The optical analogy for vector fields

NASA Technical Reports Server (NTRS)

Parker, E. N. (Editor)

1991-01-01

This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.

How random is a random vector?

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2015-12-01

Over 80 years ago Samuel Wilks proposed that the "generalized variance" of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the "Wilks standard deviation" -the square root of the generalized variance-is indeed the standard deviation of a random vector. We further establish that the "uncorrelation index" -a derivative of the Wilks standard deviation-is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: "randomness measures" and "independence indices" of random vectors. In turn, these general notions give rise to "randomness diagrams"-tangible planar visualizations that answer the question: How random is a random vector? The notion of "independence indices" yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

Antisymmetric tensor generalizations of affine vector fields.

PubMed

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

Vector models and generalized SYK models

DOE PAGES

Peng, Cheng

2017-05-23

Here, we consider the relation between SYK-like models and vector models by studying a toy model where a tensor field is coupled with a vector field. By integrating out the tensor field, the toy model reduces to the Gross-Neveu model in 1 dimension. On the other hand, a certain perturbation can be turned on and the toy model flows to an SYK-like model at low energy. Furthermore, a chaotic-nonchaotic phase transition occurs as the sign of the perturbation is altered. We further study similar models that possess chaos and enhanced reparameterization symmetries.

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

Stable solutions of inflation driven by vector fields

NASA Astrophysics Data System (ADS)

Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li

2017-03-01

Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.

Representation and display of vector field topology in fluid flow data sets

NASA Technical Reports Server (NTRS)

Helman, James; Hesselink, Lambertus

1989-01-01

The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.

Cosmology in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.

Diffeomorphism invariance and black hole entropy

NASA Astrophysics Data System (ADS)

Huang, Chao-Guang; Guo, Han-Ying; Wu, Xiaoning

2003-11-01

The Noether-charge and the Hamiltonian realizations for the diff(M) algebra in diffeomorphism-invariant gravitational theories without a cosmological constant in any dimension are studied in a covariant formalism. We analyze how the Hamiltonian functionals form the diff(M) algebra under the Poisson brackets and show how the Noether charges with respect to the diffeomorphism generated by the vector fields and their variations in n-dimensional general relativity form this algebra. The asymptotic behaviors of vector fields generating diffeomorphism of the manifold with boundaries are discussed. It is shown that the “central extension” for a large class of vector fields is always zero on the Killing horizon. We also check whether choosing the vector fields near the horizon may pick up the Virasoro algebra. The conclusion is unfortunately negative in any dimension.

Field Computation and Nonpropositional Knowledge.

DTIC Science & Technology

1987-09-01

field computer It is based on xeneralization of Taylor’s theorem to continuous dimensional vector spaces. 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21...generalization of Taylor’s theorem to continuous dimensional vector -5paces A number of field computations are illustrated, including several Lransforma...paradigm. The "old" Al has been quite successful in performing a number of difficult tasks, such as theorem prov- ing, chess playing, medical diagnosis and

IIB supergravity and the E 6(6) covariant vector-tensor hierarchy

DOE PAGES

Ciceri, Franz; de Wit, Bernard; Varela, Oscar

2015-04-20

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional ‘dual graviton’. The invariant E 6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions formore » the USp(8) covariant fermion fields. Implications are further discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.« less

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

NASA Astrophysics Data System (ADS)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time

NASA Astrophysics Data System (ADS)

Benisty, David; Guendelman, E. I.

2016-09-01

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.

Generalized Legendre transformations and symmetries of the WDVV equations

NASA Astrophysics Data System (ADS)

Strachan, Ian A. B.; Stedman, Richard

2017-03-01

The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class—the so-called Legendre transformations—were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.

Cosmology in generalized Proca theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Felice, Antonio De; Mukohyama, Shinji; Heisenberg, Lavinia

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for themore » absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.« less

Z2×Z2 generalizations of 𝒩 =2 super Schrödinger algebras and their representations

NASA Astrophysics Data System (ADS)

Aizawa, N.; Segar, J.

2017-11-01

We generalize the real and chiral N =2 super Schrödinger algebras to Z2×Z2-graded Lie superalgebras. This is done by D-module presentation, and as a consequence, the D-module presentations of Z2×Z2-graded superalgebras are identical to the ones of super Schrödinger algebras. We then generalize the calculus over the Grassmann number to Z2×Z2 setting. Using it and the standard technique of Lie theory, we obtain a vector field realization of Z2×Z2-graded superalgebras. A vector field realization of the Z2×Z2 generalization of N =1 super Schrödinger algebra is also presented.

Polarization Control with Plasmonic Antenna Tips: A Universal Approach to Optical Nanocrystallography and Vector-Field Imaging

NASA Astrophysics Data System (ADS)

Park, Kyoung-Duck; Raschke, Markus B.

2018-05-01

Controlling the propagation and polarization vectors in linear and nonlinear optical spectroscopy enables to probe the anisotropy of optical responses providing structural symmetry selective contrast in optical imaging. Here we present a novel tilted antenna-tip approach to control the optical vector-field by breaking the axial symmetry of the nano-probe in tip-enhanced near-field microscopy. This gives rise to a localized plasmonic antenna effect with significantly enhanced optical field vectors with control of both \\textit{in-plane} and \\textit{out-of-plane} components. We use the resulting vector-field specificity in the symmetry selective nonlinear optical response of second-harmonic generation (SHG) for a generalized approach to optical nano-crystallography and -imaging. In tip-enhanced SHG imaging of monolayer MoS$_2$ films and single-crystalline ferroelectric YMnO$_3$, we reveal nano-crystallographic details of domain boundaries and domain topology with enhanced sensitivity and nanoscale spatial resolution. The approach is applicable to any anisotropic linear and nonlinear optical response, and provides for optical nano-crystallographic imaging of molecular or quantum materials.

Stability of Horndeski vector-tensor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia

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 tomore » 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.« less

Visualization of Morse connection graphs for topologically rich 2D vector fields.

PubMed

Szymczak, Andrzej; Sipeki, Levente

2013-12-01

Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.

A comparison of in situ measurements of vector-E and - vector-V x vector-B from Dynamics Explorer 2

NASA Technical Reports Server (NTRS)

Hanson, W. B.; Coley, W. R.; Heelis, R. A.; Maynard, N. C.; Aggson, T. L.

1993-01-01

Dynamics Explorer-2 provided the first opportunity to make a direct comparison of in situ measurements of the high-latitude convection electric field by two distinctly different techniques. The vector electric field instrument (VEFI) used antennae to measure the intrinsic electric fields and the ion drift meter (IDM) and retarding potential analyzer (RPA) measured the ion drift velocity vector, from which the convection electric field can be deduced. The data from three orbits having large electric fields at high latitude are presented, one at high, one at medium, and one at low altitudes. The general agreement between the two measurements of electric field is very good, with typical differences at high latitudes of the order of a few millivolts per meter, but there are some regions where the particle fluxes are extremely large (e.g., the cusp) and the disagreement is worse, probably because of IDM difficulties. The auroral zone potential patterns derived from the two devices are in excellent agreement for two of the cases, but not in the third, where bad attitude data may be the problem. At low latitudes there are persistent differences in the measurements of a few millivolts per meter, though these differences are quite constant from orbit to orbit. This problem seems to arise from some shortcoming in the VEFI measurments. Overall, however, these measurements confirm the concept of `frozen-in' plasma that drifts with velocity vector-E x vector-B/B(exp 2) within the measurement errors of the two techniques.

Particle production of vector fields: Scale invariance is attractive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wagstaff, Jacques M.; Dimopoulos, Konstantinos

2011-01-15

In a model of an Abelian vector boson with a Maxwell kinetic term and non-negative mass-squared it is demonstrated that, under fairly general conditions during inflation, a scale-invariant spectrum of perturbations for the components of a vector field, massive or not, whose kinetic function (and mass) is modulated by the inflaton field is an attractor solution. If the field is massless, or if it remains light until the end of inflation, this attractor solution also generates anisotropic stress, which can render inflation weakly anisotropic. The above two characteristics of the attractor solution can source (independently or combined together) significant statisticalmore » anisotropy in the curvature perturbation, which may well be observable in the near future.« less

Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium

NASA Astrophysics Data System (ADS)

Le Kien, Fam; Schneeweiss, Philipp; Rauschenbeutel, Arno

2013-05-01

We present a systematic derivation of the dynamical polarizability and the ac Stark shift of the ground and excited states of atoms interacting with a far-off-resonance light field of arbitrary polarization. We calculate the scalar, vector, and tensor polarizabilities of atomic cesium using resonance wavelengths and reduced matrix elements for a large number of transitions. We analyze the properties of the fictitious magnetic field produced by the vector polarizability in conjunction with the ellipticity of the polarization of the light field.

Conserved quantities in non-Abelian monopole fields

NASA Astrophysics Data System (ADS)

Horváthy, P. A.; Ngome, J.-P.

2009-06-01

Van Holten’s covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere, and Wilczek, a conserved angular momentum is constructed, despite the nonconservation of the electric charge. No Runge-Lenz vector has been found.

An improved exact inversion formula for solenoidal fields in cone beam vector tomography

NASA Astrophysics Data System (ADS)

Katsevich, Alexander; Rothermel, Dimitri; Schuster, Thomas

2017-06-01

In this paper we present an improved inversion formula for the 3D cone beam transform of vector fields supported in the unit ball which is exact for solenoidal fields. It is well known that only the solenoidal part of a vector field can be determined from the longitudinal ray transform of a vector field in cone beam geometry. The inversion formula, as it was developed in Katsevich and Schuster (2013 An exact inversion formula for cone beam vector tomography Inverse Problems 29 065013), consists of two parts. The first part is of the filtered backprojection type, whereas the second part is a costly 4D integration and very inefficient. In this article we tackle this second term and obtain an improved formula, which is easy to implement and saves one order of integration. We also show that the first part contains all information about the curl of the field, whereas the second part has information about the boundary values. More precisely, the second part vanishes if the solenoidal part of the original field is tangential at the boundary. A number of numerical tests presented in the paper confirm the theoretical results and the exactness of the formula. Also, we obtain an inversion algorithm that works for general convex domains.

Inhomogeneity and velocity fields effects on scattering polarization in solar prominences

NASA Astrophysics Data System (ADS)

Milić, I.; Faurobert, M.

2015-10-01

One of the methods for diagnosing vector magnetic fields in solar prominences is the so called "inversion" of observed polarized spectral lines. This inversion usually assumes a fairly simple generative model and in this contribution we aim to study the possible systematic errors that are introduced by this assumption. On two-dimensional toy model of a prominence, we first demonstrate importance of multidimensional radiative transfer and horizontal inhomogeneities. These are able to induce a significant level of polarization in Stokes U, without the need for the magnetic field. We then compute emergent Stokes spectrum from a prominence which is pervaded by the vector magnetic field and use a simple, one-dimensional model to interpret these synthetic observations. We find that inferred values for the magnetic field vector generally differ from the original ones. Most importantly, the magnetic field might seem more inclined than it really is.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

Decay width of hadronic molecule structure for quarks

NASA Astrophysics Data System (ADS)

Chen, Xiaozhao; Lü, Xiaofu

2018-06-01

Based on the general form of the Bethe-Salpeter wave functions for the bound states consisting of two vector fields, we obtain the general formulas for the decay widths of molecular states composed of two heavy vector mesons with arbitrary spin and parity into a heavy meson plus a light meson. In this approach, our attention is still focused on the internal structure of heavy vector mesons in the molecular state. According to the molecule state model of exotic meson, we give the generalized Bethe-Salpeter wave function of molecular state as a four-quark state. Then the observed Y (3940 ) state is considered as a molecular state consisting of two heavy vector mesons D*0D¯*0 and the strong Y (3940 )→J /ψ ω decay width is calculated. The numerical result is consistent with the experimental values.

Cosmology for quadratic gravity in generalized Weyl geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excludingmore » pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.« less

Vector and axial-vector decomposition of Einstein's gravitational action

NASA Astrophysics Data System (ADS)

Soh, Kwang S.

1991-08-01

Vector and axial-vector gravitational fields are introduced to express the Einstein action in the manner of electromagnetism. Their conformal scaling properties are examined, and the resemblance between the general coordinate and electromagnetic gauge transformation is elucidated. The chiral formulation of the gravitational action is constructed. I am deeply grateful to Professor S. Hawking, and Professor G. Lloyd for warm hospitality at DAMTP, and Darwin College, University of Cambridge, respectively. I also appreciate much help received from Dr. Q.-H. Park.

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of ½

PubMed Central

Maryasov, Alexander G.

2012-01-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or ‘powder’ sample when g tensor anisotropy is significant. PMID:22743542

Spin dynamics of paramagnetic centers with anisotropic g tensor and spin of 1/2

NASA Astrophysics Data System (ADS)

Maryasov, Alexander G.; Bowman, Michael K.

2012-08-01

The influence of g tensor anisotropy on spin dynamics of paramagnetic centers having real or effective spin of 1/2 is studied. The g anisotropy affects both the excitation and the detection of EPR signals, producing noticeable differences between conventional continuous-wave (cw) EPR and pulsed EPR spectra. The magnitudes and directions of the spin and magnetic moment vectors are generally not proportional to each other, but are related to each other through the g tensor. The equilibrium magnetic moment direction is generally parallel to neither the magnetic field nor the spin quantization axis due to the g anisotropy. After excitation with short microwave pulses, the spin vector precesses around its quantization axis, in a plane that is generally not perpendicular to the applied magnetic field. Paradoxically, the magnetic moment vector precesses around its equilibrium direction in a plane exactly perpendicular to the external magnetic field. In the general case, the oscillating part of the magnetic moment is elliptically polarized and the direction of precession is determined by the sign of the g tensor determinant (g tensor signature). Conventional pulsed and cw EPR spectrometers do not allow determination of the g tensor signature or the ellipticity of the magnetic moment trajectory. It is generally impossible to set a uniform spin turning angle for simple pulses in an unoriented or 'powder' sample when g tensor anisotropy is significant.

An application of the Braunbeck method to the Maggi-Rubinowicz field representation

NASA Technical Reports Server (NTRS)

Meneghini, R.

1982-01-01

The Braunbek method is applied to the generalized vector potential associated with the Maggi-rubinowicz representation. Under certain approximations, an asymptotic evaluation of the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. An evaluation of the field for the simple case of a plane wave normally incident on a circular aperture is presented showing that the field predicted by the Maggi-Rubinowicz theory is continuous across the shadow boundary.

An application of the Braunbeck method to the Maggi-Rubinowicz field representation

NASA Astrophysics Data System (ADS)

Meneghini, R.

1982-06-01

The Braunbek method is applied to the generalized vector potential associated with the Maggi-rubinowicz representation. Under certain approximations, an asymptotic evaluation of the vector potential is obtained. For observation points away from caustics or shadow boundaries, the field derived from this quantity is the same as that determined from the geometrical theory of diffraction on a singly diffracted edge ray. An evaluation of the field for the simple case of a plane wave normally incident on a circular aperture is presented showing that the field predicted by the Maggi-Rubinowicz theory is continuous across the shadow boundary.

Micromechanics of Composite Materials Governed by Vector Constitutive Laws

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2017-01-01

The high-fidelity generalized method of cells micromechanics theory has been extended for the prediction of the effective property tensor and the corresponding local field distributions for composites whose constituents are governed by vector constitutive laws. As shown, the shear analogy, which can predict effective transverse properties, is not valid in the general three-dimensional case. Consequently, a general derivation is presented that is applicable to both continuously and discontinuously reinforced composites with arbitrary vector constitutive laws and periodic microstructures. Results are given for thermal and electric problems, effective properties and local field distributions, ordered and random microstructures, as well as complex geometries including woven composites. Comparisons of the theory's predictions are made to test data, numerical analysis, and classical expressions from the literature. Further, classical methods cannot provide the local field distributions in the composite, and it is demonstrated that, as the percolation threshold is approached, their predictions are increasingly unreliable. XXXX It has been observed that the bonding between the fibers and matrix in composite materials can be imperfect. In the context of thermal conductivity, such imperfect interfaces have been investigated in micromechanical models by Dunn and Taya (1993), Duan and Karihaloo (2007), Nan et al. (1997) and Hashin (2001). The present HFGMC micromechanical method, derived for perfectly bonded composite materials governed by vector constitutive laws, can be easily generalized to include the effects of weak bonding between the constituents. Such generalizations, in the context of the mechanical micromechanics problem, involve introduction of a traction-separation law at the fiber/matrix interface and have been presented by Aboudi (1987), Bednarcyk and Arnold (2002), Bednarcyk et al. (2004) and Aboudi et al. (2013) and will be addressed in the future.

Towards thermodynamics of universal horizons in Einstein-æther theory.

PubMed

Berglund, Per; Bhattacharyya, Jishnu; Mattingly, David

2013-02-15

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons," which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

NASA Astrophysics Data System (ADS)

Li, Jing; Kou, Liying; Wang, Duo; Zhang, Wei

2017-12-01

In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the efficiency of the approach, a comparison of our result with others is also presented.

Weakly charged generalized Kerr-NUT-(A)dS spacetimes

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2017-08-01

We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor hab, which is present in such a spacetime, and a derivative of the primary Killing vector, associated with hab. For the vanishing cosmological constant the obtained solution reduces to the Wald's electromagnetic field generated from the primary Killing vector.

Consistent compactification of double field theory on non-geometric flux backgrounds

NASA Astrophysics Data System (ADS)

Hassler, Falk; Lüst, Dieter

2014-05-01

In this paper, we construct non-trivial solutions to the 2 D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2( D - d) internal directions with a twist U M N which is directly connected to the covariant fluxes ABC . It exhibits 2( D - d) linear independent generalized Killing vectors K I J and gives rise to a gauged supergravity in d dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For ( D - d) = 3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

On the 4D generalized Proca action for an Abelian vector field

NASA Astrophysics Data System (ADS)

Allys, Erwan; Beltrán Almeida, Juan P.; Peter, Patrick; Rodríguez, Yeinzon

2016-09-01

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 05 (2014) 015 and Phys. Lett. B 757 (2016) 405 and complements those of JCAP 02 (2016) 004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field Aμ, the Faraday tensor Fμν and its Hodge dual tilde Fμν.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emami, Razieh; Mukohyama, Shinji; Namba, Ryo

Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models,more » we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.« less

Electron in higher-dimensional weakly charged rotating black hole spacetimes

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-03-01

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with the vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first-order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in V. P. Frolov and P. Krtous [Phys. Rev. D 83, 024016 (2011)].

The canonical Lagrangian approach to three-space general relativity

NASA Astrophysics Data System (ADS)

Shyam, Vasudev; Venkatesh, Madhavan

2013-07-01

We study the action for the three-space formalism of general relativity, better known as the Barbour-Foster-Ó Murchadha action, which is a square-root Baierlein-Sharp-Wheeler action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

NASA Astrophysics Data System (ADS)

Cheng, C. H. Arthur; Shkoller, Steve

2017-09-01

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain {Ω \\subseteq R^n}, and either the normal component {{u} \\cdot {N}} or the tangential components of the vector field {{u} × {N}} are prescribed on the boundary {partial Ω}. For {k > n/2}, we prove that u is in the Sobolev space {H^k+1(Ω)} if {Ω} is an {H^k+1}-domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics.

Generalized Case ``Van Kampen theory for electromagnetic oscillations in a magnetized plasma

NASA Astrophysics Data System (ADS)

Bairaktaris, F.; Hizanidis, K.; Ram, A. K.

2017-10-01

The Case-Van Kampen theory is set up to describe electrostatic oscillations in an unmagnetized plasma. Our generalization to electromagnetic oscillations in magnetized plasma is formulated in the relativistic position-momentum phase space of the particles. The relativistic Vlasov equation includes the ambient, homogeneous, magnetic field, and space-time dependent electromagnetic fields that satisfy Maxwell's equations. The standard linearization technique leads to an equation for the perturbed distribution function in terms of the electromagnetic fields. The eigenvalues and eigenfunctions are obtained from three integrals `` each integral being over two different components of the momentum vector. Results connecting phase velocity, frequency, and wave vector will be presented. Supported in part by the Hellenic National Programme on Controlled Thermonuclear Fusion associated with the EUROfusion Consortium, and by DoE Grant DE-FG02-91ER-54109.

An Elementary Treatment of General Inner Products

ERIC Educational Resources Information Center

Graver, Jack E.

2011-01-01

A typical first course on linear algebra is usually restricted to vector spaces over the real numbers and the usual positive-definite inner product. Hence, the proof that dim(S)+ dim(S[perpendicular]) = dim("V") is not presented in a way that is generalizable to non-positive?definite inner products or to vector spaces over other fields. In this…

Dielectric and permeability

NASA Technical Reports Server (NTRS)

Cole, K. D.

1982-01-01

Using the unabridged Maxwell equations (including vectors D, E and H) new effects in collisionless plasmas are uncovered. In a steady state, it is found that spatially varying energy density of the electric field (E perpendicular) orthogonal to B produces electric current leading, under certain conditions, to the relationship P perpendicular+B(2)/8 pi-epsilon E perpendicular(2)/8 pi = constant, where epsilon is the dielectric constant of the plasma for fields orthogonal to B. In steady state quasi-two-dimensional flows in plasmas, a general relationship between the components of electric field parallel and perpendicular to B is found. These effects are significant in goephysical and astrophysical plasmas. The general conditions for a steady state in collisionless plasma are deduced. With time variations in a plasma, slow compared to ion-gyroperiod, there is a general current, (j*), which includes the well-known polarisation current, given by J*=d/dt (ExM)+(PxB)xB B(-2) where M and P are the magnetization and polarization vectors respectively.

THE EFFECT OF GRAVITATION ON THE POLARIZATION STATE OF A LIGHT RAY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Tanay; Sen, A. K.

In the present work, detailed calculations have been carried out on the rotation of the polarization vector of an electromagnetic wave due to the presence of a gravitational field of a rotating body. This has been done using the general expression of Maxwell’s equation in curved spacetime. Considering the far-field approximation (i.e., the impact parameter is greater than the Schwarzschild radius and rotation parameter), the amount of rotation of the polarization vector as a function of impact parameter has been obtained for a rotating body (considering Kerr geometry). The present work shows that the rotation of the polarization vector cannotmore » be observed in the case of Schwarzschild geometry. This work also calculates the rotational effect when considering prograde and retrograde orbits for the light ray. Although the present work demonstrates the effect of rotation of the polarization vector, it confirms that there would be no net polarization of an electromagnetic wave due to the curved spacetime geometry in a Kerr field.« less

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.

Identification of cardiac rhythm features by mathematical analysis of vector fields.

PubMed

Fitzgerald, Tamara N; Brooks, Dana H; Triedman, John K

2005-01-01

Automated techniques for locating cardiac arrhythmia features are limited, and cardiologists generally rely on isochronal maps to infer patterns in the cardiac activation sequence during an ablation procedure. Velocity vector mapping has been proposed as an alternative method to study cardiac activation in both clinical and research environments. In addition to the visual cues that vector maps can provide, vector fields can be analyzed using mathematical operators such as the divergence and curl. In the current study, conduction features were extracted from velocity vector fields computed from cardiac mapping data. The divergence was used to locate ectopic foci and wavefront collisions, and the curl to identify central obstacles in reentrant circuits. Both operators were applied to simulated rhythms created from a two-dimensional cellular automaton model, to measured data from an in situ experimental canine model, and to complex three-dimensional human cardiac mapping data sets. Analysis of simulated vector fields indicated that the divergence is useful in identifying ectopic foci, with a relatively small number of vectors and with errors of up to 30 degrees in the angle measurements. The curl was useful for identifying central obstacles in reentrant circuits, and the number of velocity vectors needed increased as the rhythm became more complex. The divergence was able to accurately identify canine in situ pacing sites, areas of breakthrough activation, and wavefront collisions. In data from human arrhythmias, the divergence reliably estimated origins of electrical activity and wavefront collisions, but the curl was less reliable at locating central obstacles in reentrant circuits, possibly due to the retrospective nature of data collection. The results indicate that the curl and divergence operators applied to velocity vector maps have the potential to add valuable information in cardiac mapping and can be used to supplement human pattern recognition.

SSM/I and ECMWF Wind Vector Comparison

NASA Technical Reports Server (NTRS)

Wentz, Frank J.; Ashcroft, Peter D.

1996-01-01

Wentz was the first to convincingly show that satellite microwave radiometers have the potential to measure the oceanic wind vector. The most compelling evidence for this conclusion was the monthly wind vector maps derived solely from a statistical analysis of Special Sensor Microwave Imager (SSM/I) observations. In a qualitative sense, these maps clearly showed the general circulation over the world's oceans. In this report we take a closer look at the SSM/I monthly wind vector maps and compare them to European Center for Medium-Range Weather Forecasts (ECMWF) wind fields. This investigation leads both to an empirical comparison of SSM/I calculated wind vectors with ECMWF wind vectors, and to an examination of possible reasons that the SSM/I calculated wind vector direction would be inherently more reliable at some locations than others.

O Electromagnetic Power Waves and Power Density Components.

NASA Astrophysics Data System (ADS)

Petzold, Donald Wayne

1980-12-01

On January 10, 1884 Lord Rayleigh presented a paper entitled "On the Transfer of Energy in the Electromagnetic Field" to the Royal Society of London. This paper had been authored by the late Fellow of Trinity College, Cambridge, Professor J. H. Poynting and in it he claimed that there was a general law for the transfer of electromagnetic energy. He argued that associated with each point in space is a quantity, that has since been called the Poynting vector, that is a measure of the rate of energy flow per unit area. His analysis was concerned with the integration of this power density vector at all points over an enclosing surface of a specific volume. The interpretation of this Poynting vector as a true measure of the local power density was viewed with great skepticism unless the vector was integrated over a closed surface, as the development of the concept required. However, within the last decade or so Shadowitz indicates that a number of prominent authors have argued that the criticism of the interpretation of Poynting's vector as a local power density vector is unjustified. The present paper is not concerned with these arguments but instead is concerned with a decomposition of Poynting's power density vector into two and only two components: one vector which has the same direction as Poynting's vector and which is called the forward power density vector, and another vector, directed opposite to the Poynting vector and called the reverse power density vector. These new local forward and reverse power density vectors will be shown to be dependent upon forward and reverse power wave vectors and these vectors in turn will be related to newly defined forward and reverse components of the electric and magnetic fields. The sum of these forward and reverse power density vectors, which is simply the original Poynting vector, is associated with the total electromagnetic energy traveling past the local point. Another vector which is the difference between the forward and reverse power density vectors and which will be shown to be associated with the total electric and magnetic field energy densities existing at a local point will also be introduced. These local forward and reverse power density vectors may be integrated over a surface to determine the forward and reverse powers and from these results problems related to maximum power transfer or efficiency of electromagnetic energy transmission in space may be studied in a manner similar to that presently being done with transmission lines, wave guides, and more recently with two port multiport lumped parameter systems. These new forward and reverse power density vectors at a point in space are analogous to the forward and revoltages or currents and power waves as used with the transmission line, waveguide, or port. These power wave vectors in space are a generalization of the power waves as developed by Penfield, Youla, and Kurokawa and used with the scattering parameters associated with transmission lines, waveguides and ports.

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; KubizÅák, David; Santos, Jorge E.

2018-06-01

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.

PubMed

Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David; Santos, Jorge E

2018-06-08

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Mosquitoes and other aquatic insects in fallow field biotopes and rice paddy fields.

PubMed

Ohba, S Y; Matsuo, T; Takagi, M

2013-03-01

Fallow field biotopes that develop from abandoned rice fields are man-made wetlands that provide new habitats for various aquatic animals. Although consideration of such biotopes generally focuses on their positive aspects, this study evaluated the negative aspects of establishing fallow field biotopes with regard to mosquito breeding sites. To determine whether fallow field biotopes become breeding habitats for vector mosquitoes, we evaluated mosquito fauna in fallow field biotopes and adjacent rice fields. We found larvae of Anopheles lesteri, Anopheles sinensis and Culex tritaeniorhynchus (all: Diptera: Culicidae) in the biotopes. Although abundances of mosquito larvae in the biotopes and rice fields were statistically similar, mosquito abundances in rice fields increased dramatically in August when the water level reduced after the rainy season. The abundance and variety of the mosquitoes' natural predators were greater in biotopes than in rice fields because the former are a permanent and stable aquatic environment. A generalized linear mixed model showed a negative effect of predator diversity on mosquito larvae abundance in both habitats. Although fallow field biotopes become breeding habitats for vector mosquitoes, establishing biotopes from fallow fields in order to protect various aquatic animals, including mosquito insect predators, may help to control mosquito breeding. © 2012 The Royal Entomological Society.

Note on the Noether charge and holographic transports

NASA Astrophysics Data System (ADS)

Fan, Zhong-Ying

2018-03-01

We clarify the relation between the Noether charge associated to an arbitrary vector field and the equations of motion by revisiting Wald formalism. For a timelike Killing vector, aspects of the Noether charge suggest that it is dual to the heat current in the boundary for general holographic theories. For a spacelike Killing vector, we interpret the Noether charge (at the transverse direction) as shear stress of the dual fluid so we can compute the ratio of shear viscosity to entropy density by simply using the infrared data on the black hole event horizon. We test the new method for Einstein gravity and Gauss-Bonnet gravity and find that it produces correct results for both cases even in the presence of additional matter fields.

Discrete Data Transfer Technique for Fluid-Structure Interaction

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2007-01-01

This paper presents a general three-dimensional algorithm for data transfer between dissimilar meshes. The algorithm is suitable for applications of fluid-structure interaction and other high-fidelity multidisciplinary analysis and optimization. Because the algorithm is independent of the mesh topology, we can treat structured and unstructured meshes in the same manner. The algorithm is fast and accurate for transfer of scalar or vector fields between dissimilar surface meshes. The algorithm is also applicable for the integration of a scalar field (e.g., coefficients of pressure) on one mesh and injection of the resulting vectors (e.g., force vectors) onto another mesh. The author has implemented the algorithm in a C++ computer code. This paper contains a complete formulation of the algorithm with a few selected results.

Field by field hybrid upwind splitting methods

NASA Technical Reports Server (NTRS)

Coquel, Frederic; Liou, Meng-Sing

1993-01-01

A new and general approach to upwind splitting is presented. The design principle combines the robustness of flux vector splitting schemes in the capture of nonlinear waves and the accuracy of some flux difference splitting schemes in the resolution of linear waves. The new schemes are derived following a general hybridization technique performed directly at the basic level of the field by field decomposition involved in FDS methods. The scheme does not use a spatial switch to be tuned up according to the local smoothness of the approximate solution.

A flippon related singlet at the LHC II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tianjun; Maxin, James A.; Mayes, Van E.

2016-06-28

Here, we consider the 750 GeV diphoton resonance at the 13 TeV LHC in the ℱ-SU(5) model with a Standard Model (SM) singlet field which couples to TeV-scale vector-like particles, dubbed flippons. This singlet field assumes the role of the 750 GeV resonance, with production via gluon fusion and subsequent decay to a diphoton via the vector-like particle loops. We present a numerical analysis showing that the observed 8 TeV and 13 TeV diphoton production cross-sections can be generated in the model space with realistic electric charges and Yukawa couplings for light vector-like masses. We further discuss the experimental viabilitymore » of light vector-like masses in a General No-Scale ℱ-SU(5) model, offering a few benchmark scenarios in this consistent GUT that can satisfy all experimental constraints imposed by the LHC and other essential experiments.« less

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.

Einstein-aether theory with a Maxwell field: General formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru; Lemos, José P.S., E-mail: joselemos@ist.utl.pt

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shearmore » and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.« less

High-efficiency and flexible generation of vector vortex optical fields by a reflective phase-only spatial light modulator.

PubMed

Cai, Meng-Qiang; Wang, Zhou-Xiang; Liang, Juan; Wang, Yan-Kun; Gao, Xu-Zhen; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2017-08-01

The scheme for generating vector optical fields should have not only high efficiency but also flexibility for satisfying the requirements of various applications. However, in general, high efficiency and flexibility are not compatible. Here we present and experimentally demonstrate a solution to directly, flexibly, and efficiently generate vector vortex optical fields (VVOFs) with a reflective phase-only liquid crystal spatial light modulator (LC-SLM) based on optical birefringence of liquid crystal molecules. To generate the VVOFs, this approach needs in principle only a half-wave plate, an LC-SLM, and a quarter-wave plate. This approach has some advantages, including a simple experimental setup, good flexibility, and high efficiency, making the approach very promising in some applications when higher power is need. This approach has a generation efficiency of 44.0%, which is much higher than the 1.1% of the common path interferometric approach.

Application of support vector regression for optimization of vibration flow field of high-density polyethylene melts characterized by small angle light scattering

NASA Astrophysics Data System (ADS)

Xian, Guangming

2018-03-01

In this paper, the vibration flow field parameters of polymer melts in a visual slit die are optimized by using intelligent algorithm. Experimental small angle light scattering (SALS) patterns are shown to characterize the processing process. In order to capture the scattered light, a polarizer and an analyzer are placed before and after the polymer melts. The results reported in this study are obtained using high-density polyethylene (HDPE) with rotation speed at 28 rpm. In addition, support vector regression (SVR) analytical method is introduced for optimization the parameters of vibration flow field. This work establishes the general applicability of SVR for predicting the optimal parameters of vibration flow field.

Projective mappings and dimensions of vector spaces of three types of Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature

NASA Astrophysics Data System (ADS)

Mikeš, Josef; Stepanov, Sergey; Hinterleitner, Irena

2012-07-01

In our paper we have determined the dimension of the space of conformal Killing-Yano tensors and the dimensions of its two subspaces of closed conformal Killing-Yano and Killing-Yano tensors on pseudo Riemannian manifolds of constant curvature. This result is a generalization of well known results on sharp upper bounds of the dimensions of the vector spaces of conformal Killing-Yano, Killing-Yano and concircular vector fields on pseudo Riemannian manifolds of constant curvature.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.

Macroscopic theory of dark sector

NASA Astrophysics Data System (ADS)

Meierovich, Boris

A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out an adequate tool for macroscopic description of the dark sector. The zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant [1]. Space-like and time-like massive vector fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves [2]. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four parametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating non-singular scenarios of evolution of the universe [3]. In particular, the singular big bang turns into a regular inflation-like transition from contraction to expansion with the accelerate expansion at late times. The fine-tuned Friedman-Robertson-Walker singular solution corresponds to the particular limiting case at the boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energy-momentum tensor allows to analyse the main properties of the dark sector analytically and avoid unnecessary model assumptions. It opens a possibility to trace how the additional attraction of the space-like dark matter, dominating in the galaxy scale, transforms into the elastic repulsion of the time-like dark matter, dominating in the scale of the Universe. 1. B. E. Meierovich. "Vector fields in multidimensional cosmology". Phys. Rev. D 84, 064037 (2011). 2. B. E. Meierovich. "Galaxy rotation curves driven by massive vector fields: Key to the theory of the dark sector". Phys. Rev. D 87, 103510, (2013). 3. B. E. Meierovich. "Towards the theory of the evolution of the Universe". Phys. Rev. D 85, 123544 (2012).

Visualizing second order tensor fields with hyperstreamlines

NASA Technical Reports Server (NTRS)

Delmarcelle, Thierry; Hesselink, Lambertus

1993-01-01

Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.

First Use of Synoptic Vector Magnetograms for Global Nonlinear, Force-Free Coronal Magnetic Field Models

NASA Technical Reports Server (NTRS)

Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A.

2014-01-01

Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) - E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.

Elliptic-symmetry vector optical fields.

PubMed

Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian

2014-08-11

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

Lie algebra of conformal Killing-Yano forms

NASA Astrophysics Data System (ADS)

Ertem, Ümit

2016-06-01

We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing-Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing-Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.

Separation of spin and orbital angular coherence momenta in the second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2007-09-15

In analogy with the separation of the total optical angular momentum into a spin and an orbital part in electrodynamics, we introduce a new concept of spin and orbital angular coherence momenta into the general coherence theory of vector electromagnetic fields. The properties of the newly introduced spin and orbital angular coherence momenta are investigated through the decomposition of the total coherence angular momentum into the sum of these two components, and their separate conservations have been derived for what is believed to be the first time.

Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

NASA Astrophysics Data System (ADS)

Johnson, Robert W.

2012-06-01

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Only at low conductivity and below, the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.

Supersymmetric solutions of N =(1 ,1 ) general massive supergravity

NASA Astrophysics Data System (ADS)

Deger, N. S.; Nazari, Z.; Sarıoǧlu, Ö.

2018-05-01

We construct supersymmetric solutions of three-dimensional N =(1 ,1 ) general massive supergravity (GMG). Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N =(1 ,1 ) new massive supergravity (NMG). In the timelike case, we find that many solutions are common with NMG, but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a nonzero vector field that preserves 1 /4 supersymmetry.

Z H η vertex in the simplest little Higgs model

NASA Astrophysics Data System (ADS)

He, Shi-Ping; Mao, Ying-nan; Zhang, Chen; Zhu, Shou-hua

2018-04-01

The issue of deriving Z H η vertex in the simplest little Higgs (SLH) model is revisited. Special attention is paid to the treatment of noncanonically-normalized scalar kinetic matrix and vector-scalar two-point transitions. We elucidate a general procedure to diagonalize a general vector-scalar system in gauge theories and apply it to the case of SLH. The resultant Z H η vertex is found to be different from those which have already existed in the literature for a long time. We also present an understanding of this issue from an effective field theory viewpoint.

FPGA Implementation of Generalized Hebbian Algorithm for Texture Classification

PubMed Central

Lin, Shiow-Jyu; Hwang, Wen-Jyi; Lee, Wei-Hao

2012-01-01

This paper presents a novel hardware architecture for principal component analysis. The architecture is based on the Generalized Hebbian Algorithm (GHA) because of its simplicity and effectiveness. The architecture is separated into three portions: the weight vector updating unit, the principal computation unit and the memory unit. In the weight vector updating unit, the computation of different synaptic weight vectors shares the same circuit for reducing the area costs. To show the effectiveness of the circuit, a texture classification system based on the proposed architecture is physically implemented by Field Programmable Gate Array (FPGA). It is embedded in a System-On-Programmable-Chip (SOPC) platform for performance measurement. Experimental results show that the proposed architecture is an efficient design for attaining both high speed performance and low area costs. PMID:22778640

Impact of Vector Dispersal and Host-Plant Fidelity on the Dissemination of an Emerging Plant Pathogen

PubMed Central

Johannesen, Jes; Foissac, Xavier; Kehrli, Patrik; Maixner, Michael

2012-01-01

Dissemination of vector-transmitted pathogens depend on the survival and dispersal of the vector and the vector's ability to transmit the pathogen, while the host range of vector and pathogen determine the breath of transmission possibilities. In this study, we address how the interaction between dispersal and plant fidelities of a pathogen (stolbur phytoplasma tuf-a) and its vector (Hyalesthes obsoletus: Cixiidae) affect the emergence of the pathogen. Using genetic markers, we analysed the geographic origin and range expansion of both organisms in Western Europe and, specifically, whether the pathogen's dissemination in the northern range is caused by resident vectors widening their host-plant use from field bindweed to stinging nettle, and subsequent host specialisation. We found evidence for common origins of pathogen and vector south of the European Alps. Genetic patterns in vector populations show signals of secondary range expansion in Western Europe leading to dissemination of tuf-a pathogens, which might be newly acquired and of hybrid origin. Hence, the emergence of stolbur tuf-a in the northern range was explained by secondary immigration of vectors carrying stinging nettle-specialised tuf-a, not by widening the host-plant spectrum of resident vectors with pathogen transmission from field bindweed to stinging nettle nor by primary co-migration from the resident vector's historical area of origin. The introduction of tuf-a to stinging nettle in the northern range was therefore independent of vector's host-plant specialisation but the rapid pathogen dissemination depended on the vector's host shift, whereas the general dissemination elsewhere was linked to plant specialisation of the pathogen but not of the vector. PMID:23284774

Impact of vector dispersal and host-plant fidelity on the dissemination of an emerging plant pathogen.

PubMed

Johannesen, Jes; Foissac, Xavier; Kehrli, Patrik; Maixner, Michael

2012-01-01

Dissemination of vector-transmitted pathogens depend on the survival and dispersal of the vector and the vector's ability to transmit the pathogen, while the host range of vector and pathogen determine the breath of transmission possibilities. In this study, we address how the interaction between dispersal and plant fidelities of a pathogen (stolbur phytoplasma tuf-a) and its vector (Hyalesthes obsoletus: Cixiidae) affect the emergence of the pathogen. Using genetic markers, we analysed the geographic origin and range expansion of both organisms in Western Europe and, specifically, whether the pathogen's dissemination in the northern range is caused by resident vectors widening their host-plant use from field bindweed to stinging nettle, and subsequent host specialisation. We found evidence for common origins of pathogen and vector south of the European Alps. Genetic patterns in vector populations show signals of secondary range expansion in Western Europe leading to dissemination of tuf-a pathogens, which might be newly acquired and of hybrid origin. Hence, the emergence of stolbur tuf-a in the northern range was explained by secondary immigration of vectors carrying stinging nettle-specialised tuf-a, not by widening the host-plant spectrum of resident vectors with pathogen transmission from field bindweed to stinging nettle nor by primary co-migration from the resident vector's historical area of origin. The introduction of tuf-a to stinging nettle in the northern range was therefore independent of vector's host-plant specialisation but the rapid pathogen dissemination depended on the vector's host shift, whereas the general dissemination elsewhere was linked to plant specialisation of the pathogen but not of the vector.

Forms of null Lagrangians in field theories of continuum mechanics

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Radaev, Yu. N.

2012-02-01

The divergence representation of a null Lagrangian that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null Lagrangian can contain up to 15 independent elements in total. The general form of a null Lagrangian in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null Lagrangian for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null Lagrangians are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.

Stealth configurations in vector-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Chagoya, Javier; Tasinato, Gianmassimo

2018-01-01

Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.

Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür; Ertem, Ümit

2016-08-01

We consider geometric and supergravity Killing spinors and the spinor bilinears constructed out of them. The spinor bilinears of geometric Killing spinors correspond to the antisymmetric generalizations of Killing vector fields which are called Killing-Yano forms. They constitute a Lie superalgebra structure in constant curvature spacetimes. We show that the Dirac currents of geometric Killing spinors satisfy a Lie algebra structure up to a condition on 2-form spinor bilinears. We propose that the spinor bilinears of supergravity Killing spinors give way to different generalizations of Killing vector fields to higher degree forms. It is also shown that those supergravity Killing forms constitute a Lie algebra structure in six- and ten-dimensional cases. For five- and eleven-dimensional cases, the Lie algebra structure depends on an extra condition on supergravity Killing forms.

General formulation for magnetohydrodynamic wave propagation, fire-hose, and mirror instabilities in Harris-type current sheets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hau, L.-N.; Department of Physics, National Central University, Jhongli, Taiwan; Lai, Y.-T.

Harris-type current sheets with the magnetic field model of B-vector=B{sub x}(z)x-caret+B{sub y}(z)y-caret have many important applications to space, astrophysical, and laboratory plasmas for which the temperature or pressure usually exhibits the gyrotropic form of p{r_reversible}=p{sub Parallel-To }b-caretb-caret+p{sub Up-Tack }(I{r_reversible}-b-caretb-caret). Here, p{sub Parallel-To} and p{sub Up-Tack} are, respectively, to be the pressure component along and perpendicular to the local magnetic field, b-caret=B-vector/B. This study presents the general formulation for magnetohydrodynamic (MHD) wave propagation, fire-hose, and mirror instabilities in general Harris-type current sheets. The wave equations are expressed in terms of the four MHD characteristic speeds of fast, intermediate, slow, and cuspmore » waves, and in the local (k{sub Parallel-To },k{sub Up-Tack },z) coordinates. Here, k{sub Parallel-To} and k{sub Up-Tack} are, respectively, to be the wave vector along and perpendicular to the local magnetic field. The parameter regimes for the existence of discrete and resonant modes are identified, which may become unstable at the local fire-hose and mirror instability thresholds. Numerical solutions for discrete eigenmodes are shown for stable and unstable cases. The results have important implications for the anomalous heating and stability of thin current sheets.« less

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Markarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc), but here we surmise its existence in the thin disk at z less than 200 pc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic, representing a rigid rotation of the stellar field about the axis -Y pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient of 6.2 +/- 0.9 km s(exp -1) kpc(exp -1) and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.

On the 4D generalized Proca action for an Abelian vector field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004.more » We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.« less

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

NASA Astrophysics Data System (ADS)

Wang, Bo; Zhang, Yang

2017-11-01

We present a systematic study of the 2nd-order scalar, vector, and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd order generated by a 1st-order vector field ξ(1 )μ and a 2nd-order ξ(2 )μ . All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ξ(2 )μ is effective in carrying out 2nd-order transformations that we consider, because ξ(1 )μ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ξ(2 )μ on the 2nd-order perturbations have the same structure as those by ξ(1 )μ on the 1st-order perturbations.

Focusing properties of arbitrary optical fields combining spiral phase and cylindrically symmetric state of polarization.

PubMed

Man, Zhongsheng; Bai, Zhidong; Zhang, Shuoshuo; Li, Jinjian; Li, Xiaoyu; Ge, Xiaolu; Zhang, Yuquan; Fu, Shenggui

2018-06-01

The tight focusing properties of optical fields combining a spiral phase and cylindrically symmetric state of polarization are presented. First, we theoretically analyze the mathematical characterization, Stokes parameters, and Poincaré sphere representations of arbitrary cylindrical vector (CV) vortex beams. Then, based on the vector diffraction theory, we derive and build an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input CV vortex beams. The calculations reveal that a generalized CV vortex beam can generate a sharper focal spot than that of a radially polarized (RP) plane beam in the focal plane. Besides, the focal size decrease accompanies its elongation along the optical axis. Hence, it seems that there is a trade-off between the transverse and axial resolutions. In addition, under the precondition that the absolute values between polarization order and topological charge are equal, a higher-order CV vortex can also achieve a smaller focal size than an RP plane beam. Further, the intensity for the sidelobe admits a significant suppression. To give a deep understanding of the peculiar focusing properties, the magnetic field and Poynting vector distributions are also demonstrated in detail. These properties may be helpful in applications such as optical trapping and manipulation of particles and superresolution microscopy imaging.

Anisotropic power spectrum and bispectrum in the f(Φ)F² mechanism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartolo, Nicola; Matarrese, Sabino; Peloso, Marco

2013-01-04

A suitable coupling of the inflaton φ to a vector kinetic term F² gives frozen and scale invariant vector perturbations. We compute the cosmological perturbations ζ that result from such coupling by taking into account the classical vector field that unavoidably gets generated at large scales during inflation. This generically results in a too-anisotropic power spectrum of ζ. Specifically, the anisotropy exceeds the 1% level (10% level) if inflation lasts ~5 e-folds (~50 e-folds) more than the minimal amount required to produce the cosmic microwave background modes. This conclusion applies, among others, to the application of this mechanism for magnetogenesis,more » for anisotropic inflation, and for the generation of anisotropic perturbations at the end of inflation through a waterfall field coupled to the vector (in this case, the unavoidable contribution that we obtain is effective all throughout inflation, and it is independent of the waterfall field). For a tuned duration of inflation, a 1% (10%) anisotropy in the power spectrum corresponds to an anisotropic bispectrum which is enhanced like the local one in the squeezed limit, and with an effective local f NL~3(~30). More in general, a significant anisotropy of the perturbations may be a natural outcome of all models that sustain higher than 0 spin fields during inflation.« less

Anisotropic power spectrum and bispectrum in the f(ϕ)F2 mechanism

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Matarrese, Sabino; Peloso, Marco; Ricciardone, Angelo

2013-01-01

A suitable coupling of the inflaton φ to a vector kinetic term F2 gives frozen and scale invariant vector perturbations. We compute the cosmological perturbations ζ that result from such coupling by taking into account the classical vector field that unavoidably gets generated at large scales during inflation. This generically results in a too-anisotropic power spectrum of ζ. Specifically, the anisotropy exceeds the 1% level (10% level) if inflation lasts ˜5 e-folds (˜50 e-folds) more than the minimal amount required to produce the cosmic microwave background modes. This conclusion applies, among others, to the application of this mechanism for magnetogenesis, for anisotropic inflation, and for the generation of anisotropic perturbations at the end of inflation through a waterfall field coupled to the vector (in this case, the unavoidable contribution that we obtain is effective all throughout inflation, and it is independent of the waterfall field). For a tuned duration of inflation, a 1% (10%) anisotropy in the power spectrum corresponds to an anisotropic bispectrum which is enhanced like the local one in the squeezed limit, and with an effective local fNL˜3(˜30). More in general, a significant anisotropy of the perturbations may be a natural outcome of all models that sustain higher than 0 spin fields during inflation.

Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t') /k⊥d -1 +ξ , where k⊥=|k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow")—the d -dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990), 10.1007/BF02161420]. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L . The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagonalized. The detailed proof of this fact is given for the correlation functions of arbitrary order.

Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

NASA Astrophysics Data System (ADS)

Choudhury, A. Ghose; Guha, Partha; Khanra, Barun

2009-10-01

The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, which has appeared in string inspired modern cosmology.

Interacting vector fields in relativity without relativity

NASA Astrophysics Data System (ADS)

Anderson, Edward; Barbour, Julian

2002-06-01

Barbour, Foster and Ó Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of three-dimensional metric-matter configurations. In fact gravity, the universal light-cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity - and more - without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang-Mills fields minimally coupled to gravity.

Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Robert W.

2012-06-15

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Onlymore » at low conductivity and below, the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.« less

Vector magnetic field and vector current density in and around the δ-spot NOAA 10808†

NASA Astrophysics Data System (ADS)

Bommier, Véronique; Landi Degl'Innocenti, Egidio; Schmieder, Brigitte; Gelly, Bernard

2011-08-01

The context is that of the so-called ``fundamental ambiguity'' (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the ``simulated annealing'' algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line (Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5).

Carter separable electromagnetic fields

NASA Astrophysics Data System (ADS)

Lynden-Bell, D.

2000-02-01

The purely electromagnetic analogue in flat space of Kerr's metric in general relativity is only rarely considered. Here we carry out in flat space a programme similar to Carter's investigation of metrics in general relativity in which the motion of a charged particle is separable. We concentrate on the separability of the motion (be it classical, relativistic or quantum) of a charged particle in electromagnetic fields that lie in planes through an axis of symmetry. In cylindrical polar coordinates (t,R,φ,z) the four-vector potential takes the form [formmu2] is the unit toroidal vector. The forms of the functions Φ(R,z) and A(R,z) are sought that allow separable motion. This occurs for relativistic motion only when AR,Φ and A2-Φ2 are all of the separable form ζ(λ)-η(μ)]/(λ-μ), where ζ and η are arbitrary functions, and λ and μ are spheroidal coordinates or degenerations thereof. The special forms of A and Φ that allow this are deduced. They include the Kerr metric analogue, with E+iB=-∇{q[(r-ia).(r-ia)]-1/2}. Rather more general electromagnetic fields allow separation when the motion is non-relativistic. The investigation is extended to fields that lie in parallel planes. Connections to Larmor's theorem are remarked upon.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Makarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

Anisotropic inflation with derivative couplings

NASA Astrophysics Data System (ADS)

Holland, Jonathan; Kanno, Sugumi; Zavala, Ivonne

2018-05-01

We study anisotropic power-law inflationary solutions when the inflaton and its derivative couple to a vector field. This type of coupling is motivated by D-brane inflationary models, in which the inflaton, and a vector field living on the D-brane, couple disformally (derivatively). We start by studying a phenomenological model where we show the existence of anisotropic solutions and demonstrate their stability via a dynamical system analysis. Compared to the case without a derivative coupling, the anisotropy is reduced and thus can be made consistent with current limits, while the value of the slow-roll parameter remains almost unchanged. We also discuss solutions for more general cases, including D-brane-like couplings.

Features of the photometry of the superposition of coherent vector electromagnetic waves

NASA Astrophysics Data System (ADS)

Sakhnovskyj, Mykhajlo Yu.; Tymochko, Bogdan M.; Rudeichuk, Volodymyr M.

2018-01-01

In the paper we propose a general approach to the calculation of the forming the intensity and polarization fields of the superposition of arbitrary coherent vector beams at points of a given reference plane. The method of measuring photometric parameters of a field, formed in the neighborhood of an arbitrary point of the plane of analysis by minimizing the values of irradiance in the vicinity of a given point (method of zero-amplitude at a given point), which is achieved by superimposing on it the reference wave with the controlled values of intensity, polarization state, phase, and angle of incidence, is proposed.

Lienard--Wiechert fields and general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Newman, E.T.

1974-01-01

An analogy is extablished between the Lienard-Weichart solutions of the Maxwell equations and the Robinson-Trautman solutions of the einstein equations by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) The field is a geodesic field, (2) it has nonvanishing divergence, (3) it is shear free, and (4) it is twist (or curl) free. (auth)

Determining conduction patterns on a sparse electrode grid: Implications for the analysis of clinical arrhythmias

NASA Astrophysics Data System (ADS)

Vidmar, David; Narayan, Sanjiv M.; Krummen, David E.; Rappel, Wouter-Jan

2016-11-01

We present a general method of utilizing bioelectric recordings from a spatially sparse electrode grid to compute a dynamic vector field describing the underlying propagation of electrical activity. This vector field, termed the wave-front flow field, permits quantitative analysis of the magnitude of rotational activity (vorticity) and focal activity (divergence) at each spatial point. We apply this method to signals recorded during arrhythmias in human atria and ventricles using a multipolar contact catheter and show that the flow fields correlate with corresponding activation maps. Further, regions of elevated vorticity and divergence correspond to sites identified as clinically significant rotors and focal sources where therapeutic intervention can be effective. These flow fields can provide quantitative insights into the dynamics of normal and abnormal conduction in humans and could potentially be used to enhance therapies for cardiac arrhythmias.

Spacetime symmetries and Kepler's third law

NASA Astrophysics Data System (ADS)

Le Tiec, Alexandre

2012-11-01

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler’s third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence and gravitational redshift.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

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 perturbationsmore » 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.« less

Conserved charge of a gravity theory with p -form gauge fields and its property under Kaluza-Klein reduction

NASA Astrophysics Data System (ADS)

Peng, Jun-Jin

2017-05-01

In this paper, we investigate the conserved charges of generally diffeomorphism invariant gravity theories with a wide variety of matter fields, particularly of the theories with multiple scalar fields and p -form potentials, in the context of the off-shell generalized Abbott-Deser-Tekin (ADT) formalism. We first construct a new off-shell ADT current that consists of the terms for the variation of a Killing vector and expressions of the field equations as well as the Lie derivative of a surface term with respect to the Killing vector within the framework of generally diffeomorphism invariant gravity theories involving various matter fields. After deriving the off-shell ADT potential corresponding to this current, we propose a formula of conserved charges for these theories. Next, we derive the off-shell ADT potential associated with the generic Lagrangian that describes a large range of gravity theories with a number of scalar fields and p -form potentials. Finally, the properties of the off-shell generalized ADT charges for the theory of Einstein gravity and the gravity theories with a single p -form potential are investigated by performing Kaluza-Klein dimensional reduction along a compactified direction. The results indicate that the charge contributed by all the fields in the lower-dimensional theory is equal to that of the higher-dimensional one at mathematical level with the hypothesis that the higher-dimensional spacetime allows for the existence of the compactified dimension. In order to illustrate our calculations, the mass and angular momentum for the five-dimensional rotating Kaluza-Klein black holes are explicitly evaluated as an example.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhatia, Harsh

This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields—an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single “correct” reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thusmore » creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of “correctness” of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (timeindependent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations.« less

Lyapounov Functions of Closed Cone Fields: From Conley Theory to Time Functions

NASA Astrophysics Data System (ADS)

Bernard, Patrick; Suhr, Stefan

2018-03-01

We propose a theory "à la Conley" for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of closed (or equivalently semi-continuous) cone fields with singularities. This setting contains (for questions which are parametrization independent such as the existence of Lyapounov functions) the case of continuous vector-fields on manifolds, of differential inclusions, of Lorentzian metrics, and of continuous cone fields. We generalize to this setting the equivalence between stable causality and the existence of temporal functions. We also generalize the equivalence between global hyperbolicity and the existence of a steep temporal function.

Changes in measured vector magnetic fields when transformed into heliographic coordinates

NASA Technical Reports Server (NTRS)

Hagyard, M. J.

1987-01-01

The changes that occur in measured magnetic fields when they are transformed into a heliographic coordinate system are investigated. To carry out this investigation, measurements of the vector magnetic field of an active region that was observed at 1/3 the solar radius from disk center are taken, and the observed field is transformed into heliographic coordinates. Differences in the calculated potential field that occur when the heliographic normal component of the field is used as the boundary condition rather than the observed line-of-sight component are also examined. The results of this analysis show: (1) that the observed fields of sunspots more closely resemble the generally accepted picture of the distribution of umbral fields if they are displayed in heliographic coordinates; (2) that the differences in the potential calculations are less than 200 G in field strength and 20 deg in field azimuth outside sunspots; and (3) that differences in the two potential calculations in the sunspot areas are no more than 400 G in field strength but range from 60 to 80 deg in field azimuth in localized umbral areas.

Nonpolynomial vector fields under the Lotka-Volterra normal form

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Fairén, Víctor

1995-02-01

We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the generalized Lotka-Volterra format. The procedure introduces appropriate auxiliary variables, and it is shown how, to a great extent, the final Lotka-Volterra system is independent of their specific definition. Conservation of the topological equivalence during the process is also demonstrated.

Attitude Determination Using Two Vector Measurements

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1998-01-01

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

General very special relativity in Finsler cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.

2009-05-15

General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

NASA Technical Reports Server (NTRS)

Gedney, Stephen D.; Lansing, Faiza

1993-01-01

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Towards an Optimal Noise Versus Resolution Trade-Off in Wind Scatterometry

NASA Technical Reports Server (NTRS)

Williams, Brent A.

2011-01-01

A scatterometer is a radar that measures the normalized radar cross section sigma(sup 0) of the Earth's surface. Over the ocean this signal is related to the wind via the geophysical model function (GMF). The objective of wind scatterometry is to estimate the wind vector field from sigma(sup 0) measurements; however, there are many subtleties that complicate this problem-making it difficult to obtain a unique wind field estimate. Conventionally, wind estimation is split into two stages: a wind retrieval stage in which several ambiguous solutions are obtained, and an ambiguity removal stage in which ambiguities are chosen to produce an appropriate wind vector field estimate. The most common approach to wind field estimation is to grid the scatterometer swath into wind vector cells and estimate wind vector ambiguities independently for each cell. Then, field wise structure is imposed on the solution by an ambiguity selection routine. Although this approach is simple and practical, it neglects field wise structure in the retrieval step and does not account for the spatial correlation imposed by the sampling. This makes it difficult to develop a theoretically appropriate noise versus resolution trade-off using pointwise retrieval. Fieldwise structure may be imposed in the retrieval step using a model-based approach. However, this approach is generally only practical if a low order wind field model is applied, which may discard more information than is desired. Furthermore, model-based approaches do not account for the structure imposed by the sampling. A more general fieldwise approach is to estimate all the wind vectors for all the WVCs simultaneously from all the measurements. This approach can account for structure of the wind field as well as structure imposed by the sampling in the wind retrieval step. Williams and Long in 2010 developed a fieldwise retrieval method based on maximum a posteriori estimation (MAP). This MAP approach can be extended to perform a noise versus resolution trade-off, and deal with ambiguity selection. This paper extends the fieldwise MAP estimation approach and investigates both the noise versus resolution trade-off as well as ambiguity removal in the fieldwise wind retrieval step. The method is then applied to the Sea Winds scatterometer and the results are analyzed. This paper extends the fieldwise MAP estimation approach and investigates both the noise versus resolution trade-off as well as ambiguity removal in the fieldwise wind retrieval step. The method is then applied to the Sea Winds scatterometer and the results are analyzed.

New Method for Solving Inductive Electric Fields in the Ionosphere

NASA Astrophysics Data System (ADS)

Vanhamäki, H.

2005-12-01

We present a new method for calculating inductive electric fields in the ionosphere. It is well established that on large scales the ionospheric electric field is a potential field. This is understandable, since the temporal variations of large scale current systems are generally quite slow, in the timescales of several minutes, so inductive effects should be small. However, studies of Alfven wave reflection have indicated that in some situations inductive phenomena could well play a significant role in the reflection process, and thus modify the nature of ionosphere-magnetosphere coupling. The input to our calculation method are the time series of the potential part of the ionospheric electric field together with the Hall and Pedersen conductances. The output is the time series of the induced rotational part of the ionospheric electric field. The calculation method works in the time-domain and can be used with non-uniform, time-dependent conductances. In addition no particular symmetry requirements are imposed on the input potential electric field. The presented method makes use of special non-local vector basis functions called Cartesian Elementary Current Systems (CECS). This vector basis offers a convenient way of representing curl-free and divergence-free parts of 2-dimensional vector fields and makes it possible to solve the induction problem using simple linear algebra. The new calculation method is validated by comparing it with previously published results for Alfven wave reflection from uniformly conducting ionosphere.

A link between torse-forming vector fields and rotational hypersurfaces

NASA Astrophysics Data System (ADS)

Chen, Bang-Yen; Verstraelen, Leopold

Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340-346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More precisely, our main result states that, for a hypersurface M of 𝔼n+1 with n ≥ 3, the tangential component xT of the position vector field of M is a proper torse-forming vector field on M if and only if M is contained in a rotational hypersurface whose axis of rotation contains the origin.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors.

PubMed

Xu, Danfeng; Gu, Bing; Rui, Guanghao; Zhan, Qiwen; Cui, Yiping

2016-02-22

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

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.

Intraventricular vector flow mapping—a Doppler-based regularized problem with automatic model selection

NASA Astrophysics Data System (ADS)

Assi, Kondo Claude; Gay, Etienne; Chnafa, Christophe; Mendez, Simon; Nicoud, Franck; Abascal, Juan F. P. J.; Lantelme, Pierre; Tournoux, François; Garcia, Damien

2017-09-01

We propose a regularized least-squares method for reconstructing 2D velocity vector fields within the left ventricular cavity from single-view color Doppler echocardiographic images. Vector flow mapping is formulated as a quadratic optimization problem based on an {{\\ell }2} -norm minimization of a cost function composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to 2D mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of the continuous problem was adopted in a polar coordinate system, leading to a sparse symmetric positive-definite system. The three regularization parameters were determined automatically by analyzing the L-hypersurface, a generalization of the L-curve. The performance of the proposed method was numerically evaluated using (1) a synthetic flow composed of a mixture of divergence-free and curl-free flow fields and (2) simulated flow data from a patient-specific CFD (computational fluid dynamics) model of a human left heart. The numerical evaluations showed that the vector flow fields reconstructed from the Doppler components were in good agreement with the original velocities, with a relative error less than 20%. It was also demonstrated that a perturbation of the domain contour has little effect on the rebuilt velocity fields. The capability of our intraventricular vector flow mapping (iVFM) algorithm was finally illustrated on in vivo echocardiographic color Doppler data acquired in patients. The vortex that forms during the rapid filling was clearly deciphered. This improved iVFM algorithm is expected to have a significant clinical impact in the assessment of diastolic function.

Design of 2D time-varying vector fields.

PubMed

Chen, Guoning; Kwatra, Vivek; Wei, Li-Yi; Hansen, Charles D; Zhang, Eugene

2012-10-01

Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects.

Euler potentials of current-free fields expressed in spherical harmonics

NASA Technical Reports Server (NTRS)

Stern, David P.

1994-01-01

Given a magnetic field B = -del(vector differential operator)(sub gamma) with gamma expanded in spherical harmonics, it is shown that analytic Euler potentials may be derived for B if gamma is asymmetrical but contains only the contribution of a single index n. This work generalizes a result for sectorial harmonics with n = m, derived by Willis and Gardiner (1988).

Analysis of a dual-reflector antenna system using physical optics and digital computers

NASA Technical Reports Server (NTRS)

Schmidt, R. F.

1972-01-01

The application of physical-optics diffraction theory to a deployable dual-reflector geometry is discussed. The methods employed are not restricted to the Conical-Gregorian antenna, but apply in a general way to dual and even multiple reflector systems. Complex vector wave methods are used in the Fresnel and Fraunhofer regions of the reflectors. Field amplitude, phase, polarization data, and time average Poynting vectors are obtained via an IBM 360/91 digital computer. Focal region characteristics are plotted with the aid of a CalComp plotter. Comparison between the GSFC Huygens wavelet approach, JPL measurements, and JPL computer results based on the near field spherical wave expansion method are made wherever possible.

Lovelock vacua with a recurrent null vector field

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello

2018-02-01

Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a "generic" base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the p p - waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions n =5 , 6 as well as for particular choices of the base manifold. The obtained solutions describe various classes of nonexpanding gravitational waves propagating, e.g., in Nariai-like backgrounds M2×Σn -2. An Appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

PubMed

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Uncertainty principles for inverse source problems for electromagnetic and elastic waves

NASA Astrophysics Data System (ADS)

Griesmaier, Roland; Sylvester, John

2018-06-01

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

NASA Astrophysics Data System (ADS)

Wen, Dan; Yu, Hongwei; Pan, Qiyuan; Lin, Kai; Qian, Wei-Liang

2018-05-01

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

Thermal noise model of antiferromagnetic dynamics: A macroscopic approach

NASA Astrophysics Data System (ADS)

Li, Xilai; Semenov, Yuriy; Kim, Ki Wook

In the search for post-silicon technologies, antiferromagnetic (AFM) spintronics is receiving widespread attention. Due to faster dynamics when compared with its ferromagnetic counterpart, AFM enables ultra-fast magnetization switching and THz oscillations. A crucial factor that affects the stability of antiferromagnetic dynamics is the thermal fluctuation, rarely considered in AFM research. Here, we derive from theory both stochastic dynamic equations for the macroscopic AFM Neel vector (L-vector) and the corresponding Fokker-Plank equation for the L-vector distribution function. For the dynamic equation approach, thermal noise is modeled by a stochastic fluctuating magnetic field that affects the AFM dynamics. The field is correlated within the correlation time and the amplitude is derived from the energy dissipation theory. For the distribution function approach, the inertial behavior of AFM dynamics forces consideration of the generalized space, including both coordinates and velocities. Finally, applying the proposed thermal noise model, we analyze a particular case of L-vector reversal of AFM nanoparticles by voltage controlled perpendicular magnetic anisotropy (PMA) with a tailored pulse width. This work was supported, in part, by SRC/NRI SWAN.

MOG without anomaly

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Ghaffary, Tooraj; Naimi, Yaghoob

2018-03-01

We obtain the action of Moffat's Modified Gravity (MOG), a scalar-tensor-vector theory of gravitation, by generalizing the Horava-Witten mechanism to fourteen dimensions. We show that the resulting theory is anomaly-free. We propose an extended version of MOG that includes fermionic fields.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Layton, E.; Huang, Y.; Chu, S.

We show that cyclic quantum evolution can be realized and the Aharonov-Anandan (AA) geometric phase can be determined for any spin-{ital j} system driven by periodic fields. Two methods are extended for the study of this problem: the generalized spin-coherent-state technique and the Floquet quasienergy approach. Using the former approach, we have developed a {ital generalized} Bloch-sphere model and presented a SU(2) Lie-group formulation of the AA geometric phase in the spin-coherent state. We show that the AA phase is equal to {ital j} times the solid angle enclosed by the trajectory traced out by the tip of a generalizedmore » Bloch vector. General analytic formulas are obtained for the Bloch vector trajectory and the AA geometric phase in terms of external physical parameters. In addition to these findings, we have also approached the same problem from an alternative but complementary point of view without recourse to the concept of coherent-state terminology. Here we first determine the Floquet quasienergy eigenvalues and eigenvectors for the spin-{ital j} system driven by periodic fields. This in turn allows the construction of the time-evolution propagator, the total wave function, and the AA geometric phase in a more general fashion.« less

Ladder operators for the Klein-Gordon equation with a scalar curvature term

NASA Astrophysics Data System (ADS)

Mück, Wolfgang

2018-01-01

Recently, Cardoso, Houri and Kimura constructed generalized ladder operators for massive Klein-Gordon scalar fields in space-times with conformal symmetry. Their construction requires a closed conformal Killing vector, which is also an eigenvector of the Ricci tensor. Here, a similar procedure is used to construct generalized ladder operators for the Klein-Gordon equation with a scalar curvature term. It is proven that a ladder operator requires the existence of a conformal Killing vector, which must satisfy an additional property. This property is necessary and sufficient for the construction of a ladder operator. For maximally symmetric space-times, the results are equivalent to those of Cardoso, Houri and Kimura.

Torsion axial vector and Yvon-Takabayashi angle: zitterbewegung, chirality and all that

NASA Astrophysics Data System (ADS)

Fabbri, Luca; da Rocha, Roldão

2018-03-01

We consider propagating torsion as a completion of gravitation in order to describe the dynamics of curved-twisted space-times filled with Dirac spinorial fields; we discuss interesting relationships of the torsion axial vector and the curvature tensor with the Yvon-Takabayashi angle and the module of the spinor field, that is the two degrees of freedom of the spinor field itself: in particular, we shall discuss in what way the torsion axial vector could be seen as the potential of a specific interaction of the Yvon-Takabayashi angle, and therefore as a force between the two chiral projections of the spinor field itself. Chiral interactions of the components of a spinor may render effects of zitterbewegung, as well as effective mass terms and other related features: we shall briefly sketch some of the analogies and differences with the similar but not identical situation given by the Yukawa interaction occurring in the Higgs sector of the standard model. We will provide some overall considerations about general consequences for contemporary physics, consequences that have never been discussed before, so far as we are aware, in the present physics literature.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hanson, J. D.

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz's theorem.

Hyperbolic-symmetry vector fields.

PubMed

Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2015-12-14

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

General Relativity

NASA Astrophysics Data System (ADS)

Hobson, M. P.; Efstathiou, G. P.; Lasenby, A. N.

2006-02-01

1. The spacetime of special relativity; 2. Manifolds and coordinates; 3. Vector calculus on manifolds; 4. Tensor calculus on manifolds; 5. Special relativity revisited; 6. Electromagnetism; 7. The equivalence principle and spacetime curvature; 8. The gravitational field equations; 9. The Schwarzschild geometry; 10. Experimental tests of general relativity; 11. Schwarzschild black holes; 12. Further spherically-symmetric geometries; 13. The Kerr geometry; 14. The Friedmann-Robertson-Walker geometry; 15. Cosmological models; 16. Inflationary cosmology; 17. Linearised general relativity; 18. Gravitational waves; 19. A variational approach to general relativity.

Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.

2018-04-01

In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.

A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

NASA Astrophysics Data System (ADS)

Carozzi, T. D.; Woan, G.

2009-05-01

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard `Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

NASA Astrophysics Data System (ADS)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Synthetic Sex Pheromone Attracts the Leishmaniasis Vector Lutzomyia longipalpis (Diptera: Psychodidae) to Traps in the Field

PubMed Central

Bray, D. P.; Bandi, K. K.; Brazil, R. P.; Oliveira, A. G.; Hamilton, J.G.C.

2011-01-01

Improving vector control remains a key goal in reducing the world’s burden of infectious diseases. More cost-effective approaches to vector control are urgently needed, particularly as vaccines are unavailable and treatment is prohibitively expensive. The causative agent of AVL, Leishmania chagasi, Cunha and Chagas (Kinetoplastida: Trypanosomatidae) is transmitted between animal and human hosts by blood-feeding female sand flies, attracted to mating aggregations formed on or above host animals by male-produced sex pheromones. Our results demonstrate the potential of using synthetic pheromones to control populations of Lutzomyia longipalpis Lutz and Neiva (Diptera: Psychodidae), the sand fly vector of one of the world’s most important neglected diseases, American visceral leishmaniasis (AVL). We showed that a synthetic pheromone, (±)-9-methylgermacrene-B, produced from a low-cost plant intermediate, attracted females in the laboratory. Then by formulating dispensers that released this pheromone at a rate similar to that released by aggregating males, we were able to attract flies of both sexes to traps in the field. These dispensers worked equally well when deployed with mechanical light traps and inexpensive sticky traps. If deployed effectively, pheromone-based traps could be used to decrease AVL transmission rates through specific targeting and reduction of L. longipalpis populations. This is the first study to show attraction of a human disease-transmitting insect to a synthetic pheromone in the field, demonstrating the general applicability of this novel approach for developing new tools for use in vector control. PMID:19496409

Synthetic sex pheromone attracts the leishmaniasis vector Lutzomyia longipalpis (Diptera: Psychodidae) to traps in the field.

PubMed

Bray, D P; Bandi, K K; Brazil, R P; Oliveira, A G; Hamilton, J G C

2009-05-01

Improving vector control remains a key goal in reducing the world's burden of infectious diseases. More cost-effective approaches to vector control are urgently needed, particularly because vaccines are unavailable and treatment is prohibitively expensive. The causative agent of American visceral leishmaniasis (AVL), Leishmania chagasi, Cunha and Chagas (Kinetoplastida: Trypanosomatidae), is transmitted between animal and human hosts by blood-feeding female sand flies attracted to mating aggregations formed on or above host animals by male-produced sex pheromones. Our results show the potential of using synthetic pheromones to control populations of Lutzomyia longipalpis Lutz and Neiva (Diptera: Psychodidae), the sand fly vector of one of the world's most important neglected diseases, AVL. We showed that a synthetic pheromone, (+/-)-9-methylgermacrene-B, produced from a low-cost plant intermediate, attracted females in the laboratory. By formulating dispensers that released this pheromone at a rate similar to that released by aggregating males, we were able to attract flies of both sexes to traps in the field. These dispensers worked equally well when deployed with mechanical light traps and inexpensive sticky traps. If deployed effectively, pheromone-based traps could be used to decrease AVL transmission rates through specific targeting and reduction of L. longipalpis populations. This is the first study to show attraction of a human disease-transmitting insect to a synthetic pheromone in the field, showing the general applicability of this novel approach for developing new tools for use in vector control.

Algebraic and radical potential fields. Stability domains in coordinate and parametric space

NASA Astrophysics Data System (ADS)

Uteshev, Alexei Yu.

2018-05-01

A dynamical system d X/d t = F(X; A) is treated where F(X; A) is a polynomial (or some general type of radical contained) function in the vectors of state variables X ∈ ℝn and parameters A ∈ ℝm. We are looking for stability domains in both spaces, i.e. (a) domain ℙ ⊂ ℝm such that for any parameter vector specialization A ∈ ℙ, there exists a stable equilibrium for the dynamical system, and (b) domain 𝕊 ⊂ ℝn such that any point X* ∈ 𝕊 could be made a stable equilibrium by a suitable specialization of the parameter vector A.

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Spacetime algebra as a powerful tool for electromagnetism

NASA Astrophysics Data System (ADS)

Dressel, Justin; Bliokh, Konstantin Y.; Nori, Franco

2015-08-01

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.

Isotropy of Angular Frequencies and Weak Chimeras with Broken Symmetry

NASA Astrophysics Data System (ADS)

Bick, Christian

2017-04-01

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.

Rotation invariants of vector fields from orthogonal moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Bo; Kostková, Jitka; Flusser, Jan

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

Huygens' optical vector wave field synthesis via in-plane electric dipole metasurface.

PubMed

Park, Hyeonsoo; Yun, Hansik; Choi, Chulsoo; Hong, Jongwoo; Kim, Hwi; Lee, Byoungho

2018-04-16

We investigate Huygens' optical vector wave field synthesis scheme for electric dipole metasurfaces with the capability of modulating in-plane polarization and complex amplitude and discuss the practical issues involved in realizing multi-modulation metasurfaces. The proposed Huygens' vector wave field synthesis scheme identifies the vector Airy disk as a synthetic unit element and creates a designed vector optical field by integrating polarization-controlled and complex-modulated Airy disks. The metasurface structure for the proposed vector field synthesis is analyzed in terms of the signal-to-noise ratio of the synthesized field distribution. The design of practical metasurface structures with true vector modulation capability is possible through the analysis of the light field modulation characteristics of various complex modulated geometric phase metasurfaces. It is shown that the regularization of meta-atoms is a key factor that needs to be considered in field synthesis, given that it is essential for a wide range of optical field synthetic applications, including holographic displays, microscopy, and optical lithography.

Rotation invariants of vector fields from orthogonal moments

DOE PAGES

Yang, Bo; Kostková, Jitka; Flusser, Jan; ...

2017-09-11

Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is so-called total rotation, where the action is applied not only on the spatial coordinates but alsomore » on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.« less

Cranking of Nuclei at Finite Temperature:

NASA Astrophysics Data System (ADS)

Bartel, J.; Bencheikh, K.; Quentin, P.

We present a generalization of the Extended Thomas Fermi (ETF) theory to fermionic systems at finite temperature and finite angular momentum. In fact the present approach is more general in the sense that it is able to treat an excited system of fermions subject to an external vector field which in the case of nuclear rotations, developed more extensively here, is simply ěc{r}×ěc{ω }.

Helicons in uniform fields. I. Wave diagnostics with hodograms

NASA Astrophysics Data System (ADS)

Urrutia, J. M.; Stenzel, R. L.

2018-03-01

The wave equation for whistler waves is well known and has been solved in Cartesian and cylindrical coordinates, yielding plane waves and cylindrical waves. In space plasmas, waves are usually assumed to be plane waves; in small laboratory plasmas, they are often assumed to be cylindrical "helicon" eigenmodes. Experimental observations fall in between both models. Real waves are usually bounded and may rotate like helicons. Such helicons are studied experimentally in a large laboratory plasma which is essentially a uniform, unbounded plasma. The waves are excited by loop antennas whose properties determine the field rotation and transverse dimensions. Both m = 0 and m = 1 helicon modes are produced and analyzed by measuring the wave magnetic field in three dimensional space and time. From Ampère's law and Ohm's law, the current density and electric field vectors are obtained. Hodograms for these vectors are produced. The sign ambiguity of the hodogram normal with respect to the direction of wave propagation is demonstrated. In general, electric and magnetic hodograms differ but both together yield the wave vector direction unambiguously. Vector fields of the hodogram normal yield the phase flow including phase rotation for helicons. Some helicons can have locally a linear polarization which is identified by the hodogram ellipticity. Alternatively the amplitude oscillation in time yields a measure for the wave polarization. It is shown that wave interference produces linear polarization. These observations emphasize that single point hodogram measurements are inadequate to determine the wave topology unless assuming plane waves. Observations of linear polarization indicate wave packets but not plane waves. A simple qualitative diagnostics for the wave polarization is the measurement of the magnetic field magnitude in time. Circular polarization has a constant amplitude; linear polarization results in amplitude modulations.

Magnetic Field, Density Current, and Lorentz Force Full Vector Maps of the NOAA 10808 Double Sunspot: Evidence of Strong Horizontal Current Flows in the Penumbra

NASA Astrophysics Data System (ADS)

Bommier, V.; Landi Degl'Innocenti, E.; Schmieder, B.; Gelly, B.

2011-04-01

The context is that of the so-called “fundamental ambiguity” (also azimuth ambiguity, or 180° ambiguity) in magnetic field vector measurements: two field vectors symmetrical with respect to the line-of-sight have the same polarimetric signature, so that they cannot be discriminated. We propose a method to solve this ambiguity by applying the “simulated annealing” algorithm to the minimization of the field divergence, added to the longitudinal current absolute value, the line-of-sight derivative of the magnetic field being inferred by the interpretation of the Zeeman effect observed by spectropolarimetry in two lines formed at different depths. We find that the line pair Fe I λ 6301.5 and Fe I λ 6302.5 is appropriate for this purpose. We treat the example case of the δ-spot of NOAA 10808 observed on 13 September 2005 between 14:25 and 15:25 UT with the THEMIS telescope. Besides the magnetic field resolved map, the electric current density vector map is also obtained. A strong horizontal current density flow is found surrounding each spot inside its penumbra, associated to a non-zero Lorentz force centripetal with respect to the spot center (i.e., oriented towards the spot center). The current wrapping direction is found to depend on the spot polarity: clockwise for the positive polarity, counterclockwise for the negative one. This analysis is made possible thanks to the UNNOFIT2 Milne-Eddington inversion code, where the usual theory is generalized to the case of a line Fe I λ 6301.5) that is not a normal Zeeman triplet line (like Fe I λ 6302.5).

General n-dimensional quadrature transform and its application to interferogram demodulation.

PubMed

Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis

2003-05-01

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Broken Symmetry

ScienceCinema

Englert, Francois

2018-05-24

- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of “massless” modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a “massive” SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic “vector” field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are “scalar’’ fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a “renormalizable” theory. From our analysis of the preserved gauge symmetry, we suggested in 1966 that this is indeed the case, in contradistinction to the aforementioned earlier theories of charged massive vector fields. The full proof of “renormalizability” is subtle and was achieved in the impressive work of ‘t Hooft and Veltman. One gains some insight into the subtleties by making explicit the equivalence of Higgs’ approach with ours. - To a large extend, the LHC was build to detect the massive SBS scalar boson, i.e. the fluctuations of the scalar field. More elaborate realizations of the mechanism without elementary scalars are possible, but their experimental confirmation may (or may not) be outside the scope of present available technology. - The mechanism of Brout, Englert and Higgs unified in the same theoretical framework short- and long-range forces. It became the cornerstone of the electroweak theory and opened the way to a modern view on unified laws of nature.

Nonlinear interactions between black holes and Proca fields

NASA Astrophysics Data System (ADS)

Zilhão, Miguel; Witek, Helvi; Cardoso, Vitor

2015-12-01

Physics beyond the standard model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle ‘forces’ all forms of matter to fall in the same way, and it is therefore natural to look for imprints of these fields in regions with strong gravitational fields, such as compact stars or black holes (BHs). Here we study general relativity minimally coupled to a massive vector field, and how BHs in this theory lose ‘hair’. Our results indicate that BHs can sustain Proca field condensates for extremely long time-scales.

Fractal vector optical fields.

PubMed

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields.

PubMed

Gu, Bing; Xu, Danfeng; Rui, Guanghao; Lian, Meng; Cui, Yiping; Zhan, Qiwen

2015-09-20

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

A note on φ-analytic conformal vector fields

NASA Astrophysics Data System (ADS)

Deshmukh, Sharief; Bin Turki, Nasser

2017-09-01

Taking clue from the analytic vector fields on a complex manifold, φ-analytic conformal vector fields are defined on a Riemannian manifold (Deshmukh and Al-Solamy in Colloq. Math. 112(1):157-161, 2008). In this paper, we use φ-analytic conformal vector fields to find new characterizations of the n-sphere Sn(c) and the Euclidean space (Rn,<,> ).

Mapping the magnetic field vector in a fountain clock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gertsvolf, Marina; Marmet, Louis

2011-12-15

We show how the mapping of the magnetic field vector components can be achieved in a fountain clock by measuring the Larmor transition frequency in atoms that are used as a spatial probe. We control two vector components of the magnetic field and apply audio frequency magnetic pulses to localize and measure the field vector through Zeeman spectroscopy.

Second level semi-degenerate fields in W_3 Toda theory: matrix element and differential equation

NASA Astrophysics Data System (ADS)

Belavin, Vladimir; Cao, Xiangyu; Estienne, Benoit; Santachiara, Raoul

2017-03-01

In a recent study we considered W_3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl_3 . We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

Analysis models for the estimation of oceanic fields

NASA Technical Reports Server (NTRS)

Carter, E. F.; Robinson, A. R.

1987-01-01

A general model for statistically optimal estimates is presented for dealing with scalar, vector and multivariate datasets. The method deals with anisotropic fields and treats space and time dependence equivalently. Problems addressed include the analysis, or the production of synoptic time series of regularly gridded fields from irregular and gappy datasets, and the estimate of fields by compositing observations from several different instruments and sampling schemes. Technical issues are discussed, including the convergence of statistical estimates, the choice of representation of the correlations, the influential domain of an observation, and the efficiency of numerical computations.

The virtual-casing principle and Helmholtz's theorem

DOE PAGES

Hanson, J. D.

2015-09-10

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz's theorem.

The virtual-casing principle and Helmholtz’s theorem

DOE PAGES

Hanson, J. D.

2015-09-10

The virtual-casing principle is used in plasma physics to convert a Biot–Savart integration over a current distribution into a surface integral over a surface that encloses the current. In many circumstances, use of virtual casing can significantly speed up the computation of magnetic fields. In this paper, a virtual-casing principle is derived for a general vector field with arbitrary divergence and curl. This form of the virtual-casing principle is thus applicable to both magnetostatic fields and electrostatic fields. The result is then related to Helmholtz’s theorem.

Numerical computation of gravitational field for general axisymmetric objects

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Nonnormal operators in physics, a singular-vectors approach: illustration in polarization optics.

PubMed

Tudor, Tiberiu

2016-04-20

The singular-vectors analysis of a general nonnormal operator defined on a finite-dimensional complex vector space is given in the frame of a pure operatorial ("nonmatrix," "coordinate-free") approach, performed in a Dirac language. The general results are applied in the field of polarization optics, where the nonnormal operators are widespread as operators of various polarization devices. Two nonnormal polarization devices representative for the class of nonnormal and even pathological operators-the standard two-layer elliptical ideal polarizer (singular operator) and the three-layer ambidextrous ideal polarizer (singular and defective operator)-are analyzed in detail. It is pointed out that the unitary polar component of the operator exists and preserves, in such pathological case too, its role of converting the input singular basis of the operator in its output singular basis. It is shown that for any nonnormal ideal polarizer a complementary one exists, so that the tandem of their operators uniquely determines their (common) unitary polar component.

Different Relative Orientation of Static and Alternative Magnetic Fields and Cress Roots Direction of Growth Changes Their Gravitropic Reaction

NASA Astrophysics Data System (ADS)

Sheykina, Nadiia; Bogatina, Nina

The following variants of roots location relatively to static and alternative components of magnetic field were studied. At first variant the static magnetic field was directed parallel to the gravitation vector, the alternative magnetic field was directed perpendicular to static one; roots were directed perpendicular to both two fields’ components and gravitation vector. At the variant the negative gravitropysm for cress roots was observed. At second variant the static magnetic field was directed parallel to the gravitation vector, the alternative magnetic field was directed perpendicular to static one; roots were directed parallel to alternative magnetic field. At third variant the alternative magnetic field was directed parallel to the gravitation vector, the static magnetic field was directed perpendicular to the gravitation vector, roots were directed perpendicular to both two fields components and gravitation vector; At forth variant the alternative magnetic field was directed parallel to the gravitation vector, the static magnetic field was directed perpendicular to the gravitation vector, roots were directed parallel to static magnetic field. In all cases studied the alternative magnetic field frequency was equal to Ca ions cyclotron frequency. In 2, 3 and 4 variants gravitropism was positive. But the gravitropic reaction speeds were different. In second and forth variants the gravitropic reaction speed in error limits coincided with the gravitropic reaction speed under Earth’s conditions. At third variant the gravitropic reaction speed was slowed essentially.

Displacement field for an edge dislocation in a layered half-space

USGS Publications Warehouse

Savage, J.C.

1998-01-01

The displacement field for an edge dislocation in an Earth model consisting of a layer welded to a half-space of different material is found in the form of a Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the layer and the Burgers vector is either parallel or perpendicular to the layer. A general two-dimensional solution for a dip-slip faulting or dike injection (arbitrary dip) can be constructed from a superposition of these elementary solutions. Surface deformations have been calculated for an edge dislocation located at the interface with Burgers vector inclined 0??, 30??, 60??, and 90?? to the interface for the case where the rigidity of the layer is half of that of the half-space and the Poisson ratios are the same. Those displacement fields have been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space. The surface displacement field produced by the edge dislocation in the layered half-space is very similar to that produced by an edge dislocation at a different depth in a uniform half-space. In general, a low-modulus (high-modulus) layer causes the half-space equivalent dislocation to appear shallower (deeper) than the actual dislocation in the layered half-space.

Discovering and understanding the vector field using simulation in android app

NASA Astrophysics Data System (ADS)

Budi, A.; Muliyati, D.

2018-05-01

An understanding of vector field’s concepts are fundamental parts of the electrodynamics course. In this paper, we use a simple simulation that can be used to show qualitative imaging results as a variation of the vector field. Android application packages the simulation with consideration of the efficiency of use during the lecture. In addition, this simulation also trying to cover the divergences and curl concepts from the same conditions that students have a complete understanding and can distinguish concepts that have been described only mathematically. This simulation is designed to show the relationship between the field magnitude and its potential. This application can show vector field simulations in various conditions that help to improve students’ understanding of vector field concepts and their relation to particle existence around the field vector.

Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for Circular Current Loops in Cylindrical Coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walstrom, Peter Lowell

A numerical algorithm for computing the field components B r and B z and their r and z derivatives with open boundaries in cylindrical coordinates for circular current loops is described. An algorithm for computing the vector potential is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations (especially for the field derivatives) are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. Since cel can evaluate complete elliptic integrals of a fairlymore » general type, in some cases the elliptic integrals can be evaluated without first reducing them to forms containing standard Legendre forms. The algorithms avoid the numerical difficulties that many of the textbook solutions have for points near the axis because of explicit factors of 1=r or 1=r 2 in the some of the expressions.« less

Path planning for assembly of strut-based structures. Thesis

NASA Technical Reports Server (NTRS)

Muenger, Rolf

1991-01-01

A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.

General Matrix Inversion Technique for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

NASA Technical Reports Server (NTRS)

Mach, D. M.; Koshak, W. J.

2007-01-01

A matrix calibration procedure has been developed that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. The calibration method can be generalized to any reasonable combination of electric field measurements and aircraft. A calibration matrix is determined for each aircraft that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or deemphasized [e.g., due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate the calibration technique, data are presented from several aircraft programs (ER-2, DC-8, Altus, and Citation).

A feature selection approach towards progressive vector transmission over the Internet

NASA Astrophysics Data System (ADS)

Miao, Ru; Song, Jia; Feng, Min

2017-09-01

WebGIS has been applied for visualizing and sharing geospatial information popularly over the Internet. In order to improve the efficiency of the client applications, the web-based progressive vector transmission approach is proposed. Important features should be selected and transferred firstly, and the methods for measuring the importance of features should be further considered in the progressive transmission. However, studies on progressive transmission for large-volume vector data have mostly focused on map generalization in the field of cartography, but rarely discussed on the selection of geographic features quantitatively. This paper applies information theory for measuring the feature importance of vector maps. A measurement model for the amount of information of vector features is defined based upon the amount of information for dealing with feature selection issues. The measurement model involves geometry factor, spatial distribution factor and thematic attribute factor. Moreover, a real-time transport protocol (RTP)-based progressive transmission method is then presented to improve the transmission of vector data. To clearly demonstrate the essential methodology and key techniques, a prototype for web-based progressive vector transmission is presented, and an experiment of progressive selection and transmission for vector features is conducted. The experimental results indicate that our approach clearly improves the performance and end-user experience of delivering and manipulating large vector data over the Internet.

Coupled B-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI.

PubMed

Amini, A A; Chen, Y; Curwen, R W; Mani, V; Sun, J

1998-06-01

Magnetic resonance imaging (MRI) is unique in its ability to noninvasively and selectively alter tissue magnetization and create tagged patterns within a deforming body such as the heart muscle. The resulting patterns define a time-varying curvilinear coordinate system on the tissue, which we track with coupled B-snake grids. B-spline bases provide local control of shape, compact representation, and parametric continuity. Efficient spline warps are proposed which warp an area in the plane such that two embedded snake grids obtained from two tagged frames are brought into registration, interpolating a dense displacement vector field. The reconstructed vector field adheres to the known displacement information at the intersections, forces corresponding snakes to be warped into one another, and for all other points in the plane, where no information is available, a C1 continuous vector field is interpolated. The implementation proposed in this paper improves on our previous variational-based implementation and generalizes warp methods to include biologically relevant contiguous open curves, in addition to standard landmark points. The methods are validated with a cardiac motion simulator, in addition to in-vivo tagging data sets.

Initial Results from the Vector Electric Field Investigation on the C/NOFS Satellite

NASA Technical Reports Server (NTRS)

Pfaff, R.; Rowland, D.; Acuna, M.; Le, G.; Farrell, W.; Holzworth, R.; Wilson, G.; Burke, W.; Freudenreich, H.; Bromund, K.;

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Numerical computation of gravitational field of general extended body and its application to rotation curve study of galaxies

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-06-01

Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface mass density distribution. Fortran 90 subroutines to execute these methods and their test programs and sample outputs are available from the author's WEB site: https://www.researchgate.net/profile/Toshio_Fukushima/

Proper projective symmetry in LRS Bianchi type V spacetimes

NASA Astrophysics Data System (ADS)

Shabbir, Ghulam; Mahomed, K. S.; Mahomed, F. M.; Moitsheki, R. J.

2018-04-01

In this paper, we investigate proper projective vector fields of locally rotationally symmetric (LRS) Bianchi type V spacetimes using direct integration and algebraic techniques. Despite the non-degeneracy in the Riemann tensor eigenvalues, we classify proper Bianchi type V spacetimes and show that the above spacetimes do not admit proper projective vector fields. Here, in all the cases projective vector fields are Killing vector fields.

Extracting remanent magnetization from magnetic data inversion

NASA Astrophysics Data System (ADS)

Liu, S.; Fedi, M.; Baniamerian, J.; Hu, X.

2017-12-01

Remanent magnetization is an important vector parameter of rocks' and ores' magnetism, which is related to the intensity and direction of primary geomagnetic fields at all geological periods and hence shows critical evidences of geological tectonic movement and sedimentary evolution. We extract the remanence information from the distributions of the inverted magnetization vector. Firstly, directions of total magnetization vector are estimated from reduced-to-pole anomaly (max-min algorithm) and by its correlations with other magnitude magnetic transforms such as magnitude magnetic anomaly and normalized source strength. Then we invert data for the magnetization intensity and finally the intensity and direction of the remanent magnetization are separated from the total magnetization vector with a generalized formula of the apparent susceptibility based on a priori information on the Koenigsberger ratio. Our approach is used to investigate the targeted resources and geologic processes of the mining areas in China.

Video-rate terahertz electric-field vector imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takai, Mayuko; Takeda, Masatoshi; Sasaki, Manabu

We present an experimental setup to dramatically reduce a measurement time for obtaining spatial distributions of terahertz electric-field (E-field) vectors. The method utilizes the electro-optic sampling, and we use a charge-coupled device to detect a spatial distribution of the probe beam polarization rotation by the E-field-induced Pockels effect in a 〈110〉-oriented ZnTe crystal. A quick rotation of the ZnTe crystal allows analyzing the terahertz E-field direction at each image position, and the terahertz E-field vector mapping at a fixed position of an optical delay line is achieved within 21 ms. Video-rate mapping of terahertz E-field vectors is likely to bemore » useful for achieving real-time sensing of terahertz vector beams, vector vortices, and surface topography. The method is also useful for a fast polarization analysis of terahertz beams.« less

The Maxwell and Navier-Stokes equations that follow from Einstein equation in a spacetime containing a Killing vector field

NASA Astrophysics Data System (ADS)

Rodrigues, Fabio Grangeiro; Rodrigues, Waldyr Alves, Jr.; da Rocha, Roldão

2012-10-01

In this paper we are concerned to reveal that any spacetime structure , which is a model of a gravitational field in General Relativity generated by an energy-momentum tensor T - and which contains at least one nontrivial Killing vector field A - is such that the 2-form field F = dA (where A = g(A,)) satisfies a Maxwell like equation - with a well determined current that contains a term of the superconducting type- which follows directly from Einstein equation. Moreover, we show that the resulting Maxwell like equations, under an additional condition imposed to the Killing vector field, may be written as a Navier-Stokes like equation as well. As a result, we have a set consisting of Einstein, Maxwell and Navier-Stokes equations, that follows sequentially from the first one under precise mathematical conditions and once some identifications about field variables are evinced, as explained in details throughout the text. We compare and emulate our results with others on the same subject appearing in the literature. In Appendix A we fix our notation and recall some necessary material concerning the theory of differential forms, Lie derivatives and the Clifford bundle formalism used in this paper. Moreover, we comment in Appendix B on some analogies (and main differences) between our results to the ones obtained long ago by Bergmann and Kommar which are reviewed and briefly criticized.

Spherical Harmonic Inductive Detection Coils and their use In Dynamic Pre-emphasis for Magnetic Resonance Imaging

NASA Astrophysics Data System (ADS)

Edler, Karl T.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field -- an inverse curl operation -- and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI. Keywords: magnetic resonance imaging, eddy currents, dynamic shimming, negative feedback, quasi-static fields, vector potential, inverse curl

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Generalized Analysis Tools for Multi-Spacecraft Missions

NASA Astrophysics Data System (ADS)

Chanteur, G. M.

2011-12-01

Analysis tools for multi-spacecraft missions like CLUSTER or MMS have been designed since the end of the 90's to estimate gradients of fields or to characterize discontinuities crossed by a cluster of spacecraft. Different approaches have been presented and discussed in the book "Analysis Methods for Multi-Spacecraft Data" published as Scientific Report 001 of the International Space Science Institute in Bern, Switzerland (G. Paschmann and P. Daly Eds., 1998). On one hand the approach using methods of least squares has the advantage to apply to any number of spacecraft [1] but is not convenient to perform analytical computation especially when considering the error analysis. On the other hand the barycentric approach is powerful as it provides simple analytical formulas involving the reciprocal vectors of the tetrahedron [2] but appears limited to clusters of four spacecraft. Moreover the barycentric approach allows to derive theoretical formulas for errors affecting the estimators built from the reciprocal vectors [2,3,4]. Following a first generalization of reciprocal vectors proposed by Vogt et al [4] and despite the present lack of projects with more than four spacecraft we present generalized reciprocal vectors for a cluster made of any number of spacecraft : each spacecraft is given a positive or nul weight. The non-coplanarity of at least four spacecraft with strictly positive weights is a necessary and sufficient condition for this analysis to be enabled. Weights given to spacecraft allow to minimize the influence of some spacecraft if its location or the quality of its data are not appropriate, or simply to extract subsets of spacecraft from the cluster. Estimators presented in [2] are generalized within this new frame except for the error analysis which is still under investigation. References [1] Harvey, C. C.: Spatial Gradients and the Volumetric Tensor, in: Analysis Methods for Multi-Spacecraft Data, G. Paschmann and P. Daly (eds.), pp. 307-322, ISSI SR-001, 1998. [2] Chanteur, G.: Spatial Interpolation for Four Spacecraft: Theory, in: Analysis Methods for Multi-Spacecraft Data, G. Paschmann and P. Daly (eds.), pp. 371-393, ISSI SR-001, 1998. [3] Chanteur, G.: Accuracy of field gradient estimations by Cluster: Explanation of its dependency upon elongation and planarity of the tetrahedron, pp. 265-268, ESA SP-449, 2000. [4] Vogt, J., Paschmann, G., and Chanteur, G.: Reciprocal Vectors, pp. 33-46, ISSI SR-008, 2008.

Spatio-temporal optimization of sampling for bluetongue vectors (Culicoides) near grazing livestock

PubMed Central

2013-01-01

Background Estimating the abundance of Culicoides using light traps is influenced by a large variation in abundance in time and place. This study investigates the optimal trapping strategy to estimate the abundance or presence/absence of Culicoides on a field with grazing animals. We used 45 light traps to sample specimens from the Culicoides obsoletus species complex on a 14 hectare field during 16 nights in 2009. Findings The large number of traps and catch nights enabled us to simulate a series of samples consisting of different numbers of traps (1-15) on each night. We also varied the number of catch nights when simulating the sampling, and sampled with increasing minimum distances between traps. We used resampling to generate a distribution of different mean and median abundance in each sample. Finally, we used the hypergeometric distribution to estimate the probability of falsely detecting absence of vectors on the field. The variation in the estimated abundance decreased steeply when using up to six traps, and was less pronounced when using more traps, although no clear cutoff was found. Conclusions Despite spatial clustering in vector abundance, we found no effect of increasing the distance between traps. We found that 18 traps were generally required to reach 90% probability of a true positive catch when sampling just one night. But when sampling over two nights the same probability level was obtained with just three traps per night. The results are useful for the design of vector monitoring programmes on fields with grazing animals. PMID:23705770

Mass and angular momentum of black holes in low-energy heterotic string theory

NASA Astrophysics Data System (ADS)

Peng, Jun-Jin

2016-04-01

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott-Deser-Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr-Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

Structuring Stokes correlation functions using vector-vortex beam

NASA Astrophysics Data System (ADS)

Kumar, Vijay; Anwar, Ali; Singh, R. P.

2018-01-01

Higher order statistical correlations of the optical vector speckle field, formed due to scattering of a vector-vortex beam, are explored. Here, we report on the experimental construction of the Stokes parameters covariance matrix, consisting of all possible spatial Stokes parameters correlation functions. We also propose and experimentally realize a new Stokes correlation functions called Stokes field auto correlation functions. It is observed that the Stokes correlation functions of the vector-vortex beam will be reflected in the respective Stokes correlation functions of the corresponding vector speckle field. The major advantage of proposing Stokes correlation functions is that the Stokes correlation function can be easily tuned by manipulating the polarization of vector-vortex beam used to generate vector speckle field and to get the phase information directly from the intensity measurements. Moreover, this approach leads to a complete experimental Stokes characterization of a broad range of random fields.

Vector optical fields with bipolar symmetry of linear polarization.

PubMed

Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian

2013-09-15

We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

NASA Astrophysics Data System (ADS)

Benioff, Paul

2015-05-01

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as just one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex number structures and vector space structures. The structures are parameterized by a real or complex scaling factor, s. A vector space at a fiber level, s, has, as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector valued fields gives the same vector fields. The derivation shows that the complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.

Nanoscale shift of the intensity distribution of dipole radiation.

PubMed

Shu, Jie; Li, Xin; Arnoldus, Henk F

2009-02-01

The energy flow lines (field lines of the Poynting vector) for radiation emitted by a dipole are in general curves, rather than straight lines. For a linear dipole the field lines are straight, but when the dipole moment of a source rotates, the field lines wind numerous times around an axis, which is perpendicular to the plane of rotation, before asymptotically approaching a straight line. We consider an elliptical dipole moment, representing the most general state of oscillation, and this includes the linear dipole as a special case. Due to the spiraling near the source, for the case of a rotating dipole moment, the field lines in the far field are displaced with respect to the outward radial direction, and this leads to a shift of the intensity distribution of the radiation in the far field. This shift is shown to be independent of the distance to the source and, although of nanoscale dimension, should be experimentally observable.

Constrains on the South Atlantic Anomaly from Réunion Island

NASA Astrophysics Data System (ADS)

Béguin, A.; de Groot, L. V.

2017-12-01

The South Atlantic Anomaly (SAA) is a region where the geomagnetic field intensity is about half as strong as would be expected from the current geomagnetic dipole moment that arises from geomagnetic field models. Those field models predict a westward movement of the SAA and predicts its origin East of Africa around 1500 AD. The onset and evolution of the SAA, however, are poorly constrained due to a lack of full-vector paleomagnetic data from Africa and the Indian Ocean for the past centuries. Here we present a full-vector paleosecular variation (PSV) curve for Réunion Island (21°S, 55°E) located East the African continent, in the region that currently shows the fastest increase in geomagnetic field strength in contrast to the average global decay. We sampled 27 sites covering the last 700 years, and subjected them to a directional and multi-method paleointensity study. The obtained directional records reveal shallower inclinations and less variation in the declination compared to current geomagnetic field model predictions. Scrutinizing the IZZI-Thellier, Multispecimen, and calibrated pseudo-Thellier results produces a coherent paleointensity record. The predicted intensity trend from the geomagnetic field models generally agrees with the trend in our data, however, the high paleointensities are higher than the models predict, and the low paleointensities are lower than the models. This illustrates the inevitable smoothing inherent to geomagnetic field modelling. We will discuss the constraints on the onset of the SAA that arise from the new full-vector PSV curve for Réunion that we present and the implications for the past and future evolution of this geomagnetic phenomenon.

Light scattering of rectangular slot antennas: parallel magnetic vector vs perpendicular electric vector

NASA Astrophysics Data System (ADS)

Lee, Dukhyung; Kim, Dai-Sik

2016-01-01

We study light scattering off rectangular slot nano antennas on a metal film varying incident polarization and incident angle, to examine which field vector of light is more important: electric vector perpendicular to, versus magnetic vector parallel to the long axis of the rectangle. While vector Babinet’s principle would prefer magnetic field along the long axis for optimizing slot antenna function, convention and intuition most often refer to the electric field perpendicular to it. Here, we demonstrate experimentally that in accordance with vector Babinet’s principle, the incident magnetic vector parallel to the long axis is the dominant component, with the perpendicular incident electric field making a small contribution of the factor of 1/|ε|, the reciprocal of the absolute value of the dielectric constant of the metal, owing to the non-perfectness of metals at optical frequencies.

Numerical simulation using vorticity-vector potential formulation

NASA Technical Reports Server (NTRS)

Tokunaga, Hiroshi

1993-01-01

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Gauge invariant fractional electromagnetic fields

NASA Astrophysics Data System (ADS)

Lazo, Matheus Jatkoske

2011-09-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

On the origin of vorticity in magnetic particle suspensions subjected to triaxial fields

DOE PAGES

Martin, James E.

2016-06-06

We have recently reported that two classes of time-dependent triaxial magnetic fields can induce vorticity in magnetic particle suspensions. The first class – symmetry-breaking fields – is comprised of two ac components and one dc component. The second class – rational triad fields – is comprised of three ac components. In both cases deterministic vorticity occurs when the ratios of the field frequencies form rational numbers. A strange aspect of these fields is that they produce fluid vorticity without generally having a circulating field vector, such as would occur in a rotating field. It has been shown, however, that themore » symmetry of the field trajectory, considered jointly with that of the converse field, allows vorticity to occur around one particular field axis. This axis might be any of the field components, and is determined by the relative frequencies of the field components. However, the symmetry theories give absolutely no insight into why vorticity should occur. In this paper we propose a particle-based model of vorticity in these driven fluids. This model proposes that particles form volatile chains that follow, but lag behind, the dynamic field vector. Furthermore, this model is consistent with the predictions of symmetry theory and gives reasonable agreement with previously reported torque density measurements for a variety of triaxial fields.« less

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure.

PubMed

Mozrzymas, Anna

2011-12-14

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant. Copyright © 2011 Elsevier Ltd. All rights reserved.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

Vector curvaton with varying kinetic function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimopoulos, Konstantinos; Karciauskas, Mindaugas; Wagstaff, Jacques M.

2010-01-15

A new model realization of the vector curvaton paradigm is presented and analyzed. The model consists of a single massive Abelian vector field, with a Maxwell-type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale-invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the spectrum and bispectrum of the curvature perturbation.more » In this case the non-Gaussianity in the curvature perturbation is predominantly anisotropic, which will be a testable prediction in the near future. If, on the other hand, the vector field is heavy at the end of inflation then it is demonstrated that particle production is approximately isotropic and the vector field alone can give rise to the curvature perturbation, without directly involving any fundamental scalar field. The parameter space for both possibilities is shown to be substantial. Finally, toy models are presented which show that the desired variation of the mass and kinetic function of the vector field can be realistically obtained, without unnatural tunings, in the context of supergravity or superstrings.« less

Uniqueness of complete maximal hypersurfaces in spatially parabolic generalized Robertson-Walker spacetimes

NASA Astrophysics Data System (ADS)

Romero, Alfonso; Rubio, Rafael M.; Salamanca, Juan J.

2013-06-01

A new technique for the study of noncompact complete spacelike hypersurfaces in generalized Robertson-Walker (GRW) spacetimes whose fiber is a parabolic Riemannian manifold is introduced. This class of spacetimes allows us to model open universes which extend to spacelike closed GRW spacetimes from the viewpoint of the geometric analysis of the fiber, and which, unlike those spacetimes, could be compatible with the holographic principle. First, under reasonable assumptions on the restriction of the warping function to the spacelike hypersurface and on the hyperbolic angle between the unit normal vector field and a certain timelike vector field, a complete spacelike hypersurface in a spatially parabolic GRW spacetime is shown to be parabolic, and the existence of a simply connected parabolic spacelike hypersurface in a GRW spacetime also leads to the parabolicity of its fiber. Then, all the complete maximal hypersurfaces in spatially parabolic GRW spacetimes are determined in several cases, extending, in particular, to this family of open cosmological models several well-known uniqueness results for the case of spatially closed GRW spacetimes. Moreover, new Calabi-Bernstein problems are solved.

Killing spinors are Killing vector fields in Riemannian supergeometry

NASA Astrophysics Data System (ADS)

Alekseevsky, D. V.; Cortés, V.; Devchand, C.; Semmelmann, U.

1998-06-01

A supermanifold M is canonically associated to any pseudo-Riemannian spin manifold ( M0, g0). Extending the metric g0 to a field g of bilinear forms g( p) on TpM, pɛM0, the pseudo-Riemannian supergeometry of ( M, g) is formulated as G-structure on M, where G is a supergroup with even part G 0 ≊ Spin(k, l); (k, l) the signature of ( M0, go). Killing vector fields on ( M, g) are, by definition, infinitesimal automorphisms of this G-structure. For every spinor field s there exists a corresponding odd vector field Xs on M. Our main result is that Xs is a Killing vector field on ( M, g) if and only if s is a twistor spinor. In particular, any Killing spinor s defines a Killing vector field Xs.

Pioneer 7 observations of plasma flow and field reversal regions in the distant geomagnetic tail

NASA Technical Reports Server (NTRS)

Walker, R. C.; Lazarus, A. J.; Villante, U.

1975-01-01

The present paper gives the results of an extensive analysis of plasma and magnetic-field data from Pioneer 7 taken in the geomagnetic tail approximately 1000 earth radii downstream from earth. The principal observations are: (1) measurable fluxes of protons in the tail, flowing away from earth, sometimes with a double-peaked velocity distribution; (2) field reversal regions in which the field changes from radial to antiradial by a vector rotation in the north-south plane; and (3) general characteristics of the tail similar to those observed near earth with good correlation between taillike magnetic fields and plasma.

On the cosmology of scalar-tensor-vector gravity theory

NASA Astrophysics Data System (ADS)

Jamali, Sara; Roshan, Mahmood; Amendola, Luca

2018-01-01

We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and μ(x), and one vector field phiα(x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θs, in MOG. We find that 8× 10‑3rad<θs<8.2× 10‑3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

Orbifold Schur index and IR formula

NASA Astrophysics Data System (ADS)

Imamura, Yosuke

2018-04-01

We discuss an orbifold version of the Schur index defined as the supersymmetric partition function in S^3/{Z}_n×{S}^1. We first give a general formula for Lagrangian theories obtained by the localization technique, and then suggest a generalization of the Cordova and Shao IR formula. We confirm that the generalized IR formula gives the correct answer for systems with free hypermultiplets if we tune the background fields so that they are invariant under the orbifold action. Unfortunately, we find disagreement for theories with dynamical vector multiplets.

Vertical amplitude phase structure of a low-frequency acoustic field in shallow water

NASA Astrophysics Data System (ADS)

Kuznetsov, G. N.; Lebedev, O. V.; Stepanov, A. N.

2016-11-01

We obtain in integral and analytic form the relations for calculating the amplitude and phase characteristics of an interference structure of orthogonal projections of the oscillation velocity vector in shallow water. For different frequencies and receiver depths, we numerically study the source depth dependences of the effective phase velocities of an equivalent plane wave, the orthogonal projections of the sound pressure phase gradient, and the projections of the oscillation velocity vector. We establish that at low frequencies in zones of interference maxima, independently of source depth, weakly varying effective phase velocity values are observed, which exceed the sound velocity in water by 5-12%. We show that the angles of arrival of the equivalent plane wave and the oscillation velocity vector in the general case differ; however, they virtually coincide in the zone of the interference maximum of the sound pressure under the condition that the horizontal projections of the oscillation velocity appreciably exceed the value of the vertical projection. We give recommendations on using the sound field characteristics in zones with maximum values for solving rangefinding and signal-detection problems.

General Matrix Inversion for the Calibration of Electric Field Sensor Arrays on Aircraft Platforms

NASA Technical Reports Server (NTRS)

Mach, D. M.; Koshak, W. J.

2006-01-01

We have developed a matrix calibration procedure that uniquely relates the electric fields measured at the aircraft with the external vector electric field and net aircraft charge. Our calibration method is being used with all of our aircraft/electric field sensing combinations and can be generalized to any reasonable combination of electric field measurements and aircraft. We determine a calibration matrix that represents the individual instrument responses to the external electric field. The aircraft geometry and configuration of field mills (FMs) uniquely define the matrix. The matrix can then be inverted to determine the external electric field and net aircraft charge from the FM outputs. A distinct advantage of the method is that if one or more FMs need to be eliminated or de-emphasized (for example, due to a malfunction), it is a simple matter to reinvert the matrix without the malfunctioning FMs. To demonstrate our calibration technique, we present data from several of our aircraft programs (ER-2, DC-8, Altus, Citation).

Toward a Quantitative Comparison of Magnetic Field Extrapolations and Observed Coronal Loops

NASA Astrophysics Data System (ADS)

Warren, Harry P.; Crump, Nicholas A.; Ugarte-Urra, Ignacio; Sun, Xudong; Aschwanden, Markus J.; Wiegelmann, Thomas

2018-06-01

It is widely believed that loops observed in the solar atmosphere trace out magnetic field lines. However, the degree to which magnetic field extrapolations yield field lines that actually do follow loops has yet to be studied systematically. In this paper, we apply three different extrapolation techniques—a simple potential model, a nonlinear force-free (NLFF) model based on photospheric vector data, and an NLFF model based on forward fitting magnetic sources with vertical currents—to 15 active regions that span a wide range of magnetic conditions. We use a distance metric to assess how well each of these models is able to match field lines to the 12202 loops traced in coronal images. These distances are typically 1″–2″. We also compute the misalignment angle between each traced loop and the local magnetic field vector, and find values of 5°–12°. We find that the NLFF models generally outperform the potential extrapolation on these metrics, although the differences between the different extrapolations are relatively small. The methodology that we employ for this study suggests a number of ways that both the extrapolations and loop identification can be improved.

Estimation of Discontinuous Displacement Vector Fields with the Minimum Description Length Criterion.

DTIC Science & Technology

1990-10-01

type of approach for finding a dense displacement vector field has a time complexity that allows a real - time implementation when an appropriate control...hardly vector fields as they appear in Stereo or motion. The reason for this is the fact that local displacement vector field ( DVF ) esti- mates bave...2 objects’ motion, but that the quantitative optical flow is not a reliable measure of the real motion [VP87, SU87]. This applies even more to the

Quasi-steady-state analysis of coupled flashing ratchets.

PubMed

Levien, Ethan; Bressloff, Paul C

2015-10-01

We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

Vector optical fields with polarization distributions similar to electric and magnetic field lines.

PubMed

Pan, Yue; Li, Si-Min; Mao, Lei; Kong, Ling-Jun; Li, Yongnan; Tu, Chenghou; Wang, Pei; Wang, Hui-Tian

2013-07-01

We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of "electric charges" and "magnetic charges" can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.

Relativistic Transverse Gravitational Redshift

NASA Astrophysics Data System (ADS)

Mayer, A. F.

2012-12-01

The parametrized post-Newtonian (PPN) formalism is a tool for quantitative analysis of the weak gravitational field based on the field equations of general relativity. This formalism and its ten parameters provide the practical theoretical foundation for the evaluation of empirical data produced by space-based missions designed to map and better understand the gravitational field (e.g., GRAIL, GRACE, GOCE). Accordingly, mission data is interpreted in the context of the canonical PPN formalism; unexpected, anomalous data are explained as similarly unexpected but apparently real physical phenomena, which may be characterized as ``gravitational anomalies," or by various sources contributing to the total error budget. Another possibility, which is typically not considered, is a small modeling error in canonical general relativity. The concept of the idealized point-mass spherical equipotential surface, which originates with Newton's law of gravity, is preserved in Einstein's synthesis of special relativity with accelerated reference frames in the form of the field equations. It was not previously realized that the fundamental principles of relativity invalidate this concept and with it the idea that the gravitational field is conservative (i.e., zero net work is done on any closed path). The ideal radial free fall of a material body from arbitrarily-large range to a point on such an equipotential surface (S) determines a unique escape-velocity vector of magnitude v collinear to the acceleration vector of magnitude g at this point. For two such points on S separated by angle dφ , the Equivalence Principle implies distinct reference frames experiencing inertial acceleration of identical magnitude g in different directions in space. The complete equivalence of these inertially-accelerated frames to their analogous frames at rest on S requires evaluation at instantaneous velocity v relative to a local inertial observer. Because these velocity vectors are not parallel, a symmetric energy potential exists between the frames that is quantified by the instantaneous Δ {v} = v\\cdot{d}φ between them; in order for either frame to become indistinguishable from the other, such that their respective velocity and acceleration vectors are parallel, a change in velocity is required. While the qualitative features of general relativity imply this phenomenon (i.e., a symmetric potential difference between two points on a Newtonian `equipotential surface' that is similar to a friction effect), it is not predicted by the field equations due to a modeling error concerning time. This is an error of omission; time has fundamental geometric properties implied by the principles of relativity that are not reflected in the field equations. Where b is the radius and g is the gravitational acceleration characterizing a spherical geoid S of an ideal point-source gravitational field, an elegant derivation that rests on first principles shows that for two points at rest on S separated by a distance d << b, a symmetric relativistic redshift exists between these points of magnitude z = gd2/bc^2, which over 1 km at Earth sea level yields z ˜{10-17}. It can be tested with a variety of methods, in particular laser interferometry. A more sophisticated derivation yields a considerably more complex predictive formula for any two points in a gravitational field.

QCD next-to-leading-order predictions matched to parton showers for vector-like quark models.

PubMed

Fuks, Benjamin; Shao, Hua-Sheng

2017-01-01

Vector-like quarks are featured by a wealth of beyond the Standard Model theories and are consequently an important goal of many LHC searches for new physics. Those searches, as well as most related phenomenological studies, however, rely on predictions evaluated at the leading-order accuracy in QCD and consider well-defined simplified benchmark scenarios. Adopting an effective bottom-up approach, we compute next-to-leading-order predictions for vector-like-quark pair production and single production in association with jets, with a weak or with a Higgs boson in a general new physics setup. We additionally compute vector-like-quark contributions to the production of a pair of Standard Model bosons at the same level of accuracy. For all processes under consideration, we focus both on total cross sections and on differential distributions, most these calculations being performed for the first time in our field. As a result, our work paves the way to precise extraction of experimental limits on vector-like quarks thanks to an accurate control of the shapes of the relevant observables and emphasise the extra handles that could be provided by novel vector-like-quark probes never envisaged so far.

Spectral flow as a map between N = (2 , 0)-models

NASA Astrophysics Data System (ADS)

Athanasopoulos, P.; Faraggi, A. E.; Gepner, D.

2014-07-01

The space of (2 , 0) models is of particular interest among all heterotic-string models because it includes the models with the minimal SO (10) unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic Z2 ×Z2 heterotic-string models revealed the existence of a new symmetry in the space of string configurations under the exchange of spinors and vectors of the SO (10) GUT group, dubbed spinor-vector duality. In this paper we generalize this idea to arbitrary internal rational conformal field theories (RCFTs). We explain how the spectral flow operator normally acting within a general (2 , 2) theory can be used as a map between (2 , 0) models. We describe the details, give an example and propose more simple currents that can be used in a similar way.

The problem of exact interior solutions for rotating rigid bodies in general relativity

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.

1993-01-01

The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.

Notes from 1999 on computational algorithm of the Local Wave-Vector (LWV) model for the dynamical evolution of the second-rank velocity correlation tensor starting from the mean-flow-coupled Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zemach, Charles; Kurien, Susan

These notes present an account of the Local Wave Vector (LWV) model of a turbulent flow defined throughout physical space. The previously-developed Local Wave Number (LWN) model is taken as a point of departure. Some general properties of turbulent fields and appropriate notation are given first. The LWV model is presently restricted to incompressible flows and the incompressibility assumption is introduced at an early point in the discussion. The assumption that the turbulence is homogeneous is also introduced early on. This assumption can be relaxed by generalizing the space diffusion terms of LWN, but the present discussion is focused onmore » a modeling of homogeneous turbulence.« less

Propagation and wavefront ambiguity of linear nondiffracting beams

NASA Astrophysics Data System (ADS)

Grunwald, R.; Bock, M.

2014-02-01

Ultrashort-pulsed Bessel and Airy beams in free space are often interpreted as "linear light bullets". Usually, interconnected intensity profiles are considered a "propagation" along arbitrary pathways which can even follow curved trajectories. A more detailed analysis, however, shows that this picture gives an adequate description only in situations which do not require to consider the transport of optical signals or causality. To also cover these special cases, a generalization of the terms "beam" and "propagation" is necessary. The problem becomes clearer by representing the angular spectra of the propagating wave fields by rays or Poynting vectors. It is known that quasi-nondiffracting beams can be described as caustics of ray bundles. Their decomposition into Poynting vectors by Shack-Hartmann sensors indicates that, in the frame of their classical definition, the corresponding local wavefronts are ambiguous and concepts based on energy density are not appropriate to describe the propagation completely. For this reason, quantitative parameters like the beam propagation factor have to be treated with caution as well. For applications like communication or optical computing, alternative descriptions are required. A heuristic approach based on vector field based information transport and Fourier analysis is proposed here. Continuity and discontinuity of far field distributions in space and time are discussed. Quantum aspects of propagation are briefly addressed.

Magnetic Helicity of Alfven Simple Waves

NASA Technical Reports Server (NTRS)

Webb, Gary M.; Hu, Q.; Dasgupta, B.; Zank, G. P.; Roberts, D.

2010-01-01

The magnetic helicity of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulas. Two basic Alfven modes are identified: (a) the plane 1D Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis, with wave phase varphi=k_0(z-lambda t), where k_0 is the wave number and lambda is the group velocity of the wave, and (b)\\ the generalized Barnes (1976) simple Alfven wave in which the wave normal {bf n} moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (a) is analogous to the slab Alfven mode and the generalized Barnes solution (b) is analogous to the 2D mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Aifvenic fluctuations and structures observed in the solar wind are discussed.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Research on soundproof properties of cylindrical shells of generalized phononic crystals

NASA Astrophysics Data System (ADS)

Liu, Ru; Shu, Haisheng; Wang, Xingguo

2017-04-01

Based on the previous studies, the concept of generalized phononic crystals (GPCs) is further introduced into the cylindrical shell structures in this paper. And a type of cylindrical shells of generalized phononic crystals (CS-GPCs) is constructed, the structural field and acoustic-structural coupled field of the composite cylindrical shells are examined respectively. For the structural field, the transfer matrix method of mechanical state vector is adopted to build the transfer matrix of radial waves propagating from inside to outside. For the acoustic-structural coupled field, the expressions of the acoustic transmission/reflection coefficients and the sound insulation of acoustic waves with the excitation of center line sound source are set up. And the acoustic transmission coefficient and the frequency response of sound insulation in this mode were numerical calculated. Furthermore, the theoretical analysis results are verified by using the method of combining the numerical calculation and finite element simulation. Finally, the effects of inner and outer fluid parameters on the transmission/reflection coefficients of CS-GPCs are analyzed in detail.

Dissipative N-point-vortex Models in the Plane

NASA Astrophysics Data System (ADS)

Shashikanth, Banavara N.

2010-02-01

A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ3. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu-Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.

UAV formation control design with obstacle avoidance in dynamic three-dimensional environment.

PubMed

Chang, Kai; Xia, Yuanqing; Huang, Kaoli

2016-01-01

This paper considers the artificial potential field method combined with rotational vectors for a general problem of multi-unmanned aerial vehicle (UAV) systems tracking a moving target in dynamic three-dimensional environment. An attractive potential field is generated between the leader and the target. It drives the leader to track the target based on the relative position of them. The other UAVs in the formation are controlled to follow the leader by the attractive control force. The repulsive force affects among the UAVs to avoid collisions and distribute the UAVs evenly on the spherical surface whose center is the leader-UAV. Specific orders or positions of the UAVs are not required. The trajectories of avoidance obstacle can be obtained through two kinds of potential field with rotation vectors. Every UAV can choose the optimal trajectory to avoid the obstacle and reconfigure the formation after passing the obstacle. Simulations study on UAV are presented to demonstrate the effectiveness of proposed method.

Electromagnetic fluctuations in magnetized plasmas. I. The rigorous relativistic kinetic theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu; Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu; School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701

2015-07-15

Using the system of the Klimontovich and Maxwell equations, the general linear fluctuation theory for magnetized plasmas is developed. General expressions for the electromagnetic fluctuation spectra (electric and magnetic fields) from uncorrelated plasma particles in plasmas with a uniform magnetic field are derived, which are covariantly correct within the theory of special relativity. The general fluctuation spectra hold for plasmas of arbitrary composition, arbitrary momentum dependences of the plasma particle distribution functions, and arbitrary orientations of the wave vector with respect to the uniform magnetic field. Moreover, no restrictions on the values of the real and the imaginary parts ofmore » the frequency are made. The derived fluctuation spectra apply to both non-collective fluctuations and collective plasma eigenmodes in magnetized plasmas. In the latter case, kinetic equations for the components of fluctuating electric and magnetic fields in magnetized plasmas are derived that include the effect of spontaneous emission and absorption. In the limiting case of an unmagnetized plasmas, the general fluctuation spectra correctly reduce to the unmagnetized fluctuation spectra derived before.« less

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=({+-}1,0)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmid, Christoph

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein's static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes. -more » The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity {omega}-vector{sub gyro} of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B-vector{sub g}{identical_to}-2{omega}-vector{sub gyro}. The gravitomagnetic field is caused by energy currents J-vector{sub {epsilon}} via the momentum constraint, Einstein's G{sup 0-}circumflex{sub i-circumflex} equation, (-{delta}+{mu}{sup 2})A-vector{sub g}=-16{pi}G{sub N}J-vector{sub {epsilon}} with B-vector{sub g}=curl A-vector{sub g}. This equation is analogous to Ampere's law, but it holds for all time-dependent situations. {delta} is the de Rham-Hodge Laplacian, and {delta}=-curl curl for the vorticity sector in Riemannian 3-space. - In the solution for an open universe the 1/r{sup 2}-force of Ampere is replaced by a Yukawa force Y{sub {mu}}(r)=(-d/dr)[(1/R)exp(-{mu}r)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2{pi}R is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and {mu}{sup 2}=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein's closed static universe.--We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.--We show that only energy currents in the toroidal vorticity sector with l=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X-vector{sub lm}{sup -} has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions. - The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenboeck formula for the difference between the de Rham-Hodge Laplacian {delta} and the ''rough'' Laplacian {nabla}{sup 2} on vector fields.« less

Poynting Theorem, Relativistic Transformation of Total Energy-Momentum and Electromagnetic Energy-Momentum Tensor

NASA Astrophysics Data System (ADS)

Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

2016-02-01

We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.

Electromagnetic potential vectors and the Lagrangian of a charged particle

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

Maxwell's equations can be shown to imply the existence of two independent three-dimensional potential vectors. A comparison between the potential vectors and the electric and magnetic field vectors, using a spatial Fourier transformation, reveals six independent potential components but only four independent electromagnetic field components for each mode. Although the electromagnetic fields determined by Maxwell's equations give a complete description of all possible classical electromagnetic phenomena, potential vectors contains more information and allow for a description of such quantum mechanical phenomena as the Aharonov-Bohm effect. A new result is that a charged particle Lagrangian written in terms of potential vectors automatically contains a 'spontaneous symmetry breaking' potential.

Adjustable vector Airy light-sheet single optical tweezers: negative radiation forces on a subwavelength spheroid and spin torque reversal

NASA Astrophysics Data System (ADS)

Mitri, Farid G.

2018-01-01

Generalized solutions of vector Airy light-sheets, adjustable per their derivative order m, are introduced stemming from the Lorenz gauge condition and Maxwell's equations using the angular spectrum decomposition method. The Cartesian components of the incident radiated electric, magnetic and time-averaged Poynting vector fields in free space (excluding evanescent waves) are determined and computed with particular emphasis on the derivative order of the Airy light-sheet and the polarization on the magnetic vector potential forming the beam. Negative transverse time-averaged Poynting vector components can arise, while the longitudinal counterparts are always positive. Moreover, the analysis is extended to compute the optical radiation force and spin torque vector components on a lossless dielectric prolate subwavelength spheroid in the framework of the electric dipole approximation. The results show that negative forces and spin torques sign reversal arise depending on the derivative order of the beam, the polarization of the magnetic vector potential, and the orientation of the subwavelength prolate spheroid in space. The spin torque sign reversal suggests that counter-clockwise or clockwise rotations around the center of mass of the subwavelength spheroid can occur. The results find useful applications in single Airy light-sheet tweezers, particle manipulation, handling, and rotation applications to name a few examples.

Evaluation of the impacts of climate change on disease vectors through ecological niche modelling.

PubMed

Carvalho, B M; Rangel, E F; Vale, M M

2017-08-01

Vector-borne diseases are exceptionally sensitive to climate change. Predicting vector occurrence in specific regions is a challenge that disease control programs must meet in order to plan and execute control interventions and climate change adaptation measures. Recently, an increasing number of scientific articles have applied ecological niche modelling (ENM) to study medically important insects and ticks. With a myriad of available methods, it is challenging to interpret their results. Here we review the future projections of disease vectors produced by ENM, and assess their trends and limitations. Tropical regions are currently occupied by many vector species; but future projections indicate poleward expansions of suitable climates for their occurrence and, therefore, entomological surveillance must be continuously done in areas projected to become suitable. The most commonly applied methods were the maximum entropy algorithm, generalized linear models, the genetic algorithm for rule set prediction, and discriminant analysis. Lack of consideration of the full-known current distribution of the target species on models with future projections has led to questionable predictions. We conclude that there is no ideal 'gold standard' method to model vector distributions; researchers are encouraged to test different methods for the same data. Such practice is becoming common in the field of ENM, but still lags behind in studies of disease vectors.

Study of Equatorial Ionospheric irregularities and Mapping of Electron Density Profiles and Ionograms

DTIC Science & Technology

2012-03-09

equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the...wave function arguments from complex scalars to complex vectors . This conversion allows us to separate the electric field vector and the imaginary...magnetic field vector , because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while ex- ponentials of imaginary

A generalized nonlocal vector calculus

NASA Astrophysics Data System (ADS)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Reconstruction of Vectorial Acoustic Sources in Time-Domain Tomography

PubMed Central

Xia, Rongmin; Li, Xu; He, Bin

2009-01-01

A new theory is proposed for the reconstruction of curl-free vector field, whose divergence serves as acoustic source. The theory is applied to reconstruct vector acoustic sources from the scalar acoustic signals measured on a surface enclosing the source area. It is shown that, under certain conditions, the scalar acoustic measurements can be vectorized according to the known measurement geometry and subsequently be used to reconstruct the original vector field. Theoretically, this method extends the application domain of the existing acoustic reciprocity principle from a scalar field to a vector field, indicating that the stimulating vectorial source and the transmitted acoustic pressure vector (acoustic pressure vectorized according to certain measurement geometry) are interchangeable. Computer simulation studies were conducted to evaluate the proposed theory, and the numerical results suggest that reconstruction of a vector field using the proposed theory is not sensitive to variation in the detecting distance. The present theory may be applied to magnetoacoustic tomography with magnetic induction (MAT-MI) for reconstructing current distribution from acoustic measurements. A simulation on MAT-MI shows that, compared to existing methods, the present method can give an accurate estimation on the source current distribution and a better conductivity reconstruction. PMID:19211344

Measuring magnetic field vector by stimulated Raman transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Wenli; Wei, Rong, E-mail: weirong@siom.ac.cn; Lin, Jinda

2016-03-21

We present a method for measuring the magnetic field vector in an atomic fountain by probing the line strength of stimulated Raman transitions. The relative line strength for a Λ-type level system with an existing magnetic field is theoretically analyzed. The magnetic field vector measured by our proposed method is consistent well with that by the traditional bias magnetic field method with an axial resolution of 6.1 mrad and a radial resolution of 0.16 rad. Dependences of the Raman transitions on laser polarization schemes are also analyzed. Our method offers the potential advantages for magnetic field measurement without requiring additional bias fields,more » beyond the limitation of magnetic field intensity, and extending the spatial measurement range. The proposed method can be widely used for measuring magnetic field vector in other precision measurement fields.« less

Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity

NASA Technical Reports Server (NTRS)

Gary, G. Allen; Hagyard, M. J.

1990-01-01

Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (September 23, 1980) and AR 4474 (April 26, 1984) from the Marshall Space Flight Center Vector magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds.

PubMed

Lu, Haishu; Wang, Zhihua

2017-01-01

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbed saddle point problem. Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities. The results presented in this paper unify and generalize many known results in the literature.

Anisotropic cosmological solutions in massive vector theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-11-01

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/H is constant, the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/H decreases with the decrease of v. As long as the conditions |Σ| ll H and v2 ll phi2 are satisfied around the onset of late-time cosmic acceleration, where phi is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state wDE in the radiation era is different from that in the isotropic case, but the approach to the isotropic value wDE(iso) typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.

Anisotropic cosmological solutions in massive vector theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji, E-mail: Lavinia.heisenberg@googlemail.com, E-mail: r.kase@rs.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp

In beyond-generalized Proca theories including the extension to theories higher than second order, we study the role of a spatial component v of a massive vector field on the anisotropic cosmological background. We show that, as in the case of the isotropic cosmological background, there is no additional ghostly degrees of freedom associated with the Ostrogradski instability. In second-order generalized Proca theories we find the existence of anisotropic solutions on which the ratio between the anisotropic expansion rate Σ and the isotropic expansion rate H remains nearly constant in the radiation-dominated epoch. In the regime where Σ/ H is constant,more » the spatial vector component v works as a dark radiation with the equation of state close to 1/3. During the matter era, the ratio Σ/ H decreases with the decrease of v . As long as the conditions |Σ| || H and v {sup 2} || φ{sup 2} are satisfied around the onset of late-time cosmic acceleration, where φ is the temporal vector component, we find that the solutions approach the isotropic de Sitter fixed point (Σ = 0 = v ) in accordance with the cosmic no-hair conjecture. In the presence of v and Σ the early evolution of the dark energy equation of state w {sub DE} in the radiation era is different from that in the isotropic case, but the approach to the isotropic value w {sub DE}{sup (iso)} typically occurs at redshifts z much larger than 1. Thus, apart from the existence of dark radiation, the anisotropic cosmological dynamics at low redshifts is similar to that in isotropic generalized Proca theories. In beyond-generalized Proca theories the only consistent solution to avoid the divergence of a determinant of the dynamical system corresponds to v = 0, so Σ always decreases in time.« less

Vector-beam solutions of Maxwell's wave equation.

PubMed

Hall, D G

1996-01-01

The Hermite-Gauss and Laguerre-Gauss modes are well-known beam solutions of the scalar Helmholtz equation in the paraxial limit. As such, they describe linearly polarized fields or single Cartesian components of vector fields. The vector wave equation admits, in the paraxial limit, of a family of localized Bessel-Gauss beam solutions that can describe the entire transverse electric field. Two recently reported solutions are members of this family of vector Bessel-Gauss beam modes.

Complex equiangular tight frames

NASA Astrophysics Data System (ADS)

Tropp, Joel A.

2005-08-01

A complex equiangular tight frame (ETF) is a tight frame consisting of N unit vectors in Cd whose absolute inner products are identical. One may view complex ETFs as a natural geometric generalization of an orthonormal basis. Numerical evidence suggests that these objects do not arise for most pairs (d, N). The goal of this paper is to develop conditions on (d, N) under which complex ETFs can exist. In particular, this work concentrates on the class of harmonic ETFs, in which the components of the frame vectors are roots of unity. In this case, it is possible to leverage field theory to obtain stringent restrictions on the possible values for (d, N).

General description of circularly symmetric Bessel beams of arbitrary order

NASA Astrophysics Data System (ADS)

Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Mädler, Lutz

2016-11-01

A general description of circularly symmetric Bessel beams of arbitrary order is derived in this paper. This is achieved by analyzing the relationship between different descriptions of polarized Bessel beams obtained using different approaches. It is shown that a class of circularly symmetric Davis Bessel beams derived using the Hertz vector potentials possesses the same general functional dependence as the aplanatic Bessel beams generated using the angular spectrum representation (ASR). This result bridges the gap between different descriptions of Bessel beams and leads to a general description of circularly symmetric Bessel beams, such that the Davis Bessel beams and the aplanatic Bessel beams are merely the two simplest cases of an infinite number of possible circularly symmetric Bessel beams. Additionally, magnitude profiles of the electric and magnetic fields, the energy density and the Poynting vector are displayed for Bessel beams in both paraxial and nonparaxial cases. The results presented in this paper provide a fresh perspective on the description of Bessel beams and cast some insights into the light scattering and light-matter interactions problems in practice.

Correlation between topological structure and its properties in dynamic singular vector fields.

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 10³  s order.

Formation of magnetic discontinuities through viscous relaxation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Sanjay; Bhattacharyya, R.; Smolarkiewicz, P. K.

2014-05-15

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach ofmore » describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topology-preserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berres, Anne Sabine

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

Amplitude-phase characteristics of electromagnetic fields diffracted by a hole in a thin film with realistic optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2009-03-01

Characteristics of a quasi-spherical wave front of an electromagnetic field diffracted by a subwavelength hole in a thin film with real optical properties are studied. Related diffraction problem is solved in general by use of the scalar and vector Green's theorems and related Green's function of a boundary-value problem. Local phase deviations of a diffracted wave front from an ideal spherical front are calculated. Diffracted patterns are calculated for the coherent incident fields in case of holes array in a screen of perfect conductivity.

A predictor-corrector scheme for vortex identification

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Banks, David C.

1994-01-01

A new algorithm for identifying and characterizing vortices in complex flows is presented. The scheme uses both the vorticity and pressure fields. A skeleton line along the center of a vortex is produced by a two-step predictor-corrector scheme. The technique uses the vector field to move in the direction of the skeleton line and the scalar field to correct the location in the plane perpendicular to the skeleton line. A general vortex cross section can be concisely defined with five parameters at each point along the skeleton line. The details of the method and examples of its use are discussed.

Origin and structures of solar eruptions II: Magnetic modeling

NASA Astrophysics Data System (ADS)

Guo, Yang; Cheng, Xin; Ding, MingDe

2017-07-01

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.

Vacuum polarization of the quantized massive fields in Friedman-Robertson-Walker spacetime

NASA Astrophysics Data System (ADS)

Matyjasek, Jerzy; Sadurski, Paweł; Telecka, Małgorzata

2014-04-01

The stress-energy tensor of the quantized massive fields in a spatially open, flat, and closed Friedman-Robertson-Walker universe is constructed using the adiabatic regularization (for the scalar field) and the Schwinger-DeWitt approach (for the scalar, spinor, and vector fields). It is shown that the stress-energy tensor calculated in the sixth adiabatic order coincides with the result obtained from the regularized effective action, constructed from the heat kernel coefficient a3. The behavior of the tensor is examined in the power-law cosmological models, and the semiclassical Einstein field equations are solved exactly in a few physically interesting cases, such as the generalized Starobinsky models.

On the presence of electric currents in the solar atmosphere. I - A theoretical framework

NASA Technical Reports Server (NTRS)

Hagyard, M.; Low, B. C.; Tandberg-Hanssen, E.

1981-01-01

The general magnetic field above the solar photosphere is divided by an elementary analysis based on Ampere's law into two parts: a potential field due to electric currents below the photosphere and a field produced by electric currents above the photosphere combined with the induced mirror currents. The latter, by symmetry, has a set of field lines lying in the plane taken to be the photosphere which may be constructed from given vector magnetograph measurements. These field lines also represent all the information on the electric currents above the photosphere that a magnetograph can provide. Theoretical illustrations are given, and implications for data analysis are discussed.

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

NASA Astrophysics Data System (ADS)

Aochi, Masataka; Endo, Ryusuke; Miura, Hikaru

2018-02-01

We present a BRST symmetric gaugeon formalism for the second-rank antisymmetric tensor gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher-derivative field equation; this property is necessary to change the gauge-fixing parameter of the antisymmetric tensor gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev-Popov ghost terms.

Microchip solid-state cylindrical vector lasers with orthogonally polarized dual laser-diode end pumping.

PubMed

Otsuka, Kenju; Chu, Shu-Chun

2013-05-01

We report a simple method for generating cylindrical vector beams directly from laser-diode (LD)-pumped microchip solid-state lasers by using dual end-pumping beams. Radially as well as azimuthally polarized vector field emissions have been generated from the common c-cut Nd:GdVO4 laser cavity merely by controlling the focus positions of orthogonally polarized LD off-axis pump beams. Hyperbolically polarized vector fields have also been observed, in which the cylindrical symmetry of vector fields is broken. Experimental results have been well reproduced by numerical simulations.

Inflation with a massive vector field nonminimally coupled to gravity

NASA Astrophysics Data System (ADS)

Páramos, J.

2018-01-01

The possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity is presented. Through an appropriate Ansatz for the vector field, the behaviour of the equations of motion is studied through the ensuing dynamical system, focusing on the characterisation of the ensuing fixed points.

Spin Chirality of Cu3 and V3 Nanomagnets. 1. Rotation Behavior of Vector Chirality, Scalar Chirality, and Magnetization in the Rotating Magnetic Field, Magnetochiral Correlations.

PubMed

Belinsky, Moisey I

2016-05-02

The rotation behavior of the vector chirality κ, scalar chirality χ, and magnetization M in the rotating magnetic field H1 is considered for the V3 and Cu3 nanomagnets, in which the Dzialoshinsky-Moriya coupling is active. The polar rotation of the field H1 of the given strength H1 results in the energy spectrum characterized by different vector and scalar chiralities in the ground and excited states. The magnetochiral correlations between the vector and scalar chiralities, energy, and magnetization in the rotating field were considered. Under the uniform polar rotation of the field H1, the ground-state chirality vector κI performs sawtooth oscillations and the magnetization vector MI performs the sawtooth oscillating rotation that is accompanied by the correlated transformation of the scalar chirality χI. This demonstrates the magnetochiral effect of the joint rotation behavior and simultaneous frustrations of the spin chiralities and magnetization in the rotating field, which are governed by the correlation between the chiralities and magnetization.

Scalar/Vector potential formulation for compressible viscous unsteady flows

NASA Technical Reports Server (NTRS)

Morino, L.

1985-01-01

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Magnetic vector field tag and seal

DOEpatents

Johnston, Roger G.; Garcia, Anthony R.

2004-08-31

One or more magnets are placed in a container (preferably on objects inside the container) and the magnetic field strength and vector direction are measured with a magnetometer from at least one location near the container to provide the container with a magnetic vector field tag and seal. The location(s) of the magnetometer relative to the container are also noted. If the position of any magnet inside the container changes, then the measured vector fields at the these locations also change, indicating that the tag has been removed, the seal has broken, and therefore that the container and objects inside may have been tampered with. A hollow wheel with magnets inside may also provide a similar magnetic vector field tag and seal. As the wheel turns, the magnets tumble randomly inside, removing the tag and breaking the seal.

Accelerating 4D flow MRI by exploiting vector field divergence regularization.

PubMed

Santelli, Claudio; Loecher, Michael; Busch, Julia; Wieben, Oliver; Schaeffter, Tobias; Kozerke, Sebastian

2016-01-01

To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields. © 2014 Wiley Periodicals, Inc.

Visualizing Vector Fields Using Line Integral Convolution and Dye Advection

NASA Technical Reports Server (NTRS)

Shen, Han-Wei; Johnson, Christopher R.; Ma, Kwan-Liu

1996-01-01

We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.

Polarization ellipse and Stokes parameters in geometric algebra.

PubMed

Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J

2012-01-01

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

Discrete symmetries in the heterotic-string landscape

NASA Astrophysics Data System (ADS)

Athanasopoulos, P.

2015-07-01

We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ2 × ℤ2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

PubMed

Chen, Rui-Pin; Chen, Zhaozhong; Chew, Khian-Hooi; Li, Pei-Gang; Yu, Zhongliang; Ding, Jianping; He, Sailing

2015-05-29

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Creating orbiting vorticity vectors in magnetic particle suspensions through field symmetry transitions–a route to multi-axis mixing

DOE PAGES

Martin, James E.; Solis, Kyle Jameson

2015-11-09

It has recently been reported that two types of triaxial electric or magnetic fields can drive vorticity in dielectric or magnetic particle suspensions, respectively. The first type-symmetry -- breaking rational fields -- consists of three mutually orthogonal fields, two alternating and one dc, and the second type -- rational triads -- consists of three mutually orthogonal alternating fields. In each case it can be shown through experiment and theory that the fluid vorticity vector is parallel to one of the three field components. For any given set of field frequencies this axis is invariant, but the sign and magnitude ofmore » the vorticity (at constant field strength) can be controlled by the phase angles of the alternating components and, at least for some symmetry-breaking rational fields, the direction of the dc field. In short, the locus of possible vorticity vectors is a 1-d set that is symmetric about zero and is along a field direction. In this paper we show that continuous, 3-d control of the vorticity vector is possible by progressively transitioning the field symmetry by applying a dc bias along one of the principal axes. Such biased rational triads are a combination of symmetry-breaking rational fields and rational triads. A surprising aspect of these transitions is that the locus of possible vorticity vectors for any given field bias is extremely complex, encompassing all three spatial dimensions. As a result, the evolution of a vorticity vector as the dc bias is increased is complex, with large components occurring along unexpected directions. More remarkable are the elaborate vorticity vector orbits that occur when one or more of the field frequencies are detuned. As a result, these orbits provide the basis for highly effective mixing strategies wherein the vorticity axis periodically explores a range of orientations and magnitudes.« less

The Curl of a Vector Field: Beyond the Formula

ERIC Educational Resources Information Center

Burch, Kimberly Jordan; Choi, Youngna

2006-01-01

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical…

Family and Children in the Attitudes and Life Plans of Russians

ERIC Educational Resources Information Center

Varlamova, Svetlana Nikolaevna; Noskova, Antonina Viacheslavovna; Sedova, Natal'ia Nikolaevna

2008-01-01

Specialists in the field of family research emphasize that the history of the family in Russia, as in all other countries of the world, is closely linked to the social, economic, and political processes of the modernization of society. The general vector of the development of the institution of the family, under the influence of processes of…

NEWTON - NEW portable multi-sensor scienTific instrument for non-invasive ON-site characterization of rock from planetary surface and sub-surfaces

NASA Astrophysics Data System (ADS)

Díaz-Michelena, M.; de Frutos, J.; Ordóñez, A. A.; Rivero, M. A.; Mesa, J. L.; González, L.; Lavín, C.; Aroca, C.; Sanz, M.; Maicas, M.; Prieto, J. L.; Cobos, P.; Pérez, M.; Kilian, R.; Baeza, O.; Langlais, B.; Thébault, E.; Grösser, J.; Pappusch, M.

2017-09-01

In space instrumentation, there is currently no instrument dedicated to susceptibly or complete magnetization measurements of rocks. Magnetic field instrument suites are generally vector (or scalar) magnetometers, which locally measure the magnetic field. When mounted on board rovers, the electromagnetic perturbations associated with motors and other elements make it difficult to reap the benefits from the inclusion of such instruments. However, magnetic characterization is essential to understand key aspects of the present and past history of planetary objects. The work presented here overcomes the limitations currently existing in space instrumentation by developing a new portable and compact multi-sensor instrument for ground breaking high-resolution magnetic characterization of planetary surfaces and sub-surfaces. This new technology introduces for the first time magnetic susceptometry (real and imaginary parts) as a complement to existing compact vector magnetometers for planetary exploration. This work aims to solve the limitations currently existing in space instrumentation by means of providing a new portable and compact multi-sensor instrument for use in space, science and planetary exploration to solve some of the open questions on the crustal and more generally planetary evolution within the Solar System.

Performance of a Bounce-Averaged Global Model of Super-Thermal Electron Transport in the Earth's Magnetic Field

NASA Technical Reports Server (NTRS)

McGuire, Tim

1998-01-01

In this paper, we report the results of our recent research on the application of a multiprocessor Cray T916 supercomputer in modeling super-thermal electron transport in the earth's magnetic field. In general, this mathematical model requires numerical solution of a system of partial differential equations. The code we use for this model is moderately vectorized. By using Amdahl's Law for vector processors, it can be verified that the code is about 60% vectorized on a Cray computer. Speedup factors on the order of 2.5 were obtained compared to the unvectorized code. In the following sections, we discuss the methodology of improving the code. In addition to our goal of optimizing the code for solution on the Cray computer, we had the goal of scalability in mind. Scalability combines the concepts of portabilty with near-linear speedup. Specifically, a scalable program is one whose performance is portable across many different architectures with differing numbers of processors for many different problem sizes. Though we have access to a Cray at this time, the goal was to also have code which would run well on a variety of architectures.

Vector critical points and generalized quasi-efficient solutions in nonsmooth multi-objective programming.

PubMed

Wang, Zhen; Li, Ru; Yu, Guolin

2017-01-01

In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate invexities assumptions, we prove that the solutions of generalized vector variational-like inequalities in terms of the generalized Jacobian are the generalized quasi-efficient solutions of nonsmooth multi-objective programming problems. Moreover, the equivalent conditions are presented, namely, a vector critical point is a weakly quasi-efficient solution of higher order with respect to a function.

Tailored optical vector fields for ultrashort-pulse laser induced complex surface plasmon structuring.

PubMed

Ouyang, J; Perrie, W; Allegre, O J; Heil, T; Jin, Y; Fearon, E; Eckford, D; Edwardson, S P; Dearden, G

2015-05-18

Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.

One-loop renormalization of Lee-Wick gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grinstein, Benjamin; O'Connell, Donal

2008-11-15

We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theorymore » than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.« less

B-physics anomalies: a guide to combined explanations

NASA Astrophysics Data System (ADS)

Buttazzo, Dario; Greljo, Admir; Isidori, Gino; Marzocca, David

2017-11-01

Motivated by additional experimental hints of Lepton Flavour Universality violation in B decays, both in charged- and in neutral-current processes, we analyse the ingredients necessary to provide a combined description of these phenomena. By means of an Effective Field Theory (EFT) approach, based on the hypothesis of New Physics coupled predominantly to the third generation of left-handed quarks and leptons, we show how this is possible. We demonstrate, in particular, how to solve the problems posed by electroweak precision tests and direct searches with a rather natural choice of model parameters, within the context of a U(2) q ×U(2)ℓ flavour symmetry. We further exemplify the general EFT findings by means of simplified models with explicit mediators in the TeV range: coloured scalar or vector leptoquarks and colour-less vectors. Among these, the case of an SU(2) L -singlet vector leptoquark emerges as a particularly simple and successful framework.

Understanding Vector Fields.

ERIC Educational Resources Information Center

Curjel, C. R.

1990-01-01

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Synthetic biology and occupational risk.

PubMed

Howard, John; Murashov, Vladimir; Schulte, Paul

2017-03-01

Synthetic biology is an emerging interdisciplinary field of biotechnology that involves applying the principles of engineering and chemical design to biological systems. Biosafety professionals have done an excellent job in addressing research laboratory safety as synthetic biology and gene editing have emerged from the larger field of biotechnology. Despite these efforts, risks posed by synthetic biology are of increasing concern as research procedures scale up to industrial processes in the larger bioeconomy. A greater number and variety of workers will be exposed to commercial synthetic biology risks in the future, including risks to a variety of workers from the use of lentiviral vectors as gene transfer devices. There is a need to review and enhance current protection measures in the field of synthetic biology, whether in experimental laboratories where new advances are being researched, in health care settings where treatments using viral vectors as gene delivery systems are increasingly being used, or in the industrial bioeconomy. Enhanced worker protection measures should include increased injury and illness surveillance of the synthetic biology workforce; proactive risk assessment and management of synthetic biology products; research on the relative effectiveness of extrinsic and intrinsic biocontainment methods; specific safety guidance for synthetic biology industrial processes; determination of appropriate medical mitigation measures for lentiviral vector exposure incidents; and greater awareness and involvement in synthetic biology safety by the general occupational safety and health community as well as by government occupational safety and health research and regulatory agencies.

The hopf algebra of vector fields on complex quantum groups

NASA Astrophysics Data System (ADS)

Drabant, Bernhard; Jurčo, Branislav; Schlieker, Michael; Weich, Wolfgang; Zumino, Bruno

1992-10-01

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A n , B n , C n , and D n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skraba, Primoz; Rosen, Paul; Wang, Bei

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with amore » guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.« less

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.

PubMed

Skraba, Primoz; Rosen, Paul; Wang, Bei; Chen, Guoning; Bhatia, Harsh; Pascucci, Valerio

2016-02-29

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.

Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

DOE PAGES

Skraba, Primoz; Rosen, Paul; Wang, Bei; ...

2016-02-29

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with amore » guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.« less

Statistics of partially-polarized fields: beyond the Stokes vector and coherence matrix

NASA Astrophysics Data System (ADS)

Charnotskii, Mikhail

2017-08-01

Traditionally, the partially-polarized light is characterized by the four Stokes parameters. Equivalent description is also provided by correlation tensor of the optical field. These statistics specify only the second moments of the complex amplitudes of the narrow-band two-dimensional electric field of the optical wave. Electric field vector of the random quasi monochromatic wave is a nonstationary oscillating two-dimensional real random variable. We introduce a novel statistical description of these partially polarized waves: the Period-Averaged Probability Density Function (PA-PDF) of the field. PA-PDF contains more information on the polarization state of the field than the Stokes vector. In particular, in addition to the conventional distinction between the polarized and depolarized components of the field PA-PDF allows to separate the coherent and fluctuating components of the field. We present several model examples of the fields with identical Stokes vectors and very distinct shapes of PA-PDF. In the simplest case of the nonstationary, oscillating normal 2-D probability distribution of the real electrical field and stationary 4-D probability distribution of the complex amplitudes, the newly-introduced PA-PDF is determined by 13 parameters that include the first moments and covariance matrix of the quadrature components of the oscillating vector field.

Spin polarized phases in strongly interacting matter: Interplay between axial-vector and tensor mean fields

NASA Astrophysics Data System (ADS)

Maruyama, Tomoyuki; Nakano, Eiji; Yanase, Kota; Yoshinaga, Naotaka

2018-06-01

The spontaneous spin polarization of strongly interacting matter due to axial-vector- and tensor-type interactions is studied at zero temperature and high baryon-number densities. We start with the mean-field Lagrangian for the axial-vector and tensor interaction channels and find in the chiral limit that the spin polarization due to the tensor mean field (U ) takes place first as the density increases for sufficiently strong coupling constants, and then the spin polarization due to the axial-vector mean field (A ) emerges in the region of the finite tensor mean field. This can be understood as making the axial-vector mean-field finite requires a broken chiral symmetry somehow, which is achieved by the finite tensor mean field in the present case. It is also found from the symmetry argument that there appear the type I (II) Nambu-Goldstone modes with a linear (quadratic) dispersion in the spin polarized phase with U ≠0 and A =0 (U ≠0 and A ≠0 ), although these two phases exhibit the same symmetry breaking pattern.

Lefschetz thimbles in fermionic effective models with repulsive vector-field

NASA Astrophysics Data System (ADS)

Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira

2018-06-01

We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion bilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This "auxiliary" sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.

A vectorized algorithm for 3D dynamics of a tethered satellite

NASA Technical Reports Server (NTRS)

Wilson, Howard B.

1989-01-01

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

High frequency vibration analysis by the complex envelope vectorization.

PubMed

Giannini, O; Carcaterra, A; Sestieri, A

2007-06-01

The complex envelope displacement analysis (CEDA) is a procedure to solve high frequency vibration and vibro-acoustic problems, providing the envelope of the physical solution. CEDA is based on a variable transformation mapping the high frequency oscillations into signals of low frequency content and has been successfully applied to one-dimensional systems. However, the extension to plates and vibro-acoustic fields met serious difficulties so that a general revision of the theory was carried out, leading finally to a new method, the complex envelope vectorization (CEV). In this paper the CEV method is described, underlying merits and limits of the procedure, and a set of applications to vibration and vibro-acoustic problems of increasing complexity are presented.

Vector solution for the mean electromagnetic fields in a layer of random particles

NASA Technical Reports Server (NTRS)

Lang, R. H.; Seker, S. S.; Levine, D. M.

1986-01-01

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.

Characteristic classes of gauge systems

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2004-12-01

We define and study invariants which can be uniformly constructed for any gauge system. By a gauge system we understand an (anti-)Poisson supermanifold provided with an odd Hamiltonian self-commuting vector field called a homological vector field. This definition encompasses all the cases usually included into the notion of a gauge theory in physics as well as some other similar (but different) structures like Lie or Courant algebroids. For Lagrangian gauge theories or Hamiltonian first class constrained systems, the homological vector field is identified with the classical BRST transformation operator. We define characteristic classes of a gauge system as universal cohomology classes of the homological vector field, which are uniformly constructed in terms of this vector field itself. Not striving to exhaustively classify all the characteristic classes in this work, we compute those invariants which are built up in terms of the first derivatives of the homological vector field. We also consider the cohomological operations in the space of all the characteristic classes. In particular, we show that the (anti-)Poisson bracket becomes trivial when applied to the space of all the characteristic classes, instead the latter space can be endowed with another Lie bracket operation. Making use of this Lie bracket one can generate new characteristic classes involving higher derivatives of the homological vector field. The simplest characteristic classes are illustrated by the examples relating them to anomalies in the traditional BV or BFV-BRST theory and to characteristic classes of (singular) foliations.

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fan Kai; Cai Wei; Ji Xia

2008-07-20

In this paper, we propose a new full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) to accurately handle the discontinuities in electromagnetic fields associated with wave propagations in inhomogeneous optical waveguides. The numerical method is a combination of the traditional beam propagation method (BPM) with a newly developed generalized discontinuous Galerkin (GDG) method [K. Fan, W. Cai, X. Ji, A generalized discontinuous Galerkin method (GDG) for Schroedinger equations with nonsmooth solutions, J. Comput. Phys. 227 (2008) 2387-2410]. The GDG method is based on a reformulation, using distributional variables to account for solution jumps across material interfaces, of Schroedinger equationsmore » resulting from paraxial approximations of vector Helmholtz equations. Four versions of the GDG-BPM are obtained for either the electric or magnetic field components. Modeling of wave propagations in various optical fibers using the full vectorial GDG-BPM is included. Numerical results validate the high order accuracy and the flexibility of the method for various types of interface jump conditions.« less

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team 1998

NASA Technical Reports Server (NTRS)

Hesselink, Lambertus

1999-01-01

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available under the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team

NASA Technical Reports Server (NTRS)

Hesselink, Lambertus

1999-01-01

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available un- der the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching an@ vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Solar monochromatic images in magneto-sensitive spectral lines and maps of vector magnetic fields

NASA Technical Reports Server (NTRS)

Shihui, Y.; Jiehai, J.; Minhan, J.

1985-01-01

A new method which allows by use of the monochromatic images in some magneto-sensitive spectra line to derive both the magnetic field strength as well as the angle between magnetic field lines and line of sight for various places in solar active regions is described. In this way two dimensional maps of vector magnetic fields may be constructed. This method was applied to some observational material and reasonable results were obtained. In addition, a project for constructing the three dimensional maps of vector magnetic fields was worked out.

Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Yamamoto, Kei

2013-04-01

Using a generalized Killing-Yano equation in the presence of torsion, spacetime metrics admitting a rank-2 generalized Killing-Yano tensor are investigated in five dimensions under the assumption that its eigenvector associated with the zero eigenvalue is a Killing vector field. It is shown that such metrics are classified into three types and the corresponding local expressions are given explicitly. It is also shown that they cover some classes of charged, rotating Kaluza-Klein black hole solutions of minimal supergravity and Abelian heterotic supergravity.

Generalization of the quasi-geostrophic Eliassen-Palm flux to include eddy forcing of condensation heating

NASA Technical Reports Server (NTRS)

Stone, P. H.; Salustri, G.

1984-01-01

A modified Eulerian form of the Eliassen-Palm flux which includes the effect of eddy forcing on condensation heating is defined. With the two-dimensional vector flux in the meridional plane which is a function of the zonal mean eddy fluxes replaced by the modified flux, both the Eliassen-Palm theorem and a modified but more general form of the nonacceleration theorem for quasi-geostrophic motion still hold. Calculations of the divergence of the modified flux and of the eddy forcing of the moisture field are presented.

On generalized Volterra systems

NASA Astrophysics Data System (ADS)

Charalambides, S. A.; Damianou, P. A.; Evripidou, C. A.

2015-01-01

We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a system to a quadratic Lotka-Volterra system. We present in detail all such systems in the cases of A3, A4 and we also give some examples from higher dimensions. We classify all possible Lotka-Volterra systems that arise via this algorithm in the An case.

Effective description of general extensions of the Standard Model: the complete tree-level dictionary

NASA Astrophysics Data System (ADS)

de Blas, J.; Criado, J. C.; Pérez-Victoria, M.; Santiago, J.

2018-03-01

We compute all the tree-level contributions to the Wilson coefficients of the dimension-six Standard-Model effective theory in ultraviolet completions with general scalar, spinor and vector field content and arbitrary interactions. No assumption about the renormalizability of the high-energy theory is made. This provides a complete ultraviolet/infrared dictionary at the classical level, which can be used to study the low-energy implications of any model of interest, and also to look for explicit completions consistent with low-energy data.

A Search for Vector Magnetic Field Variations Associated with the M-Class Flares of 1991 June 10 in AR 6659

NASA Technical Reports Server (NTRS)

Hagyard, Mona J.; Stark, B. A.; Venkatakrishnan, P.

1998-01-01

A careful analysis of a 6-hour time sequence of vector magnetograms of AR 6659, observed on 1991 June 10 with the MSFC vector magnetograph, has revealed only minor changes in the vector magnetic field azimuths in the vicinity of two M-class flares, and the association of these changes with the flares is not unambiguous. In this paper we present our analysis of the data which includes comparison of vector magnetograms prior to and during the flares, calculation of distributions of the rms variation of the azimuth at each pixel in the field of view of the active region, and examination of the variation with time of the azimuths at every pixel covered by the main flare emissions as observed with the H-alpha telescope coaligned with the vector magnetograph. We also present results of an analysis of evolutionary changes in the azimuth over the field of view of the active region.

Gravitational form factors and decoupling in 2D

NASA Astrophysics Data System (ADS)

Ribeiro, Tiago G.; Shapiro, Ilya L.; Zanusso, Omar

2018-07-01

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized "running" form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.

An age-structured extension to the vectorial capacity model.

PubMed

Novoseltsev, Vasiliy N; Michalski, Anatoli I; Novoseltseva, Janna A; Yashin, Anatoliy I; Carey, James R; Ellis, Alicia M

2012-01-01

Vectorial capacity and the basic reproductive number (R(0)) have been instrumental in structuring thinking about vector-borne pathogen transmission and how best to prevent the diseases they cause. One of the more important simplifying assumptions of these models is age-independent vector mortality. A growing body of evidence indicates that insect vectors exhibit age-dependent mortality, which can have strong and varied affects on pathogen transmission dynamics and strategies for disease prevention. Based on survival analysis we derived new equations for vectorial capacity and R(0) that are valid for any pattern of age-dependent (or age-independent) vector mortality and explore the behavior of the models across various mortality patterns. The framework we present (1) lays the groundwork for an extension and refinement of the vectorial capacity paradigm by introducing an age-structured extension to the model, (2) encourages further research on the actuarial dynamics of vectors in particular and the relationship of vector mortality to pathogen transmission in general, and (3) provides a detailed quantitative basis for understanding the relative impact of reductions in vector longevity compared to other vector-borne disease prevention strategies. Accounting for age-dependent vector mortality in estimates of vectorial capacity and R(0) was most important when (1) vector densities are relatively low and the pattern of mortality can determine whether pathogen transmission will persist; i.e., determines whether R(0) is above or below 1, (2) vector population growth rate is relatively low and there are complex interactions between birth and death that differ fundamentally from birth-death relationships with age-independent mortality, and (3) the vector exhibits complex patterns of age-dependent mortality and R(0) ∼ 1. A limiting factor in the construction and evaluation of new age-dependent mortality models is the paucity of data characterizing vector mortality patterns, particularly for free ranging vectors in the field.

An Age-Structured Extension to the Vectorial Capacity Model

PubMed Central

Novoseltsev, Vasiliy N.; Michalski, Anatoli I.; Novoseltseva, Janna A.; Yashin, Anatoliy I.; Carey, James R.; Ellis, Alicia M.

2012-01-01

Background Vectorial capacity and the basic reproductive number (R0) have been instrumental in structuring thinking about vector-borne pathogen transmission and how best to prevent the diseases they cause. One of the more important simplifying assumptions of these models is age-independent vector mortality. A growing body of evidence indicates that insect vectors exhibit age-dependent mortality, which can have strong and varied affects on pathogen transmission dynamics and strategies for disease prevention. Methodology/Principal Findings Based on survival analysis we derived new equations for vectorial capacity and R0 that are valid for any pattern of age-dependent (or age–independent) vector mortality and explore the behavior of the models across various mortality patterns. The framework we present (1) lays the groundwork for an extension and refinement of the vectorial capacity paradigm by introducing an age-structured extension to the model, (2) encourages further research on the actuarial dynamics of vectors in particular and the relationship of vector mortality to pathogen transmission in general, and (3) provides a detailed quantitative basis for understanding the relative impact of reductions in vector longevity compared to other vector-borne disease prevention strategies. Conclusions/Significance Accounting for age-dependent vector mortality in estimates of vectorial capacity and R0 was most important when (1) vector densities are relatively low and the pattern of mortality can determine whether pathogen transmission will persist; i.e., determines whether R0 is above or below 1, (2) vector population growth rate is relatively low and there are complex interactions between birth and death that differ fundamentally from birth-death relationships with age-independent mortality, and (3) the vector exhibits complex patterns of age-dependent mortality and R0∼1. A limiting factor in the construction and evaluation of new age-dependent mortality models is the paucity of data characterizing vector mortality patterns, particularly for free ranging vectors in the field. PMID:22724022

Gordan—Capelli series in superalgebras

PubMed Central

Brini, Andrea; Palareti, Aldopaolo; Teolis, Antonio G. B.

1988-01-01

We derive two Gordan—Capelli series for the supersymmetric algebra of the tensor product of two [unk]2-graded [unk]-vector spaces U and V, being [unk] a field of characteristic zero. These expansions yield complete decompositions of the supersymmetric algebra regarded as a pl(U)- and a pl(V)- module, where pl(U) and pl(V) are the general linear Lie superalgebras of U and V, respectively. PMID:16593911

Institutional Interpretations of the Relationship between Sport-Related Disciplines and Their Reference Disciplines: The Case of Sociology of Sport

ERIC Educational Resources Information Center

Ciomaga, Bogdan

2014-01-01

The sociology of sport literature is now sufficiently broad to allow a general analysis of research patterns in this field. To facilitate the identification of these vectors of expansion, sources referenced in articles published in "Sociology of Sport Journal and Journal of Sport and Social Issues" between 2003 and 2011 are examined in…

Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-10-01

In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015), 10.1103/PhysRevE.91.013002] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n , all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E ∝k⊥1 -ξ and the dispersion law ω ∝k⊥2 -η . In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale L .

Argand-plane vorticity singularities in complex scalar optical fields: an experimental study using optical speckle.

PubMed

Rothschild, Freda; Bishop, Alexis I; Kitchen, Marcus J; Paganin, David M

2014-03-24

The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as "vorticity singularities" that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.

Method and apparatuses for ion cyclotron spectrometry

DOEpatents

Dahl, David A [Idaho Falls, ID; Scott, Jill R [Idaho Falls, ID; McJunkin, Timothy R [Idaho Falls, ID

2012-03-06

An ion cyclotron spectrometer may include a vacuum chamber that extends at least along a z-axis and means for producing a magnetic field within the vacuum chamber so that a magnetic field vector is generally parallel to the z-axis. The ion cyclotron spectrometer may also include means for producing a trapping electric field within the vacuum chamber. The trapping electric field may comprise a field potential that, when taken in cross-section along the z-axis, includes at least one section that is concave down and at least one section that is concave up so that ions traversing the field potential experience a net magnetron effect on a cyclotron frequency of the ions that is substantially equal to zero. Other apparatuses and a method for performing ion cyclotron spectrometry are also disclosed herein.

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

NASA Astrophysics Data System (ADS)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.; Espley, J. R.; Joergensen, J. L.; Joergensen, P. S.; Merayo, J. M. G.; Herceg, M.; Bloxham, J.; Moore, K. M.; Bolton, S. J.; Levin, S. M.

2018-03-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of 45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

Using Redundancy To Reduce Errors in Magnetometer Readings

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2004-01-01

A method of reducing errors in noisy magnetic-field measurements involves exploitation of redundancy in the readings of multiple magnetometers in a cluster. By "redundancy"is meant that the readings are not entirely independent of each other because the relationships among the magnetic-field components that one seeks to measure are governed by the fundamental laws of electromagnetism as expressed by Maxwell's equations. Assuming that the magnetometers are located outside a magnetic material, that the magnetic field is steady or quasi-steady, and that there are no electric currents flowing in or near the magnetometers, the applicable Maxwell 's equations are delta x B = 0 and delta(raised dot) B = 0, where B is the magnetic-flux-density vector. By suitable algebraic manipulation, these equations can be shown to impose three independent constraints on the values of the components of B at the various magnetometer positions. In general, the problem of reducing the errors in noisy measurements is one of finding a set of corrected values that minimize an error function. In the present method, the error function is formulated as (1) the sum of squares of the differences between the corrected and noisy measurement values plus (2) a sum of three terms, each comprising the product of a Lagrange multiplier and one of the three constraints. The partial derivatives of the error function with respect to the corrected magnetic-field component values and the Lagrange multipliers are set equal to zero, leading to a set of equations that can be put into matrix.vector form. The matrix can be inverted to solve for a vector that comprises the corrected magnetic-field component values and the Lagrange multipliers.

Hyperuniformity and its generalizations.

PubMed

Torquato, Salvatore

2016-08-01

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

Hyperuniformity and its generalizations

NASA Astrophysics Data System (ADS)

Torquato, Salvatore

2016-08-01

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

A unified development of several techniques for the representation of random vectors and data sets

NASA Technical Reports Server (NTRS)

Bundick, W. T.

1973-01-01

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Wave scattering from a periodic dielectric surface for a general angle of incidence

NASA Technical Reports Server (NTRS)

Chuang, S. L.; Kong, J. A.

1982-01-01

Electromagnetic waves scattered from a periodic dielectric and perfectly conducting surface are studied for a general angle of incidence. It is shown that the one-dimensional corrugated surface can be solved by using two scalar functions: the components of the electric and magnetic fields along the row direction of the surface, and appropriate boundary conditions to obtain simple matrix equations. Results are compared to the case where the incident angle wave vector is perpendicular to the row direction. Numerical results demonstrate that energy conservation and reciprocity are obeyed for scattering by sinusoidal surfaces for the general case, which checks the consistency of the formalism.

Current collection in an anisotropic plasma

NASA Technical Reports Server (NTRS)

Li, Wei-Wei

1990-01-01

A general method is given to derive the current-potential relations in anisotropic plasmas. Orbit limit current is assumed. The collector is a conductive sphere or an infinite cylinder. Any distribution which is an arbitrary function of the velocity vector can be considered as a superposition of many mono-energetic beams whose current-potential relations are known. The results for two typical pitch angle distributions are derived and discussed in detail. The general properties of the current potential relations are very similar to that of a Maxwellian plasma except for an effective temperature which varies with the angle between the magnetic field and the charging surface. The conclusions are meaningful to generalized geometries.

The effect of transverse wave vector and magnetic fields on resonant tunneling times in double-barrier structures

NASA Astrophysics Data System (ADS)

Wang, Hongmei; Zhang, Yafei; Xu, Huaizhe

2007-01-01

The effect of transverse wave vector and magnetic fields on resonant tunneling times in double-barrier structures, which is significant but has been frequently omitted in previous theoretical methods, has been reported in this paper. The analytical expressions of the longitudinal energies of quasibound levels (LEQBL) and the lifetimes of quasibound levels (LQBL) in symmetrical double-barrier (SDB) structures have been derived as a function of transverse wave vector and longitudinal magnetic fields perpendicular to interfaces. Based on our derived analytical expressions, the LEQBL and LQBL dependence upon transverse wave vector and longitudinal magnetic fields has been explored numerically for a SDB structure. Model calculations show that the LEQBL decrease monotonically and the LQBL shorten with increasing transverse wave vector, and each original LEQBL splits to a series of sub-LEQBL which shift nearly linearly toward the well bottom and the lifetimes of quasibound level series (LQBLS) shorten with increasing Landau-level indices and magnetic fields.

Field Worker Evaluation of Dengue Vector Surveillance Methods: Factors That Determine Perceived Ease, Difficulty, Value, and Time Effectiveness in Australia and Malaysia.

PubMed

Azil, Aishah H; Ritchie, Scott A; Williams, Craig R

2015-10-01

This qualitative study aimed to describe field worker perceptions, evaluations of worth, and time costs of routine dengue vector surveillance methods in Cairns (Australia), Kuala Lumpur and Petaling District (Malaysia). In Cairns, the BG-Sentinel trap is a favored method for field workers because of its user-friendliness, but is not as cost-efficient as the sticky ovitrap. In Kuala Lumpur, the Mosquito Larvae Trapping Device is perceived as a solution for the inaccessibility of premises to larval surveys. Nonetheless, the larval survey method is retained in Malaysia for prompt detection of dengue vectors. For dengue vector surveillance to be successful, there needs to be not only technical, quantitative evaluations of method performance but also an appreciation of how amenable field workers are to using particular methods. Here, we report novel field worker perceptions of dengue vector surveillance methods in addition to time analysis for each method. © 2014 APJPH.

Vector boson star solutions with a quartic order self-interaction

NASA Astrophysics Data System (ADS)

Minamitsuji, Masato

2018-05-01

We investigate boson star (BS) solutions in the Einstein-Proca theory with the quartic order self-interaction of the vector field λ (AμA¯ μ)2/4 and the mass term μ A¯ μAμ/2 , where Aμ is the complex vector field and A¯μ is the complex conjugate of Aμ, and λ and μ are the coupling constant and the mass of the vector field, respectively. The vector BSs are characterized by the two conserved quantities, the Arnowitt-Deser-Misner (ADM) mass and the Noether charge associated with the global U (1 ) symmetry. We show that in comparison with the case without the self-interaction λ =0 , the maximal ADM mass and Noether charge increase for λ >0 and decrease for λ <0 . We also show that there exists the critical central amplitude of the temporal component of the vector field above which there is no vector BS solution, and for λ >0 it can be expressed by the simple analytic expression. For a sufficiently large positive coupling Λ ≔Mpl2λ /(8 π μ2)≫1 , the maximal ADM mass and Noether charge of the vector BSs are obtained from the critical central amplitude and of O [√{λ }Mpl3/μ2ln (λ Mpl2/μ2)] , which is different from that of the scalar BSs, O (√{λϕ }Mpl3/μϕ2) , where λϕ and μϕ are the coupling constant and the mass of the complex scalar field.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Magnetic Field-Vector Measurements in Quiescent Prominences via the Hanle Effect: Analysis of Prominences Observed at Pic-Du-Midi and at Sacramento Peak

NASA Technical Reports Server (NTRS)

Bommier, V.; Leroy, J. L.; Sahal-Brechot, S.

1985-01-01

The Hanle effect method for magnetic field vector diagnostics has now provided results on the magnetic field strength and direction in quiescent prominences, from linear polarization measurements in the He I E sub 3 line, performed at the Pic-du-Midi and at Sacramento Peak. However, there is an inescapable ambiguity in the field vector determination: each polarization measurement provides two field vector solutions symmetrical with respect to the line-of-sight. A statistical analysis capable of solving this ambiguity was applied to the large sample of prominences observed at the Pic-du-Midi (Leroy, et al., 1984); the same method of analysis applied to the prominences observed at Sacramento Peak (Athay, et al., 1983) provides results in agreement on the most probable magnetic structure of prominences; these results are detailed. The statistical results were confirmed on favorable individual cases: for 15 prominences observed at Pic-du-Midi, the two-field vectors are pointing on the same side of the prominence, and the alpha angles are large enough with respect to the measurements and interpretation inaccuracies, so that the field polarity is derived without any ambiguity.

Supersymmetric Dirac Born Infeld action with self-dual mass term

NASA Astrophysics Data System (ADS)

Nishino, Hitoshi; Rajpoot, Subhash; Reed, Kevin

2005-05-01

We introduce a Dirac Born Infeld action to a self-dual N = 1 supersymmetric vector multiplet in three dimensions. This action is based on the supersymmetric generalized self-duality in odd dimensions developed originally by Townsend, Pilch and van Nieuwenhuizen. Even though such a self-duality had been supposed to be very difficult to generalize to a supersymmetrically interacting system, we show that the Dirac Born Infeld action is actually compatible with supersymmetry and self-duality in three dimensions, even though the original self-duality receives corrections by the Dirac Born Infeld action. The interactions can be further generalized to arbitrary (non)polynomial interactions. As a by-product, we also show that a third-rank field strength leads to a more natural formulation of self-duality in 3D. We also show an interesting role played by the third-rank field strength leading to supersymmetry breaking, in addition to accommodating a Chern Simons form.

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Measurements of Solar Vector Magnetic Fields

NASA Technical Reports Server (NTRS)

Hagyard, M. J. (Editor)

1985-01-01

Various aspects of the measurement of solar magnetic fields are presented. The four major subdivisions of the study are: (1) theoretical understanding of solar vector magnetic fields; (3) techniques for interpretation of observational data; and (4) techniques for data display.

A New and General Formulation of the Parametric HFGMC Micromechanical Method for Three-Dimensional Multi-Phase Composites

NASA Technical Reports Server (NTRS)

Haj-Ali, Rami; Aboudi, Jacob

2012-01-01

The recent two-dimensional (2-D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3-D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2-D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3-D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2-D parametric and orthogonal HFGMC are special cases of the present 3-D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3-D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3-D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, discontinuous aligned short fiber. A 3-D repeating unit-cell for foam material composite is simulated.

Representation of magnetic fields in space

NASA Technical Reports Server (NTRS)

Stern, D. P.

1975-01-01

Several methods by which a magnetic field in space can be represented are reviewed with particular attention to problems of the observed geomagnetic field. Time dependence is assumed to be negligible, and five main classes of representation are described by vector potential, scalar potential, orthogonal vectors, Euler potentials, and expanded magnetic field.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

The synoptic maps of Br from HMI observations

NASA Astrophysics Data System (ADS)

Hayashi, Keiji; Hoeksema, J. Todd; Liu, Sun; Yang, Xudong; Centeno, Rebecca; Leka, K. D.; Barnes, Graham

2012-03-01

The vector magnetic field measurement can, in principal, give the "true" radial component of the magnetic field. We prepare 4 types of synoptic maps of the radial photospheric magnetic field, from the vector magnetic field data disambiguated by means of the minimum energy method developed at NWRA/CoRA, the vector data determined under the potential-field acute assumption, and the vector data determined under the radial-acute assumption, and the standard line-of-sight magnetogram. The models of the global corona, the MHD and the PFSS, are applied to different types of maps. Although the three-dimensional structures of the global coronal magnetic field with different maps are similar and overall agreeing well the AIA full-disk images, noticeable differences among the model outputs are found especially in the high latitude regions. We will show details of these test maps and discuss the issues in determining the radial component of the photospheric magnetic field near the poles and limb.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Vertical Wave Coupling associated with Stratospheric Sudden Warming Events analyzed in an Isentropic-Coordinate NWP Model.

NASA Astrophysics Data System (ADS)

Bleck, R.; Sun, S.; Benjamin, S.; Brown, J. M.

2017-12-01

Two- to four-week predictions of stratospheric sudden warming events during the winter seasons of 1999-2014, carried out with a high-resolution icosahedral NWP model using potential temperature as vertical coordinate, are inspected for commonalities in the evolution of both minor and major warmings. Emphasis is on the evolution of the potential vorticity field at different levels in the stratosphere, as well as on the sign and magnitude of the vertical component of the Eliassen-Palm flux vector suggestive of wave forcing in either direction. Material is presented shedding light on the skill of the model (FIM, developed at NOAA/ESRL) in predicting stratospheric warmings generally 2 weeks in advance. With an icosahedral grid ideally suited for studying polar processes, and a vertical coordinate faithfully reproducing details in the evolution of the potential vorticity and EP flux vector fields, FIM is found to be a good tool for investigating the SSW mechanism.

Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gover, A. R.; Hallowell, K.; Waldron, A.

2007-01-15

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar,more » and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.« less

Classical aspects of higher spin topologically massive gravity

NASA Astrophysics Data System (ADS)

Chen, Bin; Long, Jiang; Zhang, Jian-Dong

2012-10-01

We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern-Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors.

Fradkin-Bacry-Ruegg-Souriau perihelion vector for Gorringe-Leach equations

NASA Astrophysics Data System (ADS)

Grandati, Yves; Bérard, Alain; Mohrbach, Hervé

2010-02-01

We show that every generalized Gorringe-Leach equation admits an associated Fradkin-Bacry-Ruegg-Souriau’s vector which, in general, is only a piecewise conserved quantity. In the case of dualizable generalized Gorringe-Leach equations, which include the case of conservative motions in central power law potentials, the image sets of the FBRS vectors for dual classes are dual images of each other.

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

NASA Astrophysics Data System (ADS)

Koulouri, Alexandra; Brookes, Mike; Rimpiläinen, Ville

2017-01-01

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koulouri, Alexandra, E-mail: koulouri@uni-muenster.de; Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2BT; Brookes, Mike

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In thismore » paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field. - Highlights: • Vector tomography is used to reconstruct electric fields generated by dipole sources. • Inverse solutions are based on longitudinal and transverse line integral measurements. • Transverse line integral measurements are used as a sparsity constraint. • Numerical procedure to approximate the line integrals is described in detail. • Patterns of the studied electric fields are correctly estimated.« less

The assisted prediction modelling frame with hybridisation and ensemble for business risk forecasting and an implementation

NASA Astrophysics Data System (ADS)

Li, Hui; Hong, Lu-Yao; Zhou, Qing; Yu, Hai-Jie

2015-08-01

The business failure of numerous companies results in financial crises. The high social costs associated with such crises have made people to search for effective tools for business risk prediction, among which, support vector machine is very effective. Several modelling means, including single-technique modelling, hybrid modelling, and ensemble modelling, have been suggested in forecasting business risk with support vector machine. However, existing literature seldom focuses on the general modelling frame for business risk prediction, and seldom investigates performance differences among different modelling means. We reviewed researches on forecasting business risk with support vector machine, proposed the general assisted prediction modelling frame with hybridisation and ensemble (APMF-WHAE), and finally, investigated the use of principal components analysis, support vector machine, random sampling, and group decision, under the general frame in forecasting business risk. Under the APMF-WHAE frame with support vector machine as the base predictive model, four specific predictive models were produced, namely, pure support vector machine, a hybrid support vector machine involved with principal components analysis, a support vector machine ensemble involved with random sampling and group decision, and an ensemble of hybrid support vector machine using group decision to integrate various hybrid support vector machines on variables produced from principle components analysis and samples from random sampling. The experimental results indicate that hybrid support vector machine and ensemble of hybrid support vector machines were able to produce dominating performance than pure support vector machine and support vector machine ensemble.

Anisotropic Surface State Mediated RKKY Interaction Between Adatoms on a Hexagonal Lattice

NASA Astrophysics Data System (ADS)

Einstein, Theodore; Patrone, Paul

2012-02-01

Motivated by recent numerical studies of Ag on Pt(111), we derive a far-field expression for the RKKY interaction mediated by surface states on a (111) FCC surface, considering the effect of anisotropy in the Fermi edge. The main contribution to the interaction comes from electrons whose Fermi velocity vF is parallel to the vector R connecting the interacting adatoms; we show that in general, the corresponding Fermi wave-vector kF is not parallel to R. The interaction is oscillatory; the amplitude and wavelength of oscillations have angular dependence arising from the anisotropy of the surface state band structure. The wavelength, in particular, is determined by the component of the aforementioned kF that is parallel to R. Our analysis is easily generalized to other systems. For Ag on Pt(111), our results indicate that the RKKY interaction between pairs of adatoms should be nearly isotropic and so cannot account for the anisotropy found in the studies motivating our work.

Pinning, rotation, and metastability of BiFeO 3 cycloidal domains in a magnetic field

DOE PAGES

Fishman, Randy S.

2018-01-03

Earlier models for the room-temperature multiferroic BiFeO 3 implicitly assumed that a very strong anisotropy restricts the domain wave vectors q to the threefold-symmetric axis normal to the static polarization P. However, recent measurements demonstrate that the domain wave vectors q rotate within the hexagonal plane normal to P away from the magnetic field orientation m. In this paper, we show that the previously neglected threefold anisotropy K 3 restricts the wave vectors to lie along the threefold axis in zero field. Taking m to lie along a threefold axis, the domain with q parallel to m remains metastable belowmore » B c1≈7 T. Due to the pinning of domains by nonmagnetic impurities, the wave vectors of the other two domains start to rotate away from m above 5.6 T, when the component of the torque τ=M×B along P exceeds a threshold value τ pin. Since τ=0 when m⊥q, the wave vectors of those domains never become completely perpendicular to the magnetic field. Our results explain recent measurements of the critical field as a function of field orientation, small-angle neutron scattering measurements of the wave vectors, as well as spectroscopic measurements with m along a threefold axis. Finally, the model developed in this paper also explains how the three multiferroic domains of BiFeO 3 for a fixed P can be manipulated by a magnetic field.« less

Pinning, rotation, and metastability of BiFeO3 cycloidal domains in a magnetic field

NASA Astrophysics Data System (ADS)

Fishman, Randy S.

2018-01-01

Earlier models for the room-temperature multiferroic BiFeO3 implicitly assumed that a very strong anisotropy restricts the domain wave vectors q to the threefold-symmetric axis normal to the static polarization P . However, recent measurements demonstrate that the domain wave vectors q rotate within the hexagonal plane normal to P away from the magnetic field orientation m . We show that the previously neglected threefold anisotropy K3 restricts the wave vectors to lie along the threefold axis in zero field. Taking m to lie along a threefold axis, the domain with q parallel to m remains metastable below Bc 1≈7 T. Due to the pinning of domains by nonmagnetic impurities, the wave vectors of the other two domains start to rotate away from m above 5.6 T, when the component of the torque τ =M ×B along P exceeds a threshold value τpin. Since τ =0 when m ⊥q , the wave vectors of those domains never become completely perpendicular to the magnetic field. Our results explain recent measurements of the critical field as a function of field orientation, small-angle neutron scattering measurements of the wave vectors, as well as spectroscopic measurements with m along a threefold axis. The model developed in this paper also explains how the three multiferroic domains of BiFeO3 for a fixed P can be manipulated by a magnetic field.

Pinning, rotation, and metastability of BiFeO 3 cycloidal domains in a magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fishman, Randy S.

Earlier models for the room-temperature multiferroic BiFeO 3 implicitly assumed that a very strong anisotropy restricts the domain wave vectors q to the threefold-symmetric axis normal to the static polarization P. However, recent measurements demonstrate that the domain wave vectors q rotate within the hexagonal plane normal to P away from the magnetic field orientation m. In this paper, we show that the previously neglected threefold anisotropy K 3 restricts the wave vectors to lie along the threefold axis in zero field. Taking m to lie along a threefold axis, the domain with q parallel to m remains metastable belowmore » B c1≈7 T. Due to the pinning of domains by nonmagnetic impurities, the wave vectors of the other two domains start to rotate away from m above 5.6 T, when the component of the torque τ=M×B along P exceeds a threshold value τ pin. Since τ=0 when m⊥q, the wave vectors of those domains never become completely perpendicular to the magnetic field. Our results explain recent measurements of the critical field as a function of field orientation, small-angle neutron scattering measurements of the wave vectors, as well as spectroscopic measurements with m along a threefold axis. Finally, the model developed in this paper also explains how the three multiferroic domains of BiFeO 3 for a fixed P can be manipulated by a magnetic field.« less

USSR and Eastern Europe Scientific Abstracts- Physics - Number 45

DTIC Science & Technology

1978-10-02

compound, a function of the angle between the electrical vector of the ’ light wave and the optical c-axis of the crystal. Heterodiodes have first...of naturally radioactive U, Th and K in a 1-liter sample. USSR A VECTOR MESON IN A QUANTUM ELECTROMAGNETIC FIELD Moscow TEORETICHESKAYA I...arbitrary spin in a classical plane electromagnetic field are used to find the exact wave function of a vector meson in the quantum field of a linearly

The magnetic field investigation on Cluster

NASA Technical Reports Server (NTRS)

Balogh, A.; Cowley, S. W. H.; Southwood, D. J.; Musmann, G.; Luhr, H.; Neubauer, F. M.; Glassmeier, K.-H.; Riedler, W.; Heyn, M. F.; Acuna, M. H.

1988-01-01

The magnetic field investigation of the Cluster four-spacecraft mission is designed to provide intercalibrated measurements of the B magnetic field vector. The instrumentation and data processing of the mission are discussed. The instrumentation is identical on the four spacecraft. It consists of two triaxial fluxgate sensors and of a failure tolerant data processing unit. The combined analysis of the four spacecraft data will yield such parameters as the current density vector, wave vectors, and the geometry and structure of discontinuities.

Improvement of cardiac CT reconstruction using local motion vector fields.

PubMed

Schirra, Carsten Oliver; Bontus, Claas; van Stevendaal, Udo; Dössel, Olaf; Grass, Michael

2009-03-01

The motion of the heart is a major challenge for cardiac imaging using CT. A novel approach to decrease motion blur and to improve the signal to noise ratio is motion compensated reconstruction which takes motion vector fields into account in order to correct motion. The presented work deals with the determination of local motion vector fields from high contrast objects and their utilization within motion compensated filtered back projection reconstruction. Image registration is applied during the quiescent cardiac phases. Temporal interpolation in parameter space is used in order to estimate motion during strong motion phases. The resulting motion vector fields are during image reconstruction. The method is assessed using a software phantom and several clinical cases for calcium scoring. As a criterion for reconstruction quality, calcium volume scores were derived from both, gated cardiac reconstruction and motion compensated reconstruction throughout the cardiac phases using low pitch helical cone beam CT acquisitions. The presented technique is a robust method to determine and utilize local motion vector fields. Motion compensated reconstruction using the derived motion vector fields leads to superior image quality compared to gated reconstruction. As a result, the gating window can be enlarged significantly, resulting in increased SNR, while reliable Hounsfield units are achieved due to the reduced level of motion artefacts. The enlargement of the gating window can be translated into reduced dose requirements.

Detection of a sudden change of the field time series based on the Lorenz system.

PubMed

Da, ChaoJiu; Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance

NASA Astrophysics Data System (ADS)

Hoeksema, J. Todd; Liu, Yang; Hayashi, Keiji; Sun, Xudong; Schou, Jesper; Couvidat, Sebastien; Norton, Aimee; Bobra, Monica; Centeno, Rebecca; Leka, K. D.; Barnes, Graham; Turmon, Michael

2014-09-01

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The basic vector-field frame list cadence is 135 seconds, but to reduce noise the filtergrams are combined to derive data products every 720 seconds. The primary 720 s observables were released in mid-2010, including Stokes polarization parameters measured at six wavelengths, as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180∘ azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne-Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Definitive SHARP processing is completed only after the region rotates off the visible disk; quick-look products are produced in near real time. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report.

New post-Newtonian parameter to test Chern-Simons gravity.

PubMed

Alexander, Stephon; Yunes, Nicolas

2007-12-14

We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory.

Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability

NASA Astrophysics Data System (ADS)

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

2015-11-01

We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

Topological insulating phases from two-dimensional nodal loop semimetals

NASA Astrophysics Data System (ADS)

Li, Linhu; Araújo, Miguel A. N.

2016-10-01

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

Chromospheric Evolution and the Flare Activity of Super-Active Region NOAA 6555

NASA Technical Reports Server (NTRS)

PrasadC, Debi; Ambastha, Ashok; Srivastava, Nandita; Tripathy, Sushanta C.; Hagyard, Mona J.

1997-01-01

Super-active region NOAA 6555 was highly flare productive during the period March 21st - 27th, 1991 of its disk passage. We have studied its chromospheric activity using high spatial resolution H alpha filtergrams taken at Udaipur along with MSFC vector magnetograms. A possible relationship of flare productivity and the variation in shear has been explored. Flares were generally seen in those subareas of the active region which possessed closed magnetic field configuration, whereas only minor flares and/or surges occurred in subareas showing open magnetic field configuration. Physical mechanisms responsible for the observed surges are also discussed.

Equivalent magnetic vector potential model for low-frequency magnetic exposure assessment

NASA Astrophysics Data System (ADS)

Diao, Y. L.; Sun, W. N.; He, Y. Q.; Leung, S. W.; Siu, Y. M.

2017-10-01

In this paper, a novel source model based on a magnetic vector potential for the assessment of induced electric field strength in a human body exposed to the low-frequency (LF) magnetic field of an electrical appliance is presented. The construction of the vector potential model requires only a single-component magnetic field to be measured close to the appliance under test, hence relieving considerable practical measurement effort—the radial basis functions (RBFs) are adopted for the interpolation of discrete measurements; the magnetic vector potential model can then be directly constructed by summing a set of simple algebraic functions of RBF parameters. The vector potentials are then incorporated into numerical calculations as the equivalent source for evaluations of the induced electric field in the human body model. The accuracy and effectiveness of the proposed model are demonstrated by comparing the induced electric field in a human model to that of the full-wave simulation. This study presents a simple and effective approach for modelling the LF magnetic source. The result of this study could simplify the compliance test procedure for assessing an electrical appliance regarding LF magnetic exposure.

Circular Conditional Autoregressive Modeling of Vector Fields.

PubMed

Modlin, Danny; Fuentes, Montse; Reich, Brian

2012-02-01

As hurricanes approach landfall, there are several hazards for which coastal populations must be prepared. Damaging winds, torrential rains, and tornadoes play havoc with both the coast and inland areas; but, the biggest seaside menace to life and property is the storm surge. Wind fields are used as the primary forcing for the numerical forecasts of the coastal ocean response to hurricane force winds, such as the height of the storm surge and the degree of coastal flooding. Unfortunately, developments in deterministic modeling of these forcings have been hindered by computational expenses. In this paper, we present a multivariate spatial model for vector fields, that we apply to hurricane winds. We parameterize the wind vector at each site in polar coordinates and specify a circular conditional autoregressive (CCAR) model for the vector direction, and a spatial CAR model for speed. We apply our framework for vector fields to hurricane surface wind fields for Hurricane Floyd of 1999 and compare our CCAR model to prior methods that decompose wind speed and direction into its N-S and W-E cardinal components.

Equivalent magnetic vector potential model for low-frequency magnetic exposure assessment.

PubMed

Diao, Y L; Sun, W N; He, Y Q; Leung, S W; Siu, Y M

2017-09-21

In this paper, a novel source model based on a magnetic vector potential for the assessment of induced electric field strength in a human body exposed to the low-frequency (LF) magnetic field of an electrical appliance is presented. The construction of the vector potential model requires only a single-component magnetic field to be measured close to the appliance under test, hence relieving considerable practical measurement effort-the radial basis functions (RBFs) are adopted for the interpolation of discrete measurements; the magnetic vector potential model can then be directly constructed by summing a set of simple algebraic functions of RBF parameters. The vector potentials are then incorporated into numerical calculations as the equivalent source for evaluations of the induced electric field in the human body model. The accuracy and effectiveness of the proposed model are demonstrated by comparing the induced electric field in a human model to that of the full-wave simulation. This study presents a simple and effective approach for modelling the LF magnetic source. The result of this study could simplify the compliance test procedure for assessing an electrical appliance regarding LF magnetic exposure.

Circular Conditional Autoregressive Modeling of Vector Fields*

PubMed Central

Modlin, Danny; Fuentes, Montse; Reich, Brian

2013-01-01

As hurricanes approach landfall, there are several hazards for which coastal populations must be prepared. Damaging winds, torrential rains, and tornadoes play havoc with both the coast and inland areas; but, the biggest seaside menace to life and property is the storm surge. Wind fields are used as the primary forcing for the numerical forecasts of the coastal ocean response to hurricane force winds, such as the height of the storm surge and the degree of coastal flooding. Unfortunately, developments in deterministic modeling of these forcings have been hindered by computational expenses. In this paper, we present a multivariate spatial model for vector fields, that we apply to hurricane winds. We parameterize the wind vector at each site in polar coordinates and specify a circular conditional autoregressive (CCAR) model for the vector direction, and a spatial CAR model for speed. We apply our framework for vector fields to hurricane surface wind fields for Hurricane Floyd of 1999 and compare our CCAR model to prior methods that decompose wind speed and direction into its N-S and W-E cardinal components. PMID:24353452

Spatial Distribution of Phase Singularities in Optical Random Vector Waves.

PubMed

De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

2016-08-26

Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in random light fields. While in scalar random waves phase singularities exhibit spatial distributions reminiscent of particles in isotropic liquids, in vector fields their distribution for the different vector components becomes anisotropic due to the direct relation between propagation and field direction. By incorporating this relation in the theory for scalar fields by Berry and Dennis [Proc. R. Soc. A 456, 2059 (2000)], we quantitatively describe our experiments.

Satellite-borne study of seismic phenomena by low frequency magnetic field observations

NASA Astrophysics Data System (ADS)

Schwingenschuh, Konrad; Magnes, Werner; Xuhui, Shen; Wang, Jindong; Pollinger, Andreas; Hagen, Christian; Prattes, Gustav; Eichelberger, Hans-Ulrich; Wolbang, Daniel; Boudjada, Mohammed Y.; Besser, Bruno P.; Rozhnoi, Alexander A.; Zhang, Tielong

2015-04-01

A combined scalar-vector magnetic field experiment will be flown on the upcoming CSES mission (China Seismo-Electromagnetic Satellite). Magnetic field data from DC to 30 Hz will be measured with an accuracy of about 10 pT. A fluxgate instrument will provide the 3 magnetic field components and a new type of an optically pumped magnetometer [see Pollinger, 2010] will measure the magnitude of the ambient magnetic field. The satellite will operate in a Sun synchronous polar orbit at an altitude of about 500 km and with an inclination of 97°. We present a model of magnetic field fluctuations in the upper ionosphere based on previous satellite observations and on a model of the lithospheric-atmospheric-ionospheric coupling. Pollinger et al., CDSM-a new scalar magnetometer, EGU General Assembly 2010

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces.

PubMed

Datsyuk, Vitaly V; Pavlyniuk, Oleg R

2017-12-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces

NASA Astrophysics Data System (ADS)

Datsyuk, Vitaly V.; Pavlyniuk, Oleg R.

2017-08-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

Quantization of Electromagnetic Fields in Cavities

NASA Technical Reports Server (NTRS)

Kakazu, Kiyotaka; Oshiro, Kazunori

1996-01-01

A quantization procedure for the electromagnetic field in a rectangular cavity with perfect conductor walls is presented, where a decomposition formula of the field plays an essential role. All vector mode functions are obtained by using the decomposition. After expanding the field in terms of the vector mode functions, we get the quantized electromagnetic Hamiltonian.

Analyzing neural responses with vector fields.

PubMed

Buneo, Christopher A

2011-04-15

Analyzing changes in the shape and scale of single cell response fields is a key component of many neurophysiological studies. Typical analyses of shape change involve correlating firing rates between experimental conditions or "cross-correlating" single cell tuning curves by shifting them with respect to one another and correlating the overlapping data. Such shifting results in a loss of data, making interpretation of the resulting correlation coefficients problematic. The problem is particularly acute for two dimensional response fields, which require shifting along two axes. Here, an alternative method for quantifying response field shape and scale based on correlation of vector field representations is introduced. The merits and limitations of the methods are illustrated using both simulated and experimental data. It is shown that vector correlation provides more information on response field changes than scalar correlation without requiring field shifting and concomitant data loss. An extension of this vector field approach is also demonstrated which can be used to identify the manner in which experimental variables are encoded in studies of neural reference frames. Copyright © 2011 Elsevier B.V. All rights reserved.

Attitude Estimation for Large Field-of-View Sensors

NASA Technical Reports Server (NTRS)

Cheng, Yang; Crassidis, John L.; Markley, F. Landis

2005-01-01

The QUEST measurement noise model for unit vector observations has been widely used in spacecraft attitude estimation for more than twenty years. It was derived under the approximation that the noise lies in the tangent plane of the respective unit vector and is axially symmetrically distributed about the vector. For large field-of-view sensors, however, this approximation may be poor, especially when the measurement falls near the edge of the field of view. In this paper a new measurement noise model is derived based on a realistic noise distribution in the focal-plane of a large field-of-view sensor, which shows significant differences from the QUEST model for unit vector observations far away from the sensor boresight. An extended Kalman filter for attitude estimation is then designed with the new measurement noise model. Simulation results show that with the new measurement model the extended Kalman filter achieves better estimation performance using large field-of-view sensor observations.

Constraints on primordial magnetic fields from inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, Daniel; Kobayashi, Takeshi, E-mail: drgreen@cita.utoronto.ca, E-mail: takeshi.kobayashi@sissa.it

2016-03-01

We present generic bounds on magnetic fields produced from cosmic inflation. By investigating field bounds on the vector potential, we constrain both the quantum mechanical production of magnetic fields and their classical growth in a model independent way. For classical growth, we show that only if the reheating temperature is as low as T{sub reh} ∼< 10{sup 2} MeV can magnetic fields of 10{sup −15} G be produced on Mpc scales in the present universe. For purely quantum mechanical scenarios, even stronger constraints are derived. Our bounds on classical and quantum mechanical scenarios apply to generic theories of inflationary magnetogenesis with a two-derivative timemore » kinetic term for the vector potential. In both cases, the magnetic field strength is limited by the gravitational back-reaction of the electric fields that are produced simultaneously. As an example of quantum mechanical scenarios, we construct vector field theories whose time diffeomorphisms are spontaneously broken, and explore magnetic field generation in theories with a variable speed of light. Transitions of quantum vector field fluctuations into classical fluctuations are also analyzed in the examples.« less

Experience with a vectorized general circulation weather model on Star-100

NASA Technical Reports Server (NTRS)

Soll, D. B.; Habra, N. R.; Russell, G. L.

1977-01-01

A version of an atmospheric general circulation model was vectorized to run on a CDC STAR 100. The numerical model was coded and run in two different vector languages, CDC and LRLTRAN. A factor of 10 speed improvement over an IBM 360/95 was realized. Efficient use of the STAR machine required some redesigning of algorithms and logic. This precludes the application of vectorizing compilers on the original scalar code to achieve the same results. Vector languages permit a more natural and efficient formulation for such numerical codes.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity

NASA Astrophysics Data System (ADS)

Sato, N.; Yoshida, Z.

2018-02-01

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Transcranial Magnetic Stimulation: An Automated Procedure to Obtain Coil-specific Models for Field Calculations.

PubMed

Madsen, Kristoffer H; Ewald, Lars; Siebner, Hartwig R; Thielscher, Axel

2015-01-01

Field calculations for transcranial magnetic stimulation (TMS) are increasingly implemented online in neuronavigation systems and in more realistic offline approaches based on finite-element methods. They are often based on simplified and/or non-validated models of the magnetic vector potential of the TMS coils. To develop an approach to reconstruct the magnetic vector potential based on automated measurements. We implemented a setup that simultaneously measures the three components of the magnetic field with high spatial resolution. This is complemented by a novel approach to determine the magnetic vector potential via volume integration of the measured field. The integration approach reproduces the vector potential with very good accuracy. The vector potential distribution of a standard figure-of-eight shaped coil determined with our setup corresponds well with that calculated using a model reconstructed from x-ray images. The setup can supply validated models for existing and newly appearing TMS coils. Copyright © 2015 Elsevier Inc. All rights reserved.

Evaluation method for in situ electric field in standardized human brain for different transcranial magnetic stimulation coils

NASA Astrophysics Data System (ADS)

Iwahashi, Masahiro; Gomez-Tames, Jose; Laakso, Ilkka; Hirata, Akimasa

2017-03-01

This study proposes a method to evaluate the electric field induced in the brain by transcranial magnetic stimulation (TMS) to realize focal stimulation in the target area considering the inter-subject difference of the brain anatomy. The TMS is a non-invasive technique used for treatment/diagnosis, and it works by inducing an electric field in a specific area of the brain via a coil-induced magnetic field. Recent studies that report on the electric field distribution in the brain induced by TMS coils have been limited to simplified human brain models or a small number of detailed human brain models. Until now, no method has been developed that appropriately evaluates the coil performance for a group of subjects. In this study, we first compare the magnetic field and the magnetic vector potential distributions to determine if they can be used as predictors of the TMS focality derived from the electric field distribution. Next, the hotspots of the electric field on the brain surface of ten subjects using six coils are compared. Further, decisive physical factors affecting the focality of the induced electric field by different coils are discussed by registering the computed electric field in a standard brain space for the first time, so as to evaluate coil characteristics for a large population of subjects. The computational results suggest that the induced electric field in the target area cannot be generalized without considering the morphological variability of the human brain. Moreover, there was no remarkable difference between the various coils, although focality could be improved to a certain extent by modifying the coil design (e.g., coil radius). Finally, the focality estimated by the electric field was more correlated with the magnetic vector potential than the magnetic field in a homogeneous sphere.

Evaluation method for in situ electric field in standardized human brain for different transcranial magnetic stimulation coils.

PubMed

Iwahashi, Masahiro; Gomez-Tames, Jose; Laakso, Ilkka; Hirata, Akimasa

2017-03-21

This study proposes a method to evaluate the electric field induced in the brain by transcranial magnetic stimulation (TMS) to realize focal stimulation in the target area considering the inter-subject difference of the brain anatomy. The TMS is a non-invasive technique used for treatment/diagnosis, and it works by inducing an electric field in a specific area of the brain via a coil-induced magnetic field. Recent studies that report on the electric field distribution in the brain induced by TMS coils have been limited to simplified human brain models or a small number of detailed human brain models. Until now, no method has been developed that appropriately evaluates the coil performance for a group of subjects. In this study, we first compare the magnetic field and the magnetic vector potential distributions to determine if they can be used as predictors of the TMS focality derived from the electric field distribution. Next, the hotspots of the electric field on the brain surface of ten subjects using six coils are compared. Further, decisive physical factors affecting the focality of the induced electric field by different coils are discussed by registering the computed electric field in a standard brain space for the first time, so as to evaluate coil characteristics for a large population of subjects. The computational results suggest that the induced electric field in the target area cannot be generalized without considering the morphological variability of the human brain. Moreover, there was no remarkable difference between the various coils, although focality could be improved to a certain extent by modifying the coil design (e.g., coil radius). Finally, the focality estimated by the electric field was more correlated with the magnetic vector potential than the magnetic field in a homogeneous sphere.

Recent Progress on the Second Generation CMORPH: LEO-IR Based Precipitation Estimates and Cloud Motion Vector

NASA Astrophysics Data System (ADS)

Xie, Pingping; Joyce, Robert; Wu, Shaorong

2015-04-01

As reported at the EGU General Assembly of 2014, a prototype system was developed for the second generation CMORPH to produce global analyses of 30-min precipitation on a 0.05olat/lon grid over the entire globe from pole to pole through integration of information from satellite observations as well as numerical model simulations. The second generation CMORPH is built upon the Kalman Filter based CMORPH algorithm of Joyce and Xie (2011). Inputs to the system include rainfall and snowfall rate retrievals from passive microwave (PMW) measurements aboard all available low earth orbit (LEO) satellites, precipitation estimates derived from infrared (IR) observations of geostationary (GEO) as well as LEO platforms, and precipitation simulations from numerical global models. Key to the success of the 2nd generation CMORPH, among a couple of other elements, are the development of a LEO-IR based precipitation estimation to fill in the polar gaps and objectively analyzed cloud motion vectors to capture the cloud movements of various spatial scales over the entire globe. In this presentation, we report our recent work on the refinement for these two important algorithm components. The prototype algorithm for the LEO IR precipitation estimation is refined to achieve improved quantitative accuracy and consistency with PMW retrievals. AVHRR IR TBB data from all LEO satellites are first remapped to a 0.05olat/lon grid over the entire globe and in a 30-min interval. Temporally and spatially co-located data pairs of the LEO TBB and inter-calibrated combined satellite PMW retrievals (MWCOMB) are then collected to construct tables. Precipitation at a grid box is derived from the TBB through matching the PDF tables for the TBB and the MWCOMB. This procedure is implemented for different season, latitude band and underlying surface types to account for the variations in the cloud - precipitation relationship. At the meantime, a sub-system is developed to construct analyzed fields of cloud motion vectors from the GEO/LEO IR based precipitation estimates and the CFS Reanalysis (CFSR) precipitation fields. Motion vectors are first derived separately from the satellite IR based precipitation estimates and the CFSR precipitation fields. These individually derived motion vectors are then combined through a 2D-VAR technique to form an analyzed field of cloud motion vectors over the entire globe. Error function is experimented to best reflect the performance of the satellite IR based estimates and the CFSR in capturing the movements of precipitating cloud systems over different regions and for different seasons. Quantitative experiments are conducted to optimize the LEO IR based precipitation estimation technique and the 2D-VAR based motion vector analysis system. Detailed results will be reported at the EGU.

New Materials, Techniques and Device Concepts for Organic NLO Chromophore-based Electrooptic Devices. Part 1

DTIC Science & Technology

2006-08-23

polarization the electric field vector is parallel to the substrate, for TM polarization the magnetic field vector is parallel to the substrate. Figure...section can be obtained for the case of the two electromagnetic field polarization vectors λ and µ describing the two photons being absorbed (of the same or... polarization effects on two-photon absorption as investigated by the technique of thermal lensing detected absorption of a mode- locked laser beam. This

Electromagnetic Fields of a Uniform Sphere in a Uniform Conducting Medium with Application to Dipole Sources

DTIC Science & Technology

1991-09-01

12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (Maximum 200 words) Vector spherical harmonic expansions are...electric and magnetic field vectors from E rand B - r alone. Genural expressions are given relating the scattered field expansion coefficients to the source...Prescnbed by ANSI Std. Z39-18 29W-102 NCSC TR 426-90 CONTENTS Pag o INTRODUCTION 1 BACKGROUND 1 ANGULAR MOMENTUM OPERATOR AND VECTOR SPHERICAL

Magnetic field vector and electron density diagnostics from linear polarization measurements in 14 solar prominences

NASA Technical Reports Server (NTRS)

Bommier, V.

1986-01-01

The Hanle effect is the modification of the linear polarization parameters of a spectral line due to the effect of the magnetic field. It has been successfully applied to the magnetic field vector diagnostic in solar prominences. The magnetic field vector is determined by comparing the measured polarization to the polarization computed, taking into account all the polarizing and depolarizing processes in line formation and the depolarizing effect of the magnetic field. The method was applied to simultaneous polarization measurements in the Helium D3 line and in the hydrogen beta line in 14 prominences. Four polarization parameters are measured, which lead to the determination of the three coordinates of the magnetic field vector and the electron density, owing to the sensitivity of the hydrogen beta line to the non-negligible effect of depolarizing collisions with electrons and protons of the medium. A mean value of 1.3 x 10 to the 10th power cu. cm. is derived in 14 prominences.

On the concept of a filtered bundle

NASA Astrophysics Data System (ADS)

Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz

We present the notion of a filtered bundle as a generalization of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include affine bundles and various jet bundles, both of which play fundamental roles in geometric mechanics and classical field theory. We also present the notion of double filtered bundles which provide natural generalizations of double vector bundles and double affine bundles. Furthermore, we show that the linearization of a filtered bundle — which can be seen as a partial polarization of the admissible changes of local coordinates — is well defined.

Learning with LOGO: Logo and Vectors.

ERIC Educational Resources Information Center

Lough, Tom; Tipps, Steve

1986-01-01

This is the first of a two-part series on the general concept of vector space. Provides tool procedures to allow investigation of vector properties, vector addition and subtraction, and X and Y components. Lists several sources of additional vector ideas. (JM)

Partition function of free conformal fields in 3-plet representation

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Tseytlin, Arkady A.

2017-05-01

Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS d+1. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental ("3-plet") representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS7 dual. We compute the singlet partition function Z on S 1 × S d-1 for a free field in 3-plet representation of U( N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector ( T c ˜ N γ , γ > 0) and adjoint ( T c ˜ 1) cases are finite, we find that in the 3-plet case T c ˜ (log N)-1, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U( N) or O( N) and also to the free p-tensor theories invariant under [U( N)] p or [ O( N)] p with p ≥ 3.

Lorentzian Goldstone modes shared among photons and gravitons

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.; Jejelava, J.; Kepuladze, Z.

2018-02-01

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{μ }2=± MA2 and H_{μ ν }2=± MH2 (MA and MH are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Eisenhart lifts and symmetries of time-dependent systems

NASA Astrophysics Data System (ADS)

Cariglia, M.; Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2016-10-01

Certain dissipative systems, such as Caldirola and Kannai's damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n + 2 dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola-Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space. Time-dependent Lagrangians arise naturally also in cosmology and give rise to the phenomenon of Hubble friction. We provide an account of this for Friedmann-Lemaître and Bianchi cosmologies and how it fits in with our previous discussion in the non-relativistic limit.

Electric control of wave vector filtering in a hybrid magnetic-electric-barrier nanostructure

NASA Astrophysics Data System (ADS)

Kong, Yong-Hong; Lu, Ke-Yu; He, Ya-Ping; Liu, Xu-Hui; Fu, Xi; Li, Ai-Hua

2018-06-01

We theoretically investigate how to manipulate the wave vector filtering effect by a traverse electric field for electrons across a hybrid magnetic-electric-barrier nanostructure, which can be experimentally realized by depositing a ferromagnetic stripe and a Schottky-metal stripe on top and bottom of a GaAs/Al x Ga1- x As heterostructure, respectively. The wave vector filtering effect is found to be related closely to the applied electric field. Moreover, the wave vector filtering efficiency can be manipulated by changing direction or adjusting strength of the traverse electric field. Therefore, such a nanostructure can be employed as an electrically controllable electron-momentum filter for nanoelectronics applications.

Higher-dimensional generalizations of the Watanabe–Strogatz transform for vector models of synchronization

NASA Astrophysics Data System (ADS)

Lohe, M. A.

2018-06-01

We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d  =  2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d  =  2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.

Current vector control challenges in the fight against malaria.

PubMed

Benelli, Giovanni; Beier, John C

2017-10-01

The effective and eco-friendly control of Anopheles vectors plays a key role in any malaria management program. Integrated Vector Management (IVM) suggests making use of the full range of vector control tools available. The strategies for IVM require novel technologies to control outdoor transmission of malaria. Despite the wide number of promising control tools tested against mosquitoes, current strategies for malaria vector control used in most African countries are not sufficient to achieve successful malaria control. The majority of National Malaria Control Programs in Africa still rely on indoor residual spraying (IRS) and long-lasting insecticidal nets (LLINs). These methods reduce malaria incidence but generally have little impact on malaria prevalence. In addition to outdoor transmission, growing levels of insecticide resistance in targeted vectors threaten the efficacy of LLINs and IRS. Larvicidal treatments can be useful, but are not recommended for rural areas. The research needed to improve the quality and delivery of mosquito vector control should focus on (i) optimization of processes and methods for vector control delivery; (ii) monitoring of vector populations and biting activity with reliable techniques; (iii) the development of effective and eco-friendly tools to reduce the burden or locally eliminate malaria and other mosquito-borne diseases; (iv) the careful evaluation of field suitability and efficacy of new mosquito control tools to prove their epidemiological impact; (v) the continuous monitoring of environmental changes which potentially affect malaria vector populations; (vi) the cooperation among different disciplines, with main emphasis on parasitology, tropical medicine, ecology, entomology, and ecotoxicology. A better understanding of behavioral ecology of malaria vectors is required. Key ecological obstacles that limit the effectiveness of vector control include the variation in mosquito behavior, development of insecticide resistance, presence of behavioral avoidance, high vector biodiversity, competitive and food web interactions, lack of insights on mosquito dispersal and mating behavior, and the impact of environmental changes on mosquito ecological traits. Overall, the trans-disciplinary cooperation among parasitologists and entomologists is crucial to ensure proper evaluation of the epidemiological impact triggered by novel mosquito vector control strategies. Copyright © 2017 Elsevier B.V. All rights reserved.

Analysis of near-field components of a plasmonic optical antenna and their contribution to quantum dot infrared photodetector enhancement.

PubMed

Gu, Guiru; Vaillancourt, Jarrod; Lu, Xuejun

2014-10-20

In this paper, we analyze near-field vector components of a metallic circular disk array (MCDA) plasmonic optical antenna and their contribution to quantum dot infrared photodetector (QDIP) enhancement. The near-field vector components of the MCDA optical antenna and their distribution in the QD active region are simulated. The near-field overlap integral with the QD active region is calculated at different wavelengths and compared with the QDIP enhancement spectrum. The x-component (E(x)) of the near-field vector shows a larger intensity overlap integral and stronger correlation with the QDIP enhancement than E(z) and thus is determined to be the major near-field component to the QDIP enhancement.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

Vector fields in a tight laser focus: comparison of models.

PubMed

Peatross, Justin; Berrondo, Manuel; Smith, Dallas; Ware, Michael

2017-06-26

We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell's equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell's equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.

Differential Equations and Computational Simulations

DTIC Science & Technology

1999-06-18

divergence operator of a vector field, which can be defined in terms of the Levi - Civita connection. Let $(x, t) be the orbit passing through x g M...differential equations 31 Junping Chen and Dadi Yang The limit cycle of two species predator-prey model with general functional response > 34 S. S...analysis of two -species nonlinear competition system with periodic coefficients 286 X. H. Tang and J. S. Yu Oscillation of first order delay

Relativistic astrophysics. [studies of gravitational radiation in asymptotic de sitter space and post Newtonian approximation

NASA Technical Reports Server (NTRS)

Smalley, L. L.

1975-01-01

The coordinate independence of gravitational radiation and the parameterized post-Newtonian approximation from which it is extended are described. The general consistency of the field equations with Bianchi identities, gauge conditions, and the Newtonian limit of the perfect fluid equations of hydrodynamics are studied. A technique of modification is indicated for application to vector-metric or double metric theories, as well as to scalar-tensor theories.

Complete factorisation and analytic solutions of generalized Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Brenig, L.

1988-11-01

It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.

Outcome of capacity building intervention for malaria vector surveillance, control and research in Nigerian higher institutions.

PubMed

Oduola, Adedayo O; Obembe, Abiodun; Adelaja, Olukayode J; Adeneye, Adeniyi K; Akilah, Joel; Awolola, Taiwo S

2018-05-15

Despite the availability of effective malaria vector control intervention tools, implementation of control programmes in Nigeria is challenged by inadequate entomological surveillance data. This study was designed to assess and build the existing capacity for malaria vector surveillance, control and research (MVSC&R) in Nigerian institutions. Application call to select qualified candidates for the capacity building (CB) intervention training programme was advertised in a widely read newspaper and online platforms of national and international professional bodies. Two trainings were organized to train selected applicants on field activities, laboratory tools and techniques relevant to malaria vector surveillance and control research. A semi-structured questionnaire was administered to collect data on socio-demographic characteristics of participants, knowledge and access of participants to field and laboratory techniques in MVSC&R. Similarly, pre and post-intervention tests were conducted to assess the performance and improvement in knowledge of the participants. Mentoring activities to sustain CB activities after the training were also carried out. A total of 23 suitable applicants were shortlisted out of the 89 applications received. The South West, South East and North Central geopolitical zones of the country had the highest applications and the highest selected number of qualified applicants compared to the South South and North East geopolitical zones. The distribution with respect to gender indicated that males (72.7%) were more than females (27.3%). Mean score of participants' knowledge of field techniques was 27.8 (± 10.8) before training and 67.7 (± 9.8) after the training. Similarly, participants' knowledge on laboratory techniques also improved from 37.4 (± 5.6) to 77.2 (± 10.8). The difference in the mean scores at pre and post-test was statistically significant (p < 0.05). Access of participants to laboratory and field tools used in MVSC&R was generally low with insecticide susceptibility bioassays and pyrethrum spray collection methods being the most significant (p < 0.05). The capacity available for vector control research and surveillance at institutional level in Nigeria is weak and require further strengthening. Increased training and access of personnel to relevant tools for MVSC&R is required in higher institutions in the six geopolitical zones of the country.

The significance of vector magnetic field measurements

NASA Technical Reports Server (NTRS)

Hagyard, M. J.

1990-01-01

Observations of four flaring solar active regions, obtained during 1980-1986 with the NASA Marshall vector magnetograph (Hagyard et al., 1982 and 1985), are presented graphically and characterized in detail, with reference to nearly simultaneous Big Bear Solar Observatory and USAF ASW H-alpha images. It is shown that the flares occurred where local photospheric magnetic fields differed most from the potential field, with initial brightening on either side of a magnetic-neutral line near the point of maximum angular shear (rather than that of maximum magnetic-field strength, typically 1 kG or greater). Particular emphasis is placed on the fact that these significant nonpotential features were detected only by measuring all three components of the vector magnetic field.

Combinatorial vector fields and the valley structure of fitness landscapes.

PubMed

Stadler, Bärbel M R; Stadler, Peter F

2010-12-01

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

Detection of a sudden change of the field time series based on the Lorenz system

PubMed Central

Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series. PMID:28141832

Magnetic structure of Bayonnaise knoll caldera including Hakurei hydrothermal site obtained from near-bottom magnetic vector field mapping by autonomous underwater vehicle

NASA Astrophysics Data System (ADS)

Honsho, C.; Ura, T.; Kim, K.

2012-12-01

The Bayonnaise knoll caldera is one of the silicic submarine calderas in the Izu-Ogasawara Arc in Japan. In 2003, a large-scale hydrothermal deposit was found in the caldera, called the Hakurei deposit. The caldera had been explored by four surveys using autonomous underwater vehicles (AUVs) from 2008 to 2011, and the near-bottom magnetic field was mapped over about 75% of the caldera floor. We carried out detailed correction for the magnetic field produced by the vehicle body, which allowed us to take advantage of the vector anomaly instead of the total anomaly for the magnetic inversion. We applied the inversion method using the block model together with the Akaike's Bayesian information criterion (ABIC). One remarkable thing is that we recognized significant difference between the magnetic inversion result using the vector anomaly and that using the total anomaly: the latter result explains the observed total anomalies excellently, but does not explain the vector anomalies adequately. Except for a rare case where the vector anomaly is perpendicular to the main field throughout, the total anomaly should be sufficient for evaluating the entire field, provided that the data is collected in sufficiently high density. In fact, the track lines of our survey sometimes separate from each other by about twice the altitude of the vehicle (100 m), which can lead to considerable aliasing in the sampled field. The vector anomaly can provide vital information in such a situation. The obtained magnetization distribution is well correlated with the topography. The caldera rim and central cone have weak magnetization, which is consistent with the fact that they consist of dacite rocks. On the other hand, the caldera floor shows high magnetization, which implies the existence of basaltic rocks. The high magnetization appears to continue north and south beyond the caldera rim, forming an NS-trending high magnetization zone. Because the caldera floor is generally covered with sediment and pumice, the existence of basaltic rocks in the caldera floor has not yet been directly confirmed. As for the regional settings, however, there are NS-lined small knolls in the north and south of the caldera, which seem to continue across the caldera, and these knolls are known to consist of basaltic rocks. We postulate that the high magnetization zone of the caldera is due to basaltic volcanism, which formed the knoll chains and occurred after the formation of the silicic caldera. The Hakurei hydrothermal site is located on the southeastern rim of the caldera floor, near an inferred intersection of the caldera rim and the knoll chain. In the magnetization map, the Hakurei deposit is located near the edge of the high magnetization zone. We can clearly observe a zone of reduced magnetization associated with the deposit, probably caused by the high-temperature hydrothermal alteration of the host basaltic rock.

Remote Sensing as a Landscape Epidemiologic Tool to Identify Villages at High Risk for Malaria Transmission

NASA Technical Reports Server (NTRS)

Beck, Louisa R.; Rodriquez, Mario H.; Dister, Sheri W.; Rodriquez, Americo D.; Rejmankova, Eliska; Ulloa, Armando; Meza, Rosa A.; Roberts, Donald R.; Paris, Jack F.; Spanner, Michael A.;

A Nearest Neighbor Classifier Employing Critical Boundary Vectors for Efficient On-Chip Template Reduction.

PubMed

Xia, Wenjun; Mita, Yoshio; Shibata, Tadashi

2016-05-01

Aiming at efficient data condensation and improving accuracy, this paper presents a hardware-friendly template reduction (TR) method for the nearest neighbor (NN) classifiers by introducing the concept of critical boundary vectors. A hardware system is also implemented to demonstrate the feasibility of using an field-programmable gate array (FPGA) to accelerate the proposed method. Initially, k -means centers are used as substitutes for the entire template set. Then, to enhance the classification performance, critical boundary vectors are selected by a novel learning algorithm, which is completed within a single iteration. Moreover, to remove noisy boundary vectors that can mislead the classification in a generalized manner, a global categorization scheme has been explored and applied to the algorithm. The global characterization automatically categorizes each classification problem and rapidly selects the boundary vectors according to the nature of the problem. Finally, only critical boundary vectors and k -means centers are used as the new template set for classification. Experimental results for 24 data sets show that the proposed algorithm can effectively reduce the number of template vectors for classification with a high learning speed. At the same time, it improves the accuracy by an average of 2.17% compared with the traditional NN classifiers and also shows greater accuracy than seven other TR methods. We have shown the feasibility of using a proof-of-concept FPGA system of 256 64-D vectors to accelerate the proposed method on hardware. At a 50-MHz clock frequency, the proposed system achieves a 3.86 times higher learning speed than on a 3.4-GHz PC, while consuming only 1% of the power of that used by the PC.

A general representation scheme for crystalline solids based on Voronoi-tessellation real feature values and atomic property data

PubMed Central

Jalem, Randy; Nakayama, Masanobu; Noda, Yusuke; Le, Tam; Takeuchi, Ichiro; Tateyama, Yoshitaka; Yamazaki, Hisatsugu

2018-01-01

Abstract Increasing attention has been paid to materials informatics approaches that promise efficient and fast discovery and optimization of functional inorganic materials. Technical breakthrough is urgently requested to advance this field and efforts have been made in the development of materials descriptors to encode or represent characteristics of crystalline solids, such as chemical composition, crystal structure, electronic structure, etc. We propose a general representation scheme for crystalline solids that lifts restrictions on atom ordering, cell periodicity, and system cell size based on structural descriptors of directly binned Voronoi-tessellation real feature values and atomic/chemical descriptors based on the electronegativity of elements in the crystal. Comparison was made vs. radial distribution function (RDF) feature vector, in terms of predictive accuracy on density functional theory (DFT) material properties: cohesive energy (CE), density (d), electronic band gap (BG), and decomposition energy (Ed). It was confirmed that the proposed feature vector from Voronoi real value binning generally outperforms the RDF-based one for the prediction of aforementioned properties. Together with electronegativity-based features, Voronoi-tessellation features from a given crystal structure that are derived from second-nearest neighbor information contribute significantly towards prediction. PMID:29707064

A general representation scheme for crystalline solids based on Voronoi-tessellation real feature values and atomic property data.

PubMed

Jalem, Randy; Nakayama, Masanobu; Noda, Yusuke; Le, Tam; Takeuchi, Ichiro; Tateyama, Yoshitaka; Yamazaki, Hisatsugu

2018-01-01

Increasing attention has been paid to materials informatics approaches that promise efficient and fast discovery and optimization of functional inorganic materials. Technical breakthrough is urgently requested to advance this field and efforts have been made in the development of materials descriptors to encode or represent characteristics of crystalline solids, such as chemical composition, crystal structure, electronic structure, etc. We propose a general representation scheme for crystalline solids that lifts restrictions on atom ordering, cell periodicity, and system cell size based on structural descriptors of directly binned Voronoi-tessellation real feature values and atomic/chemical descriptors based on the electronegativity of elements in the crystal. Comparison was made vs. radial distribution function (RDF) feature vector, in terms of predictive accuracy on density functional theory (DFT) material properties: cohesive energy (CE), density ( d ), electronic band gap (BG), and decomposition energy (Ed). It was confirmed that the proposed feature vector from Voronoi real value binning generally outperforms the RDF-based one for the prediction of aforementioned properties. Together with electronegativity-based features, Voronoi-tessellation features from a given crystal structure that are derived from second-nearest neighbor information contribute significantly towards prediction.

Introduction to Electrodynamics

NASA Astrophysics Data System (ADS)

Griffiths, David J.

2017-06-01

1. Vector analysis; 2. Electrostatics; 3. Potentials; 4. Electric fields in matter; 5. Magnetostatics; 6. Magnetic fields in matter; 7. Electrodynamics; 8. Conservation laws; 9. Electromagnetic waves; 10. Potentials and fields; 11. Radiation; 12. Electrodynamics and relativity; Appendix A. Vector calculus in curvilinear coordinates; Appendix B. The Helmholtz theorem; Appendix C. Units; Index.

Non-minimally coupled tachyon field in teleparallel gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fazlpour, Behnaz; Banijamali, Ali, E-mail: b.fazlpour@umz.ac.ir, E-mail: a.banijamali@nit.ac.ir

2015-04-01

We perform a full investigation on dynamics of a new dark energy model in which the four-derivative of a non-canonical scalar field (tachyon) is non-minimally coupled to the vector torsion. Our analysis is done in the framework of teleparallel equivalent of general relativity which is based on torsion instead of curvature. We show that in our model there exists a late-time scaling attractor (point P{sub 4}), corresponding to an accelerating universe with the property that dark energy and dark matter densities are of the same order. Such a point can help to alleviate the cosmological coincidence problem. Existence of thismore » point is the most significant difference between our model and another model in which a canonical scalar field (quintessence) is used instead of tachyon field.« less

Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

NASA Astrophysics Data System (ADS)

Muniz, Sérgio R.; Bagnato, Vanderlei S.; Bhattacharya, M.

2015-06-01

In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here, we show how to calculate the general vector field inside a real (finite) solenoid, using only the magnitude of the field along the symmetry axis. Our method does not require integration or knowledge of the current distribution and is presented through practical examples, including a nonuniform finite solenoid used to produce cold atomic beams via laser cooling. These examples allow educators to discuss the nontrivial calculation of fields off-axis using concepts familiar to most students, while offering the opportunity to introduce themes of current modern research.

Rule-based fuzzy vector median filters for 3D phase contrast MRI segmentation

NASA Astrophysics Data System (ADS)

Sundareswaran, Kartik S.; Frakes, David H.; Yoganathan, Ajit P.

2008-02-01

Recent technological advances have contributed to the advent of phase contrast magnetic resonance imaging (PCMRI) as standard practice in clinical environments. In particular, decreased scan times have made using the modality more feasible. PCMRI is now a common tool for flow quantification, and for more complex vector field analyses that target the early detection of problematic flow conditions. Segmentation is one component of this type of application that can impact the accuracy of the final product dramatically. Vascular segmentation, in general, is a long-standing problem that has received significant attention. Segmentation in the context of PCMRI data, however, has been explored less and can benefit from object-based image processing techniques that incorporate fluids specific information. Here we present a fuzzy rule-based adaptive vector median filtering (FAVMF) algorithm that in combination with active contour modeling facilitates high-quality PCMRI segmentation while mitigating the effects of noise. The FAVMF technique was tested on 111 synthetically generated PC MRI slices and on 15 patients with congenital heart disease. The results were compared to other multi-dimensional filters namely the adaptive vector median filter, the adaptive vector directional filter, and the scalar low pass filter commonly used in PC MRI applications. FAVMF significantly outperformed the standard filtering methods (p < 0.0001). Two conclusions can be drawn from these results: a) Filtering should be performed after vessel segmentation of PC MRI; b) Vector based filtering methods should be used instead of scalar techniques.

[Factors for Degaussing of a Cochlear Implant Magnet in the MR Scanner].

PubMed

Koganezawa, Takumi; Uchiyama, Naoko; Teshigawara, Mai; Ogura, Akio

This study examined the conditions influencing degauss of the magnet using magnetic resonance imaging (MRI). Poly methyl methacrylate (PMMA) was used to fix the measurement magnets to the MRI bed at angles from 0° to 180° for the magnetic flux vector of static magnetic field. The PMMA was moved in the MRI magnetic field. Magnetic flux density was measured before and after bed movement, and the rate of degauss was calculated. The contents examined are as follows: (1) the angle of the magnetic flux vector of the measurement magnets for the magnetic flux vector of the static magnetic field, (2) the number of movements, (3) moving velocity, and (4) the movement on the spatial gradient of magnetic field. Mann-Whitney U test was used for statistical analysis of the data. In conclusion, the effect of the angle of the magnetic flux vector of the implant magnet was high under the conditions of degauss in this study. Therefore, during the MRI examination of a patient with a cochlear implant magnet, the operators identified the directions of the magnetic flux vector and static magnetic field of the implant magnet.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

NASA Astrophysics Data System (ADS)

Gong, Yungui; Hou, Shaoqi; Liang, Dicong; Papantonopoulos, Eleftherios

2018-04-01

In this work we discuss the polarization contents of Einstein-æther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-æther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-æther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-æther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

Electrokinetic Control of Viscous Fingering

NASA Astrophysics Data System (ADS)

Mirzadeh, Mohammad; Bazant, Martin Z.

2017-10-01

We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "vector Laplacian growth," in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend the classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic (EK) phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and EK remediation of contaminated soils.

Biot-Savart helicity versus physical helicity: A topological description of ideal flows

NASA Astrophysics Data System (ADS)

Sahihi, Taliya; Eshraghi, Homayoon

2014-08-01

For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the "Biot-Savart helicity" is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it "physical helicity" is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity in hydrodynamics and the magnetic field in MHD is presented by constant coefficients (fluxes) when expanded in terms of one of the time dependent base functions.

The history of polarisation measurements: their role in studies of magnetic fields

NASA Astrophysics Data System (ADS)

Wielebinski, R.

2015-03-01

Radio astronomy gave us new methods to study magnetic fields. Synchrotron radiation, the main cause of comic radio waves, is highly linearly polarised with the `E' vector normal to the magnetic field. The Faraday Effect rotates the `E' vector in thermal regions by the magnetic field in the line of sight. Also the radio Zeeman Effect has been observed.

Electron Beam Propagation Through a Magnetic Wiggler with Random Field Errors

DTIC Science & Technology

1989-08-21

Another quantity of interest is the vector potential 6.A,.(:) associated with the field error 6B,,,(:). Defining the normalized vector potentials ba = ebA...then follows that the correlation of the normalized vector potential errors is given by 1 . 12 (-a.(zj)a.,(z2)) = a,k,, dz’ , dz" (bBE(z’)bB , (z")) a2...Throughout the following, terms of order O(z:/z) will be neglected. Similarly, for the y-component of the normalized vector potential errors, one

High-quality and interactive animations of 3D time-varying vector fields.

PubMed

Helgeland, Anders; Elboth, Thomas

2006-01-01

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering.

Aircraft attitude measurement using a vector magnetometer

NASA Technical Reports Server (NTRS)

Peitila, R.; Dunn, W. R., Jr.

1977-01-01

The feasibility of a vector magnetometer system was investigated by developing a technique to determine attitude given magnetic field components. Sample calculations are then made using the earth's magnetic field data acquired during actual flight conditions. Results of these calculations are compared graphically with measured attitude data acquired simultaneously with the magnetic data. The role and possible implementation of various reference angles are discussed along with other pertinent considerations. Finally, it is concluded that the earth's magnetic field as measured by modern vector magnetometers can play a significant role in attitude control systems.

Preflare magnetic and velocity fields

NASA Technical Reports Server (NTRS)

Hagyard, M. J.; Gaizauskas, V.; Chapman, G. A.; Deloach, A. C.; Gary, G. A.; Jones, H. P.; Karpen, J. T.; Martres, M.-J.; Porter, J. G.; Schmeider, B.

1986-01-01

A characterization is given of the preflare magnetic field, using theoretical models of force free fields together with observed field structure to determine the general morphology. Direct observational evidence for sheared magnetic fields is presented. The role of this magnetic shear in the flare process is considered within the context of a MHD model that describes the buildup of magnetic energy, and the concept of a critical value of shear is explored. The related subject of electric currents in the preflare state is discussed next, with emphasis on new insights provided by direct calculations of the vertical electric current density from vector magnetograph data and on the role of these currents in producing preflare brightenings. Results from investigations concerning velocity fields in flaring active regions, describing observations and analyses of preflare ejecta, sheared velocities, and vortical motions near flaring sites are given. This is followed by a critical review of prevalent concepts concerning the association of flux emergence with flares

Comment on "Chiral gauge field and axial anomaly in a Weyl semimetal"

NASA Astrophysics Data System (ADS)

Zhang, Kai; Zhang, Erhu; Zhang, Shengli

2017-12-01

In Liu et al. [Phys. Rev. B 87, 235306 (2013), 10.1103/PhysRevB.87.235306], the authors obtain that the cross coupling between vector gauge field and chiral gauge field can lead to the anomaly of vector current. We demonstrate that this anomaly is not a physical effect. On one hand, it can be regulated out by the proper regulation. On the other hand, it leads to unjustifiable results, the breaking of the vector gauge symmetry and the ambiguous boundary current. Moreover, the effects associated with anomaly of vector current are understood by random phase approximation (RPA) in the paper we comment on. We point out that the RPA cannot describe the effects resulting from the quantum anomaly.

A model for predicting field-directed particle transport in the magnetofection process.

PubMed

Furlani, Edward P; Xue, Xiaozheng

2012-05-01

To analyze the magnetofection process in which magnetic carrier particles with surface-bound gene vectors are attracted to target cells for transfection using an external magnetic field and to obtain a fundamental understanding of the impact of key factors such as particle size and field strength on the gene delivery process. A numerical model is used to study the field-directed transport of the carrier particle-gene vector complex to target cells in a conventional multiwell culture plate system. The model predicts the transport dynamics and the distribution of particle accumulation at the target cells. The impact of several factors that strongly influence gene vector delivery is assessed including the properties of the carrier particles, the strength of the field source, and its extent and proximity relative to the target cells. The study demonstrates that modeling can be used to predict and optimize gene vector delivery in the magnetofection process for novel and conventional in vitro systems.

Multifractal vector fields and stochastic Clifford algebra.

PubMed

Schertzer, Daniel; Tchiguirinskaia, Ioulia

2015-12-01

In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

Energy-exchange collisions of dark-bright-bright vector solitons.

PubMed

Radhakrishnan, R; Manikandan, N; Aravinthan, K

2015-12-01

We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

A new method for distortion magnetic field compensation of a geomagnetic vector measurement system

NASA Astrophysics Data System (ADS)

Liu, Zhongyan; Pan, Mengchun; Tang, Ying; Zhang, Qi; Geng, Yunling; Wan, Chengbiao; Chen, Dixiang; Tian, Wugang

2016-12-01

The geomagnetic vector measurement system mainly consists of three-axis magnetometer and an INS (inertial navigation system), which have many ferromagnetic parts on them. The magnetometer is always distorted by ferromagnetic parts and other electric equipments such as INS and power circuit module within the system, which can lead to geomagnetic vector measurement error of thousands of nT. Thus, the geomagnetic vector measurement system has to be compensated in order to guarantee the measurement accuracy. In this paper, a new distortion magnetic field compensation method is proposed, in which a permanent magnet with different relative positions is used to change the ambient magnetic field to construct equations of the error model parameters, and the parameters can be accurately estimated by solving linear equations. In order to verify effectiveness of the proposed method, the experiment is conducted, and the results demonstrate that, after compensation, the components errors of measured geomagnetic field are reduced significantly. It demonstrates that the proposed method can effectively improve the accuracy of the geomagnetic vector measurement system.

The effect of electric field geometry on the performance of electromembrane extraction systems: footprints of a third driving force along with migration and diffusion.

PubMed

Moazami, Hamid Reza; Hosseiny Davarani, Saied Saeed; Mohammadi, Jamil; Nojavan, Saeed; Abrari, Masoud

2015-09-03

The distribution of electric field vectors was first calculated for electromembrane extraction (EME) systems in classical and cylindrical electrode geometries. The results showed that supported liquid membrane (SLM) has a general field amplifying effect due to its lower dielectric constant in comparison with aqueous donor/acceptor solutions. The calculated norms of the electric field vector showed that a DC voltage of 50 V can create huge electric field strengths up to 64 kV m(-1) and 111 kV m(-1) in classical and cylindrical geometries respectively. In both cases, the electric field strength reached its peak value on the inner wall of the SLM. In the case of classical geometry, the field strength was a function of the polar position of the SLM whereas the field strength in cylindrical geometry was angularly uniform. In order to investigate the effect of the electrode geometry on the performance of real EME systems, the analysis was carried out in three different geometries including classical, helical and cylindrical arrangements using naproxen and sodium diclofenac as the model analytes. Despite higher field strength and extended cross sectional area, the helical and cylindrical geometries gave lower recoveries with respect to the classical EME. The observed decline of the signal was proved to be against the relations governing migration and diffusion processes, which means that a third driving force is involved in EME. The third driving force is the interaction between the radially inhomogeneous electric field and the analyte in its neutral form. Copyright © 2015 Elsevier B.V. All rights reserved.

On classical mechanical systems with non-linear constraints

NASA Astrophysics Data System (ADS)

Terra, Gláucio; Kobayashi, Marcelo H.

2004-03-01

In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.

Derivation of the Lorentz force law, the magnetic field concept and the Faraday Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

NASA Astrophysics Data System (ADS)

Field, J. H.

2006-06-01

It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space time and energy momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

The evolution of adenoviral vectors through genetic and chemical surface modifications.

PubMed

Capasso, Cristian; Garofalo, Mariangela; Hirvinen, Mari; Cerullo, Vincenzo

2014-02-17

A long time has passed since the first clinical trial with adenoviral (Ad) vectors. Despite being very promising, Ad vectors soon revealed their limitations in human clinical trials. The pre-existing immunity, the marked liver tropism and the high toxicity of first generation Ad (FG-Ad) vectors have been the main challenges for the development of new approaches. Significant effort toward the development of genetically and chemically modified adenoviral vectors has enabled researchers to create more sophisticated vectors for gene therapy, with an improved safety profile and a higher transduction ability of different tissues. In this review, we will describe the latest findings in the high-speed, evolving field of genetic and chemical modifications of adenoviral vectors, a field in which different disciplines, such as biomaterial research, virology and immunology, co-operate synergistically to create better gene therapy tools for modern challenges.

Spectropolarimetric Observations of a Small Active Region with IBIS

NASA Astrophysics Data System (ADS)

Tarr, Lucas; Judge, Philip G.

2014-06-01

We have used the Interferometric BI--dimensional Spectrograph (IBIS) instrument at the Dunn Solar Telescope to measure the polarimetric Stokes IQUV signals for the small active region, NOAA 11304. We used three lines generally corresponding to three atmospheric heights ranging from the photosphere to low corona: Fe I 6302Å, NaI 5896Å, and CaII 8542Å. Each set of profiles has been inverted using the NICOLE code to determine the vector magnetic field at the three heights throughout the field of view, or the line--of--sight field, as allowed by the level of polarization signal. Comparisons are made between the magnetic and thermal structures with the goal of constraining chromospheric models with the information obtained at multiple heights.

A combined vector potential-scalar potential method for FE computation of 3D magnetic fields in electrical devices with iron cores

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1991-01-01

A method of combined use of magnetic vector potential based finite-element (FE) formulations and magnetic scalar potential (MSP) based formulations for computation of three-dimensional magnetostatic fields is introduced. In this method, the curl-component of the magnetic field intensity is computed by a reduced magnetic vector potential. This field intensity forms the basic of a forcing function for a global magnetic scalar potential solution over the entire volume of the region. This method allows one to include iron portions sandwiched in between conductors within partitioned current-carrying subregions. The method is most suited for large-scale global-type 3-D magnetostatic field computations in electrical devices, and in particular rotating electric machinery.

Characterising dark matter searches at colliders and direct detection experiments: Vector mediators

DOE PAGES

Buchmueller, Oliver; Dolan, Matthew J.; Malik, Sarah A.; ...

2015-01-09

We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models are characterised by four parameters: m DM, M med , g DM and g q, the DM and mediator masses, and the mediator couplings to DM and quarks respectively. The MSDM models accurately capture the full event kinematics, and the dependence on all masses and couplings can be systematically studied. The interpretation of mono-jet searches in this framework canmore » be used to establish an equal-footing comparison with direct detection experiments. For theories with a vector mediator, LHC mono-jet searches possess better sensitivity than direct detection searches for light DM masses (≲5 GeV). For axial-vector mediators, LHC and direct detection searches generally probe orthogonal directions in the parameter space. We explore the projected limits of these searches from the ultimate reach of the LHC and multi-ton xenon direct detection experiments, and find that the complementarity of the searches remains. In conclusion, we provide a comparison of limits in the MSDM and effective field theory (EFT) frameworks to highlight the deficiencies of the EFT framework, particularly when exploring the complementarity of mono-jet and direct detection searches.« less

Students' difficulties with vector calculus in electrodynamics

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-12-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data

NASA Technical Reports Server (NTRS)

Gottlieb, Robert G.

1993-01-01

Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.

Observation and modeling of energetic particles at synchronous orbit on July 29, 1977

NASA Technical Reports Server (NTRS)

Baker, D. N.; Higbie, P. R.; Fritz, T. A.; Wilken, B.; Kaye, S. M.; Kivelson, M. G.; Moore, T. E.; Masley, A. J.; Smith, P. H.; Vampola, A. L.

1982-01-01

In the twelve hours following a worldwide storm, there was a series of at least four magnetospheric substorms, the last and largest of which exhibited an expansion phase onset at approximately 1200 UT. Data from six spacecraft in three general local time groupings (0300, 0700, and 1300 LT) were examined and vector magnetic field data and energetic electron and ion data from approximately 15 keV to 2 MeV were employed.

Large-N -approximated field theory for multipartite entanglement

NASA Astrophysics Data System (ADS)

Facchi, P.; Florio, G.; Parisi, G.; Pascazio, S.; Scardicchio, A.

2015-12-01

We try to characterize the statistics of multipartite entanglement of the random states of an n -qubit system. Unable to solve the problem exactly we generalize it, replacing complex numbers with real vectors with Nc components (the original problem is recovered for Nc=2 ). Studying the leading diagrams in the large-Nc approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-Nc limit.

Lower-Hybrid-Drift Wave Turbulence in the Distant Magnetotail

DTIC Science & Technology

1978-05-01

kV ɘ with =• Y ~~ <» (Krall and Liewer, 1971). In this situation a Doppler shifted ,1; lower hybrid wave (u), - kV, . = ± u...satellite includes the relevant Doppler shifts since, in general, proton bulk flows are not directed parallel to the local magnetic field vector...theory of Section II predicts a relatively narrow frequency spectrum, the dominance of the Doppler shifting term k • Vp in Eq.(23)acts to

Man-Portable Vector EMI Sensor for Full UXO Characterization

DTIC Science & Technology

2012-03-01

receivers (for survey in forest and/or in steep terrain). Left inset shows data acquisition (DAQ) and power unit mounted on a backpack frame. Right panel...survey list was created such as to minimize the overall travel distance to visit every anomaly. After the daily IVS survey field operators walked to...the red star at coordinates (0, 0), is generally offset from the signal peak. This observation motivated use of a conservative 3x3-point-grid survey

Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity

NASA Astrophysics Data System (ADS)

Setare, M. R.; Adami, H.

2017-06-01

In this paper we show that warped AdS3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U(1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS3 black hole solution of GMMG is a warped CFT.

Graphic representations: keys to disclose the codex of nature

NASA Astrophysics Data System (ADS)

Caramelo, Liliana; Gonçalves, Norberto; Pereira, Mário; Soares, Armando; Naia, Marco

2010-05-01

Undergraduate and university level students present some difficulties to understand and interpret many of the geosciences concepts, in particular those represented by vector and scalar fields. Our experience reveals that these difficulties are associated with a lack in the development of their abstraction and mental picturing abilities. On the other hand, these students have easy access to communication and information technology software which can be used to built graphic representations of experimental data, time series and vector and scalar fields. This transformation allows an easiest extraction, interpretation and summary of the most important characteristics in the data. There is already commercial and open source software with graphical tools that can be used for this purpose but commercial software packs with user friendly interfaces but their price is not negligible. Open source software can circumvent this difficulty even if, in general, their graphical user interface hasn't reached the desirable level of the commercial ones. We will show a simple procedure to generate an image from the data that characterizes the generation of the suitable images illustrating the key concepts in study, using a freeware code, exactly as it is presented to the students in our open teaching sessions to the general student community. Our experience demonstrated that the students are very enthusiastic using this approach. Furthermore, the use of this software can easily be adopted by teachers and students of secondary schools as part of curricular activities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amariti, Antonio; Toldo, Chiara

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a 4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet,more » dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS 5 to AdS 3 vacua in the supergravity picture. We verify the existence of the flow to AdS 3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.« less

Betti multiplets, flows across dimensions and c-extremization

DOE PAGES

Amariti, Antonio; Toldo, Chiara

2017-07-10

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0; 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a 4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet,more » dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS 5 to AdS 3 vacua in the supergravity picture. We verify the existence of the flow to AdS 3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.« less

Betti multiplets, flows across dimensions and c-extremization

NASA Astrophysics Data System (ADS)

Amariti, Antonio; Toldo, Chiara

2017-07-01

We consider 4d N = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d N = (0, 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c 2 d , similarly to the 4d picture, where the exact R-current maximizes the central charge a 4 d . There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d N = 2 truncation of T 1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d N = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

Interplanetary medium data book, appendix

NASA Technical Reports Server (NTRS)

King, J. H.

1977-01-01

Computer generated listings of hourly average interplanetary plasma and magnetic field parameters are given. Parameters include proton temperature, proton density, bulk speed, an identifier of the source of the plasma data for the hour, average magnetic field magnitude and cartesian components of the magnetic field. Also included are longitude and latitude angles of the vector made up of the average field components, a vector standard deviation, and an identifier of the source of magnetic field data.

Mutually unbiased phase states, phase uncertainties, and Gauss sums

NASA Astrophysics Data System (ADS)

Planat, M.; Rosu, H.

2005-10-01

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d}, with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=pm using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitian phase operators generalizing those introduced by Pegg and Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects.

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Shu, Fu-Wen; Wu, Qiang; Wang, Anzhong

2012-02-01

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry Diff(M,F) to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet and infrared, but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.

Rotational polarities of sudden impulses in the magnetotail lobe

NASA Technical Reports Server (NTRS)

Kawano, H.; Yamamoto, T.; Kokubun, S.; Lepping, R. P.

1992-01-01

A sudden impulse (SI) is a sudden change in the magnetic field strength which is caused by a change in the solar wind pressure and is observed throughout the magnetosphere. In this report we have examined the rotations of the magnetic field vectors at times of SIs in the magnetotail lobe, by using IMP 6, 7, and 8 magnetometer data. The following properties have been found: (1) at the time of SI the arrowhead of the magnetic vector tends to rotate in one plane; (2) the plane of rotation tends to include the unperturbed magnetic field vector; (3) the plane of rotation tends to be aligned with the radial direction from the magnetotail axis; and (4) the magnetic vectors have a particular rotational polarity: when the plane of rotation is viewed so that the Sun is to the right of the viewed plane and the magnetotail axis is to the bottom, the arrowhead of the vector tends to rotate counterclockwise in this plane. These magnetic vector properties are consistent with those expected when part of an increase in solar wind lateral pressure squeezes the magnetotail axisymmetrically while moving tailward.

Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations

NASA Technical Reports Server (NTRS)

Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel

2012-01-01

Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?

An overview of gravitational physiology

NASA Technical Reports Server (NTRS)

Miquel, Jaime; Souza, Kenneth A.

1991-01-01

The focus of this review is on the response of humans and animals to the effects of the near weightless condition occurring aboard orbiting spacecraft. Gravity is an omnipresent force that has been a constant part of our lives and of the evolution of all living species. Emphasis is placed on the general mechanisms of adaptation to altered gravitational fields and vectors, i.e., both hypo- and hypergravity. A broad literature review of gravitational biology was conducted and the general state of our knowledge in this area is discussed. The review is specifically targeted at newcomers to the exciting and relatively new area of space and gravitational biology.

On twisting type [N] ⊗ [N] Ricci flat complex spacetimes with two homothetic symmetries

NASA Astrophysics Data System (ADS)

Chudecki, Adam; Przanowski, Maciej

2018-04-01

In this article, H H spaces of type [N] ⊗ [N] with twisting congruence of null geodesics defined by the 4-fold undotted and dotted Penrose spinors are investigated. It is assumed that these spaces admit two homothetic symmetries. The general form of the homothetic vector fields is found. New coordinates are introduced, which enable us to reduce the H H system of partial differential equations to one ordinary differential equation (ODE) on one holomorphic function. In a special case, this is a second-order ODE and its general solution is explicitly given. In the generic case, one gets rather involved fifth-order ODE.

[Sendai virus vector: vector development and its application to health care and biotechnology].

PubMed

Iida, Akihiro

2007-06-01

Sendai virus (SeV) is an enveloped virus with a nonsegmented negative-strand RNA genome and a member of the paramyxovirus family. We have developed SeV vector which has shown a high efficiently of gene transfer and expression of foreign genes to a wide range of dividing and non-dividing mammalian cells and tissues. One of the characteristics of the vector is that the genome is located exclusively in the cytoplasm of infected cells and does not go through a DNA phase; thus there is no concern about unwanted integration of foreign sequences into chromosomal DNA. Therefore, this new class of "cytoplasmic RNA vector", an RNA vector with cytoplasmic expression, is expected to be a safer and more efficient viral vector than existing vectors for application to human therapy in various fields including gene therapy and vaccination. In this review, I describe development of Sendai virus vector, its application in the field of biotechnology and clinical application aiming to treat for a large number of diseases including cancer, cardiovascular disease, infectious diseases and neurologic disorders.

A substructure coupling procedure applicable to general linear time-invariant dynamic systems

NASA Technical Reports Server (NTRS)

Howsman, T. G.; Craig, R. R., Jr.

1984-01-01

A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.

Trypanosomes, fleas and field voles: ecological dynamics of a host-vector--parasite interaction.

PubMed

Smith, A; Telfer, S; Burthe, S; Bennett, M; Begon, M

2005-09-01

To investigate the prevalence of a flea-borne protozoan (Trypanosoma (Herpetosoma) microti) in its field vole (Microtus agrestis) host, we monitored over a 2-year period a range of intrinsic and extrinsic parameters pertaining to host demographics, infection status and vector (flea) prevalence. Generalized Linear Mixed Modelling was used to analyse patterns of both flea and trypanosome occurrence. Overall, males of all sizes and ages were more likely to be infested with fleas than their female counterparts. Flea prevalence also showed direct density dependence during the winter, but patterns of density dependence varied amongst body mass (age) classes during the summer. Trypanosome prevalence did not vary between the sexes but was positively related to past flea prevalence with a lag of 3 months, with the highest levels occurring during the autumn season. A convex age-prevalence distribution was observed, suggesting that individuals develop a degree of immunity to trypanosome infection with age and exposure. An interaction between age and whether the individual was new or recaptured suggested that infected animals are less likely to become territory holders than their uninfected counterparts.

A SEASAT SASS simulation experiment to quantify the errors related to a + or - 3 hour intermittent assimilation technique

NASA Technical Reports Server (NTRS)

Sylvester, W. B.

1984-01-01

A series of SEASAT repeat orbits over a sequence of best Low center positions is simulated by using the Seatrak satellite calculator. These Low centers are, upon appropriate interpolation to hourly positions, Located at various times during the + or - 3 hour assimilation cycle. Error analysis for a sample of best cyclone center positions taken from the Atlantic and Pacific oceans reveals a minimum average error of 1.1 deg of Longitude and a standard deviation of 0.9 deg of Longitude. The magnitude of the average error seems to suggest that by utilizing the + or - 3 hour window in the assimilation cycle, the quality of the SASS data is degraded to the Level of the background. A further consequence of this assimilation scheme is the effect which is manifested as a result of the blending of two or more more juxtaposed vector winds, generally possessing different properties (vector quantity and time). The outcome of this is to reduce gradients in the wind field and to deform isobaric and frontal patterns of the intial field.

DIRECT OBSERVATION OF SOLAR CORONAL MAGNETIC FIELDS BY VECTOR TOMOGRAPHY OF THE CORONAL EMISSION LINE POLARIZATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kramar, M.; Lin, H.; Tomczyk, S., E-mail: kramar@cua.edu, E-mail: lin@ifa.hawaii.edu, E-mail: tomczyk@ucar.edu

We present the first direct “observation” of the global-scale, 3D coronal magnetic fields of Carrington Rotation (CR) Cycle 2112 using vector tomographic inversion techniques. The vector tomographic inversion uses measurements of the Fe xiii 10747 Å Hanle effect polarization signals by the Coronal Multichannel Polarimeter (CoMP) and 3D coronal density and temperature derived from scalar tomographic inversion of Solar Terrestrial Relations Observatory (STEREO)/Extreme Ultraviolet Imager (EUVI) coronal emission lines (CELs) intensity images as inputs to derive a coronal magnetic field model that best reproduces the observed polarization signals. While independent verifications of the vector tomography results cannot be performed, wemore » compared the tomography inverted coronal magnetic fields with those constructed by magnetohydrodynamic (MHD) simulations based on observed photospheric magnetic fields of CR 2112 and 2113. We found that the MHD model for CR 2112 is qualitatively consistent with the tomography inverted result for most of the reconstruction domain except for several regions. Particularly, for one of the most noticeable regions, we found that the MHD simulation for CR 2113 predicted a model that more closely resembles the vector tomography inverted magnetic fields. In another case, our tomographic reconstruction predicted an open magnetic field at a region where a coronal hole can be seen directly from a STEREO-B/EUVI image. We discuss the utilities and limitations of the tomographic inversion technique, and present ideas for future developments.« less

Morphology of the southern African geomagnetic field derived from observatory and repeat station survey observations: 2005-2014

NASA Astrophysics Data System (ADS)

Kotzé, P. B.; Korte, M.

2016-02-01

Geomagnetic field data from four observatories and annual field surveys between 2005 and 2015 provide a detailed description of Earth's magnetic field changes over South Africa, Namibia and Botswana on time scales of less than 1 year. The southern African area is characterized by rapid changes in the secular variation pattern and lies in close proximity to the South Atlantic Anomaly (SAA) where the geomagnetic field intensity is almost 30 % weaker than in other regions at similar latitudes around the globe. Several geomagnetic secular acceleration (SA) pulses (geomagnetic jerks) around 2007, 2010 and 2012 could be identified over the last decade in southern Africa. We present a new regional field model for declination and horizontal and vertical intensity over southern Africa (Southern African REGional (SAREG)) which is based on field survey and observatory data and covering the time interval from 2005 to 2014, i.e. including the period between 2010 and 2013 when no low Earth-orbiting vector field satellite data are available. A comparative evaluation between SAREG and global field models like CHAOS-5, the CHAMP, Orsted and SAC-C model of the Earth's magnetic field and International Geomagnetic Reference Field (IGRF-12) reveals that a simple regional field model based on a relatively dense ground network is able to provide a realistic representation of the geomagnetic field in this area. We particularly note that a global field model like CHAOS-5 does not always indicate similar short-period patterns in the field components as revealed by observatory data, while representing the general secular variation reasonably well during the time interval without near-Earth satellite vector field data. This investigation further shows the inhomogeneous occurrence and distribution of secular variation impulses in the different geomagnetic field components and at different locations in southern African.

SOLAR FLARE PREDICTION USING SDO/HMI VECTOR MAGNETIC FIELD DATA WITH A MACHINE-LEARNING ALGORITHM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bobra, M. G.; Couvidat, S., E-mail: couvidat@stanford.edu

2015-01-10

We attempt to forecast M- and X-class solar flares using a machine-learning algorithm, called support vector machine (SVM), and four years of data from the Solar Dynamics Observatory's Helioseismic and Magnetic Imager, the first instrument to continuously map the full-disk photospheric vector magnetic field from space. Most flare forecasting efforts described in the literature use either line-of-sight magnetograms or a relatively small number of ground-based vector magnetograms. This is the first time a large data set of vector magnetograms has been used to forecast solar flares. We build a catalog of flaring and non-flaring active regions sampled from a databasemore » of 2071 active regions, comprised of 1.5 million active region patches of vector magnetic field data, and characterize each active region by 25 parameters. We then train and test the machine-learning algorithm and we estimate its performances using forecast verification metrics with an emphasis on the true skill statistic (TSS). We obtain relatively high TSS scores and overall predictive abilities. We surmise that this is partly due to fine-tuning the SVM for this purpose and also to an advantageous set of features that can only be calculated from vector magnetic field data. We also apply a feature selection algorithm to determine which of our 25 features are useful for discriminating between flaring and non-flaring active regions and conclude that only a handful are needed for good predictive abilities.« less

Achievement of needle-like focus by engineering radial-variant vector fields.

PubMed

Gu, Bing; Wu, Jia-Lu; Pan, Yang; Cui, Yiping

2013-12-16

We present and demonstrate a novel method for engineering the radial-variant polarization on the incident field to achieve a needle of transversally polarized field without any pupil filters. We generate a new kind of localized linearly-polarized vector fields with distributions of states of polarization (SoPs) describing by the radius to the power p and explore its tight focusing, nonparaxial focusing, and paraxial focusing properties. By tuning the power p, we obtain the needle-like focal field with hybrid SoPs and give the formula for describing the length of the needle. Experimentally, we systematically investigate both the intensity distributions and the polarization evolution of the optical needle by paraxial focusing the generated vector field. Such an optical needle, which enhances the light-matter interaction, has intriguing applications in optical microma-chining and nonlinear optics.

Computation of Surface Integrals of Curl Vector Fields

ERIC Educational Resources Information Center

Hu, Chenglie

2007-01-01

This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…

Jupiter Environment Tool

NASA Technical Reports Server (NTRS)

Sturm, Erick J.; Monahue, Kenneth M.; Biehl, James P.; Kokorowski, Michael; Ngalande, Cedrick,; Boedeker, Jordan

2012-01-01

The Jupiter Environment Tool (JET) is a custom UI plug-in for STK that provides an interface to Jupiter environment models for visualization and analysis. Users can visualize the different magnetic field models of Jupiter through various rendering methods, which are fully integrated within STK s 3D Window. This allows users to take snapshots and make animations of their scenarios with magnetic field visualizations. Analytical data can be accessed in the form of custom vectors. Given these custom vectors, users have access to magnetic field data in custom reports, graphs, access constraints, coverage analysis, and anywhere else vectors are used within STK.

On the origin of Poincaré gauge gravity

NASA Astrophysics Data System (ADS)

Chkareuli, J. L.

2017-06-01

We argue that the origin of Poincaré gauge gravity (PGG) may be related to spontaneous violation of underlying spacetime symmetries involved and appearance of gauge fields as vector Goldstone bosons. In essence, we start with an arbitrary theory of some vector and fermion fields which possesses only global spacetime symmetries, such as Lorentz and translational invariance, in flat Minkowski space. The two vector field multiplets involved are assumed to belong, respectively, to the adjoint (Aμij) and vector (eμi) representations of the starting global Lorentz symmetry. We propose that these prototype vector fields are covariantly constrained, Aμij Aijμ = ±MA2 and eμi eiμ = ±Me2 , that causes a spontaneous violation of the accompanying global symmetries (MA,e are their presumed violation scales). It then follows that the only possible theory compatible with these length-preserving constraints is turned out to be the gauge invariant PGG, while the corresponding massless (pseudo)Goldstone modes are naturally collected in the emergent gauge fields of tetrads and spin-connections. In a minimal theory case being linear in a curvature we unavoidably come to the Einstein-Cartan theory. The extended theories with propagating spin-connection and tetrad modes are also considered and their possible unification with the Standard Model is briefly discussed.

Selection of optimum median-filter-based ambiguity removal algorithm parameters for NSCAT. [NASA scatterometer

NASA Technical Reports Server (NTRS)

Shaffer, Scott; Dunbar, R. Scott; Hsiao, S. Vincent; Long, David G.

1989-01-01

The NASA Scatterometer, NSCAT, is an active spaceborne radar designed to measure the normalized radar backscatter coefficient (sigma0) of the ocean surface. These measurements can, in turn, be used to infer the surface vector wind over the ocean using a geophysical model function. Several ambiguous wind vectors result because of the nature of the model function. A median-filter-based ambiguity removal algorithm will be used by the NSCAT ground data processor to select the best wind vector from the set of ambiguous wind vectors. This process is commonly known as dealiasing or ambiguity removal. The baseline NSCAT ambiguity removal algorithm and the method used to select the set of optimum parameter values are described. An extensive simulation of the NSCAT instrument and ground data processor provides a means of testing the resulting tuned algorithm. This simulation generates the ambiguous wind-field vectors expected from the instrument as it orbits over a set of realistic meoscale wind fields. The ambiguous wind field is then dealiased using the median-based ambiguity removal algorithm. Performance is measured by comparison of the unambiguous wind fields with the true wind fields. Results have shown that the median-filter-based ambiguity removal algorithm satisfies NSCAT mission requirements.

Symmetries and stochastic symmetry breaking in multifractal geophysics: analysis and simulation with the help of the Lévy-Clifford algebra of cascade generators..

NASA Astrophysics Data System (ADS)

Schertzer, D. J. M.; Tchiguirinskaia, I.

2016-12-01

Multifractal fields, whose definition is rather independent of their domain dimension, have opened a new approach of geophysics enabling to explore its spatial extension that is of prime importance as underlined by the expression "spatial chaos". However multifractals have been until recently restricted to be scalar valued, i.e. to one-dimensional codomains. This has prevented to deal with the key question of complex component interactions and their non trivial symmetries. We first emphasize that the Lie algebra of stochastic generators of cascade processes enables us to generalize multifractals to arbitrarily large codomains, e.g. flows of vector fields on large dimensional manifolds. In particular, we have recently investigated the neat example of stable Levy generators on Clifford algebra that have a number of seductive properties, e.g. universal statistical and robust algebra properties, both defining the basic symmetries of the corresponding fields (Schertzer and Tchiguirinskaia, 2015). These properties provide a convenient multifractal framework to study both the symmetries of the fields and how they stochastically break the symmetries of the underlying equations due to boundary conditions, large scale rotations and forcings. These developments should help us to answer to challenging questions such as the climatology of (exo-) planets based on first principles (Pierrehumbert, 2013), to fully address the question of the limitations of quasi- geostrophic turbulence (Schertzer et al., 2012) and to explore the peculiar phenomenology of turbulent dynamics of the atmosphere or oceans that is neither two- or three-dimensional. Pierrehumbert, R.T., 2013. Strange news from other stars. Nature Geoscience, 6(2), pp.8183. Schertzer, D. et al., 2012. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos. Chem. Phys., 12, pp.327336. Schertzer, D. & Tchiguirinskaia, I., 2015. Multifractal vector fields and stochastic Clifford algebra. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p.123127

Proper Conformal Killing Vectors in Kantowski-Sachs Metric

NASA Astrophysics Data System (ADS)

Hussain, Tahir; Farhan, Muhammad

2018-04-01

This paper deals with the existence of proper conformal Killing vectors (CKVs) in Kantowski-Sachs metric. Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal factor is presented. The integrability conditions are solved generally as well as in some particular cases to show that the non-conformally flat Kantowski-Sachs metric admits two proper CKVs, while it admits a 15-dimensional Lie algebra of CKVs in the case when it becomes conformally flat. The inheriting conformal Killing vectors (ICKVs), which map fluid lines conformally, are also investigated.

Supermodes in Coupled Multi-Core Waveguide Structures

DTIC Science & Technology

2016-04-01

and therefore can be treated as linear polarization (LP) modes. In essence, the LP modes are scalar approximations of the vector mode fields and contain...field, including the discovery of optical discrete solitons , Bragg and vector solitons in fibers, nonlinear surface waves, and the discovery of self...increased for an isolated core, it can guide high-order modes. For optical fibers with low re- fractive index contrast, the vector modes are weakly guided

Dual and mixed nonsymmetric stress-based variational formulations for coupled thermoelastodynamics with second sound effect

NASA Astrophysics Data System (ADS)

Tóth, Balázs

2018-03-01

Some new dual and mixed variational formulations based on a priori nonsymmetric stresses will be developed for linearly coupled irreversible thermoelastodynamic problems associated with second sound effect according to the Lord-Shulman theory. Having introduced the entropy flux vector instead of the entropy field and defining the dissipation and the relaxation potential as the function of the entropy flux, a seven-field dual and mixed variational formulation will be derived from the complementary Biot-Hamilton-type variational principle, using the Lagrange multiplier method. The momentum-, the displacement- and the infinitesimal rotation vector, and the a priori nonsymmetric stress tensor, the temperature change, the entropy field and its flux vector are considered as the independent field variables of this formulation. In order to handle appropriately the six different groups of temporal prescriptions in the relaxed- and/or the strong form, two variational integrals will be incorporated into the seven-field functional. Then, eliminating the entropy from this formulation through the strong fulfillment of the constitutive relation for the temperature change with the use of the Legendre transformation between the enthalpy and Gibbs potential, a six-field dual and mixed action functional is obtained. As a further development, the elimination of the momentum- and the velocity vector from the six-field principle through the a priori satisfaction of the kinematic equation and the constitutive relation for the momentum vector leads to a five-field variational formulation. These principles are suitable for the transient analyses of the structures exposed to a thermal shock of short temporal domain or a large heat flux.

Resolving the 180-degree ambiguity in vector magnetic field measurements: The 'minimum' energy solution

NASA Technical Reports Server (NTRS)

Metcalf, Thomas R.

1994-01-01

I present a robust algorithm that resolves the 180-deg ambiguity in measurements of the solar vector magnetic field. The technique simultaneously minimizes both the divergence of the magnetic field and the electric current density using a simulated annealing algorithm. This results in the field orientation with approximately minimum free energy. The technique is well-founded physically and is simple to implement.

Low-Angle Radar Tracking

DTIC Science & Technology

1976-02-01

Transition from Specular Reflection to Diffuse Scattering. . . 10 Composition of the Electric-Field Vector as Seen at the Radar...r t (16) R • FIGURE P COMPOSITION OF THE ELECTRIC-FIELD VECTOR AS SEEN AT THE RADAR, R, IN FIG. 2. The electric field at the radar, E, is the sum...wavelengths in the VHP and UHF ranges even subsurface characteristics can be important. So in a field experiment one must be careful to measure

Electromagnetically induced transparency in the case of elliptic polarization of interacting fields

NASA Astrophysics Data System (ADS)

Parshkov, Oleg M.

2018-04-01

The theoretical investigation results of disintegration effect of elliptic polarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed elliptic polarized control field and in weak probe field approximation are presented. It is shown that this disintegration occurs because the probe field in the medium is the sum of two normal modes, which correspond to elliptic polarized pulses with different speeds of propagation. The polarization ellipses of normal modes have equal eccentricities and mutually perpendicular major axes. Major axis of polarization ellipse of one normal mode is parallel to polarization ellipse major axis of control field, and electric vector of this mode rotates in the opposite direction, than electric vector of the control field. The electric vector other normal mode rotates in the same direction that the control field electric vector. The normal mode speed of the first type aforementioned is less than that of the second type. The polarization characteristics of the normal mode depend uniquely on the polarization characteristics of elliptic polarized control field and remain changeless in the propagation process. The theoretical investigation is performed for Λ-scheme of degenerated quantum transitions between 3P0, 3P10 and 3P2 energy levels of 208Pb isotope.

Radar observations of density gradients, electric fields, and plasma irregularities near polar cap patches in the context of the gradient-drift instability

NASA Astrophysics Data System (ADS)

Lamarche, Leslie J.; Makarevich, Roman A.

2017-03-01

We present observations of plasma density gradients, electric fields, and small-scale plasma irregularities near a polar cap patch made by the Super Dual Auroral Radar Network radar at Rankin Inlet (RKN) and the northern face of Resolute Bay Incoherent Scatter Radar (RISR-N). RKN echo power and occurrence are analyzed in the context of gradient-drift instability (GDI) theory, with a particular focus on the previously uninvestigated 2-D dependencies on wave propagation, electric field, and gradient vectors, with the latter two quantities evaluated directly from RISR-N measurements. It is shown that higher gradient and electric field components along the wave vector generally lead to the higher observed echo occurrence, which is consistent with the expected higher GDI growth rate, but the relationship with echo power is far less straightforward. The RKN echo power increases monotonically as the predicted linear growth rate approaches zero from negative values but does not continue this trend into positive growth rate values, in contrast with GDI predictions. The observed greater consistency of echo occurrence with GDI predictions suggests that GDI operating in the linear regime can control basic plasma structuring, but measured echo strength may be affected by other processes and factors, such as multistep or nonlinear processes or a shear-driven instability.

Superconducting dark energy

NASA Astrophysics Data System (ADS)

Liang, Shi-Dong; Harko, Tiberiu

2015-04-01

Based on the analogy with superconductor physics we consider a scalar-vector-tensor gravitational model, in which the dark energy action is described by a gauge invariant electromagnetic type functional. By assuming that the ground state of the dark energy is in a form of a condensate with the U(1) symmetry spontaneously broken, the gauge invariant electromagnetic dark energy can be described in terms of the combination of a vector and of a scalar field (corresponding to the Goldstone boson), respectively. The gravitational field equations are obtained by also assuming the possibility of a nonminimal coupling between the cosmological mass current and the superconducting dark energy. The cosmological implications of the dark energy model are investigated for a Friedmann-Robertson-Walker homogeneous and isotropic geometry for two particular choices of the electromagnetic type potential, corresponding to a pure electric type field, and to a pure magnetic field, respectively. The time evolutions of the scale factor, matter energy density and deceleration parameter are obtained for both cases, and it is shown that in the presence of the superconducting dark energy the Universe ends its evolution in an exponentially accelerating vacuum de Sitter state. By using the formalism of the irreversible thermodynamic processes for open systems we interpret the generalized conservation equations in the superconducting dark energy model as describing matter creation. The particle production rates, the creation pressure and the entropy evolution are explicitly obtained.

Far-field radially polarized focal spot from plasmonic spiral structure combined with central aperture antenna

PubMed Central

Mao, Lei; Ren, Yuan; Lu, Yonghua; Lei, Xinrui; Jiang, Kang; Li, Kuanguo; Wang, Yong; Cui, Chenjing; Wen, Xiaolei; Wang, Pei

2016-01-01

Manipulation of a vector micro-beam with an optical antenna has significant potentials for nano-optical technology applications including bio-optics, optical fabrication, and quantum information processing. We have designed and demonstrated a central aperture antenna within an Archimedean spiral that extracts the bonding plasmonic field from a surface to produce a new vector focal spot in far-field. The properties of this vector focal field are revealed by confocal microscopy and theoretical simulations. The pattern, polarization and phase of the focal field are determined by the incident light and by the chirality of the Archimedean spiral. For incident light with right-handed circular polarization, the left-handed spiral (one-order chirality) outputs a micro-radially polarized focal field. Our results reveal the relationship between the near-field and far-field distributions of the plasmonic spiral structure, and the structure has the potential to lead to advances in diverse applications such as plasmonic lenses, near-field angular momentum detection, and optical tweezers. PMID:27009383

How effective is integrated vector management against malaria and lymphatic filariasis where the diseases are transmitted by the same vector?

PubMed

Stone, Christopher M; Lindsay, Steve W; Chitnis, Nakul

2014-12-01

The opportunity to integrate vector management across multiple vector-borne diseases is particularly plausible for malaria and lymphatic filariasis (LF) control where both diseases are transmitted by the same vector. To date most examples of integrated control targeting these diseases have been unanticipated consequences of malaria vector control, rather than planned strategies that aim to maximize the efficacy and take the complex ecological and biological interactions between the two diseases into account. We developed a general model of malaria and LF transmission and derived expressions for the basic reproductive number (R0) for each disease. Transmission of both diseases was most sensitive to vector mortality and biting rate. Simulating different levels of coverage of long lasting-insecticidal nets (LLINs) and larval control confirms the effectiveness of these interventions for the control of both diseases. When LF was maintained near the critical density of mosquitoes, minor levels of vector control (8% coverage of LLINs or treatment of 20% of larval sites) were sufficient to eliminate the disease. Malaria had a far greater R0 and required a 90% population coverage of LLINs in order to eliminate it. When the mosquito density was doubled, 36% and 58% coverage of LLINs and larval control, respectively, were required for LF elimination; and malaria elimination was possible with a combined coverage of 78% of LLINs and larval control. Despite the low level of vector control required to eliminate LF, simulations suggest that prevalence of LF will decrease at a slower rate than malaria, even at high levels of coverage. If representative of field situations, integrated management should take into account not only how malaria control can facilitate filariasis elimination, but strike a balance between the high levels of coverage of (multiple) interventions required for malaria with the long duration predicted to be required for filariasis elimination.

Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties

NASA Technical Reports Server (NTRS)

Guertin, R. F.; Wilson, T. L.

1977-01-01

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

Rotation Detection Using the Precession of Molecular Electric Dipole Moment

NASA Astrophysics Data System (ADS)

Ke, Yi; Deng, Xiao-Bing; Hu, Zhong-Kun

2017-11-01

We present a method to detect the rotation by using the precession of molecular electric dipole moment in a static electric field. The molecular electric dipole moments are polarized under the static electric field and a nonzero electric polarization vector emerges in the molecular gas. A resonant radio-frequency pulse electric field is applied to realize a 90° flip of the electric polarization vector of a particular rotational state. After the pulse electric field, the electric polarization vector precesses under the static electric field. The rotation induces a shift in the precession frequency which is measured to deduce the angular velocity of the rotation. The fundamental sensitivity limit of this method is estimated. This work is only a proposal and does not involve experimental results.

Rational Development of A Polycistronic Plasmid with A CpG-Free Bacterial Backbone as A Potential Tool for Direct Reprogramming.

PubMed

Dormiani, Kianoush; Mir Mohammad Sadeghi, Hamid; Sadeghi-Aliabadi, Hojjat; Forouzanfar, Mahboobeh; Baharvand, Hossein; Ghaedi, Kamran; Nasr-Esfahani, Mohammad Hossein

2017-01-01

Induced pluripotent stem cells are generated from somatic cells by direct reprogramming. These reprogrammed pluripotent cells have different applications in biomedical fields such as regenerative medicine. Although viral vectors are widely used for efficient reprogramming, they have limited applications in the clinic due to the risk for immunogenicity and insertional mutagenesis. Accordingly, we designed and developed a small, non-integrating plasmid named pLENSO/Zeo as a 2A-mediated polycistronic expression vector. In this experimental study, we developed a single plasmid which includes a single expression cassette containing open reading frames of human LIN28, NANOG, SOX2 and OCT4 along with an EGFP reporter gene. Each reprogramming factor is separated by an intervening sequence that encodes a 2A self-processing peptide. The reprogramming cassette is located downstream of a CMV promoter. The vector is easily propagated in the E. coli GT115 strain through a CpG-depleted vector backbone. We evaluated the stability of the constructed vector bioinformatically, and its ability to stoichiometric expression of the reprogramming factors using quantitative molecular methods analysis after transient transfection into HEK293 cells. In the present study, we developed a nonviral episomal vector named pLENSO/ Zeo. Our results demonstrated the general structural stability of the plasmid DNA. This relatively small vector showed concomitant, high-level expression of the four reprogramming factors with similar titers, which are considered as the critical parameters for efficient and consistent reprogramming. According to our experimental results, this stable extrachromosomal plasmid expresses reliable amounts of four reprogramming factors simultaneously. Consequently, these promising results encouraged us to evaluate the capability of pLENSO/Zeo as a simple and feasible tool for generation of induced pluripotent stem cells from primary cells in the future.

Radiation and matter: Electrodynamics postulates and Lorenz gauge

NASA Astrophysics Data System (ADS)

Bobrov, V. B.; Trigger, S. A.; van Heijst, G. J.; Schram, P. P.

2016-11-01

In general terms, we have considered matter as the system of charged particles and quantized electromagnetic field. For consistent description of the thermodynamic properties of matter, especially in an extreme state, the problem of quantization of the longitudinal and scalar potentials should be solved. In this connection, we pay attention that the traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. The Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics may be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorenz gauge is valid for the averages potentials (and provides the implementation of the Maxwell equations for averages). The suggested concept overcomes difficulties under the electromagnetic field quantization procedure being in accordance with the results of quantum electrodynamics. As a result, longitudinal and scalar photons become real rather than virtual and may be observed in principle. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.

Strongly nonlinear composite dielectrics: A perturbation method for finding the potential field and bulk effective properties

NASA Astrophysics Data System (ADS)

Blumenfeld, Raphael; Bergman, David J.

1991-10-01

A class of strongly nonlinear composite dielectrics is studied. We develop a general method to reduce the scalar-potential-field problem to the solution of a set of linear Poisson-type equations in rescaled coordinates. The method is applicable for a large variety of nonlinear materials. For a power-law relation between the displacement and the electric fields, it is used to solve explicitly for the value of the bulk effective dielectric constant ɛe to second order in the fluctuations of its local value. A simlar procedure for the vector potential, whose curl is the displacement field, yields a quantity analogous to the inverse dielectric constant in linear dielectrics. The bulk effective dielectric constant is given by a set of linear integral expressions in the rescaled coordinates and exact bounds for it are derived.

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.; Hooshmandasl, M. R.

2013-05-01

In this paper, the interaction between a $\\Lambda$-type three-level atom and two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account and it is assumed that atom-field coupling and Kerr medium to be $f$-deformed. Even though the system seems to be complicated, the analytical form of the state vector of the entire system for considered model is exactly obtained. The time evolution of nonclassical properties such as quantum entanglement and position-momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the latter nonclassicality signs are analyzed, in detail.

Design of a Two-level Adaptive Multi-Agent System for Malaria Vectors driven by an ontology

PubMed Central

Koum, Guillaume; Yekel, Augustin; Ndifon, Bengyella; Etang, Josiane; Simard, Frédéric

2007-01-01

Background The understanding of heterogeneities in disease transmission dynamics as far as malaria vectors are concerned is a big challenge. Many studies while tackling this problem don't find exact models to explain the malaria vectors propagation. Methods To solve the problem we define an Adaptive Multi-Agent System (AMAS) which has the property to be elastic and is a two-level system as well. This AMAS is a dynamic system where the two levels are linked by an Ontology which allows it to function as a reduced system and as an extended system. In a primary level, the AMAS comprises organization agents and in a secondary level, it is constituted of analysis agents. Its entry point, a User Interface Agent, can reproduce itself because it is given a minimum of background knowledge and it learns appropriate "behavior" from the user in the presence of ambiguous queries and from other agents of the AMAS in other situations. Results Some of the outputs of our system present a series of tables, diagrams showing some factors like Entomological parameters of malaria transmission, Percentages of malaria transmission per malaria vectors, Entomological inoculation rate. Many others parameters can be produced by the system depending on the inputted data. Conclusion Our approach is an intelligent one which differs from statistical approaches that are sometimes used in the field. This intelligent approach aligns itself with the distributed artificial intelligence. In terms of fight against malaria disease our system offers opportunities of reducing efforts of human resources who are not obliged to cover the entire territory while conducting surveys. Secondly the AMAS can determine the presence or the absence of malaria vectors even when specific data have not been collected in the geographical area. In the difference of a statistical technique, in our case the projection of the results in the field can sometimes appeared to be more general. PMID:17605778

The Sequential Implementation of Array Processors when there is Directional Uncertainty

DTIC Science & Technology

1975-08-01

University of Washington kindly supplied office space and ccputing facilities. -The author hat, benefited greatly from discussions with several other...if i Q- inverse of Q I L general observation space R general vector of observation _KR general observation vector of dimension K Exiv] "Tf -- ’ -"-T’T...7" i ’i ’:"’ - ’ ; ’ ’ ’ ’ ’ ’" ’"- Glossary of Symbols (continued) R. ith observation 1 Rm real vector space of dimension m R(T) autocorrelation

Electric fields and vector potentials of thin cylindrical antennas

NASA Astrophysics Data System (ADS)

King, Ronold W. P.

1990-09-01

The vector potential and electric field generated by the current in a center-driven or parasitic dipole antenna that extends from z = -h to z = h are investigated for each of the several components of the current. These include sin k(h - absolute value of z), sin k (absolute value of z) - sin kh, cos kz - cos kh, and cos kz/2 - cos kh/2. Of special interest are the interactions among the variously spaced elements in parallel nonstaggered arrays. These depend on the mutual vector potentials. It is shown that at a radial distance rho approximately = h and in the range z = -h to h, the vector potentials due to all four components become alike and have an approximately plane-wave form. Simple approximate formulas for the electric fields and vector potentials generated by each of the four distributions are derived and compared with the exact results. The application of the new formulas to large arrays is discussed.

Limits on new forces coexisting with electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kloor, H.; Fischbach, E.; Talmadge, C.

1994-02-15

We consider the limits arising from different electromagnetic systems on the existence of a possible new electromagnetic analogue of the fifth force. Although such a force may have no intrinsic connection to electromagnetism (or gravity), its effects could be manifested through various anomalies in electromagnetic systems, for appropriate values of the coupling strength and range. Our work generalizes that of Bartlett and Loegl (who considered the case of a massive vector field coexisting with massless electrodynamics) to encompass a broad class of phenomenological interactions mediated by both scalar and vector exchanges. By combining data from both gravitational and electromagnetic systems,more » one can eventually set limits on a new force whose range [lambda] extends from the subatomic scale ([lambda][approx]10[sup [minus]15] m) to the astrophysical scale ([lambda][approx]10[sup 12] m).« less

Validation of SplitVectors Encoding for Quantitative Visualization of Large-Magnitude-Range Vector Fields

PubMed Central

Zhao, Henan; Bryant, Garnett W.; Griffin, Wesley; Terrill, Judith E.; Chen, Jian

2017-01-01

We designed and evaluated SplitVectors, a new vector field display approach to help scientists perform new discrimination tasks on large-magnitude-range scientific data shown in three-dimensional (3D) visualization environments. SplitVectors uses scientific notation to display vector magnitude, thus improving legibility. We present an empirical study comparing the SplitVectors approach with three other approaches - direct linear representation, logarithmic, and text display commonly used in scientific visualizations. Twenty participants performed three domain analysis tasks: reading numerical values (a discrimination task), finding the ratio between values (a discrimination task), and finding the larger of two vectors (a pattern detection task). Participants used both mono and stereo conditions. Our results suggest the following: (1) SplitVectors improve accuracy by about 10 times compared to linear mapping and by four times to logarithmic in discrimination tasks; (2) SplitVectors have no significant differences from the textual display approach, but reduce cluttering in the scene; (3) SplitVectors and textual display are less sensitive to data scale than linear and logarithmic approaches; (4) using logarithmic can be problematic as participants' confidence was as high as directly reading from the textual display, but their accuracy was poor; and (5) Stereoscopy improved performance, especially in more challenging discrimination tasks. PMID:28113469

Validation of SplitVectors Encoding for Quantitative Visualization of Large-Magnitude-Range Vector Fields.

PubMed

Henan Zhao; Bryant, Garnett W; Griffin, Wesley; Terrill, Judith E; Jian Chen

2017-06-01

We designed and evaluated SplitVectors, a new vector field display approach to help scientists perform new discrimination tasks on large-magnitude-range scientific data shown in three-dimensional (3D) visualization environments. SplitVectors uses scientific notation to display vector magnitude, thus improving legibility. We present an empirical study comparing the SplitVectors approach with three other approaches - direct linear representation, logarithmic, and text display commonly used in scientific visualizations. Twenty participants performed three domain analysis tasks: reading numerical values (a discrimination task), finding the ratio between values (a discrimination task), and finding the larger of two vectors (a pattern detection task). Participants used both mono and stereo conditions. Our results suggest the following: (1) SplitVectors improve accuracy by about 10 times compared to linear mapping and by four times to logarithmic in discrimination tasks; (2) SplitVectors have no significant differences from the textual display approach, but reduce cluttering in the scene; (3) SplitVectors and textual display are less sensitive to data scale than linear and logarithmic approaches; (4) using logarithmic can be problematic as participants' confidence was as high as directly reading from the textual display, but their accuracy was poor; and (5) Stereoscopy improved performance, especially in more challenging discrimination tasks.

Lorentz violation and gravity

NASA Astrophysics Data System (ADS)

Bailey, Quentin G.

2007-08-01

This work explores the theoretical and experimental aspects of Lorentz violation in gravity. A set of modified Einstein field equations is derived from the general Lorentz-violating Standard-Model Extension (SME). Some general theoretical implications of these results are discussed. The experimental consequences for weak-field gravitating systems are explored in the Earth- laboratory setting, the solar system, and beyond. The role of spontaneous Lorentz-symmetry breaking is discussed in the context of the pure-gravity sector of the SME. To establish the low-energy effective Einstein field equations, it is necessary to take into account the dynamics of 20 coefficients for Lorentz violation. As an example, the results are compared with bumblebee models, which are general theories of vector fields with spontaneous Lorentz violation. The field equations are evaluated in the post- newtonian limit using a perfect fluid description of matter. The post-newtonian metric of the SME is derived and compared with some standard test models of gravity. The possible signals for Lorentz violation due to gravity-sector coefficients are studied. Several new effects are identified that have experimental implications for current and future tests. Among the unconventional effects are a new type of spin precession for a gyroscope in orbit and a modification to the local gravitational acceleration on the Earth's surface. These and other tests are expected to yield interesting sensitivities to dimensionless gravity- sector coefficients.

Dark matter as a ghost free conformal extension of Einstein theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barvinsky, A.O., E-mail: barvin@td.lpi.ru

We discuss ghost free models of the recently suggested mimetic dark matter theory. This theory is shown to be a conformal extension of Einstein general relativity. Dark matter originates from gauging out its local Weyl invariance as an extra degree of freedom which describes a potential flow of the pressureless perfect fluid. For a positive energy density of this fluid the theory is free of ghost instabilities, which gives strong preference to stable configurations with a positive scalar curvature and trace of the matter stress tensor. Instabilities caused by caustics of the geodesic flow, inherent in this model, serve asmore » a motivation for an alternative conformal extension of Einstein theory, based on the generalized Proca vector field. A potential part of this field modifies the inflationary stage in cosmology, whereas its rotational part at the post inflationary epoch might simulate rotating flows of dark matter.« less

Theoretical frameworks for testing relativistic gravity. IV - A compendium of metric theories of gravity and their post-Newtonian limits.

NASA Technical Reports Server (NTRS)

Ni, W.-T.

1972-01-01

Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.

The generalized formula for angular velocity vector of the moving coordinate system

NASA Astrophysics Data System (ADS)

Ermolin, Vladislav S.; Vlasova, Tatyana V.

2018-05-01

There are various ways for introducing the concept of the instantaneous angular velocity vector. In this paper we propose a method based on introducing of this concept by construction of the solution for the system of kinematic equations. These equations connect the function vectors defining the motion of the basis, and their derivatives. Necessary and sufficient conditions for the existence and uniqueness of the solution of this system are established. The instantaneous angular velocity vector is a solution of the algebraic system of equations. It is built explicitly. The derived formulas for the angular velocity vector generalize the earlier results, both for a basis of an affine oblique coordinate system and for an orthonormal basis.

Crustal block structure by GPS data using neural network in the Northern Tien Shan

NASA Astrophysics Data System (ADS)

Kostuk, A.; Carmenate, D.

2010-05-01

For over ten years regular GPS measurements have been carried out by Research Station RAS in the Central Asia. The results of these measurements have not only proved the conclusion that the Earth's crust meridional compression equals in total about 17 mm/year from the Tarim massif to the Kazakh shield, but have also allowed estimating deformation behavior in the region. As is known, deformation behavior of continental crust is an actively discussed issue. On the one hand, the Earth's crust is presented as a set of microplates (blocks) and deformation here is a result of shifting along the blocks boundaries, on the other hand, lithospheric deformation is distributed by volume and meets the rheological model of nonlinear viscous fluid. This work represents an attempt to detect the block structure of the surface of the Northern Tien Shan using GPS velocity fields. As a significant difference from analogous works, appears the vector field clustering with the help of neural network used as a classifier by many criteria that allows dividing input space into areas and using of all three components of GPS velocity. In this case, we use such a feature of neural networks as self-organization. Among the mechanisms of self-organization there are two main classes: self-organization based on the Hebb associative rule and the mechanism of neuronal competition based on the generalized Kohonen rule. In this case, we use an approach of self-organizing networks in which we take neuronal competition as an algorithm for their training. As a rule, these are single-layer networks where each neuron is connected to all components of m-dimensional input vector. GPS vectors of the Central Asian velocity field located within the territory of the Northern Tien Shan were used as input patterns. Measurements at GPS sites were fulfilled in 36 hour-long sessions by double-frequency receivers Trimble and Topcon. In so doing, measurement discreteness equaled 30 seconds; the data were processed by GAMITGLOBK programs. An overall period of measurements lasted from 1995 to 2005. Those GPS vectors were admitted to processing that had an estimated error no more than 1 mm per year for each of the three components. In general, an obtained cluster structure reflecting the block structure of the Earth's crust of the Northern Tien Shan is proved by the location of active faults. Certainly, the structure analysis of GPS velocity field is a rather complicated task that yet does not have a definite solution; however, obtained results indicate the possibility of using of neural networks for solving such a problem.

Weighted K-means support vector machine for cancer prediction.

PubMed

Kim, SungHwan

2016-01-01

To date, the support vector machine (SVM) has been widely applied to diverse bio-medical fields to address disease subtype identification and pathogenicity of genetic variants. In this paper, I propose the weighted K-means support vector machine (wKM-SVM) and weighted support vector machine (wSVM), for which I allow the SVM to impose weights to the loss term. Besides, I demonstrate the numerical relations between the objective function of the SVM and weights. Motivated by general ensemble techniques, which are known to improve accuracy, I directly adopt the boosting algorithm to the newly proposed weighted KM-SVM (and wSVM). For predictive performance, a range of simulation studies demonstrate that the weighted KM-SVM (and wSVM) with boosting outperforms the standard KM-SVM (and SVM) including but not limited to many popular classification rules. I applied the proposed methods to simulated data and two large-scale real applications in the TCGA pan-cancer methylation data of breast and kidney cancer. In conclusion, the weighted KM-SVM (and wSVM) increases accuracy of the classification model, and will facilitate disease diagnosis and clinical treatment decisions to benefit patients. A software package (wSVM) is publicly available at the R-project webpage (https://www.r-project.org).

Burgers Vector Analysis of Vertical Dislocations in Ge Crystals by Large-Angle Convergent Beam Electron Diffraction.

PubMed

Groiss, Heiko; Glaser, Martin; Marzegalli, Anna; Isa, Fabio; Isella, Giovanni; Miglio, Leo; Schäffler, Friedrich

2015-06-01

By transmission electron microscopy with extended Burgers vector analyses, we demonstrate the edge and screw character of vertical dislocations (VDs) in novel SiGe heterostructures. The investigated pillar-shaped Ge epilayers on prepatterned Si(001) substrates are an attempt to avoid the high defect densities of lattice mismatched heteroepitaxy. The Ge pillars are almost completely strain-relaxed and essentially defect-free, except for the rather unexpected VDs. We investigated both pillar-shaped and unstructured Ge epilayers grown either by molecular beam epitaxy or by chemical vapor deposition to derive a general picture of the underlying dislocation mechanisms. For the Burgers vector analysis we used a combination of dark field imaging and large-angle convergent beam electron diffraction (LACBED). With LACBED simulations we identify ideally suited zeroth and second order Laue zone Bragg lines for an unambiguous determination of the three-dimensional Burgers vectors. By analyzing dislocation reactions we confirm the origin of the observed types of VDs, which can be efficiently distinguished by LACBED. The screw type VDs are formed by a reaction of perfect 60° dislocations, whereas the edge types are sessile dislocations that can be formed by cross-slips and climbing processes. The understanding of these origins allows us to suggest strategies to avoid VDs.

A compositional reservoir simulator on distributed memory parallel computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rame, M.; Delshad, M.

1995-12-31

This paper presents the application of distributed memory parallel computes to field scale reservoir simulations using a parallel version of UTCHEM, The University of Texas Chemical Flooding Simulator. The model is a general purpose highly vectorized chemical compositional simulator that can simulate a wide range of displacement processes at both field and laboratory scales. The original simulator was modified to run on both distributed memory parallel machines (Intel iPSC/960 and Delta, Connection Machine 5, Kendall Square 1 and 2, and CRAY T3D) and a cluster of workstations. A domain decomposition approach has been taken towards parallelization of the code. Amore » portion of the discrete reservoir model is assigned to each processor by a set-up routine that attempts a data layout as even as possible from the load-balance standpoint. Each of these subdomains is extended so that data can be shared between adjacent processors for stencil computation. The added routines that make parallel execution possible are written in a modular fashion that makes the porting to new parallel platforms straight forward. Results of the distributed memory computing performance of Parallel simulator are presented for field scale applications such as tracer flood and polymer flood. A comparison of the wall-clock times for same problems on a vector supercomputer is also presented.« less

Sensitivity of rough differential equations: An approach through the Omega lemma

NASA Astrophysics Data System (ADS)

Coutin, Laure; Lejay, Antoine

2018-03-01

The Itô map gives the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniqueness hold. By studying how a path is transformed through the vector field which is integrated, we prove that the Itô map is Hölder or Lipschitz continuous with respect to all its parameters. This result unifies and weakens the hypotheses of the regularity results already established in the literature.

s-Ordered Exponential of Quadratic Forms Gained via IWSOP Technique

NASA Astrophysics Data System (ADS)

Bazrafkan, M. R.; Shähandeh, F.; Nahvifard, E.

2012-11-01

Using the generalized bar{s}-ordered Wigner operator, in which bar{s} is a vector over the field of complex numbers, the technique of integration within an s-ordered product of operators (IWSOP) has been extended to multimode case. We derive the bar{s}-ordered form of the widely applicable multimode exponential of quadratic form exp\\{sum_{i,j = 1}n ai^{dag}\\varLambda_{ij}{aj}\\} , each mode being in some particular order s i , applying this method.

A note on ‘gaugings’ in four spacetime dimensions and electric-magnetic duality

NASA Astrophysics Data System (ADS)

Henneaux, Marc; Julia, Bernard; Lekeu, Victor; Ranjbar, Arash

2018-02-01

The variety of consistent ‘gauging’ deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper n v abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to n s uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by \

Thermofield duality for higher spin Rindler Gravity

DOE PAGES

Jevicki, Antal; Suzuki, Kenta

2016-02-15

In this paper, we study the Thermo-field realization of the duality between the Rindler-AdS higher spin theory and O(N) vector theory. The CFT represents a decoupled pair of free O(N) vector field theories. It is shown how this decoupled domain CFT is capable of generating the connected Rindler-AdS background with the full set of Higher Spin fields.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fogh, Ellen; Toft-Petersen, Rasmus; Ressouche, Eric

Here, the magnetic phase diagram of magnetoelectric LiCoPO 4 is established using neutron diffraction and magnetometry in fields up to 25.9T applied along the crystallographic b axis. For fields greater than 11.9T, the magnetic unit cell triples in size with propagation vector Q = (0,1/3,0). A magnetized elliptic cycloid is formed with spins in the (b,c) plane and the major axis oriented along b. Such a structure allows for the magnetoelectric effect with an electric polarization along c induced by magnetic fields applied along b. Intriguingly, additional ordering vectors Q ≈ (0,1/4,0) and Q ≈ (0,1/2,0) appear for increasing fieldsmore » in the hysteresis region below the transition field. Traces of this behavior are also observed in the magnetization. A simple model based on a mean-field approach is proposed to explain these additional ordering vectors. In the field interval 20.5–21.0T, the propagation vector Q = (0,1/3,0) remains but the spins orient differently compared to the cycloid phase. Furthermore, above 21.0T and up until saturation, a commensurate magnetic structure exists with a ferromagnetic component along b and an antiferromagnetic component along« less

An MHD Simulation of Solar Active Region 11158 Driven with a Time-dependent Electric Field Determined from HMI Vector Magnetic Field Measurement Data

NASA Astrophysics Data System (ADS)

Hayashi, Keiji; Feng, Xueshang; Xiong, Ming; Jiang, Chaowei

2018-03-01

For realistic magnetohydrodynamics (MHD) simulation of the solar active region (AR), two types of capabilities are required. The first is the capability to calculate the bottom-boundary electric field vector, with which the observed magnetic field can be reconstructed through the induction equation. The second is a proper boundary treatment to limit the size of the sub-Alfvénic simulation region. We developed (1) a practical inversion method to yield the solar-surface electric field vector from the temporal evolution of the three components of magnetic field data maps, and (2) a characteristic-based free boundary treatment for the top and side sub-Alfvénic boundary surfaces. We simulate the temporal evolution of AR 11158 over 16 hr for testing, using Solar Dynamics Observatory/Helioseismic Magnetic Imager vector magnetic field observation data and our time-dependent three-dimensional MHD simulation with these two features. Despite several assumptions in calculating the electric field and compromises for mitigating computational difficulties at the very low beta regime, several features of the AR were reasonably retrieved, such as twisting field structures, energy accumulation comparable to an X-class flare, and sudden changes at the time of the X-flare. The present MHD model can be a first step toward more realistic modeling of AR in the future.

Long-term vacuum tests of single-mode vertical cavity surface emitting laser diodes used for a scalar magnetometer

NASA Astrophysics Data System (ADS)

Hagen, C.; Ellmeier, M.; Piris, J.; Lammegger, R.; Jernej, I.; Magnes, W.; Murphy, E.; Pollinger, A.; Erd, C.; Baumjohann, W.

2017-11-01

Scalar magnetometers measure the magnitude of the magnetic field, while vector magnetometers (mostly fluxgate magnetometers) produce three-component outputs proportional to the magnitude and the direction of the magnetic field. While scalar magnetometers have a high accuracy, vector magnetometers suffer from parameter drifts and need to be calibrated during flight. In some cases, full science return can only be achieved by a combination of vector and scalar magnetometers.

Advanced Techniques for Scene Analysis

DTIC Science & Technology

2010-06-01

robustness prefers a bigger intergration window to handle larger motions. The advantage of pyramidal implementation is that, while each motion vector dL...labeled SAR images. Now the previous algorithm leads to a more dedicated classifier for the particular target; however, our algorithm trades generality for...accuracy is traded for generality. 7.3.2 I-RELIEF Feature weighting transforms the original feature vector x into a new feature vector x′ by assigning each

Analysis of the vector magnetic fields of complex sunspots

NASA Technical Reports Server (NTRS)

Patty, S. R.

1981-01-01

An analysis of the vector magnetic field in the delta-configurations of two complex sunspot groups is presented, noting several characteristics identified in the delta-configurations. The observations of regions 2469 (S12E80) and 2470 (S21E83) took place in May, 1980 with a vector magnetograph, verified by optical viewing. Longitudinal magnetic field plots located the delta-configurations in relation to the transverse field neutral line. It is shown that data on the polarization yields qualitative information on the magnetic field strengths, while the azimuth of the transverse field can be obtained from the relative intensities of linear polarization measurements aligned with respect to the magnetograph analyses axis at 0 and 90 deg, and at the plus and minus 45 deg positions. Details of the longitudinal fields are discussed. A strong, sheared transverse field component is found to be a signature of strong delta. A weak delta is accompanied by a weak longitudinal gradient with an unsheared transverse component of variable strength.

Stress field modelling from digital geological map data

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián

2016-04-01

To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is calculated from the fracture criterion. The calculation includes the gravitational acceleration, the average density of rocks and the experimental 60 degree of the fracture angle from the normal of the fault plane. This way, the stress tensors are calculated as absolute pressure values per square meters on both sides of the faults. If the stress from the overburden is greater than 1 bar (i.e. the faults are buried), a confined compression would be present. Modelling this state of stress may result a confusing pattern of vectors, because in a confined position the horizontal stress vectors may point towards structures primarily associated with extension. To step over this, and to highlight the variability in the stress-field, the model calculates the vectors directly from the differential stress (practically subtracting the minimum principal stress from the critical stress). The result of the modelling is a vector map, which theoretically represents the minimum tectonic pressure in the moment, when the rock body breaks from an initial state. This map - together with the original fault-map - is suitable for determining those areas where unrevealed tectonic, sedimentary and lithological structures are possibly present (e.g. faults, sub-basins and intrusions). With modelling different deformational phases on the same area, change of the stress vectors can be detected which reveals not only the varying directions of the principal stresses, but the tectonic-driven sedimentation patterns too. The decrease of necessary critical stress in the case of a possible reactivation of a fault in subsequent deformation phase can be managed with the down-ranking of the concerning structural elements. Reference: Albert G., Ungvári ZS., Szentpéteri K. 2014: Modeling the present day stress field of the Pannonian Basin from neotectonic maps - In: Beqiraj A, Ionescu C, Christofides G, Uta A, Beqiraj Goga E, Marku S (eds.) Proceedings XX Congress of the Carpathian-Balkan Geological Association. Tirana: p. 2.

Evolution of vector magnetic fields and the August 27 1990 X-3 flare

NASA Technical Reports Server (NTRS)

Wang, Haimin

1992-01-01

Vector magnetic fields in an active region of the sun are studied by means of continuous observations of magnetic-field evolution emphasizing magnetic shear build-up. The vector magnetograms are shown to measure magnetic fields correctly based on concurrent observations and a comparison of the transverse field with the H alpha fibril structure. The morphology and velocity pattern are examined, and these data and the shear build-up suggest that the active region's two major footprints are separated by a region with flows, new flux emergence, and several neutral lines. The magnetic shear appears to be caused by the collision and shear motion of two poles of opposite polarities. The transverse field is shown to turn from potential to sheared during the process of flux cancellation, and this effect can be incorporated into existing models of magnetic flux cancellation.

Comparative field trial of alternative vector control strategies for non-domiciliated Triatoma dimidiata.

PubMed

Ferral, Jhibran; Chavez-Nuñez, Leysi; Euan-Garcia, Maria; Ramirez-Sierra, Maria Jesus; Najera-Vazquez, M Rosario; Dumonteil, Eric

2010-01-01

Chagas disease is a major vector-borne disease, and regional initiatives based on insecticide spraying have successfully controlled domiciliated vectors in many regions. Non-domiciliated vectors remain responsible for a significant transmission risk, and their control is a challenge. We performed a proof-of-concept field trial to test alternative strategies in rural Yucatan, Mexico. Follow-up of house infestation for two seasons following the interventions confirmed that insecticide spraying should be performed annually for the effective control of Triatoma dimidiata; however, it also confirmed that insect screens or long-lasting impregnated curtains may represent good alternative strategies for the sustained control of these vectors. Ecosystemic peridomicile management would be an excellent complementary strategy to improve the cost-effectiveness of interventions. Because these strategies would also be effective against other vector-borne diseases, such as malaria or dengue, they could be integrated within a multi-disease control program.

Vector disformal transformation of cosmological perturbations

NASA Astrophysics Data System (ADS)

Papadopoulos, Vassilis; Zarei, Moslem; Firouzjahi, Hassan; Mukohyama, Shinji

2018-03-01

We study disformal transformations of cosmological perturbations by vector fields in theories invariant under U (1 ) gauge transformations. Three types of vector disformal transformations are considered: (i) disformal transformations by a single timelike vector; (ii) disformal transformations by a single spacelike vector; and (iii) disformal transformations by three spacelike vectors. We show that transformations of type (i) do not change either curvature perturbation or gravitational waves; that those of type (ii) do not change curvature perturbation but change gravitational waves; and that those of type (iii) change both curvature perturbation and gravitational waves. Therefore, coupling matter fields to the metric after disformal transformations of type (ii) or (iii) in principle have observable consequences. While the recent multi-messenger observation of binary neutron stars has singled out a proper disformal frame at the present epoch with a high precision, the result of the present paper may thus help distinguishing disformal frames in the early universe.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

NASA Technical Reports Server (NTRS)

Ronan, R. S.; Mickey, D. L.; Orrall, F. Q.

1987-01-01

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Index formulas for higher order Loewner vector fields

NASA Astrophysics Data System (ADS)

Broad, Steven

Let ∂ be the Cauchy-Riemann operator and f be a C real-valued function in a neighborhood of 0 in R in which ∂z¯nf≠0 for all z≠0. In such cases, ∂z¯nf is known as a Loewner vector field due to its connection with Loewner's conjecture that the index of such a vector field is bounded above by n. The n=2 case of Loewner's conjecture implies Carathéodory's conjecture that any C-immersion of S into R must have at least two umbilics. Recent work of F. Xavier produced a formula for computing the index of Loewner vector fields when n=2 using data about the Hessian of f. In this paper, we extend this result and establish an index formula for ∂z¯nf for all n⩾2. Structurally, our index formula provides a defect term, which contains geometric data extracted from Hessian-like objects associated with higher order derivatives of f.

Lie-Hamilton systems on the plane: Properties, classification and applications

NASA Astrophysics Data System (ADS)

Ballesteros, A.; Blasco, A.; Herranz, F. J.; de Lucas, J.; Sardón, C.

2015-04-01

We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. We start with the local classification of finite-dimensional real Lie algebras of vector fields on the plane obtained in González-López, Kamran, and Olver (1992) [23] and we interpret their results as a local classification of Lie systems. By determining which of these real Lie algebras consist of Hamiltonian vector fields relative to a Poisson structure, we provide the complete local classification of Lie-Hamilton systems on the plane. We present and study through our results new Lie-Hamilton systems of interest which are used to investigate relevant non-autonomous differential equations, e.g. we get explicit local diffeomorphisms between such systems. We also analyse biomathematical models, the Milne-Pinney equations, second-order Kummer-Schwarz equations, complex Riccati equations and Buchdahl equations.

Spatial attenuation of different sound field components in a water layer and shallow-water sediments

NASA Astrophysics Data System (ADS)

Belov, A. I.; Kuznetsov, G. N.

2017-11-01

The paper presents the results of an experimental study of spatial attenuation of low-frequency vector-scalar sound fields in shallow water. The experiments employed a towed pneumatic cannon and spatially separated four-component vector-scalar receiver modules. Narrowband analysis of received signals made it possible to estimate the attenuation coefficients of the first three modes in the frequency of range of 26-182 Hz and calculate the frequency dependences of the sound absorption coefficients in the upper part of bottom sediments. We analyze the experimental and calculated (using acoustic calibration of the waveguide) laws of the drop in sound pressure and orthogonal vector projections of the oscillation velocity. It is shown that the vertical projection of the oscillation velocity vector decreases significantly faster than the sound pressure field.