polarization cannot self-consistently support the wormhole.
Effenberger, F.; Fichtner, H.; Scherer, K.; Barra, S.; Kleimann, J.; Strauss, R. D.
2012-05-10
The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e., one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the diffusion tensor from this local to a global frame, in which the Parker transport equation for energetic particles is usually formulated and solved. Particularly, we generalize the transformation formulae to allow for an explicit choice of two principal local perpendicular diffusion axes. This generalization includes the 'traditional' diffusion tensor in the special case of isotropic perpendicular diffusion. For the local frame, we describe the motivation for the choice of the Frenet-Serret trihedron, which is related to the intrinsic magnetic field geometry. We directly compare the old and the new tensor elements for two heliospheric magnetic field configurations, namely the hybrid Fisk and Parker fields. Subsequently, we examine the significance of the different formulations for the diffusion tensor in a standard three-dimensional model for the modulation of galactic protons. For this, we utilize a numerical code to evaluate a system of stochastic differential equations equivalent to the Parker transport equation and present the resulting modulated spectra. The computed differential fluxes based on the new tensor formulation deviate from those obtained with the 'traditional' one (only valid for isotropic perpendicular diffusion) by up to 60% for energies below a few hundred MeV depending on heliocentric distance.
Yamaguchi, Yoshiyuki Y
2015-09-01
We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions. PMID:26465428
NASA Astrophysics Data System (ADS)
Yamaguchi, Yoshiyuki Y.
2015-09-01
We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions.
Relativistic second-order dissipative fluid dynamics at finite chemical potential
NASA Astrophysics Data System (ADS)
Jaiswal, Amaresh; Friman, Bengt; Redlich, Krzysztof
2016-07-01
We employ a Chapman-Enskog like expansion for the distribution function close to equilibrium to solve the Boltzmann equation in the relaxation time approximation and subsequently derive second-order evolution equations for dissipative charge currentand shear stress tensor for a system of massless quarks and gluons. We use quantum statistics for the phase space distribution functions to calculate the transport coefficients. We show that, the second-order evolution equations for the dissipative charge current and the shear stress tensor can be decoupled. We find that, for large chemical potential, the charge conductivity is small compared to the shear viscosity. Moreover, we demonstrate that the limiting behaviour of the ratio of heat conductivity to shear viscosity is identicalto that obtained for a strongly coupled conformal plasma.
Scalar-tensor gravity with a non-minimally coupled Higgs field and accelerating universe
NASA Astrophysics Data System (ADS)
Sim, Jonghyun; Lee, Tae Hoon
2016-03-01
We consider general couplings, including non-minimal derivative coupling, of a Higgs boson field to scalar-tensor gravity and calculate their contributions to the energy density and pressure in Friedmann-Robertson-Walker spacetime. In a special case where the kinetic term of the Higgs field is non-minimally coupled to the Einstein tensor, we seek de Sitter solutions for the cosmic scale factor and discuss the possibility that the late-time acceleration and the inflationary era of our universe can be described by means of scalar fields with self-interactions and the Yukawa potential.
A preliminary compressible second-order closure model for high speed flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1989-01-01
A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.
Second-Order Fermi Acceleration and Emission in Blazar Jets
NASA Astrophysics Data System (ADS)
Asano, Katsuaki; Takahara, Fumio; Toma, Kenji; Kusunose, Masaaki; Kakuwa, Jun
The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations, adopt it for 1ES 1101-232, and Mrk 421. The Fermi-II model with radial evolution of the electron injection rate and/or diffusion coefficient can reproduce the spectra from the radio to the gamma-ray regime. For Mrk 421, an external radio photon field with a luminosity of 4.9 begin{math} {times} 10 (38) erg s (-1) is required to agree with the observed GeV flux. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.
Magnetic Compensation for Second-Order Doppler Shift in LITS
NASA Technical Reports Server (NTRS)
Burt, Eric; Tjoelker, Robert
2008-01-01
The uncertainty in the frequency of a linear-ion-trap frequency standard (LITS) can be reduced substantially by use of a very small magnetic inhomogeneity tailored to compensate for the residual second-order Doppler shift. An effect associated with the relativistic time dilatation, one cause of the second-order Doppler shift, is ion motion that is attributable to the trapping radio-frequency (RF)electromagnetic field used to trap ions. The second-order Doppler shift is reduced by using a multi-pole trap; however it is still the largest source of systematic frequency shift in the latest generation of LITSs, which are among the most stable clocks in the world. The present compensation scheme reduces the frequency instability of the affected LITS to about a tenth of its previous value. The basic principles of prior generation LITSs were discussed in several prior NASA Tech Briefs articles. Below are recapitulated only those items of basic information necessary to place the present development in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of the ground state hyperfine transition of 199Hg+ ions. The comparison involves a combination of optical and microwave excitation and interrogation of the ions in a linear ion trap in the presence of a nominally uniform magnetic field. In the current version of the LITS, there are two connected traps (see figure): (1) a quadrupole trap wherein the optical excitation and measurement take place and (2) a 12-pole trap (denoted the resonance trap), wherein the microwave interrogation takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. Shuttling ions into the resonance trap allows sensitive microwave interrogation to take place well away from loading interference. The axial magnetic field for the resonance trap is generated by an electric current in a finely wound wire coil surrounded by
Second order closure modeling of turbulent buoyant wall plumes
NASA Technical Reports Server (NTRS)
Zhu, Gang; Lai, Ming-Chia; Shih, Tsan-Hsing
1992-01-01
Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.
Effect of carbazole as a donor moiety on the second-order nonlinearity of organic molecules
NASA Astrophysics Data System (ADS)
Meshulam, Guilia; Berkovic, Garry; Kotler, Zvi; Ben-Asuly, Amos; Mazor, Royi; Shapiro, Lev; Khodorkovsky, Vladimir
1999-10-01
The second order nonlinearity of conjugated organic molecules involving, 1,3 indandione derivatives as an acceptor moiety has been studied. Varying the donor from dialkylamino to the chemically similar substituent, N- carbazolyl resulted in a drastic reduction of electric field induced second harmonic (beta) values. For some molecules, even a small negative value of (beta) was received. Quantum chemical calculations indicate that the decrease occurs as a result of two overlapping transitions, which contribute to (beta) with opposite signs. The charge transfer band gives a positive (beta) zzz along the molecular long axis, while a transition essentially within the carbazole moiety provides a negative (beta zzz contribution to (beta EFISH. Thus, these molecules must be described with a 2D model as opposed to the 'classical' model of 1D nonlinear optical chromophores. The prediction of the 2D model was verified experimentally by using a combination of two methods, EFISH and Hyper-Rayleigh Scattering, which probe different combination of the (beta) tensor elements.
Second-order estimates for the large-deformation response of particle-reinforced rubbers
NASA Astrophysics Data System (ADS)
Lopez-Pamies, Oscar; Ponte Castañeda, Pedro
2003-01-01
This paper presents the application of a recently proposed 'second-order' homogenization method (J. Mech. Phys. Solids 50 (2002) 737-757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of 'generalized' secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin-Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389-1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).
Compact Two-State-Variable Second-Order Memristor Model.
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2016-06-01
A key requirement for using memristors in functional circuits is a predictive physical model to capture the resistive switching behavior, which shall be compact enough to be implemented using a circuit simulator. Although a number of memristor models have been developed, most of these models (i.e., first-order memristor models) have utilized only a one-state-variable. However, such simplification is not adequate for accurate modeling because multiple mechanisms are involved in resistive switching. Here, a two-state-variable based second-order memristor model is presented, which considers the axial drift of the charged vacancies in an applied electric field and the radial vacancy motion caused by the thermophoresis and diffusion. In particular, this model emulates the details of the intrinsic short-term dynamics, such as decay and temporal heat summation, and therefore, it accurately predicts the resistive switching characteristics for both DC and AC input signals. PMID:27152649
Gravitational Microlensing by Ellis Wormhole: Second Order Effects
NASA Astrophysics Data System (ADS)
Lukmanova, Regina; Kulbakova, Aliya; Izmailov, Ramil; Potapov, Alexander A.
2016-07-01
Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.
Compact Two-State-Variable Second-Order Memristor Model.
Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin
2016-06-01
A key requirement for using memristors in functional circuits is a predictive physical model to capture the resistive switching behavior, which shall be compact enough to be implemented using a circuit simulator. Although a number of memristor models have been developed, most of these models (i.e., first-order memristor models) have utilized only a one-state-variable. However, such simplification is not adequate for accurate modeling because multiple mechanisms are involved in resistive switching. Here, a two-state-variable based second-order memristor model is presented, which considers the axial drift of the charged vacancies in an applied electric field and the radial vacancy motion caused by the thermophoresis and diffusion. In particular, this model emulates the details of the intrinsic short-term dynamics, such as decay and temporal heat summation, and therefore, it accurately predicts the resistive switching characteristics for both DC and AC input signals.
NASA Astrophysics Data System (ADS)
Reina, Borja; Vera, Raül
2015-08-01
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in general relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function m0 (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass δ M needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.
Energy-momentum tensors in classical field theories — A modern perspective
NASA Astrophysics Data System (ADS)
Voicu, Nicoleta
2016-04-01
The paper presents a general geometric approach to energy-momentum tensors in Lagrangian field theories, based on a global Hilbert-type definition. The approach is consistent with the ones defining energy-momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian — and, in a sense, complementary to these, with the advantage of an increased simplicity of proofs and also, opening up new insights on the topic. A special attention is paid to the particular cases of metric and metric-affine theories.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Building a holographic superconductor with a scalar field coupled kinematically to Einstein tensor
NASA Astrophysics Data System (ADS)
Kuang, Xiao-Mei; Papantonopoulos, Eleftherios
2016-08-01
We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.
A second order accurate embedded boundary method for the wave equation with Dirichlet data
Kreiss, H O; Petersson, N A
2004-03-02
The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.
Method to render second order beam optics programs symplectic
Douglas, D.; Servranckx, R.V.
1984-10-01
We present evidence that second order matrix-based beam optics programs violate the symplectic condition. A simple method to avoid this difficulty, based on a generating function approach to evaluating transfer maps, is described. A simple example illustrating the non-symplectricity of second order matrix methods, and the effectiveness of our solution to the problem, is provided. We conclude that it is in fact possible to bring second order matrix optics methods to a canonical form. The procedure for doing so has been implemented in the program DIMAT, and could be implemented in programs such as TRANSPORT and TURTLE, making them useful in multiturn applications. 15 refs.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Second-order model selection in mixture experiments
Redgate, P.E.; Piepel, G.F.; Hrma, P.R.
1992-07-01
Full second-order models for q-component mixture experiments contain q(q+l)/2 terms, which increases rapidly as q increases. Fitting full second-order models for larger q may involve problems with ill-conditioning and overfitting. These problems can be remedied by transforming the mixture components and/or fitting reduced forms of the full second-order mixture model. Various component transformation and model reduction approaches are discussed. Data from a 10-component nuclear waste glass study are used to illustrate ill-conditioning and overfitting problems that can be encountered when fitting a full second-order mixture model. Component transformation, model term selection, and model evaluation/validation techniques are discussed and illustrated for the waste glass example.
Energy-momentum tensor of the electromagnetic field in dispersive media
NASA Astrophysics Data System (ADS)
Toptygin, I. N.; Levina, K.
2016-02-01
We study the relation between the energy-momentum tensor of the electromagnetic field and the group velocity of quasi-monochromatic waves in a nonabsorptive, isotropic, spatially and temporally dispersive dielectric. It is shown that the Abraham force acting on a dielectric is not needed for the momentum conservation law to hold if the dielectric is free of external charges and currents and if the Abraham momentum density is used. The energy-momentum tensor turns out to be symmetric, and the Maxwell stress tensor is expressed either in terms of the momentum density vector and the group velocity or in terms of the energy density and the group velocity. The stress tensor and the energy density are essentially dependent on the frequency and wave vector derivatives of the functions that describe the electromagnetic properties of the medium (i.e., the dielectric permittivity and the magnetic permeability). The obtained results are applicable to both ordinary and left-handed media. The results are compared with those of other authors. The pressure a wave exerts on the interface between two media is calculated. For both ordinary and left-handed media, either 'radiation pressure' or 'radiation attraction' can occur at the interface, depending on the material parameters of the two media. For liquid dielectrics, the striction effect is considered.
Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Dvoeglazov, V. V.
Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.
a Second Order Born Calculation for Charge Transfer.
NASA Astrophysics Data System (ADS)
Simony, Paul Richard
Charge transfer cross sections, from the ground state of the target to the ground state of the projectile, have been computed in a second order Born approximation for protons incident upon hydrogen at energies of 1, 10, and 50 MeV. The exact second order matrix element is evaluated numerically, and the results are compared to a standard peaking approximation (SP), as well as to a new peaking approximation (LP) developed herein. At 50 MeV two distinct second order effects are evident in the differential cross section. For very small (center of mass) scattering angles ((theta) (DBLTURN) .032(DEGREES)) the second order cross section is smaller than the first order cross section, while at larger angles ((theta) (DBLTURN) .054(DEGREES)) a second Born peak occurs. This peak can be kinematically associated with a classical two step process which gives rise to the well known dominating v('-11) asymptotic velocity dependence of the total cross section. The reduction of the differential cross section at smaller angles serves to decrease the total cross section, as is predicted by the asymptotic expression. At 10 MeV second order effects become less important, and at 1 MeV the kinematic peak has all but disappeared, while the second order cross section has here become larger than the first order cross section. At intermediate energies experimental results indicate that the first order cross section used here is itself too large.
[Second-order retrospective revaluation in human contingency learning].
Numata, Keitaro; Shimazaki, Tsuneo
2009-04-01
We demonstrated second-order retrospective revaluation with three cues (T1, T2, and C) and an outcome, in human contingency learning. Experimental task, PC-controlled video game in which participants were required to observe about the relations between firing missiles and the tank destruction, consisted of three training phases and two rating phases. Groups C+ and C- consisted of same first two training phases, CT+ (cues C and T with an outcome) and T1T2+ followed by C+, or C- training for Groups C+, C-, respectively. In rating phases, it is clearly demonstrated that the judgment of predictive value for the outcome of the T2 were higher by C+ training (second-order unovershadowing) and lowered by C- training (second-order backward blocking). The results for Groups RC+ and RC-, in which the orders of the first two training phase for Groups C+ and C- were interchanged, also showed second-order unovershadowing and second-order backward blocking. These results, the robustness of second-order retrospective revaluation against the order of the first training phases, can be explained by the extended comparator hypothesis and probabilistic contrast model. However, these results cannot be explained by traditional associative learning models. PMID:19489431
Second order anisotropy contribution in perpendicular magnetic tunnel junctions
Timopheev, A. A.; Sousa, R.; Chshiev, M.; Nguyen, H. T.; Dieny, B.
2016-01-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form −K2cos4θ must be added to the conventional uniaxial –K1cos2θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated −K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from “easy-axis” to “easy-cone” regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface. PMID:27246631
Second order anisotropy contribution in perpendicular magnetic tunnel junctions
NASA Astrophysics Data System (ADS)
Timopheev, A. A.; Sousa, R.; Chshiev, M.; Nguyen, H. T.; Dieny, B.
2016-06-01
Hard-axis magnetoresistance loops were measured on perpendicular magnetic tunnel junction pillars of diameter ranging from 50 to 150 nm. By fitting these loops to an analytical model, the effective anisotropy fields in both free and reference layers were derived and their variations in temperature range between 340 K and 5 K were determined. It is found that a second-order anisotropy term of the form ‑K2cos4θ must be added to the conventional uniaxial –K1cos2θ term to explain the experimental data. This higher order contribution exists both in the free and reference layers. At T = 300 K, the estimated ‑K2/K1 ratios are 0.1 and 0.24 for the free and reference layers, respectively. The ratio is more than doubled at low temperatures changing the ground state of the reference layer from “easy-axis” to “easy-cone” regime. The easy-cone regime has clear signatures in the shape of the hard-axis magnetoresistance loops. The existence of this higher order anisotropy was also confirmed by ferromagnetic resonance experiments on FeCoB/MgO sheet films. It is of interfacial nature and is believed to be due to spatial fluctuations at the nanoscale of the first order anisotropy parameter at the FeCoB/MgO interface.
Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Wang, Yi-Nan
2015-04-01
We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.
Continuum tensor network field states, path integral representations and spatial symmetries
NASA Astrophysics Data System (ADS)
Jennings, David; Brockt, Christoph; Haegeman, Jutho; Osborne, Tobias J.; Verstraete, Frank
2015-06-01
A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class’ definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas
2016-01-01
Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics. PMID:26529741
Second order multidimensional sign-preserving remapping for ALE methods
Hill, Ryan N; Szmelter, J.
2010-12-15
A second-order conservative sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods is developed utilising concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The algorithm is inherently multidimensional, and so does not introduce splitting errors. The remapping is implemented in a two-dimensional, finite element ALE solver employing staggered quadrilateral meshes. The MPDATA remapping uses a finite volume discretization developed for volume coordinates. It is applied for the remapping of density and internal energy arranged as cell centered, and velocity as nodal, dependent variables. In the paper, the advection of scalar fields is examined first for test cases with prescribed mesh movement. A direct comparison of MPDATA with the performance of the van Leer MUSCL scheme indicates advantages of a multidimensional approach. Furthermore, distinctly different performance between basic MPDATA and the infinite gauge option is illustrated using benchmarks involving transport of a sign changing velocity field. Further development extends the application of MPDATA remapping to the full ALE solver with a staggered mesh arrangement for density, internal energy and momentum using volume coordinates. At present, two options of the algorithm - basic and infinite gauge - are implemented. To ensure a meaningful assessment, an identical Lagrangian solver and computational mesh update routines are used with either MPDATA or van Leer MUSCL remapping. The evaluation places particular focus on the abilities of both schemes to accurately model multidimensional problems. Theoretical considerations are supported with numerical examples. In addition to the prescribed mesh movement cases for advection of scalars, the demonstrations include two-dimensional Eulerian and ALE flow simulations on quadrilateral meshes with both fixed and variable timestep control. The key comparisons include the standard test cases of Sod and Noh
Tensor of the nonlinear polarizability of anisotropic medium and ``local'' field method
NASA Astrophysics Data System (ADS)
Lavric, V. V.; Ovander, L. N.; Shunyakov, V. T.
1983-08-01
The nonlinear polarizability tensor (NPT) for a molecular crystal of arbitrary symmetry has been obtained within the framework of polariton theory. Use of the Göppert-Mayer unitary transformation for the Hamiltonian of the crystal plus quantized electromagnetic field system made it possible to represent finally the result for the NPT in a compact form and to compare with results of semiphenomenological calculation of the NPT and to go out of the framework of the Gaitler-London approximation.
Second-order conditioning with and without unconditioned stimulus presentation.
Holland, P C
1980-07-01
The effects of presenting various episodes after serial presentation of two conditioned stimuli (CS2-CS1 sequences) on second-order conditioning to CS2 were examined in three experiments using rat subjects in an appetitive conditioning situation. In Experiment 1, presentation of food unconditioned stimuli (USs) immediately after CS2-CS1 sequences interfered with second-order conditioning of CS2. In Experiment 2, postsequence presentation of a "surprising" US interfered with second-order conditioning more than did presentation of an "expected" US; similarly, less second-order conditioning of CS2 was observed when postsequence nonpresentation of a US was surprising than when US omission was expected. In Experiment 3, the interfering effect of US presentation on second-order conditioning was smaller when a brief delay was introduced between presentation of the CS2-CS-1 sequence and the US. The results are discussed in terms of an information-processing theory recently proposed by Wagner and his colleagues.
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.
The gauge structure of exceptional field theories and the tensor hierarchy
NASA Astrophysics Data System (ADS)
Aldazabal, G.; Graña, M.; Marqués, D.; Rosabal, J. A.
2014-04-01
We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E 11 and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.
Deflection of light to second order in conformal Weyl gravity
NASA Astrophysics Data System (ADS)
Sultana, Joseph
2013-04-01
We reexamine the deflection of light in conformal Weyl gravity obtained in Sultana and Kazanas (2010), by extending the calculation based on the procedure by Rindler and Ishak, for the bending angle by a centrally concentrated spherically symmetric matter distribution, to second order in M/R, where M is the mass of the source and R is the impact parameter. It has recently been reported in Bhattacharya et al. (JCAP 09 (2010) 004; JCAP 02 (2011) 028), that when this calculation is done to second order, the term γr in the Mannheim-Kazanas metric, yields again the paradoxical contribution γR (where the bending angle is proportional to the impact parameter) obtained by standard formalisms appropriate to asymptotically flat spacetimes. We show that no such contribution is obtained for a second order calculation and the effects of the term γr in the metric are again insignificant as reported in our earlier work.
Some restrictions on the existence of second order limit language
NASA Astrophysics Data System (ADS)
Ahmad, Muhammad Azrin; Sarmin, Nor Haniza; Yusof, Yuhani; Fong, Wan Heng
2015-10-01
The cut and paste phenomenon on DNA molecules with the presence of restriction enzyme and appropriate ligase has led to the formalism of mathematical modelling of splicing system. A type of splicing system named Yusof-Goode splicing system is used to present the transparent behaviour of the DNA splicing process. The limit language that is defined as the leftover molecules after the system reaches its equilibrium point has been extended to a second order limit language. The non-existence of the second order limit language biologically has lead to this study by using mathematical approach. In this paper, the factors that restrict the formation of the second order limit language are discussed and are presented as lemmas and theorem using Y-G approach. In addition, the discussion focuses on Yusof- Goode splicing system with at most two initial strings and two rules with one cutting site and palindromic crossing site and recognition sites.
Weak value amplification via second-order correlated technique
NASA Astrophysics Data System (ADS)
Ting, Cui; Jing-Zheng, Huang; Xiang, Liu; Gui-Hua, Zeng
2016-02-01
We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification (WVA) experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed. Project supported by the Union Research Centre of Advanced Spaceflight Technology (Grant No. USCAST2013-05), the National Natural Science Foundation of China (Grant Nos. 61170228, 61332019, and 61471239), and the High-Tech Research and Development Program of China (Grant No. 2013AA122901).
Solution of second order supersymmetrical intertwining relations in Minkowski plane
NASA Astrophysics Data System (ADS)
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Human cooperation: second-order free-riding problem solved?
Fowler, James H
2005-09-22
Panchanathan and Boyd describe a model of indirect reciprocity in which mutual aid among cooperators can promote large-scale human cooperation without succumbing to a second-order free-riding problem (whereby individuals receive but do not give aid). However, the model does not include second-order free riders as one of the possible behavioural types. Here I present a simplified version of their model to demonstrate how cooperation unravels if second-round defectors enter the population, and this shows that the free-riding problem remains unsolved.
Controlling flexible structures with second order actuator dynamics
NASA Technical Reports Server (NTRS)
Inman, Daniel J.; Umland, Jeffrey W.; Bellos, John
1989-01-01
The control of flexible structures for those systems with actuators that are modeled by second order dynamics is examined. Two modeling approaches are investigated. First a stability and performance analysis is performed using a low order finite dimensional model of the structure. Secondly, a continuum model of the flexible structure to be controlled, coupled with lumped parameter second order dynamic models of the actuators performing the control is used. This model is appropriate in the modeling of the control of a flexible panel by proof-mass actuators as well as other beam, plate and shell like structural numbers. The model is verified with experimental measurements.
Second-order subsonic airfoil theory including edge effects
NASA Technical Reports Server (NTRS)
Van Dyke, Milton D
1956-01-01
Several recent advances in plane subsonic flow theory are combined into a unified second-order theory for airfoil sections of arbitrary shape. The solution is reached in three steps: the incompressible result is found by integration, it is converted into the corresponding subsonic compressible result by means of the second-order compressibility rule, and it is rendered uniformly valid near stagnation points by further rules. Solutions for a number of airfoils are given and are compared with the results of other theories and of experiment. A straight-forward computing scheme is outlined for calculating the surface velocities and pressures on any airfoil at any angle of attack
Second-Order Conditioning during a Compound Extinction Treatment
ERIC Educational Resources Information Center
Pineno, Oskar; Zilski, Jessica M.; Schachtman, Todd R.
2007-01-01
Two conditioned taste aversion experiments with rats were conducted to establish if a target taste that had received a prior pairing with illness could be subject to second-order conditioning during extinction treatment in compound with a flavor that also received prior conditioning. In these experiments, the occurrence of second-order…
Second-order variational equations for N-body simulations
NASA Astrophysics Data System (ADS)
Rein, Hanno; Tamayo, Daniel
2016-07-01
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.
Second-order accurate difference schemes on highly irregular meshes
Manteuffel, T.A.; White, A.B. Jr.
1988-01-01
In this paper compact-as-possible second-order accurate difference schemes will be constructed for boundary-value problems of arbitrary order on highly irregular meshes. It will be shown that for equations of order (K) these schemes will have truncation error of order (3/endash/K). This phenomena is known as supraconvergence. 7 refs.
Second-order nonlinear optical metamaterials: ABC-type nanolaminates
Alloatti, L. Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.
2015-09-21
We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al{sub 2}O{sub 3}, B = TiO{sub 2}, and C = HfO{sub 2}. The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths.
Forward and Backward Second-Order Pavlovian Conditioning in Honeybees
ERIC Educational Resources Information Center
Hussaini, Syed Abid; Komischke, Bernhard; Menzel, Randolf; Lachnit, Harald
2007-01-01
Second-order conditioning (SOC) is the association of a neutral stimulus with another stimulus that had previously been combined with an unconditioned stimulus (US). We used classical conditioning of the proboscis extension response (PER) in honeybees ("Apis mellifera") with odors (CS) and sugar (US). Previous SOC experiments in bees were…
Generalized Second-Order Partial Derivatives of 1/r
ERIC Educational Resources Information Center
Hnizdo, V.
2011-01-01
The generalized second-order partial derivatives of 1/r, where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a…
Maximum principles for second order dynamic equations on time scales
NASA Astrophysics Data System (ADS)
Stehlik, Petr; Thompson, Bevan
2007-07-01
This paper establishes some new maximum principles for second order dynamic equations on time scales, including: a strong maximum principle; a generalized maximum principle; and a boundary point lemma. The new results include, as special cases, well-known ideas for ordinary differential equations and difference equations.
Second-order accurate nonoscillatory schemes for scalar conservation laws
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1989-01-01
Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.
A New Factorisation of a General Second Order Differential Equation
ERIC Educational Resources Information Center
Clegg, Janet
2006-01-01
A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…
Pecuniary Effects, Second-Order Conditions, and the LRAC Curve.
ERIC Educational Resources Information Center
Comolli, Paul M.
2000-01-01
Explores the importance of second-order conditions in the cost-minimization problem confronting the monopsonistic employer of factor inputs. Describes an alternative approach to the presence of pecuniary effects that does not depend on the assumption that firms are monopsonistic in factor markets. (CMK)
Modeling Ability Differentiation in the Second-Order Factor Model
ERIC Educational Resources Information Center
Molenaar, Dylan; Dolan, Conor V.; van der Maas, Han L. J.
2011-01-01
In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…
Solving Second-Order Differential Equations with Variable Coefficients
ERIC Educational Resources Information Center
Wilmer, A., III; Costa, G. B.
2008-01-01
A method is developed in which an analytical solution is obtained for certain classes of second-order differential equations with variable coefficients. By the use of transformations and by repeated iterated integration, a desired solution is obtained. This alternative method represents a different way to acquire a solution from classic power…
Green's function of the second order differential operator with involution
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sarsenbi, Abdisalam A.
2016-08-01
In the present paper, the Green's function of the second order differential operator L defined by formula L u =α u″ (x ) -u″ (-x ) =λ u (x ) ,-1
Second-order sliding mode control with experimental application.
Eker, Ilyas
2010-07-01
In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve the performance of control systems. A Proportional + Integral + Derivative (PID) sliding surface is used for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show the feasibility and effectiveness of the proposed second-order sliding mode control and factors involved in the design. The second-order plant parameters are experimentally determined using input-output measured data. The results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control (SMC) and PID control. It is demonstrated that the proposed 2-SMC system improves the performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability.
Hattori, Koichi; Itakura, Kazunori
2013-03-15
Photons propagating in strong magnetic fields are subject to a phenomenon called the 'vacuum birefringence' where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger's proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion-antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field. - Highlights: Black-Right-Pointing-Pointer Vacuum birefringence is studied in the presence of externally applied magnetic field. Black-Right-Pointing-Pointer A general framework is given on the basis of a vacuum polarization tensor of photon. Black-Right-Pointing-Pointer A resummed vacuum polarization tensor is calculated analytically and exactly. Black-Right-Pointing-Pointer Contributions of all the Landau levels are obtained in the form of an infinite sum. Black-Right-Pointing-Pointer Threshold behavior of real-photon decay is obtained at the each Landau level.
A New Strong Field Effect in Scalar-Tensor Gravity: Spontaneous Violation of the Energy Conditions
Whinnett, A; Torres, D F
2003-11-04
A decade ago, it was shown that a wide class of scalar-tensor theories can pass very restrictive weak field tests of gravity and yet exhibit non-perturbative strong field deviations away from General Relativity. This phenomenon was called 'Spontaneous Scalarization' and causes the (Einstein frame) scalar field inside a neutron star to rapidly become inhomogeneous once the star's mass increases above some critical value. For a star whose mass is below the threshold, the field is instead nearly uniform (a state which minimizes the star's energy) and the configuration is similar to the General Relativity one. Here, we show that the spontaneous scalarization phenomenon is linked to another strong field effect: a spontaneous violation of the weak energy condition.
Large tensor-to-scalar ratio in small-field inflation.
Kobayashi, Takeshi; Takahashi, Tomo
2013-06-01
We show that density perturbations seeded by the inflaton can be suppressed when having additional light degrees of freedom contributing to the production of perturbations. The inflaton fluctuations affect the light field dynamics by modulating the length of the inflationary period and, hence, produce additional density perturbations in the postinflationary era. Such perturbations can cancel those generated during inflation as both originate from the same inflaton fluctuations. This allows production of large gravitational waves from small-field inflation, which is normally forbidden by the Lyth bound on the inflaton field excursion. We also find that the field bound is taken over by the light scalar when the inflaton-induced perturbations are suppressed and, thus, present a generalized form of the Lyth bound that applies to the total field space. The novel mechanism allows violation of the usual consistency relation r≤-8n(T) for the tensor spectral index. PMID:25167480
Travelling-wave Green tensor and near-field Rayleigh-wave sensitivity
NASA Astrophysics Data System (ADS)
Liu, Kui; Zhou, Ying
2016-04-01
Travelling-wave Green tensor has been widely used in calculations of synthetic seismograms and finite-frequency sensitivities of surface waves. The classic travelling-wave decomposition is based on a far-field approximation and may not be valid when applied to construct sensitivity kernels in regions close to the receiver. In this paper, we calculate synthetic seismograms and finite-frequency sensitivity kernels of Rayleigh waves based on travelling-wave representation of Green tensor that fully accounts for near-field effects. We show that far-field approximation is adequate for synthetic seismograms when the source-receiver epicentral distance is greater than the dominant wavelength. Errors in Rayleigh-wave sensitivity kernels introduced by far-field approximation are in general negligible for single-station measurements except for in a small region around the station, and the errors are more significant in sensitivity kernels for interstation measurements. In addition, interstation measurements are strongly sensitive to structures outside the region between the two stations, even for two stations along the same great circle path from the seismic source.
NASA Astrophysics Data System (ADS)
Bull, James N.; Fitchett, Christopher M.; Tennant, W. Craighead
2010-06-01
This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57Fe symmetry-related sites of bar {1} Laue class in monoclinic FeCl2.4H2O at room temperature by single-crystal Mössbauer spectroscopy. Contrary to all previous work, the mean-squared-displacement matrix (tensor),
Application of edge detection to potential field data using eigenvalue analysis of structure tensor
NASA Astrophysics Data System (ADS)
Sertcelik, I.; Kafadar, O.
2012-09-01
One of the most important aims of potential field geophysicists is delineate the edges of subsurface structures. There are many methods based on horizontal and vertical derivative of potential field data for edge detection and enhancement. The structure tensor technique one of the image processing techniques is used to edge detection studies in many scientific areas. In this paper, the technique was applied to potential field data and detected edges of the subsurface lineaments using its eigenvalue analysis. Based on noise-free and noisy synthetic data sets, the technique was tested and satisfactory results were obtained. The proposed method was applied on two real potential field data which are gravity data of Konya region and magnetic data of Eastern Anatolia Region in Turkey. These examples demonstrate that the technique provides beneficial information to geoscientists for determining the horizontal location of subsurface structures such as contacts, faults or various source bodies.
Auxiliary Field Diffusion Monte Carlo Calculation of Nuclei with A{<=}40 with Tensor Interactions
Gandolfi, S.; Pederiva, F.
2007-07-13
We calculate the ground-state energy of {sup 4}He, {sup 8}He, {sup 16}O, and {sup 40}Ca using the auxiliary field diffusion Monte Carlo method in the fixed-phase approximation and the Argonne v{sub 6}{sup '} interaction which includes a tensor force. Comparison of our light nuclei results to those of Green's function Monte Carlo calculations shows the accuracy of our method for both open and closed-shell nuclei. We also apply it to {sup 16}O and {sup 40}Ca to show that quantum Monte Carlo methods are now applicable to larger nuclei.
NASA Astrophysics Data System (ADS)
Lu, Xu; Yang, Feng-Wei; Xie, Yi
2016-07-01
We analyze strong gravitational field time delay for photons coupled to the Weyl tensor in a Schwarzschild black hole. By making use of the method of strong deflection limit, we find that these time delays between relativistic images are significantly affected by polarization directions of such a coupling. A practical problem about determination of the polarization direction by observations is investigated. It is found that if the first and second relativistic images can be resolved, the measurement of time delay can more effectively improve detectability of the polarization direction.
Second-order and third-order elastic properties of diamond: An ab initio study
NASA Astrophysics Data System (ADS)
Clerc, Daryl G.; Ledbetter, Hassel
2005-10-01
Diamond's second-order elastic properties, and several third-order properties associated with uniform deformation, were calculated using ab initio all-electron density-functional theory. The predicted second-order elastic properties and equilibrium lattice parameter, in units of GPa and nm, are c11=1043(5), c12=128(5), c44=534(17), bulk modulus B=433(5), shear modulus G=502(10), Poisson ratio μ=0.082(5), and a=0.35569(2), where the parenthetic number is the uncertainty. The second-order force constants, in units of GPa, are kI=3843(108), kII=2346(17), kIII=2847(35), and kIV=5635(45). Here, subscripts I IV denote four strains whose tensor elements are [ɛ, ɛ, ɛ, 0, 0, 0], [ɛ, ɛ, 0, 0, 0, 0], [ɛ, ɛ, -ɛ, 0, 0, 0], and [ɛ, ɛ, ɛ, ɛ, ɛ, ɛ], respectively, using 6-component notation in the format [ɛ1, ɛ2, ɛ3, ɛ4, ɛ5, ɛ6]. Predicted inelastic properties include the third-order force constant corresponding to uniform dilation gI=-55,000(3,500) GPa, the bulk-modulus pressure derivative ∂B/∂P=4.7(3), and the overall Gruneisen parameter γG=0.85(15). Both our second-order and third-order properties agree well with measured values obtained by ultrasonics and by Raman spectroscopy.
NASA Astrophysics Data System (ADS)
Audemard, Franck; Zahradnik, Jiri; Assumpção, Marcelo
2016-11-01
This special issue follows from the Symposium "Regional Moment Tensor Solutions: advances and new applications" held in Bogotá, Colombia, at the I Regional Assembly of the IASPEI's Latin American and Caribbean Seismological Commission (LACSC) in 2014. Seven papers are presented dealing with determination of moment tensors, focal mechanisms and the stress field in Central and South America. The study areas of each paper are indicated in the index Map of Fig. 1.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1991-01-01
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
Second order modeling of boundary-free turbulent shear flows
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Chen, Y.-Y.; Lumley, J. L.
1991-01-01
A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.
Optimal second order sliding mode control for linear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-11-01
In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.
Second order upwind Lagrangian particle method for Euler equations
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
2016-06-01
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Experimental Measurement of the Second-Order Coherence of Supercontinuum.
Närhi, Mikko; Turunen, Jari; Friberg, Ari T; Genty, Goëry
2016-06-17
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources. PMID:27367389
A Second-Order Achromat Design Based on FODO Cell
Sun, Yipeng; /SLAC
2011-08-19
Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first order dispersion and provide betatron focusing. Similarly a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to generate an isochronous section, quadrupoles are again needed to tune the first order transfer matrix element R{sub 56} equaling zero. Usually sextupoles are needed to correct second order dispersion in the bending plane, for both the dogleg optics and the chicane (with quad) optics. In this paper, an alternative optics design is introduced, which is based on a simple FODO cell and does not need sextupoles assistance to form a second-order achromat. It may provide a similar function of either a dogleg or a bypass, by using 2 or 4 of such combined supercells.
Experimental Measurement of the Second-Order Coherence of Supercontinuum
NASA Astrophysics Data System (ADS)
Närhi, Mikko; Turunen, Jari; Friberg, Ari T.; Genty, Goëry
2016-06-01
We measure experimentally the second-order coherence properties of supercontinuum generated in a photonic crystal fiber. Our approach is based on measuring separately the quasicoherent and quasistationary contributions to the cross-spectral density and mutual coherence functions using a combination of interferometric and nonlinear gating techniques. This allows us to introduce two-dimensional coherence spectrograms which provide a direct characterization and convenient visualization of the spectrotemporal coherence properties. The measured second-order coherence functions are in very good agreement with numerical simulations based on the generalized nonlinear Schrödinger equation. Our results pave the way towards the full experimental characterization of supercontinuum coherence properties. More generally, they provide a generic approach for the complete experimental measurement of the coherence of broadband sources.
Compressible turbulence transport equations for generalized second order closure
Cloutman, L D
1999-05-01
Progress on the theory of second order closure in turbulence models of various types requires knowledge of the transport equations for various turbulence correlations. This report documents a procedure that provides such equations for a wide variety of turbulence averages for compressible flows of a multicomponent fluid. Generalizing some work by Germano for incompressible flows, we introduce an appropriate extension of his generalized second order correlations and use a generalized mass-weighted averaging procedure to derive transport equations for the correlations. The averaging procedure includes all of the commonly used averages as special cases. The resulting equations provide an internally consistent starting point for future work in developing single-point statistical turbulence transport models for fluid flows. The form invariance of the in-compressible equations also holds for the compressible case, and we discuss some of the closure issues and frequently ignored complications of statistical turbulence models of compressible flows.
Robust eigensystem assignment for second-order estimators
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Maghami, Peiman G.
1990-01-01
An approach for the robust eigensystem assignment of flexible structures using full state or output feedback is developed. Using the second-order dynamic equations, the approach can assign the eigenvalues of the system via velocity and displacement feedbacks, or acceleration and velocity feedbacks. The eigenvalues and eigenvectors of the system are assigned, via the second-order eigenvalue problem for the structural system, in two steps. First, an orthonormal basis spanning the attainable closed-loop eigenvector space corresponding to each desired closed-loop eigenvalue is generated using the Singular Value or QR decompositions. Second, a sequential procedure is used to choose a set of closed-loop eigenvectors that are as close as possible to the column space of a well-conditioned target matrix. Among the possible choices of the target matrix, the closest unitary matrix to the open-loop eigenvector matrix appears to be a suitable choice. A numerical example is given to illustrate the proposed algorithm.
Using of "pseudo-second-order model" in adsorption.
Ho, Yuh-Shan
2014-01-01
A research paper's contribution exists not only in its originality and creativity but also in its continuity and development for research that follows. However, the author easily ignores it. Citation error and quotation error occurred very frequently in a scientific paper. Numerous researchers use secondary references without knowing the original idea from authors. Sulaymon et al. (Environ Sci Pollut Res 20:3011-3023, 2013) and Spiridon et al. (Environ Sci Pollut Res 20:6367-6381, 2013) presented wrong pseudo-second-order models in Environmental Science and Pollution Research, vol. 20. This comment pointed the errors of the kinetic models and offered information for citing original idea of pseudo-second-order kinetic expression. In order to stop the proliferation of the mistake, it is suggested to cite the original paper for the kinetic model which provided greater accuracy and more details about the kinetic expression.
Transport equations with second-order differential collision operators
Cosner, C.; Lenhart, S.M.; Protopopescu, V.
1988-07-01
This paper discusses existence, uniqueness, and a priori estimates for time-dependent and time-independent transport equations with unbounded collision operators. These collision operators are described by second-order differential operators resulting from diffusion in the velocity space. The transport equations are degenerate parabolic-elliptic partial differential equations, that are treated by modifications of the Fichera-Oleinik-Radkevic Theory of second-order equations with nonnegative characteristic form. They consider weak solutions in spaces that are extensions of L/sup rho/ to include traces on certain parts of the boundary. This extension is necessary due to the nonclassical boundary conditions imposed by the transport problem, which requires a specific analysis of the behavior of our weak solutions.
Gravitational waves from global second order phase transitions
Jr, John T. Giblin; Price, Larry R.; Siemens, Xavier; Vlcek, Brian E-mail: larryp@caltech.edu E-mail: bvlcek@uwm.edu
2012-11-01
Global second-order phase transitions are expected to produce scale-invariant gravitational wave spectra. In this manuscript we explore the dynamics of a symmetry-breaking phase transition using lattice simulations. We explicitly calculate the stochastic gravitational wave background produced during the transition and subsequent self-ordering phase. We comment on this signal as it compares to the scale-invariant spectrum produced during inflation.
Asymptotic stability of second-order neutral stochastic differential equations
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ren, Yong; Kim, Hyunsoo
2010-05-01
In this paper, we study the existence and asymptotic stability in pth moment of mild solutions to second-order nonlinear neutral stochastic differential equations. Further, this result is extended to establish stability criterion for stochastic equations with impulsive effects. With the help of fixed point strategy, stochastic analysis technique, and semigroup theory, a set of novel sufficient conditions are derived for achieving the required result. Finally, an example is provided to illustrate the obtained result.
Klisch, Stephen M
2006-06-01
Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile-compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.
First- and second-order backscattering from clouds illuminated by finite beams.
Anderson, R C; Browell, E V
1972-06-01
Calculations have been carried out for first- and second-order backscattering from water clouds illuminated by a continuous 0.9-micro beam with a finite divergence angle. In the single-scattering calculations several cloud types were used, while only an approximation to fair weather cumulus clouds was used for double scattering. It was found that the intensity and hence the reflectivity varied with the transceiver-cloud distance for both orders of scattering. Second-order backscattering also varied with field of view. From these results a criterion is suggested for determining when the plane parallel atmosphere theories can be used with finite beams.
Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles
Sabitov, I Kh
2014-12-31
We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class C{sup 1} both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface. Bibliography: 15 entries.
Theoretical study of second-order hyperpolarizability for nitrogen radical cation
NASA Astrophysics Data System (ADS)
Tarazkar, Maryam; Romanov, Dmitri A.; Levis, Robert J.
2015-05-01
We report calculations of the static and dynamic hyperpolarizabilities of the nitrogen radical cation in doublet state. The electronic contributions were computed analytically using density functional theory and multi-configurational self-consistent field method with extended basis sets for non-resonant excitation. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient, {{γ }(2)}, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The second-order optical properties of nitrogen radical cation have been calculated as a function of bond length starting with the neutral molecular geometry (S0 minimum) and stretching the N-N triple bond, reaching the ionic D0 relaxed geometry all the way toward dissociation limit, to investigate the effect of internuclear bond distance on second-order hyperpolarizability.
First- or second-order transition in the melting of repeat sequence DNA.
Chen, Y Z; Prohofsky, E W
1994-01-01
Both theoretical analysis and observation of the continuity of the melted fraction of base pairs indicate that the melting transition in DNA is second order. Analysis of the salt dependence of the transition by polyelectrolyte limiting laws, however, has first-order dynamics imbedded in the analysis. This paper proposes that the observation taken to be a latent heat of melting in the limiting law analysis could instead be a specific heat anomaly associated with a second-order transition. The limiting laws can be reconstructed based on a second-order transition with a specific heat anomaly. The T2M dependence of this excess heat is also consistent with its being a specific heat anomaly of a system displaying classical critical behavior. Classical critical behavior indicates that theoretical mean field approaches such as MSPA should be particularly appropriate to helix melting studies. PMID:8130338
Feasibility of a second-order gravitational red-shift experiment
NASA Technical Reports Server (NTRS)
Jaffe, J.; Vessot, R. F. C.
1976-01-01
The number of gravitation experiments undertaken since the advent of Einstein's theory of gravitation is quite small, with, so far, only the famous perihelion-advance experiment and a recent lunar-laser-ranging experiment being capable of measuring a nonlinear, second-order effect. It now appears that another distinct test of the second-order term may be feasible through the use of very stable atomic clocks. This experiment, which would measure the second-order gravitational red-shift, is a bona fide test of the field equations of gravity, not just a test of the underlying principle of equivalence. The nature of such an experiment, the basic equations, model-orbit calculations, and some tracking-accuracy requirements are presented. It is concluded that current space-probe tracking capabilities cannot determine all the necessary orbital parameters with sufficient accuracy for this experiment at the present time.
Chen, Jiale; Gao, Zhe
2013-08-15
The second-order velocity distribution function was calculated from the second-order rf kinetic theory [Jaeger et al., Phys. Plasmas 7, 641 (2000)]. However, the nonresonant ponderomotive force in the radial direction derived from the theory is inconsistent with that from the fluid theory. The inconsistency arises from that the multiple-timescale-separation assumption fails when the second-order Vlasov equation is directly integrated along unperturbed particle orbits. A slowly ramped wave field including an adiabatic turn-on process is applied in the modified kinetic theory in this paper. Since this modification leads only to additional reactive/nonresonant response relevant with the secular resonant response from the previous kinetic theory, the correct nonresonant ponderomotive force can be obtained while all the resonant moments remain unchanged.
NASA Astrophysics Data System (ADS)
Studynka, J.; Chadima, M.; Hrouda, F.; Suza, P.
2013-12-01
Low-field magnetic susceptibility of diamagnetic and paramagnetic minerals as well as that of pure magnetite and all single-domain ferromagnetic (s.l.) minerals is field-independent. In contrast, magnetic susceptibility of multi-domain pyrrhotite, hematite and titanomagnetite may significantly depend on the field intensity. Hence, the AMS data acquired in various fields have a great potential to separate the magnetic fabric carried by the latter group of minerals from the whole-rock fabric. The determination of the field variation of AMS consist of separate measurements of each sample in several fields within the Rayleigh Law range and subsequent processing in which the field-independent and field-dependent susceptibility tensors are calculated. The disadvantage of this technique is that each sample must be measured several times in various positions, which is relatively laborious and time consuming. Recently, a new 3D rotator was developed for the MFK1 Kappabridges which rotates the sample simultaneously about two axes with different velocities. The measurement is fully automated in such a way that, once the sample is mounted into the rotator, it requires no additional positioning to measure the full AMS tensor. The important advantage of the 3D rotator is that it enables to measure AMS in a sequence of pre-set field intensities without any operator manipulation. Whole procedure is computer-controlled and, once a sequence of measurements is finished, the acquired data are immediately processed and visualized. Examples of natural rocks demonstrating various types of field dependence of AMS are given.
Rapid 3-D forward modeling of gravity and gravity gradient tensor fields
NASA Astrophysics Data System (ADS)
Longwei, C.; Dai, S.; Zhang, Q.
2014-12-01
Three-dimensional inversion are the key process in gravity exploration. In the commonly used scheme of inversion, the subsurface of the earth is usually divided into many small prism blocks (or grids) with variable density values. A key task in gravity inversion is to calculate the composite fields (gravity and gravity gradient tensor) generated by all these grids, this is known as forward modeling. In general forward modeling is memory-demanding and time-consuming. One scheme to rapidly calculate the fields is to implement it in Fourier domain and use fast Fourier transform algorithm. The advantage of the Fourier domain method is, obviously, much faster. However, the intrinsic edge effect of the Fourier domain method degrades the precision of the calculated fields. We have developed an innovative scheme to directly calculate the fields in spatial domain. There are two key points in this scheme. One key point is spatial discretization. Spatial convolution formula is discretized using an approach similar to normal difference method. A key idea during discretization is to use the analytical formula of a cubic prism, and this makes the resultant discrete formula have clear physical meaning: it embodies the superposition principle of the fields and is the exact formula to calculate the fields generated by all grids. The discretization only requires the grids have the same dimension in horizontal directions, and grids in different layers may have different dimension in vertical direction, and this offers more flexibility for inversion. Another key point is discrete convolution calculation. We invoke a high efficient two-dimensional discrete convolution algorithm, and it guarantees both time-saving and memory-saving. Its memory cost has the same order as the number of grids. Numerical test result shows that for a model with a dimension of 1000x1000x201 grids, it takes about 300s to calculate the fields on 1000x1000 field points in a personal computer with 3.4-GHz CPU
Second order distorted wave calculations for electron impact ionization processes
NASA Astrophysics Data System (ADS)
Chen, Zhangjin
Electron impact ionization of atoms provides a fundamental test of the current understanding of atomic structure as well as our understanding of the three body problem. Triple differential cross sections (TDCS), measured in the coincidence experiment, provide the most sensitive test of the theory of electron impact ionization processes. It was found two decades ago that second-order effects were crucial in explaining both the positions and magnitudes of the binary and recoil peaks in the TDCS. However, the existing theoretical calculations of second-order amplitudes typically resort to simplifying approximations, such as the closure approximation or neglecting the real part of the Green's function, to make the calculation tractable. In this work, we have developed a second-order distorted wave (DWB2) theory for atomic ionization which does not make these approximations. The DWB2 theory has been used to calculate the TDCS for electron impact ionization of hydrogen. It is found that the DWB2 results are in good agreement with absolute experimental measurements for incident energy greater than 100 eV. We have also performed DWB2 calculations for electron impact ionization of helium with the residual ion left in the n=1 and 2 states at intermediate energies in coplanar asymmetric geometry. Both the neutral and ionic distorting potentials are employed for the projectile in the final state. It has been found that the DWB2 results with the ionic distorting potential are in better agreement with experiment for the case in which the residual ion is left in the excited states. We have also performed the calculations to check the validity of the closure approximation and the simplified Green's function approximation and found that these approximations are not accurate for non-coplanar geometry and low incident energies.
Determination of robust stability margin for second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.; Kau, C.-T.; Juang, Jer-Nan
1992-01-01
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
Second-order kinetic Kohn-Sham lattice model
NASA Astrophysics Data System (ADS)
Solórzano, S.; Mendoza, M.; Herrmann, H. J.
2016-06-01
In this work, we introduce a semi-implicit second-order correction scheme to the kinetic Kohn-Sham lattice model. This approach is validated by performing realistic exchange-correlation energy calculations of atoms and dimers of the first two rows of the Periodic Table, finding good agreement with the expected values. Additionally, we simulate the ethane molecule, where we recover the bond lengths and compare the results with standard methods. Finally, we discuss the current applicability of pseudopotentials within the lattice kinetic Kohn-Sham approach.
Detection of a diffusive cloak via second-order statistics
NASA Astrophysics Data System (ADS)
Koirala, Milan; Yamilov, Alexey
2016-08-01
We propose a scheme to detect the diffusive cloak proposed by Schittny et al [Science 345, 427 (2014)]. We exploit the fact that diffusion of light is an approximation that disregards wave interference. The long-range contribution to intensity correlation is sensitive to locations of paths crossings and the interference inside the medium, allowing one to detect the size and position, including the depth, of the diffusive cloak. Our results also suggest that it is possible to separately manipulate the first- and the second-order statistics of wave propagation in turbid media.
Local second-order boundary methods for lattice Boltzmann models
Ginzbourg, I.; d`Humieres, D.
1996-09-01
A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.
Finite difference schemes for second order systems describing black holes
Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.
2006-06-15
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.
Supersonic second order analysis and optimization program user's manual
NASA Technical Reports Server (NTRS)
Clever, W. C.
1984-01-01
Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance theory was utilized to meet this objective. Numerical codes were developed for analysis and design of relatively general three dimensional geometries. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes. Case computational time of one minute on a CDC 176 are typical for practical aircraft arrangement.
Adaptive second-order sliding mode control with uncertainty compensation
NASA Astrophysics Data System (ADS)
Bartolini, G.; Levant, A.; Pisano, A.; Usai, E.
2016-09-01
This paper endows the second-order sliding mode control (2-SMC) approach with additional capabilities of learning and control adaptation. We present a 2-SMC scheme that estimates and compensates for the uncertainties affecting the system dynamics. It also adjusts the discontinuous control effort online, so that it can be reduced to arbitrarily small values. The proposed scheme is particularly useful when the available information regarding the uncertainties is conservative, and the classical `fixed-gain' SMC would inevitably lead to largely oversized discontinuous control effort. Benefits from the viewpoint of chattering reduction are obtained, as confirmed by computer simulations.
Second-Order Modeling of Low-Reynolds-Number Turbulence Near Walls
NASA Technical Reports Server (NTRS)
Shih, T.-H.; Mansour, N. N.
1989-01-01
This paper presents a set of second-order closure models for low-Reynolds-number turbulence near the wall. Existing closure models for the Reynolds-stress equations were modified to show proper near-wall behavior. A dissipation-rate equation for the turbulent kinetic energy is also reformulated. The proposed models satisfy realizability and will not produce unphysical behavior. Fully developed channel flows are used for model testing. The equations are solved for the mean velocity, the Reynolds stresses, and the dissipation rate of the turbulent kinetic energy. The calculations are compared with both direct numerical simulations and with measurements. It is shown that the present models perform well in predicting the behavior of the turbulence near a wall. Significant improvements over previous models in predicting the components of the Reynolds stress tensor are obtained in the present models.
Second-order estimates for nonlinear isotropic composites with spherical pores and rigid particles
NASA Astrophysics Data System (ADS)
Idiart, Martín; Ponte Castañeda, Pedro
2005-02-01
The 'second-order' nonlinear homogenization method (Ponte Castañeda, J. Mech. Phys. Solids 50 (2002) 737-757) is used to generate estimates of the Hashin-Shtrikman-type for the effective behavior of viscoplastic materials with isotropically distributed spherical pores or rigid particles. In the limiting case of an ideally plastic matrix with a dilute concentration of pores, the resulting estimates were found to exhibit a linear dependence on the porosity when the material is subjected to axisymmetric shear, but this dependence becomes singular for simple shear. In the process of this work, an alternative prescription for certain reference tensors used in the method is proposed, and shown to lead to more consistent estimates for the effective behavior than the earlier prescription. To cite this article: M. Idiart, P. Ponte Castañeda, C. R. Mecanique 333 (2005).
NASA Astrophysics Data System (ADS)
Matsumoto, S.
2016-09-01
The stress field is a key factor controlling earthquake occurrence and crustal evolution. In this study, we propose an approach for determining the stress field in a region using seismic moment tensors, based on the classical equation in plasticity theory. Seismic activity is a phenomenon that relaxes crustal stress and creates plastic strain in a medium because of faulting, which suggests that the medium could behave as a plastic body. Using the constitutive relation in plastic theory, the increment of the plastic strain tensor is proportional to the deviatoric stress tensor. Simple mathematical manipulation enables the development of an inversion method for estimating the stress field in a region. The method is tested on shallow earthquakes occurring on Kyushu Island, Japan.
3D extension of Tensorial Polar Decomposition. Application to (photo-)elasticity tensors
NASA Astrophysics Data System (ADS)
Desmorat, Rodrigue; Desmorat, Boris
2016-06-01
The orthogonalized harmonic decomposition of symmetric fourth-order tensors (i.e. having major and minor indicial symmetries, such as elasticity tensors) is completed by a representation of harmonic fourth-order tensors H by means of two second-order harmonic (symmetric deviatoric) tensors only. A similar decomposition is obtained for non-symmetric tensors (i.e. having minor indicial symmetry only, such as photo-elasticity tensors or elasto-plasticity tangent operators) introducing a fourth-order major antisymmetric traceless tensor Z. The tensor Z is represented by means of one harmonic second-order tensor and one antisymmetric second-order tensor only. Representations of totally symmetric (rari-constant), symmetric and major antisymmetric fourth-order tensors are simple particular cases of the proposed general representation. Closed-form expressions for tensor decomposition are given in the monoclinic case. Practical applications to elasticity and photo-elasticity monoclinic tensors are finally presented. xml:lang="fr"
Second-order analytic solutions for re-entry trajectories
NASA Astrophysics Data System (ADS)
Kim, Eun-Kyou
1993-01-01
With the development of aeroassist technology, either for near-earth orbital transfer with or without a plane change or for planetary aerocapture, it is of interest to have accurate analytic solutions for reentry trajectories in an explicit form. Starting with the equations of motion of a non-thrusting aerodynamic vehicle entering a non-rotating spherical planetary atmosphere, a normalization technique is used to transform the equations into a form suitable for an analytic integration. Then, depending on the type of planar entry modes with a constant angle-of-attack, namely, ballistic fly-through, lifting skip, and equilibrium glide trajectories, the first-order solutions are obtained with the appropriate simplification. By analytic continuation, the second-order solutions for the altitude, speed, and flight path angle are derived. The closed form solutions lead to explicit forms for the physical quantities of interest, such as the deceleration and aerodynamic heating rates. The analytic solutions for the planar case are extended to three-dimensional skip trajectories with a constant bank angle. The approximate solutions for the heading and latitude are developed to the second order. In each type of trajectory examined, explicit relations among the principal variables are in a form suitable for guidance and navigation purposes. The analytic solutions have excellent agreement with the numerical integrations. They also provide some new results which were not reported in the existing classical theory.
Adaptive suboptimal second-order sliding mode control for microgrids
NASA Astrophysics Data System (ADS)
Incremona, Gian Paolo; Cucuzzella, Michele; Ferrara, Antonella
2016-09-01
This paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary system becomes attractive. In the other two strategies, a suitable blend between two components, one mainly working during the reaching phase, the other being the predominant one in a vicinity of the sliding manifold, is generated, so as to reduce the control amplitude in steady state. The microgrid system in a grid-connected operation mode, controlled via the selected ASSOSM control strategies, exhibits appreciable stability properties, as proved theoretically and shown in simulation.
Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta
Giovannini, Massimo
2011-01-15
The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also superchaotic. Testable inequalities are derived in the limit of large-angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.
Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
Boubekeur, Lotfi; Creminelli, Paolo; D'Amico, Guido; Noreña, Jorge; Vernizzi, Filippo E-mail: creminel@ictp.it E-mail: norena@sissa.it
2009-08-01
We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result δT/T = Φ/3. The calculation is done in Poisson gauge. Besides intrinsic contributions calculated at last scattering, one must consider integrated effects. These are associated to lensing, and to the time dependence of the potentials (Rees-Sciama) and of the vector and tensor components of the metric generated at second order. The bispectrum is explicitly computed in the flat-sky approximation. It scales as l{sup −4} in the scale invariant limit and the shape dependence of its various contributions is represented in 3d plots. Although all the contributions to the bispectrum are parametrically of the same order, the full bispectrum is dominated by lensing. In the squeezed limit it corresponds to f{sub NL}{sup local} = −1/6−cos(2θ), where θ is the angle between the short and the long modes; the angle dependent contribution comes from lensing. In the equilateral limit it corresponds to f{sub NL}{sup equil} ≅ 3.13.
Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta
NASA Astrophysics Data System (ADS)
Giovannini, Massimo
2011-01-01
The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also superchaotic. Testable inequalities are derived in the limit of large-angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.
Localization and mass spectra of various matter fields on scalar-tensor brane
Xie, Qun-Ying; Zhao, Zhen-Hua; Zhong, Yi; Yang, Jie; Zhou, Xiang-Nan
2015-03-10
Recently, a new scalar-tensor braneworld model was presented in [http://dx.doi.org/10.1103/PhysRevD.86.127502]. It not only solves the gauge hierarchy problem but also reproduces a correct Friedmann-like equation on the brane. In this new model, there are two different brane solutions, for which the mass spectra of gravity on the brane are the same. In this paper, we investigate localization and mass spectra of various bulk matter fields (i.e., scalar, vector, Kalb-Ramond, and fermion fields) on the brane. It is shown that the zero modes of all the matter fields can be localized on the positive tension brane under some conditions, and the mass spectra of each kind of bulk matter field for the two brane solutions are different except for some special cases, which implies that the two brane solutions are not physically equivalent. When the coupling constants between the dilaton and bulk matter fields take special values, the mass spectra for both solutions are the same, and the scalar and vector zero modes are localized on the negative tension brane, while the KR zero mode is still localized on the positive tension brane.
Second order distorted born approximation for backscattering from a layer of discrete random medium
NASA Technical Reports Server (NTRS)
Lang, Roger H.; Saatchi, Sasan S.
1993-01-01
In recent years there has been increasing interest in scattering and depolarization characteristics of the vegetation canopies. Scattering models applied to the microwave remote sensing of vegetation canopies showed that multiple scattering effects can be important in simulating the backscattering coefficients correctly. In particular, in most applications, the cross-polarized backscattering coefficients are often underestimated by single scattering models. Recently, there have been concerted efforts to include the second order terms in the radiative transfer models of vegetation canopies in order to account for multiple scattering within the canopy. The coherent wave theory approach is extended to include multiple scattering effects to predict the coherent and incoherent backscattering contributions from a layer of vegetation canopy. The problem is initially formulated in terms of the exact equation for the correlation function of the field, i.e., the Bethe-Salpeter equation. Using fractional volume as a small parameter, a Foldy type approximation is made to obtain a more manageable correlation equation. This equation is iterated to obtain first and second order solutions. The iteration procedure assumes the variance of the field fluctuations are small compared to the coherent intensity. This assumption proved to be particularly successful in computing backscattering coefficients. First and second order backscattering coefficients are calculated from the iterants of the correlation equation. It is shown that the first order coefficients are the same as the distorted Born results used previously by the authors. These results contained enhancement terms in the direct-reflected contributions. The important contributions to second order backscattering are examined and interpreted in terms of scattering diagrams. Examples of situations in which second order backscattering coefficients are important are given.
Xu, Enhua; Zhao, Dongbo; Li, Shuhua
2015-10-13
A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.
The second-order procedure: exact vs approximate results for isotropic, two-phase composites
NASA Astrophysics Data System (ADS)
Nebozhyn, M. V.; Castañeda, P. Ponte
1999-10-01
Estimates for the effective behavior of statistically isotropic, two-phase, nonlinear elastic (or viscous) composites were given by Ponte Castañeda (1996; J. Mech. Phys. Solids44, 827), making use of the 'second-order procedure', also introduced in that reference. The actual computation of these estimates took advantage of a simplifying hypothesis consisting of taking the average strain deviators in the phases to be proportional to the macroscopic strain deviator. In this paper, a more general analysis is presented that shows that while the 'proportional strain' hypothesis does hold for some special cases, it does not in general. In fact, the average strain deviators in the phases are found to be only co-axial with the macroscopic strain deviator. On the other hand, the proportional strain hypothesis, together with an approximate form of the relevant P tensor, is found to lead to fairly small errors, relative to the exact solution of the problem. The largest errors, which occur for large phase contrast and nonlinearity, are less than about two percent. Because of this, and given the significant simplifications achieved, the use of the proportional strain hypothesis and of the approximate form of the P tensor are recommended. Certainly, these approximations are much more accurate than the isotropic-type approximations that have been used in the past in the context of other homogenization procedures.
Culzoni, María J; Damiani, Patricia C; García-Reiriz, Alejandro; Goicoechea, Héctor C; Olivieri, Alejandro C
2007-07-01
Three different experimental systems have been studied regarding the determination of analytes in complex samples, using non-linear second-order instrumental data, which are intrinsically able to provide the second-order advantage. This permits the quantitation of calibrated analytes in the presence of unexpected sample components, although a suitable algorithm is required. The recently described combination of artificial neural networks with post-training residual bilinearization has been applied to the three data sets, with successful results concerning prediction accuracy and precision, as well as profile recovery for the potential interferents in test samples. The studies involve: (1) the determination of two pharmaceuticals in the presence of an unexpected excipient by absorbance-pH matrix measurements, (2) the quantitation of iron(II) by its catalytic effect on the kinetics of the bromate oxidation of a colorant in the presence of a second interfering organic dye, and (3) the analysis of the antibiotic amoxicillin by fluorescence excitation-emission matrices in the presence of a fluorescent anti-inflammatory. The prediction results were compared and shown to be significantly better than those yielded by the unfolded partial least-squares/residual bilinearization model, due to the non-linear nature of the studied data.
Second-order 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.
Stress-dependent second-order grain statistics of polycrystals.
Kube, Christopher M; Turner, Joseph A
2015-10-01
In this article, the second-order statistics of the elastic moduli of randomly oriented grains in a polycrystal are derived for the case when an initial stress is present. The initial stress can be either residual stress or stresses generated from external loading. The initial stress is shown to increase or decrease the variability of the grain's elastic moduli from the average elastic moduli of the polycrystal. This variation in the elastic properties of the individual grains causes acoustic scattering phenomenon in polycrystalline materials to become stress-dependent. The influence of the initial stress on scattering is shown to be greater than the influence on acoustic phase velocities, which defines the acoustoelastic effect. This work helps the development of scattering based tools for the nondestructive analysis of material stresses in polycrystals.
Analysis of implicit second-order upwind-biased stencils
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Warren, Gary P.
1993-01-01
Truncation error and stability properties of several implicit upwind schemes for the two-dimensional Euler equations are examined. The schemes use linear data reconstruction methods to achieve second-order flux integrations where the implicit Jacobian operators are first order. The stability properties of the schemes are examined by a Von Neumann analysis of the linearized, constant-coefficient Euler equations. The choice of the data reconstruction method used to evaluate the flux integral has a dramatic effect on the convergence properties of the implicit solution method. In particular, the typical one-dimensional data reconstruction methods used with structured grids exhibit poor convergence properties compared to the unstructured grid method considered. Of the schemes examined, the one with the superior convergence properties is well-suited for both unstructured and structured grids, which has important implications for the design of implicit methods.
Nonoscillation for second order sublinear dynamic equations on time scales
NASA Astrophysics Data System (ADS)
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009-10-01
Consider the Emden-Fowler sublinear dynamic equation x[Delta][Delta](t)+p(t)f(x([sigma](t)))=0, where , is a time scale, , where ai>0, 0<[beta]i<1, with [beta]i the quotient of odd positive integers, 1<=i<=m. When m=1, and , (0.1) is the usual sublinear Emden-Fowler equation which has attracted the attention of many researchers. In this paper, we allow the coefficient function p(t) to be negative for arbitrarily large values of t. We extend a nonoscillation result of Wong for the second order sublinear Emden-Fowler equation in the continuous case to the dynamic equation (0.1). As applications, we show that the sublinear difference equation has a nonoscillatory solution, for b>0, c>[alpha], and the sublinear q-difference equation has a nonoscillatory solution, for , q>1, b>0, c>1+[alpha].
Second-Order Accurate Projective Integrators for Multiscale Problems
Lee, S L; Gear, C W
2005-05-27
We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution accuracy comparable to those obtained by implicit integrators. If the stiff differential equations are not directly available, our formulations and stability analysis are general enough to allow the combined outer-inner projective integrators to be applied to black-box legacy codes or perform a coarse-grained time integration of microscopic systems to evolve macroscopic behavior, for example.
Absorbing boundary conditions for second-order hyperbolic equations
NASA Technical Reports Server (NTRS)
Jiang, Hong; Wong, Yau Shu
1989-01-01
A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.
Perfectly matched layers for Maxwell's equations in second order formulation
Sjogreen, B; Petersson, A
2004-07-26
We consider the two-dimensional Maxwell's equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary condition are discretized to second order accuracy employing an embedded technique which does not suffer from a ''small-cell'' time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We derive estimates for both the error due to reflections at the outer boundary of the PML, and due to discretizing the continuous PML equations. Using these estimates, we show how the parameters of the PML can be chosen to make the discrete solution of the PML equations converge to the solution of Maxwell's equations on the unbounded domain, as the grid size goes to zero. Several numerical examples are given.
Spacetimes with Killing tensors. [for Einstein-Maxwell fields with certain spinor indices
NASA Technical Reports Server (NTRS)
Hughston, L. P.; Sommers, P.
1973-01-01
The characteristics of the Killing equation and the Killing tensor are discussed. A conformal Killing tensor is of interest inasmuch as it gives rise to a quadratic first integral for null geodesic orbits. The Einstein-Maxwell equations are considered together with the Bianchi identity and the conformal Killing tensor. Two examples for the application of the considered relations are presented, giving attention to the charged Kerr solution and the charged C-metric.
An Eulerian scheme for the second-order approximation of subsurface transport moments
NASA Astrophysics Data System (ADS)
Naff, R. L.
1994-05-01
The moments of a conservative tracer cloud migrating in a mean uniform flow field are estimated using an operator approximation scheme; results are presented for the second, third, and fourth central moments in the mean flow direction. It is assumed that the spatially variable flow field, and therefore the tracer migration problem itself, is amenable to a probabilistic description; the effects of local dispersion on cloud migration are neglected in this study. Variation in the flow field is assumed to be the result of spatial variation in the hydraulic conductivity; spatial variation in porosity is assumed negligible. The operator approximation scheme, as implemented in this study, is second-order correct, which requires a second-order correct approximation of the velocity field correlation structure. Because estimation of the velocity correlation structure is decidedly the most difficult aspect of second-order analysis, an ad hoc extension of the imperfectly stratified approximation developed earlier is implemented for this purpose. The first-order approximation resulting from the operator expansion scheme is equivalent to small perturbation Eulerian results presented earlier (Naff, 1990, 1992). The infinite-order approximation resulting from this scheme is equivalent to the exponential operator results obtained by Van Kampen (1976).
Second-order theory for nonlinear composites and application to isotropic constituents
NASA Astrophysics Data System (ADS)
Idiart, Martín I.; Danas, Kostas; Ponte Castañeda, Pedro
2006-10-01
New prescriptions are proposed for the 'reference' fields in the context of the 'second-order' nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737-757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, 'second-order' estimates of the Hashin-Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered. To cite this article: M.I. Idiart et al., C. R. Mecanique 334 (2006).
Linear ion trap for second-order Doppler shift reduction in frequency standard applications
NASA Technical Reports Server (NTRS)
Prestage, John D.; Janik, Gary R.; Dick, G. John; Maleki, Lute
1990-01-01
The authors have designed and are presently testing a novel linear ion trap that permits storage of a large number of ions with reduced susceptibility to the second-order Doppler effect caused by the RF confining fields. This new trap should store about 20 times the number of ions as a conventional RF trap with no corresponding increase in second-order Doppler shift from the confining field. In addition, the sensitivity of this shift to trapping parameters, i.e., RF voltage, RF frequency, and trap size, is greatly reduced. The authors have succeeded in trapping mercury ions and xenon ions in the presence of helium buffer gas. Trap times as long as 2000 s have been measured.
Hwang, Jai-chan; Noh, Hyerim
2007-11-15
velocity perturbations including the rotation coincide with the ones in Newton's gravity. All equations in this work include the cosmological constant in the background world model. We emphasize that our relativistic/Newtonian correspondences in several situations and pure general relativistic corrections in the context of Newtonian equations are mainly about the dynamic equations of density and velocity perturbations without using the gravitational potential (metric perturbations). Consequently, our relativistic/Newtonian correspondences do not imply the absence of many space-time (i.e., pure general relativistic) effects like frame dragging, and redshift and deflection of photons even in such cases. We also present the case of multiple minimally coupled scalar fields, and properly derive the large-scale conservation properties of curvature perturbation variable in various temporal gauge conditions to the second order.
NASA Astrophysics Data System (ADS)
Yin, Gang; Zhang, Yingtang; Mi, Songlin; Fan, Hongbo; Li, Zhining
2016-11-01
To obtain accurate magnetic gradient tensor data, a fast and robust calculation method based on regularized method in frequency domain was proposed. Using the potential field theory, the transform formula in frequency domain was deduced in order to calculate the magnetic gradient tensor from the pre-existing total magnetic anomaly data. By analyzing the filter characteristics of the Vertical vector transform operator (VVTO) and Gradient tensor transform operator (GTTO), we proved that the conventional transform process was unstable which would zoom in the high-frequency part of the data in which measuring noise locate. Due to the existing unstable problem that led to a low signal-to-noise (SNR) for the calculated result, we introduced regularized method in this paper. By selecting the optimum regularization parameters of different transform phases using the C-norm approach, the high frequency noise was restrained and the SNR was improved effectively. Numerical analysis demonstrates that most value and characteristics of the calculated data by the proposed method compare favorably with reference magnetic gradient tensor data. In addition, calculated magnetic gradient tensor components form real aeromagnetic survey provided better resolution of the magnetic sources and original profile.
Static multipole polarisabilities and second-order Stark shift in francium
NASA Technical Reports Server (NTRS)
Khan, F.; Khandelwal, G. S.; Wilson, J. W.
1988-01-01
The multipole polarizability of the ground state of francium is calculated by utilizing both the variational technique of Davison and the quantum defect theory underlying the Bates-Damgaard method. This approach is also shown to yield reasonable results for other alkali atoms. Second-order Stark shift for the ground state of francium is presented as a function of field strength for possible future experimental comparison.
Static multipole polarisabilities and second-order Stark shift in francium.
Khan, F; Khandelwal, G S; Wilson, J W
1988-01-01
The multipole polarisability of the ground state of francium is calculated by utilising both the variational technique of Davison and the quantum defect theory underlying the Bates-Damgaard method. This approach is also shown to yield reasonable results for other alkali atoms. Second-order Stark shift for the ground state of francium is presented as a function of field strength for possible future experimental comparison. PMID:11539071
Spin-S kagome quantum antiferromagnets in a field with tensor networks
NASA Astrophysics Data System (ADS)
Picot, Thibaut; Ziegler, Marc; Orús, Román; Poilblanc, Didier
2016-02-01
Spin-S Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S =2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the 1/3th ,(1-2/9S)th, and (1-1/9S)th of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-1/2 1/9 plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U (1 ) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S =2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.
Predictions of single field inflation for the tensor/scalar ratio and the running spectral index
Vega, H. J. de; Sanchez, N. G.
2006-09-15
We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn{sub s}/dlnk are studied in detail. We derive explicit formulas for n{sub s}, r and dn{sub s}/dlnk and provide relevant plots. In new inflation, and for the chosen central value n{sub s}=0.95, we predict 0.03
Second order gyrokinetic theory for particle-in-cell codes
NASA Astrophysics Data System (ADS)
Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric
2016-08-01
The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell-Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.
Second order sliding mode control for a quadrotor UAV.
Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang
2014-07-01
A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method.
On computing first and second order derivative spectra
NASA Astrophysics Data System (ADS)
Roy, Indrajit G.
2015-08-01
Enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis. First and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing. But high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data. An algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed. The algorithm is formalized in the framework of an inverse problem, where based on the fundamental theorem of calculus a matrix equation is formed using a Volterra type integral equation of first kind. A regularization technique, where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra. The higher order derivative spectra are obtained while using the algorithm in sequel. The algorithm is tested successfully with synthetically generated spectral data contaminated with additive white Gaussian noise, and also with real absorbance and reflectance spectral data for fresh and sea water respectively.
Modal cost analysis for linear matrix-second-order systems
NASA Technical Reports Server (NTRS)
Skelton, R. E.; Hughes, P. C.
1980-01-01
Reduced models and reduced controllers for systems governed by matrix-second-order differential equations are obtained by retaining those modes which make the largest contributions to quadratic control objectives. Such contributions, expressed in terms of modal data, used as mode truncation criteria, allow the statement of the specific control objectives to influence the early model reduction from very high order models which are available, for example, from finite element methods. The relative importance of damping, frequency, and eigenvector in the mode truncation decisions are made explicit for each of these control objectives: attitude control, vibration suppression and figure control. The paper also shows that using modal cost analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop modal coordinates which are most critical to the quadratic control performance criterion. In this way, the modes which should be controlled (and hence the modes which must be observable by choice of measurements), are deduced from truncations of the optimal controller.
Correction of the Chromaticity up to Second Order for MEIC
H. K. Sayed, S.A. Bogacz, P. Chevtsov
2010-03-01
The proposed electron collider lattice exhibits low β- functions at the Interaction Point (IP) (βx*100mm - βy* 20 mm) and rather large equilibrium momentum spread of the collider ring (δp/p = 0.00158). Both features make the chromatic corrections of paramount importance. Here the chromatic effects of the final focus quadruples are cor- rected both locally and globally. Local correction features symmetric sextupole families around the IP, the betatron phase advances from the IP to the sextupoles are chosen to eliminate the second order chromatic aberration. Global interleaved families of sextupoles are placed in the figure-8 arc sections, and non-interleaved families at straight sec- tion making use of the freely propagated dispersion wave from the arcs. This strategy minimizes the required sex- tupole strength and eventually leads to larger dynamic aper- ture of the collider. The resulting spherical aberrations induced by the sextupoles are mitigated by design; the straight and arc sections optics features an inverse identity transformation between sextupoles in each pair.
Second-order spatial analysis of epidermal nerve fibers.
Waller, Lance A; Särkkä, Aila; Olsbo, Viktor; Myllymäki, Mari; Panoutsopoulou, Ioanna G; Kennedy, William R; Wendelschafer-Crabb, Gwen
2011-10-15
Breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. Preliminary neurologic studies indicate qualitative differences in the spatial patterns of nerve fibers based on pathophysiologic conditions in the subjects. Of particular interest is the evolution of spatial patterns observed in the progression of diabetic neuropathy. It appears that the spatial distribution of nerve fibers becomes more 'clustered' as neuropathy advances, suggesting the possibility of diagnostic prediction based on patterns observed in skin biopsies. We consider two approaches to establish statistical inference relating to this observation. First, we view the set of locations where the nerves enter the epidermis from the dermis as a realization of a spatial point process. Secondly, we treat the set of fibers as a realization of a planar fiber process. In both cases, we use estimated second-order properties of the observed data patterns to describe the degree and scale of clustering observed in the microscope images of blister biopsies. We illustrate the methods using confocal microscopy blister images taken from the thigh of one normal (disease-free) individual and two images each taken from the thighs of subjects with mild, moderate, and severe diabetes and report measurable differences in the spatial patterns of nerve entry points/fibers associated with disease status.
Second-order perturbation theory: Problems on large scales
NASA Astrophysics Data System (ADS)
Pound, Adam
2015-11-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.
Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator
NASA Astrophysics Data System (ADS)
Doron, A.; Tamir, I.; Mitra, S.; Zeltzer, G.; Ovadia, M.; Shahar, D.
2016-02-01
In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.
Atmospheric Effects of Second Order on Cosmic Rays Intensity Measured at the South Hemisphere
NASA Astrophysics Data System (ADS)
Alvarez-Castillo, Jesús; Francisco Valdes-Galicia, Jose
In this work, we show atmospheric effects of second order on the cosmic rays intensity observed in the South Hemisphere; analysis is using meteorologic data of the TRMM satelite and others of the NOAA, and free data of the surface detectors from Pierre Auger Observatory with a resolution of 15 minutes. The time period analized was from 2006-2011. The methodology consisted in analize the anomalies in atmospheric pressure and in the corrected cosmic rays data for barometric effects considering a sigma level >|2|, the results reflecting a second order variation in the atmospheric pressure, applying digital filters and the spectrum of the data showed a trend that correspond to periodicities of the rain and electric field.
Yogarajah, M.; Focke, N. K.; Bonelli, S.; Cercignani, M.; Acheson, J.; Parker, G. J. M.; Alexander, D. C.; McEvoy, A. W.; Symms, M. R.; Koepp, M. J.
2009-01-01
Anterior temporal lobe resection is often complicated by superior quadrantic visual field deficits (VFDs). In some cases this can be severe enough to prohibit driving, even if a patient is free of seizures. These deficits are caused by damage to Meyer's loop of the optic radiation, which shows considerable heterogeneity in its anterior extent. This structure cannot be distinguished using clinical magnetic resonance imaging sequences. Diffusion tensor tractography is an advanced magnetic resonance imaging technique that enables the parcellation of white matter. Using seed voxels antero-lateral to the lateral geniculate nucleus, we applied this technique to 20 control subjects, and 21 postoperative patients. All patients had visual fields assessed with Goldmann perimetry at least three months after surgery. We measured the distance from the tip of Meyer's loop to the temporal pole and horn in all subjects. In addition, we measured the size of temporal lobe resection using postoperative T1-weighted images, and quantified VFDs. Nine patients suffered VFDs ranging from 22% to 87% of the contralateral superior quadrant. In patients, the range of distance from the tip of Meyer's loop to the temporal pole was 24–43 mm (mean 34 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was −15 to +9 mm (mean 0 mm). In controls the range of distance from the tip of Meyer's loop to the temporal pole was 24–47 mm (mean 35 mm), and the range of distance from the tip of Meyer's loop to the temporal horn was −11 to +9 mm (mean 0 mm). Both quantitative and qualitative results were in accord with recent dissections of cadaveric brains, and analysis of postoperative VFDs and resection volumes. By applying a linear regression analysis we showed that both distance from the tip of Meyer's loop to the temporal pole and the size of resection were significant predictors of the postoperative VFDs. We conclude that there is considerable variation in the
First and second-order features for detection of masses in digital breast tomosynthesis
NASA Astrophysics Data System (ADS)
Samala, Ravi K.; Wei, Jun; Chan, Heang-Ping; Hadjiiski, Lubomir; Cha, Kenny; Helvie, Mark A.
2016-03-01
We are developing novel methods for prescreening of mass candidates in computer-aided detection (CAD) system for digital breast tomosynthesis (DBT). With IRB approval and written informed consent, 186 views from 94 breasts were imaged using a GE GEN2 prototype DBT system. The data set was randomly separated into training and test sets by cases. Gradient field convergence features based on first-order features were used to select the initial set of mass candidates. Eigenvalues based on second-order features from the Hessian matrix were extracted for the mass candidate locations in the DBT volume. The features from the first- and second-order analysis form the feature vector that was input to a linear discriminant analysis (LDA) classifier to generate a candidate-likelihood score. The likelihood scores were ranked and the top N candidates were passed onto the subsequent detection steps. The improvement between using only first-order features and the combination of first and second-order features was analyzed using a rank-sensitivity plot. 3D objects were obtained with two-stage 3D clustering followed by active contour segmentation. Morphological, gradient field, and texture features were extracted and feature selection was performed using stepwise feature selection. A combination of LDA and rule-based classifiers was used for FP reduction. The LDA classifier output a masslikelihood score for each object that was used as a decision variable for FROC analysis. At breast-based sensitivities of 70% and 80%, prescreening using first-order and second-order features resulted in 0.7 and 1.0 FPs/DBT.
Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation
Petersson, N A; Sjogreen, B
2012-03-26
second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a
Concentration Problem of Tensor Fields on the Sphere for the Analysis of SGG Data
NASA Astrophysics Data System (ADS)
Seibert, Katrin
2015-04-01
Satellite gravity gradiometry data (SGG data) like the data recorded by the satellite mission GOCE is given in the form of tensors. So, an extension of the method of Slepian functions to tensors is useful. Spherical Slepian functions form a complete orthonormal basis on the unit sphere. They are a basis transformation of the spherical harmonics. Indeed, they have the advantage of the optimal concentration within a region of interest and are, thus, relevant for local problems. However, tensor Slepian functions on the sphere have only rarely been investigated so far. We construct a method for an efficient calculation of such local trial functions. They base not only on the tensor spherical harmonics (by Freeden and Schreiner) but also on the spin-weighted spherical harmonics (by Newman and Penrose).
Creating second-order nonlinearity in pure synthetic silica optical fibers by thermal poling.
An, Honglin; Fleming, Simon
2007-04-01
A twin-hole optical fiber with pure synthetic silicate glass between the two electrode holes was thermally poled. The induced second-order nonlinearity (SON) was located at the core-cladding interface sections that were nearly parallel to the poling electric field. The polarization dependence of the induced SON suggests that nonlinearity was due to the presence of a space-charge field, which was probably formed by electron migration among the defects located at the core-cladding interface. The magnitude of the induced SON was measured to be approximately 0.06 pm /V.
Quantum-enhanced tunable second-order optical nonlinearity in bilayer graphene.
Wu, Sanfeng; Mao, Li; Jones, Aaron M; Yao, Wang; Zhang, Chuanwei; Xu, Xiaodong
2012-04-11
Second order optical nonlinear processes involve the coherent mixing of two electromagnetic waves to generate a new optical frequency, which plays a central role in a variety of applications, such as ultrafast laser systems, rectifiers, modulators, and optical imaging. However, progress is limited in the mid-infrared (MIR) region due to the lack of suitable nonlinear materials. It is desirable to develop a robust system with a strong, electrically tunable second order optical nonlinearity. Here, we demonstrate theoretically that AB-stacked bilayer graphene (BLG) can exhibit a giant and tunable second order nonlinear susceptibility χ((2)) once an in-plane electric field is applied. χ((2)) can be electrically tuned from 0 to ~10(5) pm/V, 3 orders of magnitude larger than the widely used nonlinear crystal AgGaSe(2). We show that the unusually large χ((2)) arise from two different quantum enhanced two-photon processes thanks to the unique electronic spectrum of BLG. The tunable electronic bandgap of BLG adds additional tunability on the resonance of χ((2)), which corresponds to a tunable wavelength ranging from ~2.6 to ~3.1 μm for the up-converted photon. Combined with the high electron mobility and optical transparency of the atomically thin BLG, our scheme suggests a new regime of nonlinear photonics based on BLG. PMID:22369519
NASA Astrophysics Data System (ADS)
Johnson, Aaron P.; Kingdom, Frederick A. A.; Baker, Curtis L.
2005-10-01
Spatial filters that mimic receptive fields of visual cortex neurons provide an efficient representation of achromatic image structure, but the extension of this idea to chromatic information is at an early stage. Relatively few studies have looked at the statistical relationships between the modeled responses to natural scenes of the luminance (LUM), red-green (RG), and blue-yellow (BY) postreceptoral channels of the primate visual system. Here we consider the correlations among these channel responses in terms of pixel, first-order, and second-order information. First-order linear filtering was implemented by convolving the cosine-windowed images with oriented Gabor functions, whose gains were scaled to give equal amplitude response across spatial frequency to random fractal images. Second-order filtering was implemented via a filter-rectify-filter cascade, with Gabor functions for both first- and second-stage filters. Both signed and unsigned filter responses were obtained across a range of filter parameters (spatial frequency, 2-64 cycles/image orientation, 0-135°). The filter responses to the LUM channel images were larger than those for either RG or BY channel images. Cross correlations between the first-order channel responses and between the first- and second-order channel responses were measured. Results showed that the unsigned correlations between first-order channel responses were higher than expected on the basis of previous studies and that first-order channel responses were highly correlated with LUM, but not with RG or BY, second-order responses. These findings imply that course-scale color information correlates well with course-scale changes of fine-scale texture.
Crustal stress field in the Greek region inferred from inversion of moment tensor solutions
NASA Astrophysics Data System (ADS)
Konstantinou, Konstantinos; Mouslopoulou, Vasiliki; Liang, Wen-Tzong; Heidbach, Oliver; Oncken, Onno; Suppe, John
2016-04-01
The Hellenic region is the seismically most active area in Europe, having experienced numerous large magnitude catastrophic earthquakes and associated devastating tsunamis. A means of mitigating these potential hazards is by better understanding the patterns of spatial and temporal deformation of the crust across the Hellenic orogenic system, over timescales that range from individual earthquakes to several tens of years. In this study for the first time we make collective use of the Global CMT (GCMT), Regional CMT (RCMT) and National Observatory of Athens (NOA) moment tensor databases in order to extract focal mechanism solutions that will be used to infer crustal stresses in the Greek region at an unprecedented resolution. We focus on the shallow seismicity within the upper plate (down to 42 km) and select solutions with good waveform fits and well-resolved hypocentral depths. In this way we obtained 1,614 focal mechanism solutions covering western Greece up to southern Albania, central and southern Greece, northern Aegean as well as the subduction trench west and east of Crete. These solutions are used as input to a regional-scale damped stress inversion over a grid whose node spacing is 0.35 degrees for the purpose of recovering the three principal stress axes and the stress ratio R for each node. Several sensitivity tests are performed where parameters such as damping, hypocentral depth, magnitude range are varied, in order to ascertain the robustness of our results. The final stress field model is then compared to the GPS-derived strain field revealing an excellent agreement between the two datasets. Additionally, maximum and minimum stress axes orientations are correlated with the strike and dip of known faults in order to improve our understanding of future fault rupture and corresponding seismic hazard.
Quantum stress tensor for a massive vector field in the space-time of a cylindrical black hole
Fernandez Piedra, Owen Pavel; Matyjasek, Jerzy
2010-09-15
The components of the renormalized quantum energy-momentum tensor for a massive vector field coupled to the gravitational field configuration of static 3+1 dimensional black strings in anti-de Sitter space are analytically evaluated using the Schwinger-DeWitt approximation. The general results are employed to investigate the pointwise energy conditions for the quantized matter field, and it is shown that they are violated at some regions of the space-time, in particular the horizon of the black hole.
Unconventional photon blockade in doubly resonant microcavities with second-order nonlinearity
NASA Astrophysics Data System (ADS)
Gerace, Dario; Savona, Vincenzo
2014-03-01
It is shown that noncentrosymmetric materials with bulk second-order nonlinear susceptibility can be used to generate strongly antibunched radiation at an arbitrary wavelength, solely determined by the resonant behavior of suitably engineered coupled microcavities. The proposed scheme exploits the unconventional photon blockade of a coherent driving field at the input of a coupled cavity system, where one of the two cavities is engineered to resonate at both fundamental and second harmonic frequencies, respectively. Remarkably, the unconventional blockade mechanism occurs with reasonably low quality factors at both harmonics, and does not require a sharp doubly resonant condition for the second cavity, thus proving its feasibility with current semiconductor technology.
Action approach to cosmological perturbations: the second-order metric in matter dominance
Boubekeur, Lotfi; Creminelli, Paolo; Vernizzi, Filippo; Norena, Jorge
2008-08-15
We study nonlinear cosmological perturbations during post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-({partial_derivative}{phi}){sup 2}]{sup (1+w)/2w}. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second-order metric during matter dominance in the comoving gauge directly as a function of the primordial inflationary perturbation {zeta}. Going to Poisson gauge, we recover the metric previously derived in the literature.
Invariant slow-roll parameters in scalar-tensor theories
NASA Astrophysics Data System (ADS)
Kuusk, Piret; Rünkla, Mihkel; Saal, Margus; Vilson, Ott
2016-10-01
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan frames using quantities that are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field. By comparing spectral indices, calculated up to second order, we find that the frames are equivalent up to this order, due to the underlying assumptions.
Decanini, Yves; Folacci, Antoine
2008-08-15
We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.
NASA Astrophysics Data System (ADS)
Burgos, Gaël.; Capdeville, Yann; Guillot, Laurent
2016-06-01
We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.
NASA Astrophysics Data System (ADS)
Yang, C. J.; Grasso, M.; Roca-Maza, X.; Colò, G.; Moghrabi, K.
2016-09-01
We evaluate the second-order (beyond-mean-field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero-range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond-mean-field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated with the density-dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second-order calculations in nuclear matter.
Magnetic dipole localization based on magnetic gradient tensor data at a single point
NASA Astrophysics Data System (ADS)
Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li
2014-01-01
Magnetic dipole localization methods that rely on measurement of the magnetic field vector are compromised by the relatively strong background geomagnetic field. A localization method that uses only magnetic gradient tensor data is proposed. The localization equations are established by transforming Euler's equation of degree -3 into degree -4 and using the orthogonality of the intermediate eigenvector of the magnetic gradient tensor that is produced by a magnetic dipole and the source-sensor displacement vector. To measure the quantities required in the localization equations, we designed a magnetic gradient tensor system in which finite differences are used to approximate the first- and second-order spatial gradients of magnetic field components. Numerical simulations show that the proposed method can accurately and uniquely solve for the location of a magnetic dipole in the presence of the geomagnetic field, and the experimental results show the superiority and the practicability of the proposed method.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
NASA Astrophysics Data System (ADS)
Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes
2016-08-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.
Effects of Deception on Children's Understanding of Second-Order False Belief
ERIC Educational Resources Information Center
Miller, Scott A.
2013-01-01
This research examined two questions: effects of deception on children's understanding of second-order false belief, and possible effects of number of siblings on second-order performance. Kindergarten children responded to 3 second-order problems that varied in the presence and the nature of deception. Performance was better on the problems…
Newtonian limit of conformal gravity and the lack of necessity of the second order Poisson equation
Mannheim, P.D. ); Kazanas, D. )
1994-04-01
In this work, the authors study the interior structure of a locally conformal invariant fourth order theory of gravity in the presence of a static, spherically symmetric gravitational source. It is found, quite remarkably, that the associated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes both the strong and weak field limits of the theory in this static case. The authors present the solutions of this fourth order equation and find that they are able to recover all of the standard Newton-Euler gravitational phenomenology in the weak gravity limit, to thus establish the observational viability of the weak field limit of the fourth order theory. Additionally, the authors make a critical analysis of the second order Poisson equation, and find that the currently available experimental evidence for its validity is not as clearcut and definitive as is commonly believed, with there not apparently being any conclusive observational support for it at all either on the very largest distance scales for outside of fundamental sources, or on the very smallest ones within their interiors. This study enables the deduction that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary. 17 refs., 1 fig.
Optimization of microscopic and macroscopic second order optical nonlinearities
NASA Technical Reports Server (NTRS)
Marder, Seth R.; Perry, Joseph W.
1993-01-01
Nonlinear optical materials (NLO) can be used to extend the useful frequency range of lasers. Frequency generation is important for laser-based remote sensing and optical data storage. Another NLO effect, the electro-optic effect, can be used to modulate the amplitude, phase, or polarization state of an optical beam. Applications of this effect in telecommunications and in integrated optics include the impression of information on an optical carrier signal or routing of optical signals between fiber optic channels. In order to utilize these effects most effectively, it is necessary to synthesize materials which respond to applied fields very efficiently. In this talk, it will be shown how the development of a fundamental understanding of the science of nonlinear optics can lead to a rational approach to organic molecules and materials with optimized properties. In some cases, figures of merit for newly developed materials are more than an order of magnitude higher than those of currently employed materials. Some of these materials are being examined for phased-array radar and other electro-optic switching applications.
The John equation for tensor tomography in three-dimensions
NASA Astrophysics Data System (ADS)
Nadirashvili, Nikolai S.; Sharafutdinov, Vladimir A.; Vlăduţ, Serge G.
2016-10-01
John proved that a function φ on the manifold of lines in {{{R}}}3 belongs to the range of the x-ray transform if and only if φ satisfies some second order differential equation and obeys some smoothness and decay conditions. We generalize the John equation to the case of the x-ray transform on arbitrary rank symmetric tensor fields: a function φ on the manifold of lines in {{{R}}}3 belongs to the range of the x-ray transform on rank m symmetric tensor fields if and only if φ satisfies some differential equation of order 2(m+1) and obeys some smoothness and decay conditions. The second author was supported by RFBR, Grant 15-01-05929-a.
Optical flow based deformable volume registration using a novel second-order regularization prior
NASA Astrophysics Data System (ADS)
Grbić, Saša; Urschler, Martin; Pock, Thomas; Bischof, Horst
2010-03-01
Nonlinear image registration is an initial step for a large number of medical image analysis applications. Optical flow based intensity registration is often used for dealing with intra-modality applications involving motion differences. In this work we present an energy functional which uses a novel, second-order regularization prior of the displacement field. Compared to other methods our scheme is robust to non-Gaussian noise and does not penalize locally affine deformation fields in homogeneous areas. We propose an efficient and stable numerical scheme to find the minimizer of the presented energy. We implemented our algorithm using modern consumer graphics processing units and thereby increased the execution performance dramatically. We further show experimental evaluations on clinical CT thorax data sets at different breathing states and on dynamic 4D CT cardiac data sets.
Enhancement of Second-Order Nonlinear-Optical Signals by Optical Stimulation
NASA Astrophysics Data System (ADS)
Goodman, A. J.; Tisdale, W. A.
2015-05-01
Second-order nonlinear optical interactions such as sum- and difference-frequency generation are widely used for bioimaging and as selective probes of interfacial environments. However, inefficient nonlinear optical conversion often leads to poor signal-to-noise ratio and long signal acquisition times. Here, we demonstrate the dramatic enhancement of weak second-order nonlinear optical signals via stimulated sum- and difference-frequency generation. We present a conceptual framework to quantitatively describe the interaction and show that the process is highly sensitive to the relative optical phase of the stimulating field. To emphasize the utility of the technique, we demonstrate stimulated enhancement of second harmonic generation (SHG) from bovine collagen-I fibrils. Using a stimulating pulse fluence of only 3 nJ /cm2 , we obtain an SHG enhancement >104 relative to the spontaneous signal. The stimulation enhancement is greatest in situations where spontaneous signals are the weakest—such as low laser power, small sample volume, and weak nonlinear susceptibility—emphasizing the potential for this technique to improve signal-to-noise ratios in biological imaging and interfacial spectroscopy.
First and second order derivatives for optimizing parallel RF excitation waveforms
NASA Astrophysics Data System (ADS)
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.
First and second order derivatives for optimizing parallel RF excitation waveforms.
Majewski, Kurt; Ritter, Dieter
2015-09-01
For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations. PMID:26232364
Li, Yuan-Na; Wu, Hai-Long; Qing, Xiang-Dong; Nie, Chong-Chong; Li, Shu-Fang; Yu, Yong-Jie; Zhang, Shu-Rong; Yu, Ru-Qin
2011-07-15
A rapid non-separative spectrofluorometric method based on the second-order calibration of excitation-emission matrix (EEM) fluorescence was proposed for the determination of napropamide (NAP) in soil, river sediment, and wastewater as well as river water samples. With 0.10 mol L(-1) sodium citrate-hydrochloric acid (HCl) buffer solution of pH 2.2, the system of NAP has a large increase in fluorescence intensity. To handle the intrinsic fluorescence interferences of environmental samples, the alternating penalty trilinear decomposition (APTLD) algorithm as an efficient second-order calibration method was employed. Satisfactory results have been achieved for NAP in complex environmental samples. The limit of detection obtained for NAP in soil, river sediment, wastewater and river water samples were 0.80, 0.24, 0.12, 0.071 ng mL(-1), respectively. Furthermore, in order to fully investigate the performance of second-order calibration method, we test the second-order calibration method using different calibration approaches including the single matrix model, the intra-day various matrices model and the global model based on the APTLD algorithm with nature environmental datasets. The results showed the second-order calibration methods also enable one or more analyte(s) of interest to be determined simultaneously in the samples with various types of matrices. The maintenance of second-order advantage has been demonstrated in simultaneous determinations of the analyte of interests in the environmental samples of various matrices. PMID:21645706
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2016-08-01
We study SU(8) symmetry breaking induced by minimizing the Coleman-Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking {SU}(8)\\supset {SU}(3)× {SU}(5), we find that the stable minimum of the potential breaks the original symmetry according to {SU}(8)\\supset {SU}(3)× {Sp}(4). Using both numerical and analytical methods, we present results for the potential minimum, the corresponding Goldstone boson structure and BEH mechanism, and the group-theoretic classification of the residual states after symmetry breaking.
Multipole theory and the Hehl-Obukhov decomposition of the electromagnetic constitutive tensor
NASA Astrophysics Data System (ADS)
de Lange, O. L.; Raab, R. E.
2015-05-01
The Hehl-Obukhov decomposition expresses the 36 independent components of the electromagnetic constitutive tensor for a local linear anisotropic medium in a useful general form comprising seven macroscopic property tensors: four of second rank, two vectors, and a four-dimensional (pseudo)scalar. We consider homogeneous media and show that in semi-classical multipole theory, the first full realization of this formulation is obtained (in terms of molecular polarizability tensors) at third order (electric octopole-magnetic quadrupole order). The calculations are an extension of a direct method previously used at second order (electric quadrupole-magnetic dipole order). We consider in what sense this theory is independent of the choice of molecular coordinate origins relative to which polarizabilities are evaluated. The pseudoscalar (axion) observable is expressed relative to the crystallographic origin. The other six property tensors are invariant (with respect to an arbitrary choice of each molecular coordinate origin), or zero, at first and second orders. At third order, this invariance has to be imposed (by transformation of the response fields)—an aspect that is required by consideration of isotropic fluids and is consistent with the invariance of transmission phenomena in dielectrics. Alternative derivations of the property tensors are reviewed, with emphasis on the pseudoscalar, constraint-breaking, translational invariance, and uniqueness.
Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio
NASA Astrophysics Data System (ADS)
Germán, Gabriel; Herrera-Aguilar, Alfredo; Hidalgo, Juan Carlos; Sussman, Roberto A.
2016-05-01
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter epsilon(phi) and its derivatives epsilon'(phi) and epsilon''(phi), thereby extracting general conditions on the tensor-to-scalar ratio r and the running nsk at phiH where the perturbations are produced, some 50-60 e-folds before the end of inflation. We find quite generally that for models where epsilon(phi) develops a maximum, a relatively large r is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter ξ2(phi). To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic epsilon(phi) decreasing during most part of inflation. Since at phiH the slow-roll parameter epsilon(phi) is increasing, we thus require that epsilon(phi) develops a maximum for phi > phiH after which epsilon(phi) decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion Δphie ≡ |phiH-phie| is obtained with a sufficiently thin profile for epsilon(phi) which, however, should not conflict with the second slow-roll parameter η(phi). As a consequence of this analysis we find bounds for Δphie, rH and for the scalar spectral index nsH. Finally we provide examples where these considerations are explicitly realised.
Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio
NASA Astrophysics Data System (ADS)
Germán, Gabriel; Herrera-Aguilar, Alfredo; Hidalgo, Juan Carlos; Sussman, Roberto A.
2016-05-01
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter epsilon(phi) and its derivatives epsilon'(phi) and epsilon''(phi), thereby extracting general conditions on the tensor-to-scalar ratio r and the running nsk at phiH where the perturbations are produced, some 50–60 e-folds before the end of inflation. We find quite generally that for models where epsilon(phi) develops a maximum, a relatively large r is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter ξ2(phi). To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic epsilon(phi) decreasing during most part of inflation. Since at phiH the slow-roll parameter epsilon(phi) is increasing, we thus require that epsilon(phi) develops a maximum for phi > phiH after which epsilon(phi) decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion Δphie ≡ |phiH‑phie| is obtained with a sufficiently thin profile for epsilon(phi) which, however, should not conflict with the second slow-roll parameter η(phi). As a consequence of this analysis we find bounds for Δphie, rH and for the scalar spectral index nsH. Finally we provide examples where these considerations are explicitly realised.
NASA Astrophysics Data System (ADS)
Sadoudi, J.; Duguet, T.; Meyer, J.; Bender, M.
2013-12-01
Background: In one way or another, all modern parametrizations of the nuclear energy density functional (EDF) do not respect the exchange symmetry associated with Pauli's principle. It has been recently shown that this practice jeopardizes multireference (MR) EDF calculations by contaminating the energy with spurious self-interactions that, for example, lead to finite steps or even divergences when plotting it as a function of collective coordinates [J. Dobaczewski , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.76.054315 76, 054315 (2007); D. Lacroix , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.79.044318 79, 044318 (2009)]. As of today, the only viable option to bypass these pathologies is to rely on EDF kernels that enforce Pauli's principle from the outset by strictly and exactly deriving from a genuine, i.e., density-independent, Hamilton operator.Purpose: The objective is to build cutting-edge parametrizations of the EDF kernel deriving from a pseudopotential that can be safely employed in symmetry restoration and configuration mixing calculations.Methods: We wish to develop the most general Skyrme-like EDF parametrization containing linear, bilinear, and trilinear terms in the density matrices with up to two gradients, under the key constraint that it derives strictly from an effective Hamilton operator. While linear and bilinear terms are obtained from a standard one-body kinetic energy operator and a (density-independent) two-body Skyrme pseudopotential, the most general three-body Skyrme-like pseudopotential containing up to two gradient operators is constructed to generate the trilinear part. The present study is limited to central terms. Spin orbit and tensor will be addressed in a forthcoming paper.Results: The most general central Skyrme-type zero-range three-body interaction is built up to second order in derivatives. The complete trilinear EDF, including time-odd and T=1 pairing parts, is derived along with the corresponding normal and anomalous
NASA Astrophysics Data System (ADS)
Belardini, A.; Dominici, L.; Larciprete, M. C.; Michelotti, F.; Rousseau, A.; Ratsimihety, A.
2006-12-01
In this work the authors investigated the second order nonlinear optical properties of a group of Disperse Red 1 based electro-optic fluorinated copolymers, synthesized with two fluorinated monomers: the α-fluoroacrylate monomer bearing an adamantane side group and the α-fluoroacrylate monomer bearing the Disperse Red 1 chromophore. By means of nonlinear ellipsometry at λ =1550nm, the poling induced electro-optic tensor main component r33 was determined. The polymer's thermostability was investigated by means of the temperature scanning and isothermal relaxation techniques, leading to the determination of the depolarization temperature Tdep=136°C, corresponding to an activation energy for the relaxation of the orientational distribution of the active chromophores EA=105kcal/mol. The increased thermostability of the copolymer, given by the adamantane side group, is then compared with that of other two groups of fluorinated copolymers.
Bioethics as a second-order discipline: who is not a bioethicist?
Kopelman, Loretta M
2006-12-01
A dispute exists about whether bioethics should become a new discipline with its own methods, competency standards, duties, honored texts, and core curriculum. Unique expertise is a necessary condition for disciplines. Using the current literature, different views about the sort of expertise that might be unique to bioethicists are critically examined to determine if there is an expertise that might meet this requirement. Candidates include analyses of expertise based in "philosophical ethics," "casuistry," "atheoretical or situation ethics," "conventionalist relativism," "institutional guidance," "regulatory guidance and compliance," "political advocacy," "functionalism," and "principlism." None succeed in identifying a unique area of expertise for successful bioethicists that could serve as a basis for making it a new discipline. Rather expertise in bioethics is rooted in many professions, disciplines and fields and best understood as a second-order discipline.
NASA Astrophysics Data System (ADS)
Ito, Kazuma; Sato, Yasuaki; Takasu, Ryosuke; Mase, Nobuyuki; Kawata, Yoshimasa; Tasaka, Shigeru; Sugita, Atsushi
2014-01-01
In this manuscript, we describe the current manuscript describes the second-order nonlinear optical susceptibility of guest-host polymers possessing chromophores with strongly electron-accepting tricyanofuran (TCF). Chromophores substituted with different numbers of hydroxyl groups were prepared. Our experimental results demonstrated that the guest-host polymers exhibited nonlinear optical susceptibilities simply upon annealing at temperatures higher than the glass transition point of the host polymers even in the absence of applied external DC electric fields. Nonelectrical poling behaviors were only available for the materials possessing hydroxyl-group-functionalized chromophores. The results indicate that chemisorption of the hydroxyl groups on the substrate led to the orientation order of the guest chromophores. The orientation order of the chromophores was reproduced well by the model of poled polymers in previous studies.
Possible second-order phase transition in strongly coupled unquenched planar four-dimensional QED
Oliensis, J. ); Johnson, P.W. )
1990-07-15
We study chiral-symmetry breaking in four-dimensional QED with {ital N} fermion species using truncated Schwinger-Dyson equations, and taking vacuum-polarization effects into account via a momentum-dependent gauge coupling. These effects transmute the infinite-order phase transition found previously for the case of a fixed gauge coupling into a second-order phase transition. For large {ital N}, the phase transition may not exist, as it is determined primarily by the physics at the cutoff. We also carry out a preliminary renormalization-group analysis of the theory near the critical coupling: the results are compatible with the existence of a nontrivial continuum limit for the planar theory at the critical value, with an effectively dimensionless fermion field.
Linear matrix inequalities for analysis and control of linear vector second-order systems
Adegas, Fabiano D.; Stoustrup, Jakob
2014-10-06
Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form.
NASA Astrophysics Data System (ADS)
Aissani, Sarra; Guendouz, Laouès; Canet, Daniel
2014-02-01
The electric field gradient tensor (considered here at the level of a nitrogen nucleus) can be described by two parameters: the largest element in the (x, y, z) principal axis system, denoted by Vzz, and the asymmetry parameter η=(Vyy-Vxx)/Vzz. The frequencies of the three nitrogen-14 NQR transitions depend on both parameters and two of them are, a priori, necessary for their determination. We demonstrate that, if a weak static magnetic field is applied during a NQR experiment, both parameters can be obtained from a single transition thus alleviating the difficulties for finding out 14N Quadrupole Resonance lines.
Chen Songbai; Jing Jiliang
2010-10-15
We study the dynamical evolution of a scalar field coupling to Einstein's tensor in the background of a Reissner-Nordstroem black hole. Our results show that the coupling constant {eta} imprints in the wave dynamics of a scalar perturbation. In the weak coupling, we find that with the increase of the coupling constant {eta} the real parts of the fundamental quasinormal frequencies decrease and the absolute values of imaginary parts increase for fixed charge q and multipole number l. In the strong coupling, we find that for l{ne}0 the instability occurs when {eta} is larger than a certain threshold value {eta}{sub c} which deceases with the multipole number l and charge q. However, for the lowest l=0, we find that there does not exist such a threshold value and the scalar field always decays for arbitrary coupling constant.
Stability of Horndeski vector-tensor interactions
Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel E-mail: ruth.durrer@unige.ch E-mail: mikjel.thorsrud@astro.uio.no
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
NASA Technical Reports Server (NTRS)
Jin, Y. Q.; Kong, J. A.
1985-01-01
In the strong fluctuation theory for a bounded layer of random discrete scatterers, the second moments of the fields in the second-order distorted Born approximation are obtained for copolarized and cross-polarized fields. The backscattering cross sections per unit area are calculated by including the mutual coherence of the fields due to the coincidental ray paths, and that due to the opposite ray paths, corresponding to the ladder and cross terms in the Feynman diagramatic representation. It is proved that the contributions from ladder and cross terms for the copolarized backscattering cross sections are the same, while the contributions for the cross-polarized backscattering cross sections are of the same order. The bistatic scattering coefficients in the second-order approximation for both the ladder and cross terms are also obtained. The contributions from the cross terms explain the enhancement in the backscattering direction.
Post processing with first- and second-order hidden Markov models
NASA Astrophysics Data System (ADS)
Taghva, Kazem; Poudel, Srijana; Malreddy, Spandana
2013-01-01
In this paper, we present the implementation and evaluation of first order and second order Hidden Markov Models to identify and correct OCR errors in the post processing of books. Our experiments show that the first order model approximately corrects 10% of the errors with 100% precision, while the second order model corrects a higher percentage of errors with much lower precision.
The Second Order Approximation to Sample Influence Curve in Canonical Correlation Analysis.
ERIC Educational Resources Information Center
Fung, Wing K.; Gu, Hong
1998-01-01
A second order approximation to the sample influence curve (SIC) has been derived in the literature. This paper presents a more accurate second order approximation, which is exact for the SIC of the squared multiple correction coefficient. An example is presented. (SLD)
Increasing stimulus size impairs first- but not second-order motion perception.
Glasser, Davis M; Tadin, Duje
2011-11-23
As stimulus size increases, the direction of high-contrast moving stimuli becomes increasingly difficult to perceive. This counterintuitive effect, termed spatial suppression, is believed to reflect antagonistic center-surround interactions--mechanisms that play key roles in tasks requiring sensitivity to relative motion. It is unknown, however, whether second-order motion also exhibits spatial suppression. To test this hypothesis, we measured direction discrimination thresholds for first- and second-order stimuli of varying sizes. The results revealed increasing thresholds with increasing size for first-order stimuli but demonstrated no spatial suppression of second-order motion. This selective impairment of first-order motion predicts increasing predominance of second-order cues as stimulus size increases. We confirmed this prediction by utilizing compound stimuli that contain first- and second-order information moving in opposite directions. Specifically, we found that for large stimuli, motion perception becomes increasingly determined by the direction of second-order cues. Overall, our findings show a lack of spatial suppression for second-order stimuli, suggesting that the second-order system may have distinct functional roles, roles that do not require high sensitivity to relative motion.
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations
ERIC Educational Resources Information Center
Robin, W.
2007-01-01
The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…
Tomita, Kenji; Inoue, Kaiki Taro
2008-05-15
We study second order gravitational effects of local inhomogeneities on the cosmic microwave background radiation in flat universes with matter and a cosmological constant {lambda}. We find that the general relativistic correction to the Newtonian approximation is negligible at second order provided that the size of the inhomogeneous region is sufficiently smaller than the horizon scale. For a spherically symmetric top-hat type quasilinear perturbation, the first order temperature fluctuation corresponding to the linear integrated Sachs-Wolfe effect is enhanced (suppressed) by the second order one for a compensated void (lump). As a function of redshift of the local inhomogeneity, the second order temperature fluctuations due to evolution of the gravitational potential have a peak before the matter-{lambda} equality epoch for a fixed comoving size and a density contrast. The second order gravitational effects from local quasilinear inhomogeneities at a redshift z{approx}1 may significantly affect the cosmic microwave background.
Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets
Jimenez, Bienvenido Novo, Vicente
2004-03-15
We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Frechet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given.
The effects of second-order hydrodynamics on a semisubmersible floating offshore wind turbine
NASA Astrophysics Data System (ADS)
Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A.
2014-06-01
The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of a floating system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at the Maritime Research Institute Netherlands (MARIN) offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method was applied to the Offshore Code Comparison Collaboration Continuation OC4-DeepCwind semisubmersible platform, supporting the National Renewable Energy Laboratory's 5-MW baseline wind turbine. In this paper, the loads and response of the system caused by the second-order hydrodynamics are analysed and compared to the first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads
Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine: Preprint
Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A.
2014-07-01
The objective of this paper is to assess the second-order hydrodynamic effects on a semisubmersible floating offshore wind turbine. Second-order hydrodynamics induce loads and motions at the sum- and difference-frequencies of the incident waves. These effects have often been ignored in offshore wind analysis, under the assumption that they are significantly smaller than first-order effects. The sum- and difference-frequency loads can, however, excite eigenfrequencies of the system, leading to large oscillations that strain the mooring system or vibrations that cause fatigue damage to the structure. Observations of supposed second-order responses in wave-tank tests performed by the DeepCwind consortium at the MARIN offshore basin suggest that these effects might be more important than originally expected. These observations inspired interest in investigating how second-order excitation affects floating offshore wind turbines and whether second-order hydrodynamics should be included in offshore wind simulation tools like FAST in the future. In this work, the effects of second-order hydrodynamics on a floating semisubmersible offshore wind turbine are investigated. Because FAST is currently unable to account for second-order effects, a method to assess these effects was applied in which linearized properties of the floating wind system derived from FAST (including the 6x6 mass and stiffness matrices) are used by WAMIT to solve the first- and second-order hydrodynamics problems in the frequency domain. The method has been applied to the OC4-DeepCwind semisubmersible platform, supporting the NREL 5-MW baseline wind turbine. The loads and response of the system due to the second-order hydrodynamics are analysed and compared to first-order hydrodynamic loads and induced motions in the frequency domain. Further, the second-order loads and induced response data are compared to the loads and motions induced by aerodynamic loading as solved by FAST.
Interactions between first- and second-order motion revealed by optokinetic nystagmus.
Harris, L R; Smith, A T
2000-01-01
A previous study has suggested that second-order motion is ineffective at driving optokinetic nystagmus (OKN) when presented alone. First- and second-order motion cues interact in creating the perception of motion. Is there an interaction between first- and second-order cues in the control of eye movements? We presented combinations of first- and second-order cues moving in the same or opposite directions and measured the eye movements evoked, to look for a modification of the oculomotor response to first-order motion by simultaneously presented second-order cues. Dynamic random noise was used as a carrier for first- and second-order drifting gratings (13.4 degrees/s; 0.25 cycles/degree; 64 x 48 degrees screen viewed at 28.5 cm). Second-order gratings were defined by spatial modulation of the luminance flicker frequency of noise pixels of constant contrast (50%). A first-order, luminance-defined grating (13.4 degrees/s; 0.25 cycles/degree; variable contrast from 4-50%) was moved in either the same or the opposite direction. Eye movements were recorded by video-oculography from six subjects as they looked straight ahead. The gain (eye velocity/stimulus velocity) of first-order-evoked OKN increased with contrast. The presence of flicker-defined second-order motion in the opposite direction attenuated this OKN below a first-order contrast of 15%, although it had little effect at higher contrasts. When first- and second-order motion were in the same direction, there was an enhancement of the OKN response. We conclude that second-order motion can modify the optokinetic response to simultaneously presented first-order motion. PMID:10638442
An efficient second-order accurate and continuous interpolation for block-adaptive grids
NASA Astrophysics Data System (ADS)
Borovikov, Dmitry; Sokolov, Igor V.; Tóth, Gábor
2015-09-01
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of the resolution changes, which allows us to employ efficient and simple linear interpolation in the majority of the computational domain. The algorithm is well suited for massively parallel computations. Our interpolation algorithm allows extracting jump-free interpolated data distribution along lines and surfaces within the computational domain. This capability is important for various applications, including kinetic particles tracking in three dimensional vector fields, visualization (i.e. surface extraction) and extracting variables along one-dimensional curves such as field lines, streamlines and satellite trajectories, etc. Particular examples are models for acceleration of solar energetic particles (SEPs) along magnetic field-lines. As such models are sensitive to sharp gradients and discontinuities the capability to interpolate the data from the AMR grid to be passed to the SEP model without producing false gradients numerically becomes crucial. We provide a complete description of the algorithm and make the code publicly available as a Fortran 90 library.
NASA Technical Reports Server (NTRS)
Gopinath, Ashok
1996-01-01
Analytical and numerical studies are to be carried out to examine time-averaged thermal effects which are induced by the interaction of strong acoustic fields with a rigid boundary (thermoacoustic streaming). Also of interest is the significance of a second-order thermal expansion coefficient that emerges from this analysis. The model problem to be considered is that of a sphere that is acoustically levitated such that it is effectively isolated in a high-intensity standing acoustic field. The solution technique involves matched asymptotic analysis along with numerical solution of the boundary layer equations. The objective of this study is to predict the thermoacoustic streaming behavior and fully understand the role of the associated second-order thermodynamic modulus.
In unison: First- and second-order information combine for integration of shape information.
Tan, Ken W S; Dickinson, J Edwin; Badcock, David R
2016-09-01
The modulation of orientation around radial frequency (RF) patterns and RF textures is globally processed in both cases. This psychophysical study investigates whether the combination-a textured RF path obtained by applying an RF texture to an RF contour-is processed like a texture or a contour when making judgements about shape. Unlike RF textures, the impression of a closed flow was not required for global integration of textured RF paths, suggesting that these paths were processed as second-order, or contrast-defined contours. Luminance-defined (LD) RF paths were shown to globally integrate but with thresholds approximately half of those for the proposed second-order textured paths. The next experiment investigated whether this benefit was due to LD stimuli possessing double the amount of information (first- and second-order information). A mixed three-part contour composed of two different second-order texture components and an LD component was then employed to determine how the different cues combined. The mixed path thresholds matched predictions derived from a linear combination of first- and second-order cues. The conclusion is that the shape of isolated contours is processed using both first- and second-order information equally and that the contribution of texture is to carry additional second-order signal. PMID:27618513
Vacuum polarization of massive spinor fields in static black-string backgrounds
Fernandez Piedra, Owen Pavel; Cabo Montes de Oca, Alejandro
2008-01-15
The renormalized mean value of the quantum Lagrangian and the corresponding components of the energy-momentum tensor for massive spinor fields coupled to an arbitrary gravitational field configuration having cylindrical symmetry are analytically evaluated using the Schwinger-DeWitt approximation, up to second order in the inverse mass value. The general results are employed to explicitly derive compact analytical expressions for the quantum mean Lagrangian and Energy-Momentum tensor in the particular background of the black-string spacetime.
Theoretical study of the relativistic molecular rotational g-tensor
Aucar, I. Agustín Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Theoretical study of the relativistic molecular rotational g-tensor.
Aucar, I Agustín; Gomez, Sergio S; Giribet, Claudia G; Ruiz de Azúa, Martín C
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH(+) (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH(+) systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Second-order schedules of drug self-administration in animals.
Schindler, Charles W; Panlilio, Leigh V; Goldberg, Steven R
2002-10-01
On a second-order schedule, a subject responds according to one schedule (the unit schedule) for a brief presentation of a stimulus such as a light. Responding by the subject on this unit schedule is then reinforced according to another schedule of reinforcement. Second-order schedules of drug injection allow the study of more complex behavioral sequences than do simple schedules and may more accurately reflect the human drug-abuse situation. Much of the early work in this area used primates as subjects and focused on the behavioral variables controlling responding. It was shown that long sequences of behavior could be maintained on second-order schedules with relatively infrequent injections of drug and that the second-order, brief-stimulus presentations were critical to the acquisition and maintenance of responding. Also, the continued presentation of the brief stimulus in extinction often led to prolonged extinction behavior. These studies clearly showed that environmental stimuli greatly influence drug self-administration behavior under second-order schedules. The focus of much of the more recent work with second-order schedules has been on the evaluation of pharmacological treatments for drug addiction, both as antagonist and substitution therapies. Both types of potential therapies have shown promise in these preclinical models of addictive behavior. The recent extension of second-order self-administration studies to rats as subjects has facilitated the investigation of neural mechanisms involved in this behavior. While this use of second-order schedules is a relatively recent phenomenon, significant contributions have already been made in identifying neural mechanisms critical to second-order schedule drug self-administration. This active area of research holds great promise for delineating specific brain regions critical to different aspects of drug addiction.
Time-dependent Models for Blazar Emission with the Second-order Fermi Acceleration
NASA Astrophysics Data System (ADS)
Asano, Katsuaki; Takahara, Fumio; Kusunose, Masaaki; Toma, Kenji; Kakuwa, Jun
2014-01-01
The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations. The hard electron spectrum predicted by the Fermi-II process agrees with the hard photon spectrum of 1ES 1101-232. For other blazars that show softer spectra, the Fermi-II model requires radial evolution of the electron injection rate and/or diffusion coefficient in the outflow. Such evolutions can yield a curved electron spectrum, which can reproduce the synchrotron spectrum of Mrk 421 from the radio to the X-ray regime. The photon spectrum in the GeV energy range of Mrk 421 is hard to fit with a synchrotron self-Compton model. However, if we introduce an external radio photon field with a luminosity of 4.9 × 1038 erg s-1, GeV photons are successfully produced via inverse Compton scattering. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.
Time-dependent models for blazar emission with the second-order Fermi acceleration
Asano, Katsuaki; Takahara, Fumio; Toma, Kenji; Kusunose, Masaaki; Kakuwa, Jun
2014-01-01
The second-order Fermi acceleration (Fermi-II) driven by turbulence may be responsible for the electron acceleration in blazar jets. We test this model with time-dependent simulations. The hard electron spectrum predicted by the Fermi-II process agrees with the hard photon spectrum of 1ES 1101–232. For other blazars that show softer spectra, the Fermi-II model requires radial evolution of the electron injection rate and/or diffusion coefficient in the outflow. Such evolutions can yield a curved electron spectrum, which can reproduce the synchrotron spectrum of Mrk 421 from the radio to the X-ray regime. The photon spectrum in the GeV energy range of Mrk 421 is hard to fit with a synchrotron self-Compton model. However, if we introduce an external radio photon field with a luminosity of 4.9 × 10{sup 38} erg s{sup –1}, GeV photons are successfully produced via inverse Compton scattering. The temporal variability of the diffusion coefficient or injection rate causes flare emission. The observed synchronicity of X-ray and TeV flares implies a decrease of the magnetic field in the flaring source region.
Ismagilov, Timur Z.
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
Bonnans, J. Frederic; Silva, Francisco J.
2012-06-15
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
NASA Astrophysics Data System (ADS)
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding
NASA Astrophysics Data System (ADS)
Antayhua-Vera, Yanet; Lermo-Samaniego, Javier; Quintanar-Robles, Luis; Campos-Enríquez, Oscar
2015-10-01
We analyze local earthquakes occurring between 2003 and 2012 at the Las Tres Vírgenes Volcanic and Geothermal Field (TVVGF) to establish their temporal and spatial distribution, and relationships with local and regional fault systems, water injection, acid stimulation and steam production tests. We obtained focal mechanisms and inverted data for the stress tensor to understand the local and regional stress fields. We analyzed 423 local earthquakes with magnitudes between 0.1 and 2.9 Mc and hypocentral depths from 0.2 to 7.4 km b.s.l. The cutoff depth at ~ 7.4 km possibly delineates the brittle-ductile transition zone. We identified seven swarms (from 1 to 7). Swarms 1 (December 2009), 2 (May 2010), 3 (June-July 2010) and 7 (December 2012) are strongly correlated with injection processes; whereas swarms 5 (April 2012) and 6 (September 2012) are correlated with local tectonic faults. Stress inversion showed NW-SE, E-W and NE-SW extensional orientations (Shmin), in agreement with the local tectonic stress field; while NE-SW compressional orientations (SHmax) are correlated with the regional tectonic stress field.
A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows
Zhou, Qiang; Fan, Liang-Shih
2014-07-01
A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered
Widdifield, Cory M; Moudrakovski, Igor; Bryce, David L
2014-07-14
Calcium is the 5th most abundant element on earth, and is found in numerous biological tissues, proteins, materials, and increasingly in catalysts. However, due to a number of unfavourable nuclear properties, such as a low magnetogyric ratio, very low natural abundance, and its nuclear electric quadrupole moment, development of solid-state (43)Ca NMR has been constrained relative to similar nuclides. In this study, 12 commonly-available calcium compounds are analyzed via(43)Ca solid-state NMR and the information which may be obtained by the measurement of both the (43)Ca electric field gradient (EFG) and chemical shift tensors (the latter of which are extremely rare with only a handful of literature examples) is discussed. Combined with density functional theory (DFT) computations, this 'tensor interplay' is, for the first time for (43)Ca, illustrated to be diagnostic in distinguishing polymorphs (e.g., calcium formate), and the degree of hydration (e.g., CaCl2·2H2O and calcium tartrate tetrahydrate). For Ca(OH)2, we outline the first example of (1)H to (43)Ca cross-polarization on a sample at natural abundance in (43)Ca. Using prior knowledge of the relationship between the isotropic calcium chemical shift and the calcium quadrupolar coupling constant (CQ) with coordination number, we postulate the coordination number in a sample of calcium levulinate dihydrate, which does not have a known crystal structure. Natural samples of CaCO3 (aragonite polymorph) are used to show that the synthetic structure is present in nature. Gauge-including projector augmented-wave (GIPAW) DFT computations using accepted crystal structures for many of these systems generally result in calculated NMR tensor parameters which are in very good agreement with the experimental observations. This combination of (43)Ca NMR measurements with GIPAW DFT ultimately allows us to establish clear correlations between various solid-state (43)Ca NMR observables and selected structural parameters
NASA Astrophysics Data System (ADS)
Minale, Mario
2016-02-01
In this paper, the generalized Brinkman's equation for a viscoelastic fluid is derived using the volume averages. Darcy's generalised equation is consequently obtained neglecting the first and the second Brinkman's correction with respect to the drag term. The latter differs from the Newtonian drag because of an additional term quadratic in the velocity and inversely proportional to a "viscoelastic" permeability defined in the paper. The viscoelastic permeability tensor can be calculated by solving a boundary value problem, but it must be in fact experimentally measured. To isolate the elastic contribution, the constitutive equation of the second order fluid of Coleman and Noll is chosen because, in simple shear at steady state, second order fluids show a constant viscosity and first and second normal stress differences quadratic in the shear rate. The model predictions are compared with data of the literature obtained in a Darcy's experiment and the agreement is good.
The making of an Alfvenic fluctuation: The resolution of a second-order analysis
NASA Technical Reports Server (NTRS)
Vasquez, Bernard J.; Hollweg, Joseph V.
1995-01-01
Ulysses observations of the high speed polar streams show that they are largely occupied by very large amplitude Alfvenic fluctuations accompanied by many rotational discontinuities. These fluctuations have a nearly constant magnetic intensity or amplitude, and the magnetic field direction per wave cycle sweeps only through a limited arc, much as a car wiperblade would do. Barnes and Hollweg (JGR, 79, 2302, 1974) suggested that this unusual waveform could arise from an obliquely propagating and linearly polarized Alfven wave of finite amplitude. From a second-order analysis, they showed that the existence of a particular solution with a constant amplitude but could not resolve the outcome of the homogeneous solution which consisted of fast waves. They suggested that Landau damping of these fast waves may be needed to get the observed waveform. We present a 1 1/2 D hybrid simulation which is fully nonlinear and correctly describes the ion kinetics for an initially monochromatic and linearly polarized Alfven wave propagating obliquely to the background magnetic field. The wave has a large amplitude and a wavelength so long that it can be considered dispersionless for simulation times. At early times, the second harmonic in density and in magnetic field transverse to the initial wave magnetic field are generated and have more power than other harmonics. Steepening is observed with a weak fast shock emerging, but no rotational discontinuity is left behind, and instead a constant amplitude and an arc-shaped waveform is made. The compressional component which develops after the shocks have dissipated is to zeroth order better described as a pure acoustic wave than as a fast wave. This might be explained by the relaxing of the Alfven wave to a state where its ponderomotive force vanishes so that the compressional component can travel almost independently of it.
Trigonometrically fitted two step hybrid method for the numerical integration of second order IVPs
NASA Astrophysics Data System (ADS)
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.
2016-06-01
In this work we consider the numerical integration of second order ODEs where the first derivative is missing. We construct trigonometrically fitted two step hybrid methods. We apply the new methods on the numerical integration of several test problems.
NASA Technical Reports Server (NTRS)
Schmidt, K. H.
1970-01-01
IBM 1620 computer prepares tables to enable fast calculation of the first- and second-order rate constants from two half-lives and the corresponding initial concentrations, obtained from either one or two decay curves.
An Example of Following Second-Order Kinetics by Simple Laboratory Means
ERIC Educational Resources Information Center
Schreiber, Gisela
1976-01-01
Describes a procedure for studying the kinetics of the second-order hydrolysis of ethylene bromohydrine in alkaline medium by incorporating a substance that changes color as one of the reacting components is depleted. (MLH)
Second-order conditioning of the pigeon's key-peck using an autoshaping procedure.
Green, L; Schweitzer, L
1980-03-01
Second-order conditioning of the pigeon's key-peck was established using an autoshaping procedure. In the first experiment, pigeons came to peck a response key, the second-order conditioned stimulus (CS2), when it was paired with another key (CS1) that had previously been paired with food delivery. In the second experiment, pigeons again came to peck a key (CS2) when it was followed by a clicker (CS1) which had been paired with food delivery, even though the clicker itself had not evoked pecking. Responses to a second-order stimulus, therefore, need not resemble responses to the first-order CS. Furthermore, in both experiments, extinction of the first-order IS led to reduction in pecking CS2. These results were discussed in terms of the nature of the associations being formed during second-order conditioning.
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.
NASA Astrophysics Data System (ADS)
Han, Daozhi; Wang, Xiaoming
2015-06-01
We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier-Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme.
Second-order small disturbance theory for hypersonic flow over power-law bodies. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1974-01-01
A mathematical method for determining the flow field about power-law bodies in hypersonic flow conditions is developed. The second-order solutions, which reflect the effects of the second-order terms in the equations, are obtained by applying the method of small perturbations in terms of body slenderness parameter to the zeroth-order solutions. The method is applied by writing each flow variable as the sum of a zeroth-order and a perturbation function, each multiplied by the axial variable raised to a power. The similarity solutions are developed for infinite Mach number. All results obtained are for no flow through the body surface (as a boundary condition), but the derivation indicates that small amounts of blowing or suction through the wall can be accommodated.
NASA Astrophysics Data System (ADS)
Karakas, Asli; Unver, Huseyin; Elmali, Ayhan
To investigate the microscopic second-order nonlinear optical (NLO) behavior of the 1-salicylidene-3-thio-semicarbazone Schiff base compound, the electric dipole moments (μ), linear static polarizabilities (α) and first static hyperpolarizabilites (β) have been calculated using finite field second-order Møller-Plesset perturbation (FF MP2) theory. The ab-initio results on (hyper)polarizabilities show that the investigated molecule might have microscopic NLO properties with non-zero values. To understand the NLO behavior in the context of molecular orbital structure, we have also examined the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and the HOMO-LUMO gap in the same theoretical framework as the (hyper)polarizability calculations. In addition to the NLO properties, the electronic transition spectra have been computed using a semi-empirical method (ZINDO). ZINDO calculation results show that the electronic transition wavelengths have been estimated to be shorter than 400 nm.
Algorithms and design for a second-order automatic differentiation module
Abate, J.; Bischof, C.; Roh, L.; Carle, A.
1997-07-01
This article describes approaches to computing second-order derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given that show the speedup possible with these techniques relative to existing approaches. The authors also describe a new source transformation AD module for computing second-order derivatives of C and Fortran codes and the underlying infrastructure used to create a language-independent translation tool.
An alternative assessment of second-order closure models in turbulent shear flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Gatski, Thomas B.
1994-01-01
The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.
Exponential stability of second-order stochastic evolution equations with Poisson jumps
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ren, Y.
2012-12-01
This paper is concerned with the exponential stability problem of second-order nonlinear stochastic evolution equations with Poisson jumps. By using the stochastic analysis theory, a set of novel sufficient conditions are derived for the exponential stability of mild solutions to the second-order nonlinear stochastic differential equations with infinite delay driven by Poisson jumps. An example is provided to demonstrate the effectiveness of the proposed result.
NASA Astrophysics Data System (ADS)
Shodja, H. M.; Khorshidi, A.
2013-04-01
Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).
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.
ACKS2: Atom-condensed Kohn-Sham DFT approximated to second order
NASA Astrophysics Data System (ADS)
Verstraelen, T.; Ayers, P. W.; Van Speybroeck, V.; Waroquier, M.
2013-02-01
A new polarizable force field (PFF), namely atom-condensed Kohn-Sham density functional theory approximated to second order (ACKS2), is proposed for the efficient computation of atomic charges and linear response properties of extended molecular systems. It is derived from Kohn-Sham density functional theory (KS-DFT), making use of two novel ingredients in the context of PFFs: (i) constrained atomic populations and (ii) the Legendre transform of the Kohn-Sham kinetic energy. ACKS2 is essentially an extension of the Electronegativity Equalization Method (EEM) [W. J. Mortier, S. K. Ghosh, and S. Shankar, J. Am. Chem. Soc. 108, 4315 (1986)], 10.1021/ja00275a013 in which two major EEM shortcomings are fixed: ACKS2 predicts a linear size-dependence of the dipole polarizability in the macroscopic limit and correctly describes the charge distribution when a molecule dissociates. All ACKS2 parameters are defined as atoms-in-molecules expectation values. The implementation of ACKS2 is very similar to that of EEM, with only a small increase in computational cost.
A second-order two-scale homogenization procedure using macrolevel discretization
NASA Astrophysics Data System (ADS)
Lesičar, Tomislav; Tonković, Zdenko; Sorić, Jurica
2014-08-01
The present study deals with a second-order two-scale computational homogenization procedure for modeling deformation responses of heterogeneous materials at small strains. The macro to micro transition and the application of generalized periodic boundary conditions on the representative volume element (RVE) at the microlevel are investigated. The structure at macroscale level is discretized by the two dimensional triangular finite elements, while the quadrilateral finite element is used for the discretization of the RVE. The finite element formulations and the new proposed multiscale scheme have been implemented into the finite element software ABAQUS using user subroutines derived. Due to the continuity transition, an additional integral condition on microlevel fluctuation field has to be imposed, as expected. The integration has been performed using various numerical integration techniques and the results obtained are compared in a few examples. It is concluded that only trapezoidal rule gives a physically based deformed shape of the RVE. Finally, the efficiency and accuracy of the proposed multiscale homogenization approach are demonstrated by the modeling of a shear layer problem, usually used as a benchmark in multiscale analyses.
Investigating the Dimits Shift using the Second-order Cumulant Expansion Statistical Closure
NASA Astrophysics Data System (ADS)
St-Onge, D. A.; Krommes, J. A.
2015-11-01
The Dimits shift is the nonlinear upshift of the critical temperature gradient that signals the onset of collisionless ion-temperature-gradient-driven turbulence. This phenomenon is caused by the shearing away of turbulent streamers in the radial direction by poloidal zonal flows (ZFs). While the effect is witnessed in both gyrokinetic and gyrofluid simulations, there exists no analytical model that satisfactorily describes the mechanics through which it operates. In this work, a new model is developed by applying the second-order cumulant expansion closure to a simplified set of gyrofluid equations. In particular, we calculate the threshold for the zonostrophic instability of a two-field model, generalizing the work of Parker and Krommes on the modified Hasegawa-Mima equation, and assess whether the Reynolds-stress-generated ZFs can be destabilized in the model, thus indicating a Dimits shift. This work was supported by an NSERC PGS-D scholarship, as well as by U.S. DOE contract DE-AC02-09CH11466.
Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald; Werner, Hans-Joachim
2013-03-14
We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.
Compensated second-order recoupling: application to third spin assisted recoupling†
Giffard, Mathilde; Hediger, Sabine; Lewandowski, Józef R.; Bardet, Michel; Simorre, Jean-Pierre; Griffin, Robert G.; De Paëpe, Gaël
2015-01-01
We consider the effect of phase shifts in the context of second-order recoupling techniques in solid-state NMR. Notably we highlight conditions leading to significant improvements for the Third Spin Assisted Recoupling (TSAR) mechanism and demonstrate the benefits of resulting techniques for detecting long-distance transfer in biomolecular systems. The modified pulse sequences of PAR and PAIN-CP, Phase-Shifted Proton Assisted Recoupling (AH-PS-PAR) and Phase-Shifted Proton-Assisted Insensitive Nuclei Cross Polarization (ABH-PS-PAIN-CP), still rely on cross terms between heteronuclear dipolar couplings involving assisting protons that mediate zero-quantum polarization transfer between low-γ nuclei (13C–13C, 15N–15N, 15N–13C polarization transfer). Using Average Hamiltonian Theory we show that phase inversion compensates off-resonance contributions and yields improved polarization transfer as well as substantial broadening of the matching conditions. PS-TSAR greatly improves on the standard TSAR based methods because it alleviates their sensitivity to precise RF settings which significantly enhances robustness of the experiments. We demonstrate these new methods on a 19.6 kDa protein (U–[15N, 13C]-YajG) at high magnetic fields (up to 900 MHz 1H frequency) and fast sample spinning (up to 65 kHz MAS frequency). PMID:22513727
Gravitational-wave implications for structure formation: A second-order approach
NASA Astrophysics Data System (ADS)
Pazouli, Despoina; Tsagas, Christos G.
2016-03-01
Gravitational waves are propagating undulations in the spacetime fabric, which interact very weakly with their environment. In cosmology, gravitational-wave distortions are produced by most of the inflationary scenarios and their anticipated detection should open a new window to the early Universe. Motivated by the relative lack of studies on the potential implications of gravitational radiation for the large-scale structure of the Universe, we consider its coupling to density perturbations during the postrecombination era. We do so by assuming an Einstein-de Sitter background cosmology and by employing a second-order perturbation study. At this perturbative level and on superhorizon scales, we find that gravitational radiation adds a distinct and faster growing mode to the standard linear solution for the density contrast. Given the expected weakness of cosmological gravitational waves, however, the effect of the new mode is currently subdominant and it could start becoming noticeable only in the far future. Nevertheless, this still raises the intriguing possibility that the late-time evolution of large-scale density perturbations may be dictated by the long-range (the Weyl), rather than the local (the Ricci) component of the gravitational field.
NASA Astrophysics Data System (ADS)
Pointon, T. D.
2008-10-01
A second-order, exact charge-conserving algorithm for accumulating charge and current on the spatial grid for electromagnetic particle-in-cell (EM-PIC) simulation in bounded geometry is presented. The algorithm supports standard EM-PIC exterior boundary conditions and complex internal conductors on non-uniform grids. Boundary surfaces are handled by smoothly transitioning from second to first-order weighting within half a cell of the boundary. When a particle is exactly on the boundary surface (either about to be killed, or just created), the weighting is fully first-order. This means that particle creation and particle/surface interaction models developed for first-order weighting do not need to be modified. An additional feature is the use of an energy-conserving interpolation scheme from the electric field on the grid to the particles. Results show that high-density, cold plasmas with ωΔt˜1, and Δx/λ≫1, can be modeled with reasonable accuracy and good energy conservation. This opens up a significant new capability for explicit simulation of high-density plasmas in high-power devices.
On the effective behavior of nonlinear inelastic composites: II. A second-order procedure
NASA Astrophysics Data System (ADS)
Lahellec, Noël; Suquet, Pierre
2007-09-01
A new method for determining the overall behavior of composite materials comprising nonlinear viscoelastic and elasto-viscoplastic constituents is presented. Part I of this work showed that upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In part I of this paper the nonlinearity was handled using a variational (or secant) technique. In this second part of the study, a proper modification of the second-order procedure of Ponte Castañeda is proposed and leads to replacing, at each time-step, the actual nonlinear viscoelastic composite by a linear viscoelastic one. The linearized problem is even further simplified by using an "effective internal variable" in each individual phase. The resulting predictions are in good agreement with exact results and improve on the predictions of the secant model proposed in part I of this paper.
Killing and conformal Killing tensors
NASA Astrophysics Data System (ADS)
Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe
2016-08-01
We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of conformal Killing 2-tensors on Riemannian products of compact manifolds, Weitzenböck formulas leading to non-existence results, and construct various examples of manifolds with conformal Killing tensors.
In Vivo Generalized Diffusion Tensor Imaging (GDTI) Using Higher-Order Tensors (HOT)
Liu, Chunlei; Mang, Sarah C.; Moseley, Michael E.
2009-01-01
Generalized diffusion tensor imaging (GDTI) using higher order tensor statistics (HOT) generalizes the technique of diffusion tensor imaging (DTI) by including the effect of non-Gaussian diffusion on the signal of magnetic resonance imaging (MRI). In GDTI-HOT, the effect of non-Gaussian diffusion is characterized by higher order tensor statistics (i.e. the cumulant tensors or the moment tensors) such as the covariance matrix (the second-order cumulant tensor), the skewness tensor (the third-order cumulant tensor) and the kurtosis tensor (the fourth-order cumulant tensor) etc. Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI-HOT has been reported. The primary goal of this study is to establish GDTI-HOT as a feasible in vivo technique for imaging non-Gaussian diffusion. We show that probability distribution function (PDF) of the molecular diffusion process can be measured in vivo with GDTI-HOT and be visualized with 3D glyphs. By comparing GDTI-HOT to fiber structures that are revealed by the highest resolution DWI possible in vivo, we show that the GDTI-HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible with a small statistical variation that is similar to that of DTI. PMID:19953513
Llinares, Claudio; Mota, David F
2013-04-19
Several extensions of general relativity and high energy physics include scalar fields as extra degrees of freedom. In the search for predictions in the nonlinear regime of cosmological evolution, the community makes use of numerical simulations in which the quasistatic limit is assumed when solving the equation of motion of the scalar field. In this Letter, we propose a method to solve the full equations of motion for scalar degrees of freedom coupled to matter. We run cosmological simulations which track the full time and space evolution of the scalar field, and find striking differences with respect to the commonly used quasistatic approximation. This novel procedure reveals new physical properties of the scalar field and uncovers concealed astrophysical phenomena which were hidden in the old approach. PMID:23679591
Second-Order Inference for the Mean of a Variable Missing at Random.
Díaz, Iván; Carone, Marco; van der Laan, Mark J
2016-05-01
We present a second-order estimator of the mean of a variable subject to missingness, under the missing at random assumption. The estimator improves upon existing methods by using an approximate second-order expansion of the parameter functional, in addition to the first-order expansion employed by standard doubly robust methods. This results in weaker assumptions about the convergence rates necessary to establish consistency, local efficiency, and asymptotic linearity. The general estimation strategy is developed under the targeted minimum loss-based estimation (TMLE) framework. We present a simulation comparing the sensitivity of the first and second-order estimators to the convergence rate of the initial estimators of the outcome regression and missingness score. In our simulation, the second-order TMLE always had a coverage probability equal or closer to the nominal value 0.95, compared to its first-order counterpart. In the best-case scenario, the proposed second-order TMLE had a coverage probability of 0.86 when the first-order TMLE had a coverage probability of zero. We also present a novel first-order estimator inspired by a second-order expansion of the parameter functional. This estimator only requires one-dimensional smoothing, whereas implementation of the second-order TMLE generally requires kernel smoothing on the covariate space. The first-order estimator proposed is expected to have improved finite sample performance compared to existing first-order estimators. In the best-case scenario of our simulation study, the novel first-order TMLE improved the coverage probability from 0 to 0.90. We provide an illustration of our methods using a publicly available dataset to determine the effect of an anticoagulant on health outcomes of patients undergoing percutaneous coronary intervention. We provide R code implementing the proposed estimator. PMID:27227727
Bulk antisymmetric tensor fields coupled to a dilaton in a Randall-Sundrum model
Alencar, G.; Tahim, M. O.; Landim, R. R.; Muniz, C. R.
2010-11-15
A string-inspired three-form-dilaton-gravity model is studied in a Randall-Sundrum brane world scenario. As expected, the rank-3 antisymmetric field is exponentially suppressed. For each mass level, the mass spectrum is bigger than the one for the Kalb-Ramond field. The coupling between the dilaton and the massless Kaluza-Klein mode of the three-form is calculated, and the coupling constant of the cubic interactions is obtained numerically. This coupling are of the order of Tev{sup -1}; therefore, there exists a possibility to find some signal of it at Tev scale.
NASA Astrophysics Data System (ADS)
Ezquiaga, Jose María; García-Bellido, Juan; Zumalacárregui, Miguel
2016-07-01
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under local Lorentz transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as an arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second-order equations, which can be associated with Horndeski's theory. In this process, we identify a new second-order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second-order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step, we focus on theories with second-order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories.
Hilbe, Christian; Traulsen, Arne; Röhl, Torsten; Milinski, Manfred
2014-01-14
Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all.
Hilbe, Christian; Traulsen, Arne; Röhl, Torsten; Milinski, Manfred
2014-01-14
Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all. PMID:24367116
Assessing Stability and Change in a Second-Order Confirmatory Factor Model of Meaning in Life
Hayward, R. David
2013-01-01
Research indicates that meaning in life is an important correlate of health and well-being. However, relatively little is known about the way a sense of meaning may change over time. The purpose of this study is to explore two ways of assessing change in meaning within a second-order confirmatory factor analysis framework. First, tests are conducted to see if the first and second-order factor loadings and measurement error terms are invariant over time. Second, a largely overlooked technique is used to assess change and stability in meaning at the second-order level. Findings from a nationwide survey reveal that the first and second-order factor loadings are invariant of time. Moreover, the second-order measurement error terms, but not the first-order measurement error terms, are invariant, as well. The results further reveal that standard ways of assessing stability mask significant change in meaning that is due largely to regression to the mean. PMID:24778574
Hilbe, Christian; Traulsen, Arne; Röhl, Torsten; Milinski, Manfred
2014-01-01
Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all. PMID:24367116
Development of the Tensoral Computer Language
NASA Technical Reports Server (NTRS)
Ferziger, Joel; Dresselhaus, Eliot
1996-01-01
The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.
Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration
NASA Astrophysics Data System (ADS)
Becattini, F.; Grossi, E.
2015-08-01
We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.
Beneke, M.; Fidler, C.
2010-09-15
Non-Gaussianity and B-mode polarization are particularly interesting features of the cosmic microwave background, as--at least in the standard model of cosmology--their only sources to first order in cosmological perturbation theory are primordial, possibly generated during inflation. If the primordial sources are small, the question arises how large is the non-Gaussianity and B-mode background induced in second order from the initially Gaussian and scalar perturbations. In this paper we derive the Boltzmann hierarchy for the microwave background photon phase-space distributions at second order in cosmological perturbation theory including the complete polarization information, providing the basis for further numerical studies. As an aside we note that the second-order collision term contains new sources of B-mode polarization and that no polarization persists in the tight-coupling limit.
New second order Mumford-Shah model based on Γ-convergence approximation for image processing
NASA Astrophysics Data System (ADS)
Duan, Jinming; Lu, Wenqi; Pan, Zhenkuan; Bai, Li
2016-05-01
In this paper, a second order variational model named the Mumford-Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford-Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H1 regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss-Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.
NASA Astrophysics Data System (ADS)
Farahani, K.; Bahai, H.
2004-07-01
This paper extends the first order formulations presented in Part I to second order methods for relocation of structural natural frequencies from their initial design values to new modified frequencies. The method is based on an inverse formulation and solution algorithm of the eigenvalue problem. Using the second order Taylor's expansion series, the required parameter variation to achieve a desired natural frequency shift for the structure is computed through second order differential or binomial equations. The proposed technique can also incorporate the design constraints or objective functions in the system equations. The formulations are quite generic and applicable to all finite element structures. The accuracy of the proposed methods is tested by conducting several case studies, the results of which demonstrate the validity of the technique for a wide range of practical problems.
Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence
NASA Astrophysics Data System (ADS)
Li, Yang; Gao, Zhe; Chen, Jiale
2016-08-01
A second order kinetic model for turbulent ion parallel momentum transport is presented. A new nonresonant second order parallel momentum flux term is calculated. The resonant component of the ion parallel electrostatic force is the momentum source, while the nonresonant component of the ion parallel electrostatic force compensates for that of the nonresonant second order parallel momentum flux. The resonant component of the kinetic momentum flux can be divided into three parts, including the pinch term, the diffusive term, and the residual stress. By reassembling the pinch term and the residual stress, the residual stress can be considered as a pinch term of parallel wave-particle resonant velocity, and, therefore, may be called as "resonant velocity pinch" term. Considering the resonant component of the ion parallel electrostatic force is the transfer rate between resonant ions and waves (or, equivalently, nonresonant ions), a conservation equation of the parallel momentum of resonant ions and waves is obtained.
Encoding and estimation of first- and second-order binocular disparity in natural images
Hibbard, Paul B.; Goutcher, Ross; Hunter, David W.
2016-01-01
The first stage of processing of binocular information in the visual cortex is performed by mechanisms that are bandpass-tuned for spatial frequency and orientation. Psychophysical and physiological evidence have also demonstrated the existence of second-order mechanisms in binocular processing, which can encode disparities that are not directly accessible to first-order mechanisms. We compared the responses of first- and second-order binocular filters to natural images. We found that the responses of the second-order mechanisms are to some extent correlated with the responses of the first-order mechanisms, and that they can contribute to increasing both the accuracy, and depth range, of binocular stereopsis. PMID:26731646
Nie, Xiaobing; Cao, Jinde
2011-11-01
In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.
Second-order systematic errors in Mueller matrix dual rotating compensator ellipsometry.
Broch, Laurent; En Naciri, Aotmane; Johann, Luc
2010-06-10
We investigate the systematic errors at the second order for a Mueller matrix ellipsometer in the dual rotating compensator configuration. Starting from a general formalism, we derive explicit second-order errors in the Mueller matrix coefficients of a given sample. We present the errors caused by the azimuthal inaccuracy of the optical components and their influences on the measurements. We demonstrate that the methods based on four-zone or two-zone averaging measurement are effective to vanish the errors due to the compensators. For the other elements, it is shown that the systematic errors at the second order can be canceled only for some coefficients of the Mueller matrix. The calibration step for the analyzer and the polarizer is developed. This important step is necessary to avoid the azimuthal inaccuracy in such elements. Numerical simulations and experimental measurements are presented and discussed.
Second order gauge invariant measure of a tidally deformed black hole
Ahmadi, Nahid
2012-08-01
In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.
Use of the particle swarm optimization algorithm for second order design of levelling networks
NASA Astrophysics Data System (ADS)
Yetkin, Mevlut; Inal, Cevat; Yigit, Cemal Ozer
2009-08-01
The weight problem in geodetic networks can be dealt with as an optimization procedure. This classic problem of geodetic network optimization is also known as second-order design. The basic principles of geodetic network optimization are reviewed. Then the particle swarm optimization (PSO) algorithm is applied to a geodetic levelling network in order to solve the second-order design problem. PSO, which is an iterative-stochastic search algorithm in swarm intelligence, emulates the collective behaviour of bird flocking, fish schooling or bee swarming, to converge probabilistically to the global optimum. Furthermore, it is a powerful method because it is easy to implement and computationally efficient. Second-order design of a geodetic levelling network using PSO yields a practically realizable solution. It is also suitable for non-linear matrix functions that are very often encountered in geodetic network optimization. The fundamentals of the method and a numeric example are given.
Mean-value second-order uncertainty analysis method: application to water quality modelling
NASA Astrophysics Data System (ADS)
Mailhot, Alain; Villeneuve, Jean-Pierre
Uncertainty analysis in hydrology and water quality modelling is an important issue. Various methods have been proposed to estimate uncertainties on model results based on given uncertainties on model parameters. Among these methods, the mean-value first-order second-moment (MFOSM) method and the advanced mean-value first-order second-moment (AFOSM) method are the most common ones. This paper presents a method based on a second-order approximation of a model output function. The application of this method requires the estimation of first- and second-order derivatives at a mean-value point in the parameter space. Application to a Streeter-Phelps prototype model is presented. Uncertainties on two and six parameters are considered. Exceedance probabilities (EP) of dissolved oxygen concentrations are obtained and compared with EP computed using Monte Carlo, AFOSM and MFOSM methods. These results show that the mean-value second-order method leads to better estimates of EP.
Spectral methods for the wave equation in second-order form
Taylor, Nicholas W.; Teukolsky, Saul A.; Kidder, Lawrence E.
2010-07-15
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semidiscrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multidomain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.
NASA Astrophysics Data System (ADS)
Jayabalan, J.; Singh, Manoranjan P.; Banerjee, Arup; Rustagi, K. C.
2008-01-01
In this paper, we present results of calculations of linear and second-order nonlinear polarizabilities of sector-shaped metallic nanoparticles (hemisphere is a special case) using free electron theory. The dependences of the ground state electron density distribution and polarizabilities on various shape parameters of sector are analyzed. The ground state electron densities near the corners and edges of sector-shaped nanoparticle are very low and do not contribute to the linear and second-order polarizabilities. The second-order polarizability is found to depend strongly on the angle of the sector and is shown to be proportional to the product of an appropriately defined asymmetric volume of the particle and the third power of the electron cloud length.
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Guha, Partha; de Lucas, Javier
2013-03-01
A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geometric way. This allows us to study the transformation of these equations into simpler canonical forms, which solves a gap in the previous literature, and other relevant differential equations, which leads to derive new constants of motion for families of second-order Gambier equations. Additionally, we describe general solutions of certain second-order Gambier equations in terms of particular solutions of Riccati equations, linear systems, and t-dependent frequency harmonic oscillators.
Aissani, Sarra; Guendouz, Laouès; Marande, Pierre-Louis; Canet, Daniel
2015-01-01
As demonstrated before, the application of a weak static B0 magnetic field (less than 10 G) may produce definite effects on the ¹⁴N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. Here, we address more precisely the problem of the relative orientation of the two magnetic fields (the static field and the radio-frequency field of the pure NQR experiment). For a field of 6G, the evolution of the signal intensity, as a function of this relative orientation, is in very good agreement with the theoretical predictions. There is in particular an intensity loss by a factor of three when going from the parallel configuration to the perpendicular configuration. By contrast, when dealing with a very weak magnetic field (as the earth field, around 0.5 G), this effect drops to ca. 1.5 in the case Hexamethylenetetramine (HMT).This is explained by the fact that the Zeeman shift (due to the very weak magnetic field) becomes comparable to the natural line-width. The latter can therefore be determined by accounting for this competition. Still in the case of HMT, the estimated natural line-width is half the observed line-width. The extra broadening is thus attributed to earth magnetic field. The latter constitutes therefore the main cause of the difference between the natural transverse relaxation time (T₂) and the transverse relaxation time derived from the observed line-width (T₂(⁎)). PMID:25910551
Infrared second-order optical susceptibility in InAs/GaAs self-assembled quantum dots
NASA Astrophysics Data System (ADS)
Brunhes, T.; Boucaud, P.; Sauvage, S.; Lemaıtre, A.; Gérard, J.-M.; Glotin, F.; Prazeres, R.; Ortega, J.-M.
2000-02-01
We have investigated the second-order nonlinear susceptibility in self-assembled quantum dots. The nonlinear susceptibility associated with intraband transitions in the conduction band and in the valence band is theoretically estimated for lens-shaped InAs/GaAs self-assembled quantum dots. The confined energy levels in the dots are calculated in the effective-mass approximation by solving the three-dimensional Schrödinger equation. Giant values of nonlinear susceptibility, about six orders of magnitude larger than the bull GaAs susceptibility, are predicted. We show that this enhancement results from three key features: (i) the achievement of the double resonance condition, (ii) the specific polarization selection rules of intraband transitions that allow both in-plane and z-polarized transitions with large dipole matrix elements to be optically active, and (iii) the small homogeneous linewidth of the intraband transitions. The conclusions of the calculations are supported by the measurement of the midinfrared nonlinear susceptibility in the valence band. The measurements have been performed using a picosecond free-electron laser. Both χ(2)zzz and χ(2)zxx components of the susceptibility tensor are observed. A satisfying agreement is found between theoretical and experimental values.
Second-order discrete Kalman filtering equations for control-structure interaction simulations
NASA Technical Reports Server (NTRS)
Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.
1991-01-01
A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.
Effective second-order susceptibility in photonic crystals mode of centrosymmetric materials
NASA Astrophysics Data System (ADS)
Feigel, A.; Kotler, Z.; Sfez, B.
2002-02-01
A technique for obtaining efficient bulk second-order susceptibility in noncentrosymmetric photonic crystals (PC) made of centrosymmetric materials is discussed. The effect is based on the electric quadrupole effect, strong electromagnetic mode deformation, and nonhomogeneous contribution to volume polarization from different parts of the PC. The required symmetry breaking is introduced on the macroscale of the PC unit cell. The obtained structural χ(2)str is comparable with the second-order susceptibility of ordinary nonlinear materials. Phase matching can be achieved by introducing symmetry modulation (quasi-phase-matching) during fabrication of the PC.
Observed galaxy number counts on the lightcone up to second order: I. Main result
Bertacca, Daniele; Maartens, Roy; Clarkson, Chris E-mail: roy.maartens@gmail.com
2014-09-01
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
Robust controller designs for second-order dynamic system: A virtual passive approach
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh
1990-01-01
A robust controller design is presented for second-order dynamic systems. The controller is model-independent and itself is a virtual second-order dynamic system. Conditions on actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gains are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the physical meaning of this controller design.
Anti-Stokes luminescence in the light of second order perturbation theory
Bhattacharya, Rupak Pal, Bipul Bansal, Bhavtosh
2014-11-10
Anti-Stokes photoluminescence is measured in high-quality GaAs quantum wells. The primary pathway for interband optical absorption and hence emission under subbandgap photoexcitation is the optical phonon-mediated second-order electric dipole transition. This conclusion is drawn from the remarkable agreement between predictions of second-order perturbation calculation and the measured intensity of anti-Stokes photoluminescence, both as function of the detuning wavelength and temperature. The results are of direct relevance to laser cooling of solids where phonon-assisted upconversion is a necessary condition.
First- and second-order error estimates in Monte Carlo integration
NASA Astrophysics Data System (ADS)
Bakx, R.; Kleiss, R. H. P.; Versteegen, F.
2016-11-01
In Monte Carlo integration an accurate and reliable determination of the numerical integration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In contrast to the usual (first-order) error estimator, this second-order estimator can be shown to be not necessarily positive in an actual Monte Carlo computation. We propose an alternative and indicate how this can be computed in linear time without risk of large rounding errors. In addition, we comment on the relatively very slow convergence of the second-order error estimate.
Imaging of biological tissues with pixel-level analysis of second-order susceptibility
NASA Astrophysics Data System (ADS)
Hu, Po-Sheng; Ghazaryan, Ara; Hovhannisyan, Vladimir; Chen, Shean-Jen; Chen, Yang-Fang; Kim, Chang-Seok; Tsai, Tsung-Hua; Dong, Chen-Yuan
2013-03-01
We discuss the recent advances in the development and applications of second-order susceptibility as a contrast mechanism in optical microscopy for biological tissues. We review nonlinear optical methods and approaches for differentiation of tissue structures and discrimination of normal and pathological skin tissues, which have been demonstrated for the potential use in clinical diagnosis. In addition, the potential of second-order susceptibility imaging, encompassing applications in differentiating various types of collagen molecules for clinical diagnosis, is demonstrated. Finally, we discuss future development and application of this technique.
Approximate Controllability of Second-Order Stochastic Differential Equations with Impulsive Effects
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Ren, Yong; Mahmudov, N. I.
Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.
NASA Astrophysics Data System (ADS)
Wang, Zhengzi
2015-08-01
The influence of ambient temperature is a big challenge to robust infrared face recognition. This paper proposes a new ambient temperature normalization algorithm to improve the performance of infrared face recognition under variable ambient temperatures. Based on statistical regression theory, a second order polynomial model is learned to describe the ambient temperature's impact on infrared face image. Then, infrared image was normalized to reference ambient temperature by the second order polynomial model. Finally, this normalization method is applied to infrared face recognition to verify its efficiency. The experiments demonstrate that the proposed temperature normalization method is feasible and can significantly improve the robustness of infrared face recognition.
Second order nonlinear optical properties of In-doped lithium niobate
NASA Astrophysics Data System (ADS)
Xue, D.; Betzler, K.; Hesse, H.
2001-01-01
Second order nonlinear optical properties of In-doped lithium niobate crystals have been quantitatively studied from the chemical bond viewpoint. The results show that the second order nonlinear optical response of In-doped lithium niobate crystals at 1079 nm decreases remarkably with increasing In concentration in the crystal. This approximately linear composition-property correlation in In-doped lithium niobate crystals is quantitatively expressed in the current work. Furthermore, the different influences of Mg, Zn, and In dopants, respectively, on the nonlinear susceptibility of lithium niobate single crystals are also compared in the present work.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
NASA Astrophysics Data System (ADS)
Jameel, A. F.; Ismail, Ahmad Izani Md
2014-07-01
In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The effectiveness of the algorithm is demonstrated by solving nonlinear second order fuzzy Riccati equation. The results indicate that the method is very effective and simple to apply.
Robust controller designs for second-order dynamic systems - A virtual passive approach
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Phan, Minh
1991-01-01
A robust controller design is presented for second-order dynamic systems. The controller is model-independent and itself is a virtual second-order dynamic system. Conditions on actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gians are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the physical meaning of this controller design.
Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass.
Choi, Jiyeon; Bellec, Matthieu; Royon, Arnaud; Bourhis, Kevin; Papon, Gautier; Cardinal, Thierry; Canioni, Lionel; Richardson, Martin
2012-03-15
We demonstrate that direct femtosecond laser writing in silver-containing zinc and gallium phosphate glass enables generation of three-dimensional (3D) optical second-order nonlinear microstructures having an χ(2) value about 2.5 times that of quartz. The proposed physical model involves photo-reduction, photo-dissociation, and migration of silver species within the glass matrix. 3D laser-written second-order nonlinear structures could become a new class of nonlinear optical components. PMID:22446213
On the second-order homogenization of wave motion in periodic media and the sound of a chessboard
NASA Astrophysics Data System (ADS)
Wautier, Antoine; Guzina, Bojan B.
2015-05-01
The goal of this study is to better understand the mathematical structure and ramifications of the second-order homogenization of low-frequency wave motion in periodic solids. To this end, multiple-scales asymptotic approach is applied to the scalar wave equation (describing anti-plane shear motion) in one and two spatial dimensions. In contrast to previous studies where the second-order homogenization has lead to the introduction of a single fourth-order derivative in the governing equation, present investigation demonstrates that such (asymptotic) approach results in a family of field equations uniting spatial, temporal, and mixed fourth-order derivatives - that jointly control incipient wave dispersion. Given the consequent freedom in selecting the affiliated lengthscale parameters, the notion of an optimal asymptotic model is next considered in a one-dimensional setting via its ability to capture the salient features of wave propagation within the first Brillouin zone, including the onset and magnitude of the phononic band gap. In the context of two-dimensional wave propagation, on the other hand, the asymptotic analysis is first established in a general setting, exposing the constant shear modulus as sufficient condition under which the second-order approximation of a bi-periodic elastic solid is both isotropic and limited to even-order derivatives. On adopting a chessboard-like periodic structure (with contrasts in both modulus and mass density) as a testbed for in-depth analytical treatment, it is next shown that the second-order approximation of germane wave motion is governed by a family fourth-order differential equations that: (i) entail exclusively even-order derivatives and homogenization coefficients that depend explicitly on the contrast in mass density; (ii) describe anisotropic wave dispersion characterized by the "sin4 θ +cos4 θ" term, and (iii) include the asymptotic model for a square lattice of circular inclusions as degenerate case. For
Guendouz, Laouès; Aissani, Sarra; Marêché, Jean-François; Retournard, Alain; Marande, Pierre-Louis; Canet, Daniel
2013-01-01
The application of a weak static B0 magnetic field (less than 1 mT) may produce a well-defined splitting of the (14)N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B0, (ii) the amplitude and pulse duration of the radio-frequency field, B1, used for detecting the NQR signal, and (iii) the relative orientation of B0 and B1. For instance, when B0 is parallel to B1 and regardless of the B0 value, the signal intensity is three times larger than when B0 is perpendicular to B1. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained. PMID:24183810
NASA Astrophysics Data System (ADS)
Kinscher, J.; Krüger, F.; Woith, H.; Lühr, B. G.; Hintersberger, E.; Irmak, T. S.; Baris, S.
2013-11-01
The Armutlu peninsula, located in the eastern Marmara Sea, coincides with the western end of the rupture of the 17 August 1999, İzmit MW 7.6 earthquake which is the penultimate event of an apparently westward migrating series of strong and disastrous earthquakes along the NAFZ during the past century. We present new seismotectonic data of this key region in order to evaluate previous seismotectonic models and their implications for seismic hazard assessment in the eastern Marmara Sea. Long term kinematics were investigated by performing paleo strain reconstruction from geological field investigations by morphotectonic and kinematic analysis of exposed brittle faults. Short term kinematics were investigated by inverting for the moment tensor of 13 small to moderate recent earthquakes using surface wave amplitude spectra. Our results confirm previous models interpreting the eastern Marmara Sea Region as an active transtensional pull-apart environment associated with significant NNE-SSW extension and vertical displacement. At the northern peninsula, long term deformation pattern did not change significantly since Pliocene times contradicting regional tectonic models which postulate a newly formed single dextral strike slip fault in the Marmara Sea Region. This area is interpreted as a horsetail splay fault structure associated with a major normal fault segment that we call the Waterfall Fault. Apart from the Waterfall Fault, the stress strain relation appears complex associated with a complicated internal fault geometry, strain partitioning, and reactivation of pre-existing plane structures. At the southern peninsula, recent deformation indicates active pull-apart tectonics constituted by NE-SW trending dextral strike slip faults. Earthquakes generated by stress release along large rupture zones seem to be less probable at the northern, but more probable at the southern peninsula. Additionally, regional seismicity appears predominantly driven by plate boundary
Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields
NASA Astrophysics Data System (ADS)
Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs
2015-12-01
We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.
Armas-Pérez, Julio C; Londono-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortiz, Juan P; de Pablo, Juan J
2015-07-28
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
Armas-Perez, Julio C.; Londono-Hurtado, Alejandro; Guzman, Orlando; Hernandez-Ortiz, Juan P.; de Pablo, Juan J.
2015-07-27
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortiz, Juan P.; Pablo, Juan J. de
2015-07-28
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
Beidenkopf, H; Avraham, N; Myasoedov, Y; Shtrikman, H; Zeldov, E; Rosenstein, B; Brandt, E H; Tamegai, T
2005-12-16
The thermodynamic phase diagram of Bi2Sr2CaCu2O8 was mapped by measuring local equilibrium magnetization M(H,T) in the presence of vortex shaking. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium M(T) slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.
Employment of Second Order Ruled Surfaces in Design of Sheet Beam Guns
Krasnykh, Anatoly; /SLAC
2007-03-05
A novel 3D method of sheet beam gun design has recently been developed. Second order ruled surfaces (SORS) can be used to define the geometry of the gun electrodes. The gun design process is made simpler if SORS are derived from analytical formulas. A proposed method is discussed and illustrated.
On types of the resolvent of a complete second order differential operator
Ospanov, Kordan Nauryzkhanovich
2015-09-18
In this work we consider the complete second order differential operator, the intermediate coefficient of which is growing rapidly. We find the conditions when its resolvent is compact or belongs to Schatten class, in particular, it is a nuclear operator. The most accurate results are obtained when the coefficient oscillates weakly. In this case we shown that the operator is separable.
ERIC Educational Resources Information Center
Papa, Frank J.; And Others
1997-01-01
Chest pain was identified as a specific medical problem space, and disease classes were modeled to define it. Results from a test taken by 628 medical residents indicate a second-order factor structure that suggests that chest pain is a multidimensional problem space. Implications for medical education are discussed. (SLD)
Control by Contextual Stimuli in Novel Second-Order Conditional Discriminations
ERIC Educational Resources Information Center
Perez-Gonzalez, Luis Antonio; Martinez, Hector
2007-01-01
Eighteen undergraduates participated in studies designed to examine the factors that produce transfer of contextual functions to novel stimuli in second-order conditional discriminations. In Study 1, participants selected comparison B1 given sample A1 and comparison B2 given sample A2 in a matching-to-sample procedure. Contextual stimuli X1 or X2…
Concurrent Second-Order Schedules: Some Effects of Variations in Response Number and Duration
ERIC Educational Resources Information Center
Sealey, Diane M.; Sumpter, Catherine E.; Temple, W.; Foster, T. Mary
2005-01-01
To examine the effects on concurrent performance of independent manipulations of response-unit duration and number, 6 hens were exposed to concurrent second- order schedules of reinforcement. Each first-order operant unit required completion of a fixed-ratio schedule within the time specified by a fixed- interval schedule, with one further…
Second-Order Factor Structure of the MBTI: A Construct Validity Assessment.
ERIC Educational Resources Information Center
Thompson, Bruce; Borrello, Gloria M.
1986-01-01
Factor adequacy and other results based on data from college students (N=359) provided positive evidence regarding the construct validity of the Myers-Briggs Type Indicator (MBTI). Second order factor analysis supported the appropriateness of the MBTI item weighting procedures. (Author/ABB)
Temporal Frequency Modulates Reaction Time Responses to First-Order and Second-Order Motion
ERIC Educational Resources Information Center
Hutchinson, Claire V.; Ledgeway, Tim
2010-01-01
This study investigated the effect of temporal frequency and modulation depth on reaction times for discriminating the direction of first-order (luminance-defined) and second-order (contrast-defined) motion, equated for visibility using equal multiples of direction-discrimination threshold. Results showed that reaction times were heavily…
Second-order cascading in third-order nonlinear optical processes
NASA Astrophysics Data System (ADS)
Meredith, Gerald R.
1982-12-01
Because cascaded second-order processes make substantial qualitative and quanitative differences to the results of third-order nonlinear optical experiments, a formalism for their treatment is presented. The symmetry dictates concerning the occurrence and relationships of magnitudes of cascading are tabulated for the higher symmetry crystal classes. Angular momentum considerations are applied to the situations allowing circularly polarized light waves.
Do Children with Autism Perceive Second-Order Relational Features? The Case of the Thatcher Illusion
ERIC Educational Resources Information Center
Rouse, Helen; Donnelly, Nick; Hadwin, Julie A.; Brown, Tony
2004-01-01
Background: This study presents two experiments that investigated whether children with autism were susceptible to the Thatcher illusion. Perception of the Thatcher illusion requires being able to compute second-order configural relations for facial stimuli. Method: In both experiments children with autism were matched for non-verbal and verbal…
ERIC Educational Resources Information Center
Facao, M.; Lopes, A.; Silva, A. L.; Silva, P.
2011-01-01
We propose an undergraduate numerical project for simulating the results of the second-order correlation function as obtained by an intensity interference experiment for two kinds of light, namely bunched light with Gaussian or Lorentzian power density spectrum and antibunched light obtained from single-photon sources. While the algorithm for…
Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1
NASA Technical Reports Server (NTRS)
Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany
1990-01-01
A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.
The Development of Perceptual Sensitivity to Second-Order Facial Relations in Children
ERIC Educational Resources Information Center
Baudouin, Jean-Yves; Gallay, Mathieu; Durand, Karine; Robichon, Fabrice
2010-01-01
This study investigated children's perceptual ability to process second-order facial relations. In total, 78 children in three age groups (7, 9, and 11 years) and 28 adults were asked to say whether the eyes were the same distance apart in two side-by-side faces. The two faces were similar on all points except the space between the eyes, which was…
Validity of a Measure of Children's Health Locus of Control: A Second-Order Factor Analysis.
ERIC Educational Resources Information Center
Thompson, Bruce; And Others
The study reported in this paper investigated the structure of the health locus of control beliefs of elementary school children using second-order factor analysis and the measurement characteristics of the Multidimensional Health Locus of Control (MHLC) Scales. Changes of wording were made in 10 of the MHLC Scales items in order to improve the…
Second-Order Schedules of Token Reinforcement with Pigeons: Implications for Unit Price
ERIC Educational Resources Information Center
Bullock, Christopher E.; Hackenberg, Timothy D.
2006-01-01
Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio).…
Keep Your Distance! Using Second-Order Ordinary Differential Equations to Model Traffic Flow
ERIC Educational Resources Information Center
McCartney, Mark
2004-01-01
A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…
Independence of First- and Second-Order Memories in Newborn Rabbits
ERIC Educational Resources Information Center
Coureaud, Gerard; Languille, Solene; Joly, Virginie; Schaal, Benoist; Hars, Bernard
2011-01-01
The mammary pheromone promotes the acquisition of novel odorants (CS1) in newborn rabbits. Here, experiments pinpoint that CS1 becomes able to support neonatal learning of other odorants (CS2). We therefore evaluated whether these first- and second-order memories remained dependent after reactivation. Amnesia induced after CS2 recall selectively…
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
Phillips, Steven; Wilson, William H.
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other “structurally related” cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
NASA Technical Reports Server (NTRS)
Pflaum, Christoph
1996-01-01
A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
ERIC Educational Resources Information Center
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
Multidimensional first and second order symmetric strang splitting for hyperbolic systems
Kucharik, Milan; Wendroff, Burton
2008-01-01
We propose an algebraic basis for symmetric Strang splitting for first and second order accurate schemes for hyperbolic systems in N dimensions. Examples are given for two and three dimensions. Optimal stability is shown for symmetric systems. Lack of strong stability is shown for a non-symmetric example. Some numerical examples are presented for some Euler-like constant coefficient problems.
Phillips, Steven; Wilson, William H
2016-01-01
Systematicity is a property of cognitive architecture whereby having certain cognitive capacities implies having certain other "structurally related" cognitive capacities. The predominant classical explanation for systematicity appeals to a notion of common syntactic/symbolic structure among the systematically related capacities. Although learning is a (second-order) cognitive capacity of central interest to cognitive science, a systematic ability to learn certain cognitive capacities, i.e., second-order systematicity, has been given almost no attention in the literature. In this paper, we introduce learned associations as an instance of second-order systematicity that poses a paradox for classical theory, because this form of systematicity involves the kinds of associative constructions that were explicitly rejected by the classical explanation. Our category theoretic explanation of systematicity resolves this problem, because both first and second-order forms of systematicity are derived from the same categorical construction: universal morphisms, which generalize the notion of compositionality of constituent representations to (categorical) compositionality of constituent processes. We derive a model of systematic associative learning based on (co)recursion, which is an instance of a universal construction. These results provide further support for a category theory foundation for cognitive architecture. PMID:27505411
NASA Astrophysics Data System (ADS)
Sun, Yuan Gong; Wong, James S. W.
2007-10-01
We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities: where , p(t) is positive and differentiable, [alpha]1>...>[alpha]m>1>[alpha]m+1>...>[alpha]n. No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n=1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc. Amer. Math. Soc. 118 (1993) 813-817], Wong [J.S.W. Wong, Oscillation criteria for a forced second linear differential equations, J. Math. Anal. Appl. 231 (1999) 235-240], Sun, Ou and Wong [Y.G. Sun, C.H. Ou, J.S.W. Wong, Interval oscillation theorems for a linear second order differential equation, Comput. Math. Appl. 48 (2004) 1693-1699] for the linear equation, Nazr [A.H. Nazr, Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. Math. Soc. 126 (1998) 123-125] for the superlinear equation, and Sun and Wong [Y.G. Sun, J.S.W. Wong, Note on forced oscillation of nth-order sublinear differential equations, JE Math. Anal. Appl. 298 (2004) 114-119] for the sublinear equation.
Enhancement of linear and second-order hyperpolarizabilities in wedge-shaped nanostructures
NASA Astrophysics Data System (ADS)
Jayabalan, J.; Singh, Manoranjan P.; Rustagi, K. C.
2003-08-01
Analytical solutions for the wave functions for free electrons inside a wedge-shaped quantum dot are reported. For silver wedge-shaped quantum dots, linear and second-order hyperpolarizabilities are calculated for various apex angles. It is found that linear and nonlinear hyperpolarizabilities both increase with decreasing apex angle.
Carborane tuning on iridium complexes: redox-switchable second-order NLO responses.
Wang, Jiao; Wang, Wen-Yong; Fang, Xin-Yan; Qiu, Yong-Qing
2015-04-01
Much effort has been devoted to investigating the molecular geometries, electronic structures, redox properties and nonlinear optical (NLO) properties of Ir complexes involving o-, m- or p-carborane groups by density functional theory (DFT) methods. Switchable second-order NLO properties were induced by redox processes involving these complexes, and it was found that mainly the coordination bonds of Ir complexes changed during the oxidation process. Our calculations revealed that oxidation reactions have a significant influence on the second-order NLO response owing to the change in charge transfer pattern. The β tot values of oxidized species are at least ∼9 times larger for set I and ∼5 times larger for set II than those of the corresponding parent complexes. Introduction of carborane groups into ppy (phenylpyridine) ligands can enhance the second-order NLO response by 1.2- 1.6 times by a metal-to-ligand charge transfer (MLCT) transition between the Ir atom and carborane. The β tot of complex 2 [(ppy)2Ir(phen)](+) (phen = phenanthroline) is 3.3 times larger than that of complex 1 (ppy)2Ir(acce) (acce = acetylacetonate), which is caused by ligand-to-ligand charge transfer (LLCT) between ppy ligands and the ancillary ligand. Therefore, it can be concluded that the second-order NLO response can be effectively enhanced by oxidation reactions.
Time domain reflectometry waveform analysis with second order bounded mean oscillation
Technology Transfer Automated Retrieval System (TEKTRAN)
Tangent-line methods and adaptive waveform interpretation with Gaussian filtering (AWIGF) have been proposed for determining reflection positions of time domain reflectometry (TDR) waveforms. However, the accuracy of those methods is limited for short probe TDR sensors. Second order bounded mean osc...
NASA Astrophysics Data System (ADS)
Pokharel, Rajendra K.
Relativistic heavy ion collision experiments show clear evidence of creation of a very short-lived phase of nuclear matter consisting of color-deconfined quarks and gluons. This matter is known as the quark-gluon plasma (QGP). Fluctuation and correlation measurements of the detected particles have played a very important role in revealing the properties of QGP. In particular, these measurements have shown that the QGP behaves like a nearly perfect liquid. Relativistic hydrodynamics has been successfully used to study how the QGP evolves before the system hadronizes and ultimately produces the final state particles. Transport properties like shear viscosity constitute an important part in such studies. This work is focused on developing a second order hydrodynamic theory for the evolution of two-particle transverse momentum correlations. We use general temperature dependent transport and relaxation coefficients as well as the latest information on equations of state and use both first and second order relativistic viscous hydrodynamics to compute experimentally measurable observables. We will show that our computations using the second order viscous hydrodynamics are in good agreement with experimental data. We also highlight some features that distinguish the second order viscous hydrodynamic evolution of QGP from the first order.
NASA Astrophysics Data System (ADS)
Morshed, Khandakar Niaz; Dasi, Lakshmi Prasad
2013-05-01
We study the variations in second-order velocity structure functions (SFs) in the strongly anisotropic turbulent flow past a backward facing step. Time-resolved particle image velocimetry measurements were taken in a stationary turbulent flow past a backward facing step at Reynolds numbers 13,600, 9,000, and 5,500 based on the maximum velocity and step size. Large-scale anisotropic properties of the flow along with local small-scale turbulence characteristics were characterized in detail. Seven interrogation points distributed along points of different large-scale anisotropic characteristics systematically probed the influence of large-scale anisotropy on the second-order SFs. The velocity SFs at each interrogation point represent variance of velocity increments in the streamwise, transverse (wall normal), and the two principle directions of local deformation field. Logarithmic derivatives of the SFs captured the scale-dependent scaling characteristics at the small scales. Measurements revealed a strongly anisotropic large-scale flow with an intense turbulent free-shear layer downstream of the step. Comparison among second-order SFs reveals a mechanistic relationship between the mean flow deformation field, defined by the principle axis of deformation and the magnitude of eigenvalues, to the characteristic influence on SF scaling in the dissipative and non-dissipative scales. Specifically, we report that non-dissipative scaling between orthogonal directions does not differentially saturate if these directions are aligned with the principle axis of deformation. We also show that the relative root mean square of velocity components influences the level of exponent saturation in the dissipative scale regime.
Reviewing the active stress field in Central Asia by using a modified stress tensor approach
NASA Astrophysics Data System (ADS)
Karagianni, I.; Papazachos, C. B.; Scordilis, E. M.; Karakaisis, G. F.
2015-04-01
Central Asia and its surroundings constitute a geodynamically complicated region, where almost all types of tectonic patterns can be observed. A triple junction, collision, and subduction zones, as well as extended fault systems of all types prevail in different parts of this region and compose one of the most interesting and complex geotectonic environments on Earth. This complicated setting is also associated with intense deformation, resulting in a large number of high seismicity zones, where numerous strong earthquakes occur, also extending, in some cases, to intermediate depths. Several previous studies have focused on specific seismotectonic zones in order to assess the active tectonic setting and the associated stress regime. We attempt to provide a unified but detailed picture of the stress field variability for the entire central Asia region, using the well-known inversion method proposed by Gephart and Forsyth (1984), modified in the present work on the basis of Fisher statistics. For this application, we employ a large number of focal mechanisms, spatially separated in 138 data groups. Τhe proposed modified algorithm (FD-BSM) examines the Fisher distribution of all possible stress principal axes solutions and select the one that: (a) shows the smallest angle variation from the Fisher mean in all three principal distributions and (b) minimizes the difference between the theoretical and observed slip vectors of the employed fault plane solution data. Synthetic tests and comparison of the corresponding results with real data show that, in cases where the stress regime is not clearly uniform or the number of available data is rather small, the models selected by the modified approach (FD-BSM) are more robust and show better spatial coherence compared to the initial Gephart and Forsyth (1984) method or alternative techniques such as the method of Michael (1984, 1987) as adapted by Vavrycuk (2014).
Kolda, Tamara G.; Bader, Brett W.
2006-08-03
This software provides a collection of MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. We have also added support for sparse tensor, tensors in Kruskal or Tucker format, and tensors stored as matrices (both dense and sparse).
The role of ion pairs in the second-order NLO response of 4-X-1-methylpiridinium salts.
Tessore, Francesca; Cariati, Elena; Cariati, Franco; Roberto, Dominique; Ugo, Renato; Mussini, Patrizia; Zuccaccia, Cristiano; Macchioni, Alceo
2010-02-01
A series of 4-X-1-methylpyridinium cationic nonlinear optical (NLO) chromophores (X = (E)-CH=CHC(6)H(5); (E)-CH=CHC(6)H(4)-4'-C(CH(3))(3); (E)-CH=CHC(6)H(4)-4'-N(CH(3))(2); (E)-CH=CHC(6)H(4)-4'-N(C(4)H(9))(2); (E,E)-(CH=CH)(2)C(6)H(4)-4'-N(CH(3))(2)) with various organic (CF(3)SO(3)(-), p-CH(3)C(6)H(4)SO(3)(-)), inorganic (I(-), ClO(4)(-), SCN(-), [Hg(2)I(6)](2-)) and organometallic (cis-[Ir(CO)(2)I(2)](-)) counter anions are studied with the aim of investigating the role of ion pairing and of ionic dissociation or aggregation of ion pairs in controlling their second-order NLO response in anhydrous chloroform solution. The combined use of electronic absorption spectra, conductimetric measurements and pulsed field gradient spin echo (PGSE) NMR experiments show that the second-order NLO response, investigated by the electric-field-induced second harmonic generation (EFISH) technique, of the salts of the cationic NLO chromophores strongly depends upon the nature of the counter anion and concentration. The ion pairs are the major species at concentration around 10(-3) M, and their dipole moments were determined. Generally, below 5x10(-4) M, ion pairs start to dissociate into ions with parallel increase of the second-order NLO response, due to the increased concentration of purely cationic NLO chromophores with improved NLO response. At concentration higher than 10(-3) M, some multipolar aggregates, probably of H type, are formed, with parallel slight decrease of the second-order NLO response. Ion pairing is dependent upon the nature of the counter anion and on the electronic structure of the cationic NLO chromophore. It is very strong for the thiocyanate anion in particular and, albeit to a lesser extent, for the sulfonated anions. The latter show increased tendency to self-aggregate.
NASA Astrophysics Data System (ADS)
Li, Zhi-Hui; Ma, Qiang; Cui, Junzhi
2016-06-01
The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment.
NASA Astrophysics Data System (ADS)
Bijlani, Bhavin J.
2011-07-01
This thesis explored the theory, design, fabrication and characterization of AlGaAs Bragg reflection waveguides (BRW) towards the goal of a platform for monolithic integration of active and optically nonlinear devices. Through integration of a diode laser and nonlinear phase-matched cavity, the possibility of on-chip nonlinear frequency generation was explored. Such integrated devices would be highly useful as a robust, alignment free, small footprint and electrically injected alternative to bulk optic systems. A theoretical framework for modal analysis of arbitrary 1-D photonic crystal defect waveguides is developed. This method relies on the transverse resonance condition. It is then demonstrated in the context of several types of Bragg reflection waveguides. The framework is then extended to phase-match second-order nonlinearities and incorporating quantum-wells for diode lasers. Experiments within a slab and ridge waveguide demonstrated phase-matched Type-I second harmonic generation at fundamental wavelength of 1587 and 1600 nm, respectively; a first for this type of waveguide. For the slab waveguide, conversion efficiency was 0.1 %/W. In the more strongly confined ridge waveguides, efficiency increased to 8.6 %/W owing to the increased intensity. The normalized conversion efficiency was estimated to be at 600 %/Wcm2. Diode lasers emitting at 980 nm in the BRW mode were also fabricated. Verification of the Bragg mode was performed through imaging the near- field of the mode. Propagation loss of this type of mode was measured directly for the first time at ≈ 14 cm-1. The lasers were found to be very insensitive with characteristic temperature at 215 K. Two designs incorporating both laser and phase-matched nonlinearity within the same cavity were fabricated, for degenerate and non-degenerate down-conversion. Though the lasers were sub-optimal, a parametric fluorescence signal was readily detected. Fluorescence power as high as 4 nW for the degenerate design
The second order effects on commercial shipping of restrictions on the use of TBT.
Strandenes, S P
2000-08-21
Increased hull roughness reduces vessel speed and increases fuel consumption. These are first order effects of restricting or prohibiting the use of antifouling paints. Reduced transport capacity and increased capital costs are frequently recognised as second order effects of such reductions in fleet efficiency. This paper focuses on other second order effects of prohibiting or restricting the use of TBT-based antifoulings. The potential cost increases will affect high-speed vessels most severely. These vessels are the segment of the shipping industry that is most relevant to the political drive in Europe towards shifting the balance of transport of goods towards sea rather than road transport for environmental reasons. Any decision to restrict or prohibit these paints would tend also to induce a shift from local to global environmental problems, which would be more difficult to manage.
Comprehensive investigation about the second order term of thermodynamic perturbation expansion
NASA Astrophysics Data System (ADS)
Zhou, Shiqi; Solana, J. R.
2009-10-01
Monte Carlo simulations are carried out for the second order term in the thermodynamic perturbation expansion around a hard sphere reference fluid. The sample potentials considered cover a wide spectrum: From two frequently employed, namely hard sphere plus square well potential and hard core attractive Yukawa potential, to two kinds of repulsive potentials, namely hard sphere plus square shoulder potential and hard sphere plus triangle shoulder potential; the investigated potential range also extends from extremely short range to rather long range. The obtained simulation data are used to evaluate performance of two theoretical approaches, i.e., a traditional macroscopic compressibility approximation (MCA) and a recent coupling parameter expansion. Extensive comparison shows that the coupling parameter expansion provides a reliable method for accurately calculating the second order term of the high temperature series expansion, while the widely accepted MCA fails quantitatively or even qualitatively for most of the situations investigated.
Direct method for second-order sensitivity analysis of modal assurance criterion
NASA Astrophysics Data System (ADS)
Lei, Sheng; Mao, Kuanmin; Li, Li; Xiao, Weiwei; Li, Bin
2016-08-01
A Lagrange direct method is proposed to calculate the second-order sensitivity of modal assurance criterion (MAC) values of undamped systems. The eigenvalue problem and normalizations of eigenvectors, which augmented by using some Lagrange multipliers, are used as the constraints of the Lagrange functional. Once the Lagrange multipliers are determined, the sensitivities of MAC values can be evaluated directly. The Lagrange direct method is accurate, efficient and easy to implement. A simply supported beam is utilized to check the accuracy of the proposed method. A frame is adopted to validate the predicting capacity of the first- and second-order sensitivities of MAC values. It is shown that the computational costs of the proposed method can be remarkably reduced in comparison with those of the indirect method without loss of accuracy.
A second-order closure analysis of turbulent diffusion flames. [combustion physics
NASA Technical Reports Server (NTRS)
Varma, A. K.; Fishburne, E. S.; Beddini, R. A.
1977-01-01
A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.
Beyond the G W approximation: A second-order screened exchange correction
NASA Astrophysics Data System (ADS)
Ren, Xinguo; Marom, Noa; Caruso, Fabio; Scheffler, Matthias; Rinke, Patrick
2015-08-01
Motivated by the recently developed renormalized second-order perturbation theory for ground-state energy calculations, we propose a second-order screened exchange correction (SOSEX) to the G W self-energy. This correction follows the spirit of the SOSEX correction to the random-phase approximation for the electron correlation energy and can be clearly represented in terms of Feynman diagrams. We benchmark the performance of the perturbative G0W0 +SOSEX scheme for a set of molecular systems, including the G2 test set from quantum chemistry as well as benzene and tetracyanoethylene. We find that G0W0 +SOSEX improves over G0W0 for the energy levels of the highest occupied and lowest unoccupied molecular orbitals. In addition, it can resolve some of the difficulties encountered by the G W method for relative energy positions as exemplified by benzene where the energy spacing between certain valence orbitals is severely underestimated.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Second-order cone programming formulation for consolidation analysis of saturated porous media
NASA Astrophysics Data System (ADS)
Zhang, Xue; Sheng, Daichao; Sloan, Scott W.; Krabbenhoft, Kristian
2016-07-01
In this paper, the incremental problem for consolidation analysis of elastoplastic saturated porous media is formulated and solved using second-order cone programming. This is achieved by the application of the Hellinger-Reissner variational theorem, which casts the governing equations of Biot's consolidation theory as a min-max optimisation problem. The min-max problem is then discretised using the finite element method and converted into a standard second-order cone programming problem that can be solved efficiently using modern optimisation algorithms (such as the primal-dual interior-point method). The proposed computational formulation is verified against a number of benchmark examples and also applied to simulate the construction of a road embankment on soft clay.
Stable surface relief grating with second-order nonlinearity on urethane urea copolymer film
NASA Astrophysics Data System (ADS)
Che, Yanlong; Sugihara, Okihiro; Fujimura, Hisashi; Okamoto, Naomichi; Egami, Chikara; Kawata, Yoshimasa; Tsuchimori, Masaaki; Watanabe, Osamu
2003-01-01
Surface relief gratings (SRGs) on azobenzene-contained urethane-urea copolymer film with second-order nonlinearity are fabricated by laser-interferometric method. The surface relief structures are obtained upon exposure an interference pattern of a CW Ar + laser and a single-pulse UV laser. The SRG is thermally stable even at Tg of the copolymer. The mechanism of the stability is investigated by comparing the pulse UV laser inscribed SRG. It is suggested that laser ablation of the copolymer surface by the high-power laser irradiation is taken into account. Second-order nonlinearity is induced by corona-poling process after grating formation. Diffraction of second-harmonic generation (SHG) is observed by inserting a fundamental beam, which is in agreement with vector diagram.
Improved Global Soft Decision Incorporating Second-Order Conditional MAP in Speech Enhancement
NASA Astrophysics Data System (ADS)
Kum, Jong-Mo; Chang, Joon-Hyuk
In this paper, we propose a novel method based on the second-order conditional maximum a posteriori (CMAP) to improve the performance of the global soft decision in speech enhancement. The conventional global soft decision scheme is found through investigation to have a disadvantage in that the global speech absence probability (GSAP) in that scheme is adjusted by a fixed parameter, which could be a restrictive assumption in the consecutive occurrences of speech frames. To address this problem, we devise a method to incorporate the second-order CMAP in determining the GSAP, which is clearly different from the previous approach in that not only current observation but also the speech activity decisions of the previous two frames are exploited. Performances of the proposed method are evaluated by a number of tests in various environments and show better results than previous work.
Sustainable institutionalized punishment requires elimination of second-order free-riders
NASA Astrophysics Data System (ADS)
Perc, Matjaž
2012-03-01
Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the ``punishment pool'' from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.
Second-order two-scale method for bending behaviors of composite plate with periodic configuration
NASA Astrophysics Data System (ADS)
Zhu, Guoqing; Cui, Junzhi
2010-06-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
Second-Order Two-Scale Method for Bending Behaviors of Composite Plate with Periodic Configuration
NASA Astrophysics Data System (ADS)
Zhu, Guoqing; Cui, Junzhi
2010-05-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
Yield criteria for porous media in plane strain: second-order estimates versus numerical results
NASA Astrophysics Data System (ADS)
Pastor, Joseph; Ponte Castañeda, Pedro
2002-11-01
This Note presents a comparison of some recently developed "second-order" homogenization estimates for two-dimensional, ideally plastic porous media subjected to plane strain conditions with corresponding yield analysis results using a new linearization technique and systematically optimized finite elements meshes. Good qualitative agreement is found between the second-order theory and the yield analysis results for the shape of the yield surfaces, which exhibit a corner on the hydrostatic axis, as well as for the dependence of the effective flow stress in shear on the porosity, which is found to be non-analytic in the dilute limit. Both of these features are inconsistent with the predictions of the standard Gurson model. To cite this article: J. Pastor, P. Ponte Castañeda, C. R. Mecanique 330 (2002) 741-747.
Second-order discretization in space and time for radiation hydrodynamics
Edwards, J. D.; Morel, J. E.; Lowrie, R. B.
2013-07-01
We present a method for solving the equations of radiation hydrodynamics that is second-order accurate in space and time. This method combines the MUSCL-Hancock method for solving the Euler equations with the TR/BDF2 scheme in time for solving the equations of radiative transfer. We use an LDFEM to discretize the radiative transfer equations in space, which, though uncommon for radiation diffusion calculations, is a standard for radiation transport applications. We address the challenges inherent to using different spatial discretizations for the hydrodynamics and radiation and demonstrate how these may be overcome. We define our method for a 1-D model of compressible fluid dynamics coupled with grey radiation diffusion. Using the method of manufactured solutions, we show that the method is second-order accurate in space and time for both the equilibrium diffusion and streaming limit. (authors)
NASA Astrophysics Data System (ADS)
Shay, W. A.; Schultz, D. H.
1985-05-01
The present investigation is concerned with a problem described by Schultz (1973), who provided a numerical solution for the flow of a fluid in a heated closed cavity. The procedures employed by various investigators to obtain numerical results for this problem are evaluated. No evidence is found that any one of the considered methods have produced results for large Rayleigh numbers and small Prandtl numbers with small grids and second order boundary approximations. The current investigation provides a method which produces such results. The selected procedure involves the use of a rectangular array of nodes which is placed over the region considered in the problem. The solution of the obtained difference equations is discussed, and the results are presented in a number of tables and graphs. It is found that the employed second-order method is superior to the method used by Schultz.
Quasidegenerate second-order perturbation corrections to single excitation configuration interaction
NASA Astrophysics Data System (ADS)
Head-Gordon, Martin
1999-02-01
A family of quasidegenerate second-order perturbation theories that correct excitation energies from single-excitation configuration interaction (CIS) are introduced which generalize the earlier non-degenerate second-order method, CIS(D). The new methods are termed CIS(D), where n ranges from 0 to x, according to the number of terms retained in a doubles denominator expansion. Truncation at either n = 0 or n = 1 yields methods which involve the diagonalization of a dressed singles-only response matrix, where the dressing is state-independent. Hence CIS(D0) and CIS(D1) can be implemented efficiently using semidirect methods, which are discussed. Test calculations on formaldehyde, ethylene, chlorine nitrate, styrene, benzaldehyde, and chalcone are presented to assess the performance of these methods. CIS(D0) and CIS(D1) both show significant improvements relative to CIS(D) in cases of near-degeneracy.
Temporal second-order coherence function for displaced-squeezed thermal states
NASA Astrophysics Data System (ADS)
Alexanian, Moorad
2016-05-01
We calculate the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz. a displaced-squeezed thermal state. The calculation involves first dynamical generation at time t of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time ? apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on ?, via ?, for the given Gaussian state parameters, Gaussian state preparation time t, and average number ? of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in ? rather than an exponential one as is the case for general, displaced-squeezed thermal states.
Optical implementation of a second-order translation-invariant network algorithm
NASA Astrophysics Data System (ADS)
Horan, Paul; Jennings, Andrew; Kelly, Brian; Hegarty, John
1993-03-01
Higher-order networks, particularly second-order translation-invariant networks, are introduced, and their suitability for optical implementation is outlined. The algorithm is implemented with a conventional liquid-crystal display, permitting on-line learning and updating of weights. The basic operation of the optical system is demonstrated, and the ability of the system to adapt to system nonuniformities is illustrated. The implementation with an integrated optoelectronic array of asymmetric Fabry-Perot modulators containing a GaAs/AlGaAs multiple-quantum-well active region is described. The principles of operation and operating characteristics of the device array are outlined. The use of the array in an optical system to calculate the autocorrelation matrix necessary for a second-order network is demonstrated.
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
NASA Astrophysics Data System (ADS)
Basin, Michael; Bharath Panathula, Chandrasekhara; Shtessel, Yuri
2016-09-01
This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.
A second-order characteristic line scheme for solving a juvenile-adult model of amphibians.
Deng, Keng; Wang, Yi
2015-01-01
In this paper, we develop a second-order characteristic line scheme for a nonlinear hierarchical juvenile-adult population model of amphibians. The idea of the scheme is not to follow the characteristics from the initial data, but for each time step to find the origins of the grid nodes at the previous time level. Numerical examples are presented to demonstrate the accuracy of the scheme and its capability to handle solutions with singularity.
Singh, Sanjay; Caron, Luana; D'Souza, Sunil Wilfred; Fichtner, Tina; Porcari, Giacomo; Fabbrici, Simone; Shekhar, Chandra; Chadov, Stanislav; Solzi, Massimo; Felser, Claudia
2016-05-01
In contrast to rare-earth-based materials, cheaper and more environmentally friendly candidates for cooling applications are found within the family of Ni-Mn Heusler alloys. Initial interest in these materials is focused on the first-order magnetostructural transitions. However, large hysteresis makes a magnetocaloric cycle irreversible. Alternatively, here it is shown how the Heusler family can be used to optimize reversible second-order magnetic phase transitions for magnetocaloric applications. PMID:26928954
Dal Cappello, C.; Champion, C.; Kada, I.; Mansouri, A.
2011-06-15
The double ionization of isolated water molecules fixed in space is investigated within a theoretical approach based on the second-order Born approximation. Electron angular distributions have been studied for specific kinematical conditions. The three usual mechanisms, the shake-off and the two two-step mechanisms, have been identified. A significant contribution of the two-step mechanism is clearly visible for some particular kinematics.
Observation of second-order kinetic damage in sodium salicylate due to soft x rays
NASA Astrophysics Data System (ADS)
Husk, D. E.; Tarrio, C.; Benitez, E. L.; Schnatterly, S. E.
1991-10-01
We have observed the dose dependence of the bulk quantum efficiency for luminescence of sodium salicylate as a function of the photon energy from 7 to 150 eV. We show that the damage is a second-order or higher kinetic process in the number of electron-hole pairs and is not reversible. We predict that the threshold for damage occurs at 7.2 eV, or twice the band gap of sodium salicylate.
Singh, Sanjay; Caron, Luana; D'Souza, Sunil Wilfred; Fichtner, Tina; Porcari, Giacomo; Fabbrici, Simone; Shekhar, Chandra; Chadov, Stanislav; Solzi, Massimo; Felser, Claudia
2016-05-01
In contrast to rare-earth-based materials, cheaper and more environmentally friendly candidates for cooling applications are found within the family of Ni-Mn Heusler alloys. Initial interest in these materials is focused on the first-order magnetostructural transitions. However, large hysteresis makes a magnetocaloric cycle irreversible. Alternatively, here it is shown how the Heusler family can be used to optimize reversible second-order magnetic phase transitions for magnetocaloric applications.
An approach for generation of second order RC-active filters.
NASA Technical Reports Server (NTRS)
Dunn, W. R., Jr.
1972-01-01
It is shown that node (or loop) matrix equations can be written which yield second order low-pass, band-pass, and high-pass network functions. Networks corresponding to the equations can in turn be formulated by inspection of the equations. The networks employ ideal VCT or CVT sources which can be physically realized using transistors and/or operational amplifiers. The technique yields several structures which are believed to be new.
Solution of second-order linear system by matched asymptotic expansions
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1982-01-01
Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.
Sherman, L.L.; Taylor, A.C. III; Hou, G.W.; Korivi, V.M.
1996-12-01
The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained. The basic equations for second-order sensitivity derivatives are presented, which results in a comparison of four different methods. Each of these four schemes for second-order derivatives requires that large systems are solved first for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first-order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent-flow example. In each of these two sample problems, three dependent variables (coefficients of lift, drag, and pitching-moment) and six independent variables (three geometric-shape and three flow-condition design variables) are considered. Several different procedures are tested, and results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method. Furthermore, it is at least two to four times faster than central finite differences, without an overwhelming penalty in computer memory. 23 refs., 14 tabs.
Mitigation of Second-Order Ionospheric Error for Real-Time PPP Users in Europe
NASA Astrophysics Data System (ADS)
Abdelazeem, Mohamed
2016-07-01
Currently, the international global navigation satellite system (GNSS) real-time service (IGS-RTS) products are used extensively for real-time precise point positioning and ionosphere modeling applications. The major challenge of the dual frequency real-time precise point positioning (RT-PPP) is that the solution requires relatively long time to converge to the centimeter-level accuracy. This relatively long convergence time results essentially from the un-modeled high-order ionospheric errors. To overcome this challenge, a method for the second-order ionospheric delay mitigation, which represents the bulk of the high-order ionospheric errors, is proposed for RT-PPP users in Europe. A real-time regional ionospheric model (RT-RIM) over Europe is developed using the IGS-RTS precise satellite orbit and clock products. GPS observations from a regional network consisting of 60 IGS and EUREF reference stations are processed using the Bernese 5.2 software package in order to extract the real-time vertical total electron content (RT-VTEC). The proposed RT-RIM has spatial and temporal resolution of 1º×1º and 15 minutes, respectively. In order to investigate the effect of the second-order ionospheric delay on the RT-PPP solution, new GPS data sets from another reference stations are used. The examined stations are selected to represent different latitudes. The GPS observations are corrected from the second-order ionospheric errors using the extracted RT-VTEC values. In addition, the IGS-RTS precise orbit and clock products are used to account for the satellite orbit and clock errors, respectively. It is shown that the RT-PPP convergence time and positioning accuracy are improved when the second-order ionospheric delay is accounted for.
Second-order virial expansion for an atomic gas in a harmonic waveguide
NASA Astrophysics Data System (ADS)
Kristensen, Tom; Leyronas, Xavier; Pricoupenko, Ludovic
2016-06-01
The virial expansion for cold two-component Fermi and Bose atomic gases is considered in the presence of a waveguide and in the vicinity of a Feshbach resonance. The interaction between atoms and the coupling with the Feshbach molecules is modeled using a quantitative separable two-channel model. The scattering phase shift in an atomic waveguide is defined. This permits us to extend the Beth-Uhlenbeck formula for the second-order virial coefficient to this inhomogeneous case.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps.
Finite amplitude instability of second-order fluids in plane Poiseuille flow.
NASA Technical Reports Server (NTRS)
Mcintire, L. V.; Lin, C. H.
1972-01-01
The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.
A second-order pressure-correction method for viscous incompressible flow
NASA Astrophysics Data System (ADS)
Vankan, J.
An ADI scheme with pressure correction which is second order consistent in space and time is presented. It is shown that the pressure correction method in a system of constrained ordinary differential equations under reasonably weak assumptions leads to a solution with 0 (Delta t sq) accuracy. It is proved that in a linearized simplified case pressure correction does not affect the unconditional stability of the underlying scheme. Application to flow in a glass furnace is illustrated.
Second-order Born approximation for the ionization of molecules by electron and positron impact
Dal Cappello, C.; Rezkallah, Z.; Houamer, S.; Charpentier, I.; Hervieux, P. A.; Ruiz-Lopez, M. F.; Dey, R.; Roy, A. C.
2011-09-15
Second-order Born approximation is applied to study the ionization of molecules. The initial and final states are described by single-center wave functions. For the initial state a Gaussian wave function is used while for the ejected electron it is a distorted wave. Results of the present model are compared with recent (e,2e) experiments on the water molecule. Preliminary results are also presented for the ionization of the thymine molecule by electrons and positrons.
Dynamic gain aperture modelocking in picosecond regime based on cascaded second-order nonlinearity.
Mondal, Shyamal; Mukherjee, Shouvik; Singh, Satya Pratap; Rand, Stephen C; Bhattacharya, Sayantan; Das, Amit C; Datta, Prasanta Kumar
2016-07-11
The operation of a cascaded second-order mode-locked Nd:YVO_{4} laser has been investigated considering it as a soft-aperture Kerr lens type and using complex beam parameters. A self consistent complex beam propagation method is used to incorporate the effect of cascaded Kerr nonlinearity on radially varying gain aperturing. The analysis deduces a stable pulsewidth of ~9.5 ps which agrees well with the experimental value of 10.3 ps. PMID:27410804
On the basic equations for the second-order modeling of compressible turbulence
NASA Technical Reports Server (NTRS)
Liou, W. W.; Shih, T.-H.
1991-01-01
Equations for the mean and turbulent quantities for compressible turbulent flows are derived. Both the conventional Reynolds average and the mass-weighted, Favre average were employed to decompose the flow variable into a mean and a turbulent quality. These equations are to be used later in developing second order Reynolds stress models for high speed compressible flows. A few recent advances in modeling some of the terms in the equations due to compressibility effects are also summarized.
Assessment of the second-order perturbative corrections to PNOF5
NASA Astrophysics Data System (ADS)
Piris, M.; Ruipérez, F.; Matxain, J. M.
2014-03-01
In a recent paper (J. Chem. Phys. 139, 064111, 2013), an antisymmetrised product of strongly orthogonal geminals with the expansion coefficients explicitly expressed by means of the occupation numbers was used to generate the Piris natural orbital functional 5 (PNOF5). This functional describes most of the non-dynamical effects, but also an important part of the intrapair (intrageminal) electron correlation. Second-order corrections to the generating PNOF5 wave function were derived using the multiconfigurational perturbation theory size consistent at the second order (SC2-MCPT) to include the missing interpair (intergeminal) electron correlation. A modified version of the SC2-MCPT involving double excitations only from different geminals was introduced and denoted as PNOF5-PT2. In this paper, the ground-state energies of 36 closed-shell species belonging to the G2/97 test set of molecules are studied by the PNOF5-PT2 and PNOF5-SC2-MCPT methods. The numerical performance of both methods on eight dimers, with different strength of hydrogen bonds, and 13 isogyric reactions is also assessed. The results are in reasonable agreement with those obtained using the complete active space second-order perturbation theory and coupled-cluster method with singles, doubles, and noniterative triples corrections.
NASA Astrophysics Data System (ADS)
Sigalotti, L. Di G.; Klapp, J.
1997-03-01
A new second-order Eulerian code is compared with a version of the TREESPH code formulated by Hernquist and Katz (1989) for the standard isothermal collapse test. The results indicate that both codes produce a very similar evolution ending with the formation of a protostellar binary system. Contrary to previous first-order calculations, the binary forms by direct fragmentation, i.e. without the occurrence of an intermediate bar configuration. A similar trend was also found in second-order Eulerian calculations (Myhill and Boss 1993), suggesting that it is a result of the decreased numerical diffusion associated with the new second-order schemes. The results have also implications on the differences between the finite difference methods and the particle method SPH, raised by Monaghan and Lattanzio (1986) for this problem. In particular, the Eulerian calculation does not result in a run-away collapse of the fragments, and as found in the TREESPH evolution, they also show a clear tendency to get closer together. In agreement with previous SPH calculations (Monaghan and Lattanzio 1986), the results of the long term evolution with code TREESPH show that the gravitational interaction between the two fragments may become important, and eventually induce the binary to coalesce. However, SPH calculations by Bate, Bonnell and Price (1995) indicate that the two fragments, after having reached a minimum separation distance, do not merge but continue to orbit each other.
Second-order autoshaped key pecking based on an auditory stimulus.
Burt, J S; Westbrook, R F
1980-11-01
In Experiment 1, pigeons were exposed either to paired or to unpaired presentations of a tone and grain, and then to paired presentations of a keylight with the tone. Substantial second-order conditioned pecking to the keylight was produced in the birds that had received paired presentations of tone and grain. In Experiment 2, second-order pecking to the keylight increased in probability across four groups that had received, respectively, 20, 80, 140, or 200 paired presentations of tone and grain. In Experiment 3, the amount of pecking directed towards a keylight which predicted the first-order, tone CS was as substantial in birds without a prior history of key pecking as in birds with such a history. A further experiment failed to discover any significant differences in the levels of second-order pecking to a keylight paired with a first-order tone CS or with a first-order keylight CS. Thus, an auditory signal that does not itself support pecking may enable a localized visual stimulus to evoke key pecking.
NASA Astrophysics Data System (ADS)
Ahn, Kyoung-Pyo; Ishikawa, Ryo; Saitou, Akira; Honjo, Kazuhiko
This paper describes the characteristic of negative group delay (NGD) circuits for various configurations including first-order, distributed, and second-order RC circuit configurations. This study includes locus, magnitude, and phase characteristics of the NGD circuits. The simplest NGD circuit is available using first-order RC or RL configuration. As an example of distributed circuit configuration, it is verified that losses in a distributed line causes NGD characteristic at higher cut-off band of a coupled four-line bandpass filter. Also, novel wideband NGD circuits using second-order RC configuration, instead of conventional RLC configuration, are proposed. Adding a parallel resistor to a parallel-T filter enables NGD characteristic to it. Also, a Wien-Robinson bridge is modified to have NGD characteristic by controlling the voltage division ratio. They are fabricated on MMIC substrate, and their NGD characteristics are verified with measured results. They have larger insertion loss than multi-stage RLC NGD circuits, however they can realize second-order NGD characteristic without practical implementation of inductors.
Chen, Chao-Yin; Bonham, Ann C; Dean, Caron; Hopp, Francis A; Hillard, Cecilia J; Seagard, Jeanne L
2010-12-01
In prior studies, we found that activation of cannabinoid-1 receptors in the nucleus tractus solitarii (NTS) prolonged baroreflex-induced sympathoinhibition in rats. In many regions of the central nervous system, activation of cannabinoid-1 receptors presynaptically inhibits γ-aminobutyric acid (GABA) release, disinhibiting postsynaptic neurons. To determine if cannabinoid-1 receptor-mediated presynaptic inhibition of GABA release occurs in the NTS, we recorded miniature inhibitory postsynaptic currents in anatomically identified second-order baroreceptive NTS neurons in the presence of ionotropic glutamate receptor antagonists and tetrodotoxin. The cannabinoid-1 receptor agonists, WIN 55212-2 (0.3-30 μM) and methanandamide (3 μM) decreased the frequency of miniature inhibitory postsynaptic currents in a concentration-dependent manner, an effect that was blocked by the cannabinoid-1 receptor antagonist, N-(piperidin-1-yl)-5-(4-iodophenyl)-1-(2,4-dichlorophenyl)-4-methyl-1H-pyrazole-3-carboxamide (AM 251, 5 μM). Importantly, depolarization of second-order baroreceptive neurons decreased the frequency of miniature inhibitory postsynaptic currents; an effect which was blocked by the cannabinoid-1 receptor antagonist. The data indicate that depolarization of second-order baroreceptive NTS neurons induces endocannabinoid release from the neurons, leading to activation of presynaptic cannabinoid-1 receptors, inhibition of GABA release and subsequent enhanced baroreflex signaling in the NTS. The data suggest that endocannabinoid signaling in the NTS regulates short-term synaptic plasticity and provide a mechanism for endocannabinoid modulation of central baroreflex control.
Effects of Second-Order Hydrodynamic Forces on Floating Offshore Wind Turbines
Duarte, T.; Sarmento, A. J. N. A.; Jonkman, J.
2014-04-01
Relative to first-order, second-order wave-excitation loads are known to cause significant motions and additional loads in offshore oil and gas platforms. The design of floating offshore wind turbines was partially inherited from the offshore oil and gas industry. Floating offshore wind concepts have been studied with powerful aero-hydro-servo-elastic tools; however, most of the existing work on floating offshore wind turbines has neglected the contribution of second-order wave-excitation loads. As a result, this paper presents a computationally efficient methodology to consider these loads within FAST, a wind turbine computer-aided engineering tool developed by the National Renewable Energy Laboratory. The method implemented was verified against the commercial OrcaFlex tool, with good agreement, and low computational time. A reference floating offshore wind turbine was studied under several wind and wave load conditions, including the effects of second-order slow-drift and sum-frequency loads. Preliminary results revealed that these loads excite the turbine's natural frequencies, namely the surge and pitch natural frequencies.
Treatment of Second Order Structures of Protein on Medical Equipments Using Oxygen Plasma
NASA Astrophysics Data System (ADS)
Hayashi, Nobuya; Kitazaki, Satoshi; Goto, Masaaki; Yagyu, Yoshihito; Yonesu, Akira
2009-10-01
Removal of proteins from the surface of medical equipments are attempted using an RF plasma. Oxygen gas is introduced into a vacuum chamber with dimensions of 450 mm in length, 200 mm in diameter and 20L of capacity. When an RF power (13.56 MHz, 60W) is applied to an ICP type antenna, oxygen radicals (atomic oxygen and excited oxygen molecule) are produced below the antenna. The characteristics of removing protein from the medical equipments was investigated using casein and heat-resistive keratin proteins. Initial concentration of the proteins on a CaF2 substrate is several mg/cm2. The treatment effect of proteins is determined by the peak height of chemical bonds in amide and second order structures appeared on FTIR spectra. The second order structure of a protein such as alpha-helix and beta-sheet are decomposed with the treatment period. Complete treatment of proteins including the second order structure requires several hours avoiding the damage to medical equipments.
Second-order estimates for the effective behaviour of viscoplastic polycrystalline materials
NASA Astrophysics Data System (ADS)
Bornert, M.; Masson, R.; Castañeda, P. Ponte; Zaoui, A.
2001-11-01
This paper is concerned with the application of the "second-order" nonlinear homogenisation procedure (Ponte Castañeda, J. Mech. Phys. Solids 44 (6) (1996) 827) to generate estimates of the self-consistent type for the effective behaviour of fcc and hcp viscoplastic polycrystals. The method has the distinctive property that it leads to estimates that are exact to second-order in the heterogeneity contrast, and which are expected to be more accurate, particularly when compared to rigorous bounds, than those resulting from earlier homogenisation schemes such as the Hill "incremental" method or its "total" formulation (Hutchinson) for pure power-law viscous materials. Special attention is paid to large grain anisotropy leading to correspondingly large heterogeneity contrast, and to highly nonlinear behaviour. Comparisons are also carried out with estimates derived from other more recent homogenisation schemes such as the "tangent" and "affine" methods. The results, illustrated for zirconium- and ice-type polycrystals, show that the second-order procedure offers the potential for significantly improved results, at least relative to the Hill incremental formulation.
Effect of Second-Order Hydrodynamics on Floating Offshore Wind Turbines: Preprint
Roald, L.; Jonkman, J.; Robertson, A,; Chokani, N.
2013-07-01
Offshore winds are generally stronger and more consistent than winds on land, making the offshore environment attractive for wind energy development. A large part of the offshore wind resource is however located in deep water, where floating turbines are the only economical way of harvesting the energy. The design of offshore floating wind turbines relies on the use of modeling tools that can simulate the entire coupled system behavior. At present, most of these tools include only first-order hydrodynamic theory. However, observations of supposed second-order hydrodynamic responses in wave-tank tests performed by the DeepCwind consortium suggest that second-order effects might be critical. In this paper, the methodology used by the oil and gas industry has been modified to apply to the analysis of floating wind turbines, and is used to assess the effect of second-order hydrodynamics on floating offshore wind turbines. The method relies on combined use of the frequency-domain tool WAMIT and the time-domain tool FAST. The proposed assessment method has been applied to two different floating wind concepts, a spar and a tension-leg-platform (TLP), both supporting the NREL 5-MW baseline wind turbine. Results showing the hydrodynamic forces and motion response for these systems are presented and analysed, and compared to aerodynamic effects.
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Imtiaz, Maria; Alsaedi, Ahmed
2015-12-01
This paper addresses the steady three-dimensional boundary layer flow of viscous nanofluid. The flow is caused by a permeable stretching surface with second order velocity slip and homogeneous-heterogeneous reactions. Water is treated as base fluid and copper as nanoparticle. An incompressible fluid fills the porous space. The fluid is electrically conducting in the presence of an applied magnetic field. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived. Impact of various pertinent parameters on the velocity, concentration and skin friction coefficient is discussed. Analysis of the obtained results shows that the flow field is influenced appreciably by the presence of velocity slip parameters. Also concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.
Thellamurege, Nandun M; Si, Dejun; Cui, Fengchao; Li, Hui
2014-05-01
A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.
Wang, Jing; Zhu, Shijun; Wang, Haiyan; Cai, Yangjian; Li, Zhenhua
2016-05-30
Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications. PMID:27410089
The Cauchy problem of scalar tensor theories of gravity
NASA Astrophysics Data System (ADS)
Salgado, Marcelo
2006-07-01
The 3 + 1 formulation of scalar tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4 + 0 covariant field equations. Contrary to common belief (folklore), the new system of ADM-like equations shows that the Cauchy problem of STT is well formulated (in the sense that the whole system of evolution equations is of first order in the time derivative). This is the first step towards a full first-order (in time and space) formulation from which a subsequent hyperbolicity analysis (a well-posedness determination) can be performed. Several gauge (lapse and shift) conditions are considered and implemented for STT. In particular, a generalization of the harmonic gauge for STT allows us to prove the well posedness of the STT using a second-order analysis which is very similar to the one employed in general relativity. Several appendices complement the ideas of the main part of the paper.
Ethanol Self-Administration in Mice under a Second-Order Schedule
Lamb, Richard J.; Pinkston, Jonathan W.; Ginsburg, Brett C.
2015-01-01
Long Fixed-Interval (FI) schedules, particularly second-order schedules, can engender substantial responding before drug or ethanol delivery that is uninfluenced by the direct effects of the drug or ethanol. Thus, these schedules can be used to study the effects of medications upon drug- or ethanol-seeking, uninfluenced by the direct effects of the self-administered drug or ethanol. Long FI second-order schedules are frequently used in primates and occasionally in rats. Under second-order schedules, completion of one response requirement, e.g., a Fixed Ratio 10 (FR10:S), produces a brief stimulus presentation, e.g., a 1-sec 80-dB 4-kHZ tone, and this FR10:S serves as the response unit under another schedule, e.g., a FI 1800-sec. Thus, the first FR10 completed after 1800 sec would result in delivery both of the tone and of reinforcement, e.g., 10 × 0.01 mL 16% (w/v) ethanol. To examine if such schedules could be effectively used in mice, which have advantages in neurobiological and genetic studies, we trained eight C57BL/6J mice to respond under the schedule just described. This schedule maintained substantial responding. The temporal pattern of behavior was typical of an FI schedule with responding accelerating across the interval. We also examined the effects of acute and chronic administration of fluvoxamine on this responding, and these were modest. Finally, we examined responding when alcohol and/or tone deliveries were withheld, and found that extinction occurred most rapidly when both were withheld. This work demonstrates that long FI schedules of ethanol delivery may be useful in studying ethanol seeking in mice. PMID:26254963
NASA Astrophysics Data System (ADS)
Di G. Sigalotti, L.; Klapp, J.
1997-03-01
A new second-order Eulerian code is compared with a version of the TREESPH code formulated by Hernquist & Katz (1989ApJS...70..419H) for the standard isothermal collapse test. The results indicate that both codes produce a very similar evolution ending with the formation of a protostellar binary system. Contrary to previous first-order calculations, the binary forms by direct fragmentation, i.e., without the occurrence of an intermediate bar configuration. A similar trend was also found in recent second-order Eulerian calculations (Myhill & Boss 1993ApJS...89..345M), suggesting that it is a result of the decreased numerical diffusion associated with the new second-order schemes. The results have also implications on the differences between the finite difference methods and the particle method SPH, raised by Monaghan & Lattanzio (1986A&A...158..207M) for this problem. In particular, the Eulerian calculation does not result in a run-away collapse of the fragments, and as found in the TREESPH evolution, they also show a clear tendency to get closer together. In agreement with previous SPH calculations (Monaghan & Lattanzio 1986A&A...158..207M), the results of the long term evolution with code TREESPH show that the gravitational interaction between the two fragments may become important, and eventually induce the binary to coalesce. However, most recent SPH calculations (Bate, Bonnell & Price 1995MNRAS.277..362B ) indicate that the two fragments, after having reached a minimum separation distance, do not merge but continue to orbit each other.
NASA Astrophysics Data System (ADS)
Ren, Xinguo; Rinke, Patrick; Scuseria, Gustavo E.; Scheffler, Matthias
2013-07-01
We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as ``renormalization'' of the second-order direct, exchange, and single-excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on a KS reference. In this work, we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well-balanced performance [J. Paier , New J. Phys.1367-263010.1088/1367-2630/14/4/043002 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to noncovalent interactions, including the rare-gas dimers, and the S22 and S66 test sets, as well as the cohesive energy of small copper clusters, and the equilibrium geometry of 10 diatomic molecules. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different electronic situations, and is a promising step towards a generally applicable electronic-structure approach.
Robustness improvement of hyperspectral image unmixing by spatial second-order regularization.
Bauer, Sebastian; Stefan, Johannes; Michelsburg, Matthias; Laengle, Thomas; León, Fernando Puente
2014-12-01
The acquisition of hundreds of images of a scene, each at a different wavelength, is known as hyperspectral imaging. This high amount of data allows the extraction of much more information from hyperspectral images compared with conventional color images. The forward-looking imaging approach emerged from remote sensing, but is still not very widespread in industrial and other practical applications. Spectral unmixing, in particular, aims at the determination of the components present in a scene as well as the abundance to which each component contributes. This information is valuable, for instance, when discrimination tasks are to be performed. Involving not only spectral, but also spatial information was found to have the potential to improve the unmixing results. Several publications use spatial first-order regularization (closely related to the total variation approach) to incorporate this spatial information. Like in classical image processing, this approach favors piecewise constant pixel transitions. This is why it was proposed in the literature to use second-order regularization instead of first order to approach piecewise-linear transitions. Therefore, we introduce Hessian-based regularization to hyperspectral unmixing and propose an algorithm to calculate the regularized result. We use simulated data and images measured in our laboratory to show that both the first- and second-order approaches share many properties and produce similar results. The second-order approach, however, is more robust and thus more accurate in finding the minimum. Both methods smoothen the images in the case of supervised unmixing (i.e., the component spectra are known beforehand) and enhance unsupervised unmixing (when the spectra are not known).
NASA Astrophysics Data System (ADS)
Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng
2016-09-01
In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we firstly propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML (ADEPML). Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: 1) For an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; 2) Unlike the M-PML with high-order damping profile, the M-PML with 2nd-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; 3) In an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with 2nd-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.
Enhancing second-order conditioning with lesions of the basolateral amygdala.
Holland, Peter C
2016-04-01
Because the occurrence of primary reinforcers in natural environments is relatively rare, conditioned reinforcement plays an important role in many accounts of behavior, including pathological behaviors such as the abuse of alcohol or drugs. As a result of pairing with natural or drug reinforcers, initially neutral cues acquire the ability to serve as reinforcers for subsequent learning. Accepting a major role for conditioned reinforcement in everyday learning is complicated by the often-evanescent nature of this phenomenon in the laboratory, especially when primary reinforcers are entirely absent from the test situation. Here, I found that under certain conditions, the impact of conditioned reinforcement could be extended by lesions of the basolateral amygdala (BLA). Rats received first-order Pavlovian conditioning pairings of 1 visual conditioned stimulus (CS) with food prior to receiving excitotoxic or sham lesions of the BLA, and first-order pairings of another visual CS with food after that surgery. Finally, each rat received second-order pairings of a different auditory cue with each visual first-order CS. As in prior studies, relative to sham-lesioned control rats, lesioned rats were impaired in their acquisition of second-order conditioning to the auditory cue paired with the first-order CS that was trained after surgery. However, lesioned rats showed enhanced and prolonged second-order conditioning to the auditory cue paired with the first-order CS that was trained before amygdala damage was made. Implications for an enhanced role for conditioned reinforcement by drug-related cues after drug-induced alterations in neural plasticity are discussed. (PsycINFO Database Record PMID:26795578
Ethanol self-administration in mice under a second-order schedule.
Lamb, Richard J; Pinkston, Jonathan W; Ginsburg, Brett C
2015-09-01
Long Fixed-Interval (FI) schedules, particularly second-order schedules, can engender substantial responding before drug or ethanol delivery that is uninfluenced by the direct effects of the drug or ethanol. Thus, these schedules can be used to study the effects of medications upon drug- or ethanol-seeking, uninfluenced by the direct effects of the self-administered drug or ethanol. Long FI second-order schedules are frequently used in primates and occasionally in rats. Under second-order schedules, completion of one response requirement, e.g., a Fixed Ratio 10 (FR10:S), produces a brief stimulus presentation, e.g., a 1-s 80-dB 4-kHZ tone, and this FR10:S serves as the response unit under another schedule, e.g., an FI 1800-s. Thus, the first FR10 completed after 1800 s would result in delivery both of the tone and of reinforcement, e.g., 10 × 0.01 mL 16% (w/v) ethanol. To examine if such schedules could be effectively used in mice, which have advantages in neurobiological and genetic studies, we trained eight C57BL/6J mice to respond under the schedule just described. This schedule maintained substantial responding. The temporal pattern of behavior was typical of an FI schedule with responding accelerating across the interval. We also examined the effects of acute and chronic administration of fluvoxamine on this responding, and these were modest. Finally, we examined responding when alcohol and/or tone deliveries were withheld, and found that extinction occurred most rapidly when both were withheld. This work demonstrates that long FI schedules of ethanol delivery may be useful in studying ethanol seeking in mice.
Comparison of Second-Order Loads on a Semisubmersible Floating Wind Turbine: Preprint
Gueydon, S.; Duarte, T.; Jonkman, J.; Bayati, I.; Sarmento, A.
2014-03-01
As offshore wind projects move to deeper waters, floating platforms become the most feasible solution for supporting the turbines. The oil and gas industry has gained experience with floating platforms that can be applied to offshore wind projects. This paper focuses on the analysis of second-order wave loading on semisubmersible platforms. Semisubmersibles, which are being chosen for different floating offshore wind concepts, are particularly prone to slow-drift motions. The slack catenary moorings usually result in large natural periods for surge and sway motions (more than 100 s), which are in the range of the second-order difference-frequency excitation force. Modeling these complex structures requires coupled design codes. Codes have been developed that include turbine aerodynamics, hydrodynamic forces on the platform, restoring forces from the mooring lines, flexibility of the turbine, and the influence of the turbine control system. In this paper two different codes are employed: FAST, which was developed by the National Renewable Energy Laboratory, and aNySIM, which was developed by the Maritime Research Institute Netherlands. The hydrodynamic loads are based on potential-flow theory, up to the second order. Hydrodynamic coefficients for wave excitation, radiation, and hydrostatic forces are obtained with two different panel codes, WAMIT (developed by the Massachusetts Institute of Technology) and DIFFRAC (developed by MARIN). The semisubmersible platform, developed for the International Energy Agency Wind Task 30 Offshore Code Comparison Collaboration Continuation project is used as a reference platform. Irregular waves are used to compare the behavior of this platform under slow-drift excitation loads. The results from this paper highlight the effects of these loads on semisubmersible-type platforms, which represent a promising solution for the commercial development of the offshore deepwater wind resource.
Second-order Poisson-Nernst-Planck solver for ion transport
NASA Astrophysics Data System (ADS)
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
2011-06-01
The Poisson-Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second-order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are
Nontrivial Bloch oscillations in waveguide arrays with second-order coupling.
Wang, Gang; Huang, Ji Ping; Yu, Kin Wah
2010-06-01
Under the influence of the next-nearest-neighbor interaction, we theoretically investigate the occurrence of Bloch oscillations in zigzag waveguide arrays. Because of the special topological configuration of the lattice itself, the second-order coupling (SOC) can be enhanced significantly and leads to the band alteration beyond the nearest-neighbor model, i.e., the offset of minimum value from the band edge. Contrary to the behavior in the vanishing SOC, the oscillation patterns exhibit new features, namely, a double turning-back occurs when the beam approaches the band edge. Our results can be applied to some ordered-lattice systems.
An invariant asymptotic formula for solutions of second-order linear ODE's
NASA Technical Reports Server (NTRS)
Gingold, H.
1988-01-01
An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).
Kim, Sungho; Du, Chao; Sheridan, Patrick; Ma, Wen; Choi, ShinHyun; Lu, Wei D
2015-03-11
Memristors have been extensively studied for data storage and low-power computation applications. In this study, we show that memristors offer more than simple resistance change. Specifically, the dynamic evolutions of internal state variables allow an oxide-based memristor to exhibit Ca(2+)-like dynamics that natively encode timing information and regulate synaptic weights. Such a device can be modeled as a second-order memristor and allow the implementation of critical synaptic functions realistically using simple spike forms based solely on spike activity. PMID:25710872
Kohn–Sham exchange-correlation potentials from second-order reduced density matrices
Cuevas-Saavedra, Rogelio; Staroverov, Viktor N.; Ayers, Paul W.
2015-12-28
We describe a practical algorithm for constructing the Kohn–Sham exchange-correlation potential corresponding to a given second-order reduced density matrix. Unlike conventional Kohn–Sham inversion methods in which such potentials are extracted from ground-state electron densities, the proposed technique delivers unambiguous results in finite basis sets. The approach can also be used to separate approximately the exchange and correlation potentials for a many-electron system for which the reduced density matrix is known. The algorithm is implemented for configuration-interaction wave functions and its performance is illustrated with numerical examples.
A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes
NASA Technical Reports Server (NTRS)
Carpenter, Russell; Lee, Taesul
2008-01-01
Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.
Reconstruction of discontinuous parameters in a second order impedance boundary operator
NASA Astrophysics Data System (ADS)
Chaabane, S.; Charfi, B.; Haddar, H.
2016-10-01
We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Kohn-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of an unknown number of discontinuity points.
Solution of second order quasi-linear boundary value problems by a wavelet method
Zhang, Lei; Zhou, Youhe; Wang, Jizeng
2015-03-10
A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.
Second-order bosonic Kadanoff-Baym equations for plasmon-accompanied optical absorption
NASA Astrophysics Data System (ADS)
Schüler, Michael; Pavlyukh, Yaroslav
2016-03-01
The availability of ultra-short and strong light sources opens the door for a variety of new experiments such as transient absorption, where optical properties of systems can be studied in extreme nonequilibrium situations. The nonequilibrium Green's function formalism is an efficient approach to investigate these processes theoretically. Here we apply the method to the light-matter interaction of the magnesium 2p core level accompanied by electron-plasmon interaction due to collective excitations in the conduction band. The plasmons are described as massive bosonic quasi-particle excitations, leading to a second-order equations of motion, requiring a new approach for their propagation.
Second-order Bragg gratings in single-mode chalcogenide fibres
Bernier, M; Asatryan, K E; Vallee, R; Galstian, T M; Vasil'ev, Sergei A; Medvedkov, O I; Plotnichenko, V G; Gnusin, P I; Dianov, Evgenii M
2011-05-31
Bragg gratings with a second-order resonance wavelength in the near-IR spectral region have been inscribed into single-mode chalcogenide (As{sub 2}S{sub 3}) glass fibre by a He - Ne laser beam using a configuration typical of Bragg grating fabrication in germanosilicate fibre, with the use of a phase mask that ensures effective diffraction of the writing light into the +1 and -1 orders. The spectra of the inscribed gratings show no resonances due to cladding mode excitation because the cladding material is photosensitive. (fibre optics)
Second-order nonlinear optical susceptibilities of AIIBVI and AIIIBV semiconductors
NASA Astrophysics Data System (ADS)
Kumar, V.; Sinha, Anita; Singh, B. P.; Chandra, S.
2016-10-01
The second-order nonlinear optical (NLO) susceptibilities χ123(2) of AIIBVI and AIIIBV groups of semiconductors with zincblende (ZB) structure have been studied. Two relations have been proposed for the calculation of χ123(2) (0) at zero frequency. One is based on bond charge model of Levine and the other is based on plasma oscillations theory of solids. Calculated values of χ123(2) (0) for all compounds are in fair agreement with the available experimental and reported values.
NASA Astrophysics Data System (ADS)
Umezawa, Hirohito; Jackson, Matthew; Lebel, Olivier; Nunzi, Jean-Michel; Sabat, Ribal Georges
2016-10-01
The second-order nonlinear optical coefficients of thin films of mexylaminotriazine-functionalized azobenzene molecular glass derivatives were measured using second harmonic generation. The thin films were poled using a custom corona poling set-up and the second harmonic light from a pulsed 1064-nm laser was detected. Four out of the six tested compounds showed optical nonlinearity and a maximum coefficient of 75 pm/V was obtained. The time dependence of the nonlinear coefficients was studied under ambient light and under dark; the second harmonic generation intensity stayed constant for thiazole-containing derivatives while a significant decay was measured for the other compounds.
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Tetikoglu, Fatih Sabahattin
2015-09-01
In this study, the Green's function of the second order differential operator Ax defined by the formula Axu =-a (x )ux x(x )+δ u (x ), δ ≥0 , a (x )=a (x +2 π ), x ∈ℝ1 with domain D (Ax)={ u (x ):u (x ),u '(x ),u″(x )∈C (ℝ1),u (x )=u (x +2 π ), x ∈ℝ1,∫0 2 π u (x )d x =0 } is presented. The estimates for the Green's function and it's derivative are obtained. The positivity of the operator Ax is proved.
The decoupling of second-order linear systems with a singular mass matrix
NASA Astrophysics Data System (ADS)
Kawano, Daniel T.; Morzfeld, Matthias; Ma, Fai
2013-12-01
It was demonstrated in earlier work that a nondefective, linear dynamical system with an invertible mass matrix in free or forced motion may be decoupled in the configuration space by a real and isospectral transformation. We extend this work by developing a procedure for decoupling a linear dynamical system with a singular mass matrix in the configuration space, transforming the original differential-algebraic system into decoupled sets of real, independent, first- and second-order differential equations. Numerical examples are provided to illustrate the application of the decoupling procedure.
Second-order time delay by a radially moving Kerr-Newman black hole
NASA Astrophysics Data System (ADS)
He, Guansheng; Lin, Wenbin
2016-09-01
We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Schäfer's formulation which is based on the retarded Liénard-Wiechert potential.
Ultra-fast digital holography of the femto-second order
NASA Astrophysics Data System (ADS)
Zhai, Hongchen; Wang, Xiaolei; Mu, Guoguang
2007-01-01
We report on pulsed digital micro holographic systems recording ultra-fast process of the femto-second order, by spatially angular division multiplexing (SADM) and wavelength division multiplexing (WDM), respectively. Both intensity and phase images of the digitally reconstructed images are obtained through Fourier transformation and digital filtering, which show clearly the plasma forming and propagating dynamic process of laser induced ionization of ambient air at the wavelength of 800 nm, with a time resolution of 50 fs and frame intervals of 300 to 550 fs.
Kim, Sungho; Du, Chao; Sheridan, Patrick; Ma, Wen; Choi, ShinHyun; Lu, Wei D
2015-03-11
Memristors have been extensively studied for data storage and low-power computation applications. In this study, we show that memristors offer more than simple resistance change. Specifically, the dynamic evolutions of internal state variables allow an oxide-based memristor to exhibit Ca(2+)-like dynamics that natively encode timing information and regulate synaptic weights. Such a device can be modeled as a second-order memristor and allow the implementation of critical synaptic functions realistically using simple spike forms based solely on spike activity.
Treatment Characteristics of Second Order Structure of Proteins Using Low-Pressure Oxygen RF Plasma
NASA Astrophysics Data System (ADS)
Hayashi, Nobuya; Nakahigashi, Akari; Kawaguchi, Ryutaro; Goto, Masaaki
2010-10-01
Removal of proteins from the surface of medical equipments is attempted using oxygen plasma produced by RF discharge. FTIR spectra indicate that the bonding of C-H and N-H in the casein protein is reduced after irradiation of oxygen plasma. Also, the second order structure of a protein such as α-helix and β-sheet are modified by the oxygen plasma. Complete removal of casein protein with the concentration of 0.016 mg/cm2 that is equivalent to remnants on the medical equipment requires two hours avoiding the damage to medical equipments.
Treatment Characteristics of Second Order Structure of Proteins Using Low-Pressure Oxygen RF Plasma
Hayashi, Nobuya; Nakahigashi, Akari; Kawaguchi, Ryutaro; Goto, Masaaki
2010-10-13
Removal of proteins from the surface of medical equipments is attempted using oxygen plasma produced by RF discharge. FTIR spectra indicate that the bonding of C-H and N-H in the casein protein is reduced after irradiation of oxygen plasma. Also, the second order structure of a protein such as {alpha}-helix and {beta}-sheet are modified by the oxygen plasma. Complete removal of casein protein with the concentration of 0.016 mg/cm{sup 2} that is equivalent to remnants on the medical equipment requires two hours avoiding the damage to medical equipments.
Thermal poling induced second-order nonlinearity in femtosecond- laser-modified fused silica
An Honglin; Fleming, Simon; McMillen, Benjamin W.; Chen, Kevin P.; Snoke, David
2008-08-11
Thermal poling was utilized to induce second-order nonlinearity in regions of fused silica modified by 771 nm femtosecond laser pulses. With second-harmonic microscopy, it was found that the nonlinearity in the laser-modified region was much lower than that in nonmodified regions. This is attributed to a more rigid glass network after irradiation by the femtosecond laser pulses and/or lack of mobile alkali ions. Measurement of the distribution of chemical elements in the femtosecond-laser-modified region in a soda lime glass revealed a lower level of sodium ions.
Analysis and design of a second-order digital phase-locked loop
NASA Technical Reports Server (NTRS)
Blasche, P. R.
1979-01-01
A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.
Effect of Second-Order Hydrodynamics on a Floating Offshore Wind Turbine
Roald, L.; Jonkman, J.; Robertson, A.
2014-05-01
The design of offshore floating wind turbines uses design codes that can simulate the entire coupled system behavior. At the present, most codes include only first-order hydrodynamics, which induce forces and motions varying with the same frequency as the incident waves. Effects due to second- and higher-order hydrodynamics are often ignored in the offshore industry, because the forces induced typically are smaller than the first-order forces. In this report, first- and second-order hydrodynamic analysis used in the offshore oil and gas industry is applied to two different wind turbine concepts--a spar and a tension leg platform.
Non-iterative local second order Møller-Plesset theory
NASA Astrophysics Data System (ADS)
Maslen, P. E.; Head-Gordon, M.
1998-01-01
Second order Møller-Plesset perturbation theory (MP2) is formulated in terms of atom-centred occupied and virtual orbitals. Both the occupied and the virtual orbitals are non-orthogonal. A new parameter-free atoms-in-molecules local approximation is employed to reduce the cost of the calculation to cubic scaling, and a quasi-canonical two-particle basis is introduced to enable the solution of the local MP2 equations via explicit matrix diagonalisation rather than iteration.
Second-order shaped pulsed for solid-state quantum computation
Sengupta, Pinaki
2008-01-01
We present the construction and detailed analysis of highly optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semianalytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analyzing several composite pulses designed to protect against pulse amplitude errors, and on decoupling sequences for potentially long chains of qubits with on-site and nearest-neighbor couplings.
Fast curvature matrix-vector products for second-order gradient descent.
Schraudolph, Nicol N
2002-07-01
We propose a generic method for iteratively approximating various second-order gradient steps - Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient - in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this approach. Since both were originally derived by very different routes, this offers fresh insight into their operation, resulting in further improvements to SMD.
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
2014-03-21
We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with χ{sub eff}{sup (2)} ∼ 0.6 pm V{sup −1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
Assessment of Patellar Tendon Reflex Responses Using Second-Order System Characteristics
Steineman, Brett D.; Karra, Pavan; Park, Kiwon
2016-01-01
Deep tendon reflex tests, such as the patellar tendon reflex (PTR), are widely accepted as simple examinations for detecting neurological disorders. Despite common acceptance, the grading scales remain subjective, creating an opportunity for quantitative measures to improve the reliability and efficacy of these tests. Previous studies have demonstrated the usefulness of quantified measurement variables; however, little work has been done to correlate experimental data with theoretical models using entire PTR responses. In the present study, it is hypothesized that PTR responses may be described by the exponential decay rate and damped natural frequency of a theoretical second-order system. Kinematic data was recorded from both knees of 45 subjects using a motion capture system and correlation analysis found that the mean R2 value was 0.99. Exponential decay rate and damped natural frequency ranges determined from the sample population were −5.61 to −1.42 and 11.73 rad/s to 14.96 rad/s, respectively. This study confirmed that PTR responses strongly correlate to a second-order system and that exponential decay rate and undamped natural frequency are novel measurement variables to accurately measure PTR responses. Therefore, further investigation of these measurement variables and their usefulness in grading PTR responses is warranted. PMID:27041981
Accuracy of second order perturbation theory in the polaron and variational polaron frames
NASA Astrophysics Data System (ADS)
Lee, Chee Kong; Moix, Jeremy; Cao, Jianshu
2012-05-01
In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.
Transport coefficients in second-order non-conformal viscous hydrodynamics
NASA Astrophysics Data System (ADS)
Ryblewski, Radoslaw
2015-05-01
Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory.
Second-Order Controllability of Multi-Agent Systems with Multiple Leaders
NASA Astrophysics Data System (ADS)
Liu, Bo; Shi, Yun-Tao; Su, Hou-Sheng; Han, Xiao
2016-05-01
This paper proposes a new second-order continuous-time multi-agent model and analyzes the controllability of second-order multi-agent system with multiple leaders based on the asymmetric topology. This paper considers the more general case: velocity coupling topology is different from location coupling topology. Some sufficient and necessary conditions are presented for the controllability of the system with multiple leaders. In addition, the paper studies the controllability of the system with velocity damping gain. Simulation results are given to illustrate the correctness of theoretical results. Supported by the National Natural Science Foundation of China under Grant Nos. 61473129, 61304049, 61104140, 61473002, the Beijing Natural Science Foundation Program under Grant No. 4132021, the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215, “The-Great-Wall-Scholar” Candidate Training-Plan of North China University of Technology (NX130), and the Plan Training Project of Excellent Young Teacher of North China University of Technology (NX132), the Fundamental Research Funds for the Central Universities, (HUST: Grant No. 2015TS025), the Fundamental Research Funds for the Central Universities (WUT: Grant No. 2015VI015)
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
Analysis of heart rate variability signal in meditation using second-order difference plot
NASA Astrophysics Data System (ADS)
Goswami, Damodar Prasad; Tibarewala, Dewaki Nandan; Bhattacharya, Dilip Kumar
2011-06-01
In this article, the heart rate variability signal taken from subjects practising different types of meditations have been investigated to find the underlying similarity among them and how they differ from the non-meditative condition. Four different groups of subjects having different meditation techniques are involved. The data have been obtained from the Physionet and also collected with our own ECG machine. For data analysis, the second order difference plot is applied. Each of the plots obtained from the second order differences form a single cluster which is nearly elliptical in shape except for some outliers. In meditation, the axis of the elliptical cluster rotates anticlockwise from the cluster formed from the premeditation data, although the amount of rotation is not of the same extent in every case. This form study reveals definite and specific changes in the heart rate variability of the subjects during meditation. All the four groups of subjects followed different procedures but surprisingly the resulting physiological effect is the same to some extent. It indicates that there is some commonness among all the meditative techniques in spite of their apparent dissimilarity and it may be hoped that each of them leads to the same result as preached by the masters of meditation. The study shows that meditative state has a completely different physiology and that it can be achieved by any meditation technique we have observed. Possible use of this tool in clinical setting such as in stress management and in the treatment of hypertension is also mentioned.
Seeing the unseen: Second-order correlation learning in 7- to 11-month-olds.
Yermolayeva, Yevdokiya; Rakison, David H
2016-07-01
We present four experiments with the object-examining procedure that investigated 7-, 9-, and 11-month-olds' ability to associate two object features that were never presented simultaneously. In each experiment, infants were familiarized with a number of 3D objects that incorporated different correlations among the features of those objects and the body of the objects (e.g., Part A and Body 1, and Part B and Body 1). Infants were then tested with objects with a novel body that either possessed both of the parts that were independently correlated with one body during familiarization (e.g., Part A and B on Body 3) or that were attached to two different bodies during familiarization. The experiments demonstrate that infants as young as 7months of age are capable of this kind of second-order correlation learning. Furthermore, by at least 11months of age infants develop a representation for the object that incorporates both of the features they experienced during training. We suggest that the ability to learn second-order correlations represents a powerful but as yet largely unexplored process for generalization in the first years of life.
A second order residual based predictor-corrector approach for time dependent pollutant transport
NASA Astrophysics Data System (ADS)
Pavan, S.; Hervouet, J.-M.; Ricchiuto, M.; Ata, R.
2016-08-01
We present a second order residual distribution scheme for scalar transport problems in shallow water flows. The scheme, suitable for the unsteady cases, is obtained adapting to the shallow water context the explicit Runge-Kutta schemes for scalar equations [1]. The resulting scheme is decoupled from the hydrodynamics yet the continuity equation has to be considered in order to respect some important numerical properties at discrete level. Beyond the classical characteristics of the residual formulation presented in [1,2], we introduce the possibility to iterate the corrector step in order to improve the accuracy of the scheme. Another novelty is that the scheme is based on a precise monotonicity condition which guarantees the respect of the maximum principle. We thus end up with a scheme which is mass conservative, second order accurate and monotone. These properties are checked in the numerical tests, where the proposed approach is also compared to some finite volume schemes on unstructured grids. The results obtained show the interest in adopting the predictor-corrector scheme for pollutant transport applications, where conservation of the mass, monotonicity and accuracy are the most relevant concerns.
Increasing returns to scale: The solution to the second-order social dilemma
Ye, Hang; Chen, Shu; Luo, Jun; Tan, Fei; Jia, Yongmin; Chen, Yefeng
2016-01-01
Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms. PMID:27535087
NASA Astrophysics Data System (ADS)
Castro Díaz, M. J.; Fernández-Nieto, E. D.; Narbona-Reina, G.; de la Asunción, M.
2014-04-01
In this work we propose a second order flux limiter finite volume method, named PVM-2U-FL, that only uses information of the two external waves of the hyperbolic system. This method could be seen as a natural extension of the well known WAF method introduced by E.F. Toro in [23]. We prove that independently of the number of unknowns of the 1D system, it recovers the second order accuracy at regular zones, while in presence of discontinuities, the scheme degenerates to PVM-2U method, which can be seen as an improvement of the HLL method (see [6,10]). Another interesting property of the method is that it does not need any spectral decomposition of the Jacobian or Roe matrix associated to the flux function. Therefore, it can be easily applied to systems with a large number of unknowns or in situations where no analytical expression of the eigenvalues or eigenvectors are known. In this work, we apply the proposed method to magnetohydrodynamics and to stratified multilayer flows. Comparison with the two-waves WAF and HLL-MUSCL methods are also presented. The numerical results show that PVM-2U-FL is the most efficient and accurate among them.
Seeing the unseen: Second-order correlation learning in 7- to 11-month-olds.
Yermolayeva, Yevdokiya; Rakison, David H
2016-07-01
We present four experiments with the object-examining procedure that investigated 7-, 9-, and 11-month-olds' ability to associate two object features that were never presented simultaneously. In each experiment, infants were familiarized with a number of 3D objects that incorporated different correlations among the features of those objects and the body of the objects (e.g., Part A and Body 1, and Part B and Body 1). Infants were then tested with objects with a novel body that either possessed both of the parts that were independently correlated with one body during familiarization (e.g., Part A and B on Body 3) or that were attached to two different bodies during familiarization. The experiments demonstrate that infants as young as 7months of age are capable of this kind of second-order correlation learning. Furthermore, by at least 11months of age infants develop a representation for the object that incorporates both of the features they experienced during training. We suggest that the ability to learn second-order correlations represents a powerful but as yet largely unexplored process for generalization in the first years of life. PMID:27038738
Increasing returns to scale: The solution to the second-order social dilemma.
Ye, Hang; Chen, Shu; Luo, Jun; Tan, Fei; Jia, Yongmin; Chen, Yefeng
2016-01-01
Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms.
Fast and efficient second-order method for training radial basis function networks.
Xie, Tiantian; Yu, Hao; Hewlett, Joel; Rózycki, Paweł; Wilamowski, Bogdan
2012-04-01
This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.