Visualizing Vector Fields Using Line Integral Convolution and Dye Advection

Science.gov (United States)

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.

Hyperbolic-symmetry vector fields.

Science.gov (United States)

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.

3-D Vector Flow Imaging

DEFF Research Database (Denmark)

Holbek, Simon

, if this significant reduction in the element count can still provide precise and robust 3-D vector flow estimates in a plane. The study concludes that the RC array is capable of estimating precise 3-D vector flow both in a plane and in a volume, despite the low channel count. However, some inherent new challenges...... ultrasonic vector flow estimation and bring it a step closer to a clinical application. A method for high frame rate 3-D vector flow estimation in a plane using the transverse oscillation method combined with a 1024 channel 2-D matrix array is presented. The proposed method is validated both through phantom...... hampers the task of real-time processing. In a second study, some of the issue with the 2-D matrix array are solved by introducing a 2-D row-column (RC) addressing array with only 62 + 62 elements. It is investigated both through simulations and via experimental setups in various flow conditions...

Elliptic-symmetry vector optical fields.

Science.gov (United States)

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.

Magnetosheath for almost-aligned solar wind magnetic field and flow vectors: Wind observations across the dawnside magnetosheath at X = -12 Re

Science.gov (United States)

Farrugia, C. J.; Erkaev, N. V.; Torbert, R. B.; Biernat, H. K.; Gratton, F. T.; Szabo, A.; Kucharek, H.; Matsui, H.; Lin, R. P.; Ogilvie, K. W.; Lepping, R. P.; Smith, C. W.

2010-08-01

While there are many approximations describing the flow of the solar wind past the magnetosphere in the magnetosheath, the case of perfectly aligned (parallel or anti-parallel) interplanetary magnetic field (IMF) and solar wind flow vectors can be treated exactly in a magnetohydrodynamic (MHD) approach. In this work we examine a case of nearly-opposed (to within 15°) interplanetary field and flow vectors, which occurred on October 24-25, 2001 during passage of the last interplanetary coronal mass ejection in an ejecta merger. Interplanetary data are from the ACE spacecraft. Simultaneously Wind was crossing the near-Earth (X ˜ -13 Re) geomagnetic tail and subsequently made an approximately 5-hour-long magnetosheath crossing close to the ecliptic plane (Z = -0.7 Re). Geomagnetic activity was returning steadily to quiet, “ground” conditions. We first compare the predictions of the Spreiter and Rizzi theory with the Wind magnetosheath observations and find fair agreement, in particular as regards the proportionality of the magnetic field strength and the product of the plasma density and bulk speed. We then carry out a small-perturbation analysis of the Spreiter and Rizzi solution to account for the small IMF components perpendicular to the flow vector. The resulting expression is compared to the time series of the observations and satisfactory agreement is obtained. We also present and discuss observations in the dawnside boundary layer of pulsed, high-speed (v ˜ 600 km/s) flows exceeding the solar wind flow speeds. We examine various generating mechanisms and suggest that the most likely cause is a wave of frequency 3.2 mHz excited at the inner edge of the boundary layer by the Kelvin-Helmholtz instability.

Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...

Vector Fields on Product Manifolds

OpenAIRE

Kurz, Stefan

2011-01-01

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.

2D Vector Field Simplification Based on Robustness

KAUST Repository

Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul

2014-01-01

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification

Directional Transverse Oscillation Vector Flow Estimation

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt

2017-01-01

A method for estimating vector velocities using transverse oscillation (TO) combined with directional beamforming is presented. In Directional Transverse Oscillation (DTO) a normal focused field is emitted and the received signals are beamformed in the lateral direction transverse to the ultrasound...... beam to increase the amount of data for vector velocity estimation. The approach is self-calibrating as the lateral oscillation period is estimated from the directional signal through a Fourier transform to yield quantitative velocity results over a large range of depths. The approach was extensively...... simulated using Field IIpro and implemented on the experimental SARUS scanner in connection with a BK Medical 8820e convex array transducer. Velocity estimates for DTO are found for beam-to-flow angles of 60, 75, and 90, and vessel depths from 24 to 156 mm. Using 16 emissions the Standard Deviation (SD...

Fractal vector optical fields.

Science.gov (United States)

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.

High Frame Rate Synthetic Aperture 3D Vector Flow Imaging

DEFF Research Database (Denmark)

Villagómez Hoyos, Carlos Armando; Holbek, Simon; Stuart, Matthias Bo

2016-01-01

, current volumetric ultrasonic flow methods are limited to one velocity component or restricted to a reduced field of view (FOV), e.g. fixed imaging planes, in exchange for higher temporal resolutions. To solve these problems, a previously proposed accurate 2-D high frame rate vector flow imaging (VFI...

On vector fields having properties of Reeb fields

OpenAIRE

Hajduk, Boguslaw; Walczak, Rafal

2011-01-01

We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.

Motion compensated beamforming in synthetic aperture vector flow imaging

DEFF Research Database (Denmark)

Oddershede, Niels; Jensen, Jørgen Arendt

2006-01-01

. In this paper, these motion effects are considered. A number of Field II simulations of a single scatterer moving at different velocities are performed both for axial and lateral velocities from 0 to 1 m/s. Data are simulated at a pulse repetition frequency of 5 kHz. The signal-to-noise ratio (SNR....... Here the SNR is -10 dB compared to the stationary scatterer. A 2D motion compensation method for synthetic aperture vector flow imaging is proposed, where the former vector velocity estimate is used for compensating the beamforming of new data. This method is tested on data from an experimental flow...

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

Science.gov (United States)

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.

2D Vector Field Simplification Based on Robustness

KAUST Repository

Skraba, Primoz

2014-03-01

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. These geometric metrics do not consider the flow magnitude, an important physical property of the flow. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness, which provides a complementary view on flow structure compared to the traditional topological-skeleton-based approaches. Robustness enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory, has fewer boundary restrictions, and so can handle more general cases. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. © 2014 IEEE.

New techniques in 3D scalar and vector field visualization

Energy Technology Data Exchange (ETDEWEB)

Max, N.; Crawfis, R.; Becker, B.

1993-05-05

At Lawrence Livermore National Laboratory (LLNL) we have recently developed several techniques for volume visualization of scalar and vector fields, all of which use back-to-front compositing. The first renders volume density clouds by compositing polyhedral volume cells or their faces. The second is a ``splatting`` scheme which composites textures used to reconstruct the scalar or vector fields. One version calculates the necessary texture values in software, and another takes advantage of hardware texture mapping. The next technique renders contour surface polygons using semi-transparent textures, which adjust appropriately when the surfaces deform in a flow, or change topology. The final one renders the ``flow volume`` of smoke or dye tracer swept out by a fluid flowing through a small generating polygon. All of these techniques are applied to a climate model data set, to visualize cloud density and wind velocity.

New techniques in 3D scalar and vector field visualization

International Nuclear Information System (INIS)

Max, N.; Crawfis, R.; Becker, B.

1993-01-01

At Lawrence Livermore National Laboratory (LLNL) we have recently developed several techniques for volume visualization of scalar and vector fields, all of which use back-to-front compositing. The first renders volume density clouds by compositing polyhedral volume cells or their faces. The second is a ''splatting'' scheme which composites textures used to reconstruct the scalar or vector fields. One version calculates the necessary texture values in software, and another takes advantage of hardware texture mapping. The next technique renders contour surface polygons using semi-transparent textures, which adjust appropriately when the surfaces deform in a flow, or change topology. The final one renders the ''flow volume'' of smoke or dye tracer swept out by a fluid flowing through a small generating polygon. All of these techniques are applied to a climate model data set, to visualize cloud density and wind velocity

Multi-task Vector Field Learning.

Science.gov (United States)

Lin, Binbin; Yang, Sen; Zhang, Chiyuan; Ye, Jieping; He, Xiaofei

2012-01-01

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously and identifying the shared information among tasks. Most of existing MTL methods focus on learning linear models under the supervised setting. We propose a novel semi-supervised and nonlinear approach for MTL using vector fields. A vector field is a smooth mapping from the manifold to the tangent spaces which can be viewed as a directional derivative of functions on the manifold. We argue that vector fields provide a natural way to exploit the geometric structure of data as well as the shared differential structure of tasks, both of which are crucial for semi-supervised multi-task learning. In this paper, we develop multi-task vector field learning (MTVFL) which learns the predictor functions and the vector fields simultaneously. MTVFL has the following key properties. (1) The vector fields MTVFL learns are close to the gradient fields of the predictor functions. (2) Within each task, the vector field is required to be as parallel as possible which is expected to span a low dimensional subspace. (3) The vector fields from all tasks share a low dimensional subspace. We formalize our idea in a regularization framework and also provide a convex relaxation method to solve the original non-convex problem. The experimental results on synthetic and real data demonstrate the effectiveness of our proposed approach.

Boundary conditions and dualities: vector fields in AdS/CFT

International Nuclear Information System (INIS)

Marolf, Donald; Ross, Simo F.

2006-01-01

In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the bulk spacetime using the results of Ishibashi and Wald [hep-th/0402184]. As in the context of scalar fields, general boundary conditions for vector fields involve multi-trace deformations which lead to renormalization-group flows. Such flows originate in ultra-violet CFTs which give new gauge/gravity dualities. At least for AdS 4 /CFT 3 , the dual of the bulk photon appears to be a propagating gauge field instead of the usual R-charge current. Applying similar reasoning to tensor fields suggests the existence of a duality between string theory on AdS 4 and a quantum gravity theory in three dimensions

Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena

OpenAIRE

Bayak, Igor V.

2015-01-01

In this paper we discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.

Real-time 2-D Phased Array Vector Flow Imaging

DEFF Research Database (Denmark)

Holbek, Simon; Hansen, Kristoffer Lindskov; Fogh, Nikolaj

2018-01-01

Echocardiography examination of the blood flow is currently either restricted to 1-D techniques in real-time or experimental off-line 2-D methods. This paper presents an implementation of transverse oscillation for real-time 2-D vector flow imaging (VFI) on a commercial BK Ultrasound scanner....... A large field-of-view (FOV) sequence for studying flow dynamics at 11 frames per second (fps) and a sequence for studying peak systolic velocities (PSV) with a narrow FOV at 36 fps were validated. The VFI sequences were validated in a flow-rig with continuous laminar parabolic flow and in a pulsating flow...

Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields

KAUST Repository

Skraba, Primoz

2015-08-01

© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields.

Science.gov (United States)

Skraba, Primoz; Bei Wang; Guoning Chen; Rosen, Paul

2015-08-01

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

Robustness-Based Simplification of 2D Steady and Unsteady Vector Fields

KAUST Repository

Skraba, Primoz; Wang, Bei; Chen, Guoning; Rosen, Paul

2015-01-01

© 2015 IEEE. Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness which enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory and has minimal boundary restrictions. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets. We show local and complete hierarchical simplifications for steady as well as unsteady vector fields.

Stable piecewise polynomial vector fields

Directory of Open Access Journals (Sweden)

Claudio Pessoa

2012-09-01

Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

ESTIMATING ELECTRIC FIELDS FROM VECTOR MAGNETOGRAM SEQUENCES

International Nuclear Information System (INIS)

Fisher, G. H.; Welsch, B. T.; Abbett, W. P.; Bercik, D. J.

2010-01-01

Determining the electric field distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This electric field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how observed vector magnetogram time series can be used to estimate the photospheric electric field. Our method uses a 'poloidal-toroidal decomposition' (PTD) of the time derivative of the vector magnetic field. These solutions provide an electric field whose curl obeys all three components of Faraday's Law. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD electric field without affecting consistency with Faraday's Law. We then present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique electric field, a generalization of Longcope's 'Minimum Energy Fit'. The PTD technique, the iterative technique, and the variational technique are used to estimate electric fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these fields are compared with the simulation's known electric fields. The PTD and iteration techniques compare favorably to results from existing velocity inversion techniques. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data. Careful examination of the results from all three methods indicates that evolution of the magnetic vector by itself does not provide enough information to determine the true electric field in the photosphere. Either more information from other measurements, or physical constraints other than those considered here are necessary to find

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

Science.gov (United States)

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.

Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

1975-03-01

General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

Transversals of Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...

Complex blood flow quantification using real-time in vivo vector flow ultrasound

DEFF Research Database (Denmark)

Pedersen, Mads Møller; Pihl, Michael Johannes; Per, Haugaard

A new method to define and quantify complex blood flow is presented. The standard deviations of real-time in vivo vector flow angle estimates are used. Using vector flow ultrasound imaging both carotid bifurcations of two healthy volunteers were scanned. Scanning was performed with a 7.6 MHz linear...... transducer (8670, B-K Medical, Denmark) and a commercial vector flow ultrasound scanner (ProFocus 2202, B-K Medical). Eight video sequences of one cardiac cycle were obtained. In every frame boxes were placed to define the common carotid artery(box1) and the carotid bulb(box2). The standard deviation...... for the vector angle estimates was calculated for each box in every frame. For comparison three ultrasound experts evaluated the presence of complex flow in every box. The trial was blinded. For every sequence the mean standard deviation of the vector angle estimates were calculated for box1 {39...

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

Science.gov (United States)

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.

3-D Vector Flow Using a Row-Column Addressed CMUT Array

DEFF Research Database (Denmark)

Holbek, Simon; Christiansen, Thomas Lehrmann; Engholm, Mathias

2016-01-01

This paper presents an in-house developed 2-D capacitive micromachined ultrasonic transducer (CMUT) appliedfor 3-D blood flow estimation. The probe breaks with conventional transducers in two ways; first, the ultrasonicpressure field is generated from thousands of small vibrating micromachined...... cells, and second, elements areaccessed by row and/or column indices. The 62+62 2-D row-column addressed prototype CMUT probe was usedfor vector flow estimation by transmitting focused ultrasound into a flow-rig with a fully developed parabolicflow. The beam-to-flow angle was 90◦. The received data...... was beamformed and processed offline. A transverseoscillation (TO) velocity estimator was used to estimate the 3-D vector flow along a line originating from thecenter of the transducer. The estimated velocities in the lateral and axial direction were close to zero as expected.In the transverse direction...

Preliminary examples of 3D vector flow imaging

DEFF Research Database (Denmark)

Pihl, Michael Johannes; Stuart, Matthias Bo; Tomov, Borislav Gueorguiev

2013-01-01

This paper presents 3D vector flow images obtained using the 3D Transverse Oscillation (TO) method. The method employs a 2D transducer and estimates the three velocity components simultaneously, which is important for visualizing complex flow patterns. Data are acquired using the experimental ult...... as opposed to magnetic resonance imaging (MRI). The results demonstrate that the 3D TO method is capable of performing 3D vector flow imaging.......This paper presents 3D vector flow images obtained using the 3D Transverse Oscillation (TO) method. The method employs a 2D transducer and estimates the three velocity components simultaneously, which is important for visualizing complex flow patterns. Data are acquired using the experimental...... ultrasound scanner SARUS on a flow rig system with steady flow. The vessel of the flow-rig is centered at a depth of 30 mm, and the flow has an expected 2D circular-symmetric parabolic prole with a peak velocity of 1 m/s. Ten frames of 3D vector flow images are acquired in a cross-sectional plane orthogonal...

Synthetic Aperture Vector Flow Imaging

DEFF Research Database (Denmark)

Villagómez Hoyos, Carlos Armando

The main objective of this project was to continue the development of a synthetic aperture vector flow estimator. This type of estimator is capable of overcoming two of the major limitations in conventional ultrasound systems: 1) the inability to scan large region of interest with high temporal......, this thesis showed that novel information can be obtained with vector velocity methods providing quantitative estimates of blood flow and insight into the complexity of the hemodynamics dynamics. This could give the clinician a new tool in assessment and treatment of a broad range of diseases....

Towards 2D field-flow fractionation - Vector separation over slanted open cavities

Science.gov (United States)

Bernate, Jorge A.; Yang, Mengfei; Zhao, Hong; Risbud, Sumedh; Paul, Colin; Dallas, Matthew; Konstantopoulos, Konstantinos; Drazer, German; Shaqfeh, Eric S. G.

2013-11-01

Planar microfluidic platforms for vector chromatography, in which different species fan out in different directions and can be continuously sorted, are particularly promising for the high throughput separation of multicomponent mixtures. We carry out a computational study of the vector separation of dilute suspensions of rigid and flexible particles transported by a pressure-driven flow over an array of slanted open cavities. The numerical scheme is based on a Stokes flow boundary integral equation method. The simulations are performed in a periodic system without lateral confinement, relevant to microfluidic devices with negligible recirculation in the main channel. We study the deflection of rigid spherical particles, of flexible capsules as a model of white and red blood cells, and of rigid discoidal particles as a model of platelets. We characterize the deflection of different particles as a function of their size, shape, shear elasticity, their release position, and the geometric parameters of the channel. The simulations provide insight into the separation mechanism and allow the optimization of specific devices depending on the application. Good agreement with experiments is observed.

Ultrasound Vector Flow Imaging: Part I: Sequential Systems

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt; Nikolov, Svetoslav Ivanov; Yu, Alfred C. H.

2016-01-01

, and variants of these. The review covers both 2-D and 3-D velocity estimation and gives a historical perspective on the development along with a summary of various vector flow visualization algorithms. The current state-of-the-art is explained along with an overview of clinical studies conducted and methods......The paper gives a review of the most important methods for blood velocity vector flow imaging (VFI) for conventional, sequential data acquisition. This includes multibeam methods, speckle tracking, transverse oscillation, color flow mapping derived vector flow imaging, directional beamforming...

Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

Flows of non-smooth vector fields and degenerate elliptic equations with applications to the Vlasov-Poisson and semigeostrophic systems

CERN Document Server

Colombo, Maria

2017-01-01

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.

Versatile generation of optical vector fields and vector beams using a non-interferometric approach.

Science.gov (United States)

Tripathi, Santosh; Toussaint, Kimani C

2012-05-07

We present a versatile, non-interferometric method for generating vector fields and vector beams which can produce all the states of polarization represented on a higher-order Poincaré sphere. The versatility and non-interferometric nature of this method is expected to enable exploration of various exotic properties of vector fields and vector beams. To illustrate this, we study the propagation properties of some vector fields and find that, in general, propagation alters both their intensity and polarization distribution, and more interestingly, converts some vector fields into vector beams. In the article, we also suggest a modified Jones vector formalism to represent vector fields and vector beams.

Problems of vector Lagrangians in field theories

International Nuclear Information System (INIS)

Krivsky, I.Yu.; Simulik, V.M.

1997-01-01

A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated

Estimation of Motion Vector Fields

DEFF Research Database (Denmark)

Larsen, Rasmus

1993-01-01

This paper presents an approach to the estimation of 2-D motion vector fields from time varying image sequences. We use a piecewise smooth model based on coupled vector/binary Markov random fields. We find the maximum a posteriori solution by simulated annealing. The algorithm generate sample...... fields by means of stochastic relaxation implemented via the Gibbs sampler....

Preliminary evaluation of vector flow and spectral velocity estimation

DEFF Research Database (Denmark)

Pedersen, Mads Møller; Pihl, Michael Johannes; Haugaard, Per

Spectral estimation is considered as the golden standard in ultrasound velocity estimation. For spectral velocity estimation the blood flow angle is set by the ultrasound operator. Vector flow provides temporal and spatial estimates of the blood flow angle and velocity. A comparison of vector flow...... line covering the vessel diameter. A commercial ultrasound scanner (ProFocus 2202, BK Medical, Denmark) and a 7.6 MHz linear transducer was used (8670, BK Medical). The mean vector blood flow angle estimations were calculated {52(18);55(23);60(16)}°. For comparison the fixed angles for spectral...... estimation were obtained {52;56;52}°. The mean vector velocity estimates at PS {76(15);95(17);77(16)}cm/s and at end diastole (ED) {17(6);18(6);24(6)}cm/s were calculated. For comparison spectral velocity estimates at PS {77;110;76}cm/s and ED {18;18;20}cm/s were obtained. The mean vector angle estimates...

n-Characteristic Vector Fields of Contact Manifoldss

OpenAIRE

Hassanzadeh, Babak

2017-01-01

In present paper we define and study $n$-characteristic vector fields. We present definition of Tanaka-Webster connection, then use it for studying the behavior of $n$-characteristic vector fields. Also we show some results about of these vector fields by Tanaka-Webster connection.

Novel flow quantification of the carotid bulb and the common carotid artery with vector flow ultrasound

DEFF Research Database (Denmark)

Pedersen, Mads Møller; Pihl, Michael Johannes; Haugaard, Per

2014-01-01

technique transverse oscillation the blood velocities of both the axial and the transverse directions are obtained and the complexity of blood flow can be visualized. The aim of the study was to determine the technical performance and interpretation of vector concentration as a tool for estimation of flow...... (US) using a commercial vector flow ultrasound scanner (ProFocus, BK Medical, Denmark) with a linear 5 MHz transducer transverse oscillation vector flow software. CCA and CB areas were marked in one cardiac cycle from each volunteer. The complex flow was assessed by medical expert evaluation...... and by vector concentration calculation. A vortex with complex flow was found in all carotid bulbs, whereas the CCA had mainly laminar flow. The medical experts evaluated the flow to be mainly laminar in the CCA (0.82 +/- 0.14) and mainly complex (0.23 +/- 0.22) in the CB. Likewise, the estimated vector...

Vector fields and gravity on the lattice

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

1988-01-01

The problem of discretization of vector field on Regge lattice is considered. Our approach is based on geometrical interpretation of the vector field as the field of infinitesimal coordinate transformation. A discrete version of the vector field action is obtained as a particular case of the continuum action, and it is shown to have the true continuum limit

Quantification of complex blood flow using real-time in vivo vector flow ultrasound

DEFF Research Database (Denmark)

Pedersen, Mads Møller; Pihl, Michael Johannes; Haugaard, Per

2010-01-01

A quantitative method for distinguishing complex from non-complex flow patterns in ultrasound is presented. A new commercial BK Medical ultrasound scanner uses the Transverse Oscillation vector flow technique for visualising flow patterns in real-time. In vivo vector flow data of the blood flow...... patterns of the common carotid artery and the carotid bulb were obtained simultaneously as the basis for quantifying complex flow. The carotid bifurcation of two healthy volunteers were scanned. The presence of complex flow patterns from eight cardiac cycles were evaluated by three experts in medical...... for automatic detection of complex flow patterns....

Sub-piexl methods for improving vector quality in echo PIV flow, imaging technology.

Science.gov (United States)

Niu, Lili; Wang, Jing; Qian, Ming; Zheng, Hairong

2009-01-01

Developments of many cardiovascular problems have been shown to have a close relationship with arterial flow conditions. An ultrasound-based particle image velocimetry technique(Echo PIV) was recently developed to measure multi-component velocity vectors and local shear rates in arteries and opaque fluid flows by identifying and tracking flow tracers (ultrasound contrast microbubbles) within these flow fields. To improve the measurement accuracy, sub-pixel calculation method was adopted in this paper to maximize the ultrasound RF signal and B mode image correlation accuracy and increase the image spatial resolution. This algorithm is employed in processing both computer-generated particle image patterns and the B-mode images of microbubbles in rotating flows obtained by a high frame rate (up to 1000 frames per second) ultrasound imaging system. The results show the correlation of particle patterns and individual flow vector quality are improved and the overall flow mappings are also improved significantly. This would help the Echo PIV system to provide better multi-component velocity accuracy.

Design of 2D time-varying vector fields.

Science.gov (United States)

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.

Intraoperative Vector Flow Imaging of the Heart

DEFF Research Database (Denmark)

Hansen, Kristoffer Lindskov; Møller-Sørensen, Hasse; Pedersen, Mads Møller

2013-01-01

The cardiac flow is complex and multidirectional, and difficult to measure with conventional Doppler ultrasound (US) methods due to the one-dimensional and angle-dependent velocity estimation. The vector velocity method Transverse Oscillation (TO) has been proposed as a solution to this. TO is im......The cardiac flow is complex and multidirectional, and difficult to measure with conventional Doppler ultrasound (US) methods due to the one-dimensional and angle-dependent velocity estimation. The vector velocity method Transverse Oscillation (TO) has been proposed as a solution to this....... TO is implemented on a conventional US scanner (Pro Focus 2202 UltraView, BK Medical) using a linear transducer (8670, BK Medical) and can provide real-time, angle-independent vector velocity estimates of the cardiac blood flow. During cardiac surgery, epicardiac US examinations using TO were performed on three...

Reciprocity relationships in vector acoustics and their application to vector field calculations.

Science.gov (United States)

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Weaving Knotted Vector Fields with Tunable Helicity.

Science.gov (United States)

Kedia, Hridesh; Foster, David; Dennis, Mark R; Irvine, William T M

2016-12-30

We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.

Design of 2D Time-Varying Vector Fields

KAUST Repository

Chen, Guoning

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. © 1995-2012 IEEE.

Design of 2D Time-Varying Vector Fields

KAUST Repository

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

2012-01-01

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. © 1995-2012 IEEE.

Vector fields satisfying the barycenter property

Directory of Open Access Journals (Sweden)

Lee Manseob

2018-04-01

Full Text Available We show that if a vector field X has the C1 robustly barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, if a generic C1-vector field has the barycenter property then it does not have singularities and it is Axiom A without cycles. Moreover, we apply the results to the divergence free vector fields. It is an extension of the results of the barycenter property for generic diffeomorphisms and volume preserving diffeomorphisms [1].

Magnetic vector field tag and seal

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Gauge anomaly with vector and axial-vector fields in 6D curved space

Science.gov (United States)

Yajima, Satoshi; Eguchi, Kohei; Fukuda, Makoto; Oka, Tomonori

2018-03-01

Imposing the conservation equation of the vector current for a fermion of spin 1/2 at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial-vector fields in 6D curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial-vector field is Abelian.

Euclidean fields: vector mesons and photons

International Nuclear Information System (INIS)

Loffelholz, J.

1979-01-01

Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given

Effect of orientation dynamics on the growth of a passive vector in a family of model flows

International Nuclear Information System (INIS)

Gonzalez, M

2014-01-01

The stretching properties of a parameterized model flow used to study the fast dynamo (Tanner and Hughes 2003 Astrophys. J. 586 685–91) are analyzed by paying special attention to the dependence of the growth rate of a passive vector on its orientation with respect to strain principal axes. More specifically, the study brings out that, rather than strain intensity, it is the dynamics of orientation resulting from the alternating tilting of the strain principal axes that explains the evolution of the passive vector mean growth rate in this class of flows. On a more general level, this view of stretching may bring an alternative understanding of the growth mechanisms of vectors such as the magnetic field vector. (paper)

Quantification of In Vivo 2D Vector Flow Ultrasound

DEFF Research Database (Denmark)

Pedersen, Mads Møller

2012-01-01

by the vector technique. With the conventional technique, the manual setting of the angle is operator dependent. With the calculated vector angle, this operator is relieved from the angle setting and the measurement is angle corrected by the identical method every time. With study II the carotid bifurcation...... the clinical parameters: peak systole velocity, end diastole velocity, resistive index, and the flow direction. The results showed significant difference on the velocities and the resistive index. However, no significant difference on the manually defined flow angle and the calculated mean flow angle...... including the carotid bulb and the common carotid artery were scanned on 8 healthy volunteers. The flow patterns of the two structures were outlined and presented to each of 5 experienced radiologists. The complexity of the identical areas were calculated by the vector concentration and compared...

Sensitivity Analysis of Unsteady Flow Fields and Impact of Measurement Strategy

Directory of Open Access Journals (Sweden)

Takashi Misaka

2014-01-01

Full Text Available Difficulty of data assimilation arises from a large difference between the sizes of a state vector to be determined, that is, the number of spatiotemporal mesh points of a discretized numerical model and a measurement vector, that is, the amount of measurement data. Flow variables on a large number of mesh points are hardly defined by spatiotemporally limited measurements, which poses an underdetermined problem. In this study we conduct the sensitivity analysis of two- and three-dimensional vortical flow fields within a framework of data assimilation. The impact of measurement strategy, which is evaluated by the sensitivity of the 4D-Var cost function with respect to measurements, is investigated to effectively determine a flow field by limited measurements. The assimilation experiment shows that the error defined by the difference between the reference and assimilated flow fields is reduced by using the sensitivity information to locate the limited number of measurement points. To conduct data assimilation for a long time period, the 4D-Var data assimilation and the sensitivity analysis are repeated with a short assimilation window.

Evolution of vector magnetic fields and the August 27 1990 X-3 flare

Science.gov (United States)

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.

Fluidic Vectoring of a Planar Incompressible Jet Flow

Science.gov (United States)

Mendez, Miguel Alfonso; Scelzo, Maria Teresa; Enache, Adriana; Buchlin, Jean-Marie

2018-06-01

This paper presents an experimental, a numerical and a theoretical analysis of the performances of a fluidic vectoring device for controlling the direction of a turbulent, bi-dimensional and low Mach number (incompressible) jet flow. The investigated design is the co-flow secondary injection with Coanda surface, which allows for vectoring angles up to 25° with no need of moving mechanical parts. A simple empirical model of the vectoring process is presented and validated via experimental and numerical data. The experiments consist of flow visualization and image processing for the automatic detection of the jet centerline; the numerical simulations are carried out solving the Unsteady Reynolds Average Navier- Stokes (URANS) closed with the k - ω SST turbulence model, using the PisoFoam solver from OpenFOAM. The experimental validation on three different geometrical configurations has shown that the model is capable of providing a fast and reliable evaluation of the device performance as a function of the operating conditions.

Multiresolution and Explicit Methods for Vector Field Analysis and Visualization

Science.gov (United States)

Nielson, Gregory M.

1997-01-01

This is a request for a second renewal (3d year of funding) of a research project on the topic of multiresolution and explicit methods for vector field analysis and visualization. In this report, we describe the progress made on this research project during the second year and give a statement of the planned research for the third year. There are two aspects to this research project. The first is concerned with the development of techniques for computing tangent curves for use in visualizing flow fields. The second aspect of the research project is concerned with the development of multiresolution methods for curvilinear grids and their use as tools for visualization, analysis and archiving of flow data. We report on our work on the development of numerical methods for tangent curve computation first.

Experimental demonstration of vector E x vector B plasma divertor

International Nuclear Information System (INIS)

Strait, E.J.; Kerst, D.W.; Sprott, J.C.

1977-01-01

The vector E x vector B drift due to an applied radial electric field in a tokamak with poloidal divertor can speed the flow of plasma out of the scrape-off region, and provide a means of externally controlling the flow rate and thus the width of the density fall-off. An experiment in the Wisconsin levitated toroidal octupole, using vector E x vector B drifts alone, demonstrates divertor-like behavior, including 70% reduction of plasma density near the wall and 40% reduction of plasma flux to the wall, with no adverse effects on confinement of the main plasma

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

Science.gov (United States)

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.

Controllability of linear vector fields on Lie groups

International Nuclear Information System (INIS)

Ayala, V.; Tirao, J.

1994-11-01

In this paper, we shall deal with a linear control system Σ defined on a Lie group G with Lie algebra g. The dynamic of Σ is determined by the drift vector field which is an element in the normalizer of g in the Lie algebra of all smooth vector field on G and by the control vectors which are elements in g considered as left-invariant vector fields. We characterize the normalizer of g identifying vector fields on G with C ∞ -functions defined on G into g. For this class of control systems we study algebraic conditions for the controllability problem. Indeed, we prove that if the drift vector field has a singularity then the Lie algebra rank condition is necessary for the controllability property, but in general this condition does not determine this property. On the other hand, we show that the rank (ad-rank) condition is sufficient for the controllability of Σ. In particular, we extend the fundamental Kalman's theorem when G is an Abelian connected Lie group. Our work is related with a paper of L. Markus and we also improve his results. (author). 7 refs

Effect of a spiral phase on a vector optical field with hybrid polarization states

International Nuclear Information System (INIS)

Chen, Rui-Pin; Zhao, Tingyu; Zhong, Li-Xin; Chew, Khian-Hooi; Gu, Bing; Zhou, Guoquan

2015-01-01

The propagation dynamics of a vector field with inhomogeneous states of polarization (SoP) imposed a vortex is studied using the angular spectrum method. The evolution of SoP in the cross section of the field during propagation is analyzed numerically by the Stokes polarization parameters. The results indicate that SoP in the field cross section rotate along the propagation axis during propagation due to the existence of a vortex. In addition, the interaction between the phase singularity and the polarization singularity leads to the creation or annihilation of the optical field in the central region. In particular, the distributions of the transverse energy flow and both spin and orbital optical angular momentum fluxes in the cross section of the vortex vector optical field depend sensitively on both the vortex and polarization topology charges. (paper)

Codimension-one tangency bifurcations of global Poincare maps of four-dimensional vector fields

NARCIS (Netherlands)

Krauskopf, B.; Lee, C.M.; Osinga, H.M.

2009-01-01

When one considers a Poincarreturn map on a general unbounded (n - 1)-dimensional section for a vector field in R-n there are typically points where the flow is tangent to the section. The only notable exception is when the system is (equivalent to) a periodically forced system. The tangencies can

Desingularization strategies for three-dimensional vector fields

CERN Document Server

Torres, Felipe Cano

1987-01-01

For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2s. A logarithmic point of view is taken, marking the exceptional divisor of each blowing-up and by considering only the vector fields which are tangent to this divisor, instead of the whole tangent sheaf. The first part of the book is devoted to the logarithmic background and to the permissible blowing-ups. The main part corresponds to the control of the algorithms for the desingularization strategies by means of numerical invariants inspired by Hironaka's characteristic polygon. Only basic knowledge of local algebra and algebraic geometry is assumed of the reader. The pathologies we find in the reduction of vector fields are analogous to pathologies in the pro...

Circular Conditional Autoregressive Modeling of Vector Fields.

Science.gov (United States)

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.

Measuring magnetic field vector by stimulated Raman transitions

International Nuclear Information System (INIS)

Wang, Wenli; Wei, Rong; Lin, Jinda; Wang, Yuzhu; Dong, Richang; Zou, Fan; Chen, Tingting

2016-01-01

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, 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.

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

Energy Technology Data Exchange (ETDEWEB)

Koulouri, Alexandra, E-mail: koulouri@uni-muenster.de [Institute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, D-48149 Münster (Germany); Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2BT (United Kingdom); Brookes, Mike [Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2BT (United Kingdom); Rimpiläinen, Ville [Institute for Biomagnetism and Biosignalanalysis, University of Münster, Malmedyweg 15, D-48149 Münster (Germany); Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142 (New Zealand)

2017-01-15

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. - Highlights: • Vector tomography is used to reconstruct electric fields generated by dipole

New techniques for the scientific visualization of three-dimensional multi-variate and vector fields

Energy Technology Data Exchange (ETDEWEB)

Crawfis, Roger A. [Univ. of California, Davis, CA (United States)

1995-10-01

Volume rendering allows us to represent a density cloud with ideal properties (single scattering, no self-shadowing, etc.). Scientific visualization utilizes this technique by mapping an abstract variable or property in a computer simulation to a synthetic density cloud. This thesis extends volume rendering from its limitation of isotropic density clouds to anisotropic and/or noisy density clouds. Design aspects of these techniques are discussed that aid in the comprehension of scientific information. Anisotropic volume rendering is used to represent vector based quantities in scientific visualization. Velocity and vorticity in a fluid flow, electric and magnetic waves in an electromagnetic simulation, and blood flow within the body are examples of vector based information within a computer simulation or gathered from instrumentation. Understand these fields can be crucial to understanding the overall physics or physiology. Three techniques for representing three-dimensional vector fields are presented: Line Bundles, Textured Splats and Hair Splats. These techniques are aimed at providing a high-level (qualitative) overview of the flows, offering the user a substantial amount of information with a single image or animation. Non-homogenous volume rendering is used to represent multiple variables. Computer simulations can typically have over thirty variables, which describe properties whose understanding are useful to the scientist. Trying to understand each of these separately can be time consuming. Trying to understand any cause and effect relationships between different variables can be impossible. NoiseSplats is introduced to represent two or more properties in a single volume rendering of the data. This technique is also aimed at providing a qualitative overview of the flows.

Modeling and simulation of flow field in giant magnetostrictive pump

Science.gov (United States)

Zhao, Yapeng; Ren, Shiyong; Lu, Quanguo

2017-09-01

Recent years, there has been significant research in the design and analysis of giant magnetostrictive pump. In this paper, the flow field model of giant magnetostrictive pump was established and the relationship between pressure loss and working frequency of piston was studied by numerical simulation method. Then, the influence of different pump chamber height on pressure loss in giant magnetostrictive pump was studied by means of flow field simulation. Finally, the fluid pressure and velocity vector distribution in giant magnetostrictive pump chamber were simulated.

Accuracy and Precision of Plane Wave Vector Flow Imaging for Laminar and Complex Flow In Vivo

DEFF Research Database (Denmark)

Jensen, Jonas; Traberg, Marie Sand; Villagómez Hoyos, Carlos Armando

2017-01-01

In this study, a comparison between velocity fields for a plane wave 2-D vector flow imaging (VFI) method and a computational fluid dynamics (CFD) simulation is made. VFI estimates are obtained from the scan of a flow phantom, which mimics the complex flow conditions in the carotid artery....... Furthermore, the precision of the VFI method is investigated under laminar and complex flow conditions in vivo. The carotid bifurcation of a healthy volunteer was scanned using both fast plane wave ultrasound and magnetic resonance imaging (MRI). The acquired MRI geometry of the bifurcation was used...... difference within 15 %, however, it was 23 % in the external branch. For the in vivo scan, the precision in terms of mean standard deviation (SD) of estimates aligned to the cardiac cycle was highest in the center of the common carotid artery (SD 4.7◦ for angles) and lowest in the external branch and close...

Vector Volume Flow in Arteriovenous Fistulas

DEFF Research Database (Denmark)

Hansen, Peter Møller; Heerwagen, Søren; Pedersen, Mads Møller

2013-01-01

, but is very challenging due to the angle dependency of the Doppler technique and the anatomy of the fistula. The angle independent vector ultrasound technique Transverse Oscillation provides a new and more intuitive way to measure volume flow in an arteriovenous fistula. In this paper the Transverse...

Vector fields and differential operators: noncommutative case

International Nuclear Information System (INIS)

Borowiec, A.

1997-01-01

A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed

Hairy Slices: Evaluating the Perceptual Effectiveness of Cutting Plane Glyphs for 3D Vector Fields.

Science.gov (United States)

Stevens, Andrew H; Butkiewicz, Thomas; Ware, Colin

2017-01-01

Three-dimensional vector fields are common datasets throughout the sciences. Visualizing these fields is inherently difficult due to issues such as visual clutter and self-occlusion. Cutting planes are often used to overcome these issues by presenting more manageable slices of data. The existing literature provides many techniques for visualizing the flow through these cutting planes; however, there is a lack of empirical studies focused on the underlying perceptual cues that make popular techniques successful. This paper presents a quantitative human factors study that evaluates static monoscopic depth and orientation cues in the context of cutting plane glyph designs for exploring and analyzing 3D flow fields. The goal of the study was to ascertain the relative effectiveness of various techniques for portraying the direction of flow through a cutting plane at a given point, and to identify the visual cues and combinations of cues involved, and how they contribute to accurate performance. It was found that increasing the dimensionality of line-based glyphs into tubular structures enhances their ability to convey orientation through shading, and that increasing their diameter intensifies this effect. These tube-based glyphs were also less sensitive to visual clutter issues at higher densities. Adding shadows to lines was also found to increase perception of flow direction. Implications of the experimental results are discussed and extrapolated into a number of guidelines for designing more perceptually effective glyphs for 3D vector field visualizations.

Vector optical fields with bipolar symmetry of linear polarization.

Science.gov (United States)

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.

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela

2010-09-21

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape\\'s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.

Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt

2013-01-01

A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental...... from 90 to 45 degrees in steps of 15 degrees. The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm...

Student difficulties regarding symbolic and graphical representations of vector fields

Directory of Open Access Journals (Sweden)

Laurens Bollen

2017-08-01

Full Text Available The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person’s understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

Student difficulties regarding symbolic and graphical representations of vector fields

Science.gov (United States)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-12-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

Diagnostics of vector magnetic fields

Science.gov (United States)

Stenflo, J. O.

1985-01-01

It is shown that the vector magnetic fields derived from observations with a filter magnetograph will be severely distorted if the spatially unresolved magnetic structure is not properly accounted for. Thus the apparent vector field will appear much more horizontal than it really is, but this distortion is strongly dependent on the area factor and the temperature line weakenings. As the available fluxtube models are not sufficiently well determined, it is not possible to correct the filter magnetograph observations for these effects in a reliable way, although a crude correction is of course much better than no correction at all. The solution to this diagnostic problem is to observe simultaneously in suitable combinations of spectral lines, and/or use Stokes line profiles recorded with very high spectral resolution. The diagnostic power of using a Fourier transform spectrometer for polarimetry is shown and some results from I and V spectra are illustrated. The line asymmetries caused by mass motions inside the fluxtubes adds an extra complication to the diagnostic problem, in particular as there are indications that the motions are nonstationary in nature. The temperature structure appears to be a function of fluxtube diameter, as a clear difference between plage and network fluxtubes was revealed. The divergence of the magnetic field with height plays an essential role in the explanation of the Stokes V asymmetries (in combination with the mass motions). A self consistent treatment of the subarcsec field geometry may be required to allow an accurate derivation of the spatially averaged vector magnetic field from spectrally resolved data.

Vector Fields European user group meeting

CERN Multimedia

2007-01-01

The "Vector Fields European user group meeting" will take place at CERN on 26 and 27 September 2007. Within this framework two workshops are organized at the CERN Training Centre: 24 September 2007
 Modelling Magnets with Opera 25 September 2007
Modelling of Charged Particle Beam Devices with Opera If you are interested in attending the workshop or the user group meeting please contact Julie Shepherd (Vector Fields) or Pierre Baehler (CERN) directly at: Julie.Shepherd@vectorfields.co.uk, +44 (0) 1865 854933 or +44 (0) 1865 370151 Pierre.Baehler@cern.ch, 75016 / 160156.

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

Energy Technology Data Exchange (ETDEWEB)

Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)

2010-10-21

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.

Consistent Feature Extraction From Vector Fields: Combinatorial Representations and Analysis Under Local Reference Frames

Energy Technology Data Exchange (ETDEWEB)

Bhatia, Harsh [Univ. of Utah, Salt Lake City, UT (United States)

2015-05-01

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, thus 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

Probabilistic Extraction Of Vectors In PIV

Science.gov (United States)

Humphreys, William M., Jr.

1994-01-01

Probabilistic technique for extraction of velocity vectors in particle-image velocimetry (PIV) implemented with much less computation. Double-exposure photograph of particles in flow illuminated by sheet of light provides data on velocity field of flow. Photograph converted into video image then digitized and processed by computer into velocity-field data. Velocity vectors in interrogation region chosen from magnitude and angle histograms constructed from centroid map of region.

Classification of complex polynomial vector fields in one complex variable

DEFF Research Database (Denmark)

Branner, Bodil; Dias, Kealey

2010-01-01

This paper classifies the global structure of monic and centred one-variable complex polynomial vector fields. The classification is achieved by means of combinatorial and analytic data. More specifically, given a polynomial vector field, we construct a combinatorial invariant, describing...... the topology, and a set of analytic invariants, describing the geometry. Conversely, given admissible combinatorial and analytic data sets, we show using surgery the existence of a unique monic and centred polynomial vector field realizing the given invariants. This is the content of the Structure Theorem......, the main result of the paper. This result is an extension and refinement of Douady et al. (Champs de vecteurs polynomiaux sur C. Unpublished manuscript) classification of the structurally stable polynomial vector fields. We further review some general concepts for completeness and show that vector fields...

Linearized interactions of scalar and vector fields with the higher spin field in AdSD

International Nuclear Information System (INIS)

Mkrtchyan, K.

2011-01-01

The explicit form of linearized gauge and generalized 'Weyl invariant' interactions of scalar and general higher even spin fields in the AdS D space is reviewed. Also a linearized interaction of vector field with general higher even spin gauge field is obtained. It is shown that the gauge-invariant action of linearized vector field interacting with the higher spin field also includes the whole tower of invariant actions for couplings of the same vector field with the gauge fields of smaller even spin

A Chargeless Complex Vector Matter Field in Supersymmetric Scenario

Directory of Open Access Journals (Sweden)

L. P. Colatto

2015-01-01

Full Text Available We construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two nochiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms into matter fields by a global U1 gauge symmetry. For the aim of dealing with consistent terms without breaking the global U1 symmetry we imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminates the extra degrees of freedom which is consistent with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca’s type field for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the first steps to extend the analysis of charged massive vector field in a supersymmetric scenario.

Deformation structure analysis of material at fatigue on the basis of the vector field

Science.gov (United States)

Kibitkin, Vladimir V.; Solodushkin, Andrey I.; Pleshanov, Vasily S.

2017-12-01

In the paper, spatial distributions of deformation, circulation, and shear amplitudes and shear angles are obtained from the displacement vector field measured by the DIC technique. This vector field and its characteristics of shears and vortices are given as an example of such approach. The basic formulae are also given. The experiment shows that honeycomb deformation structures can arise in the center of a macrovortex at developed plastic flow. The spatial distribution of local circulation and shears is discovered, which coincides with the deformation structure but their amplitudes are different. The analysis proves that the spatial distribution of shear angles is a result of maximum tangential and normal stresses. The anticlockwise circulation of most local vortices obeys the normal Gaussian law in the area of interest.

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

Science.gov (United States)

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.

A temporal subtraction method for thoracic CT images based on generalized gradient vector flow

International Nuclear Information System (INIS)

Miyake, Noriaki; Kim, H.; Maeda, Shinya; Itai, Yoshinori; Tan, J.K.; Ishikawa, Seiji; Katsuragawa, Shigehiko

2010-01-01

A temporal subtraction image, which is obtained by subtraction of a previous image from a current one, can be used for enhancing interval changes (such as formation of new lesions and changes in existing abnormalities) on medical images by removing most of the normal structures. If image registration is incorrect, not only the interval changes but also the normal structures would be appeared as some artifacts on the temporal subtraction image. In a temporal subtraction technique for 2-D X-ray image, the effectiveness is shown through a lot of clinical evaluation experiments, and practical use is advancing. Moreover, the MDCT (Multi-Detector row Computed Tomography) can easily introduced on medical field, the development of a temporal subtraction for thoracic CT Images is expected. In our study, a temporal subtraction technique for thoracic CT Images is developed. As the technique, the vector fields are described by use of GGVF (Generalized Gradient Vector Flow) from the previous and current CT images. Afterwards, VOI (Volume of Interest) are set up on the previous and current CT image pairs. The shift vectors are calculated by using nearest neighbor matching of the vector fields in these VOIs. The search kernel on previous CT image is set up from the obtained shift vector. The previous CT voxel which resemble standard the current voxel is detected by voxel value and vector of the GGVF in the kernel. And, the previous CT image is transformed to the same coordinate of standard voxel. Finally, temporal subtraction image is made by subtraction of a warping image from a current one. To verify the proposal method, the result of application to 7 cases and the effectiveness are described. (author)

Conformal Vector Fields on Doubly Warped Product Manifolds and Applications

Directory of Open Access Journals (Sweden)

H. K. El-Sayied

2016-01-01

Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.

Measurements of Solar Vector Magnetic Fields

Science.gov (United States)

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.

Measurements of Solar Vector Magnetic Fields

International Nuclear Information System (INIS)

Hagyard, M.J.

1985-05-01

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

On Discrete Killing Vector Fields and Patterns on Surfaces

KAUST Repository

Ben-Chen, Mirela; Butscher, Adrian; Solomon, Justin; Guibas, Leonidas

2010-01-01

, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal

Decompositions of bubbly flow PIV velocity fields using discrete wavelets multi-resolution and multi-section image method

International Nuclear Information System (INIS)

Choi, Je-Eun; Takei, Masahiro; Doh, Deog-Hee; Jo, Hyo-Jae; Hassan, Yassin A.; Ortiz-Villafuerte, Javier

2008-01-01

Currently, wavelet transforms are widely used for the analyses of particle image velocimetry (PIV) velocity vector fields. This is because the wavelet provides not only spatial information of the velocity vectors, but also of the time and frequency domains. In this study, a discrete wavelet transform is applied to real PIV images of bubbly flows. The vector fields obtained by a self-made cross-correlation PIV algorithm were used for the discrete wavelet transform. The performances of the discrete wavelet transforms were investigated by changing the level of power of discretization. The images decomposed by wavelet multi-resolution showed conspicuous characteristics of the bubbly flows for the different levels. A high spatial bubble concentrated area could be evaluated by the constructed discrete wavelet transform algorithm, in which high-leveled wavelets play dominant roles in revealing the flow characteristics

Efficient morse decompositions of vector fields.

Science.gov (United States)

Chen, Guoning; Mischaikow, Konstantin; Laramee, Robert S; Zhang, Eugene

2008-01-01

Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG's, while fast, are overly conservative and usually results in MCG's that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of tau-maps, which typically provides finer MCG's than existing techniques. Furthermore, the choice of tau provides a natural tradeoff between the fineness of the MCG's and the computational costs. We provide efficient implementations of Morse decomposition based on tau-maps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.. Furthermore, we propose the use of spatial tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.

Multifractal vector fields and stochastic Clifford algebra.

Science.gov (United States)

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.

Multifractal vector fields and stochastic Clifford algebra

Energy Technology Data Exchange (ETDEWEB)

Schertzer, Daniel, E-mail: Daniel.Schertzer@enpc.fr; Tchiguirinskaia, Ioulia, E-mail: Ioulia.Tchiguirinskaia@enpc.fr [University Paris-Est, Ecole des Ponts ParisTech, Hydrology Meteorology and Complexity HM& Co, Marne-la-Vallée (France)

2015-12-15

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.

Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...

African Journals Online (AJOL)

In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...

''Massless'' vector field in de Sitter universe

International Nuclear Information System (INIS)

Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.

2008-01-01

We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ''massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ''massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function

``Massless'' vector field in de Sitter universe

Science.gov (United States)

Garidi, T.; Gazeau, J.-P.; Rouhani, S.; Takook, M. V.

2008-03-01

We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al., ibid. 43, 6379 (2002).] The term ``massless'' is used by reference to conformal invariance and propagation on the dS lightcone whereas ``massive'' refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta-Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function.

Interpolation of vector fields from human cardiac DT-MRI

International Nuclear Information System (INIS)

Yang, F; Zhu, Y M; Rapacchi, S; Robini, M; Croisille, P; Luo, J H

2011-01-01

There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of localizing the noise-corrupted vectors using the local statistical properties of vector fields, removing the noise-corrupted vectors and reconstructing them by using the thin plate spline (TPS) model, and finally applying global TPS interpolation to increase the resolution in the spatial domain. Experiments on 17 human hearts show that the proposed method allows us to obtain higher resolution while reducing noise, preserving details and improving direction coherence (DC) of vector fields as well as fiber tracking. Moreover, the proposed method perfectly reconstructs azimuth and elevation angle maps.

Properties of invariant modelling and invariant glueing of vector fields

International Nuclear Information System (INIS)

Petukhov, V.R.

1987-01-01

Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields

Massive vector fields and black holes

International Nuclear Information System (INIS)

Frolov, V.P.

1977-04-01

A massive vector field inside the event horizon created by the static sources located outside the black hole is investigated. It is shown that the back reaction of such a field on the metric near r = 0 cannot be neglected. The possibility of the space-time structure changing near r = 0 due to the external massive field is discussed

Research on Duct Flow Field Optimisation of a Robot Vacuum Cleaner

Directory of Open Access Journals (Sweden)

Xiao-bo Lai

2011-11-01

Full Text Available The duct of a robot vacuum cleaner is the length of the flow channel between the inlet of the rolling brush blower and the outlet of the vacuum blower. To cope with the pressure drop problem of the duct flow field in a robot vacuum cleaner, a method based on Pressure Implicit with Splitting of Operators (PRISO algorithm is introduced and the optimisation design of the duct flow field is implemented. Firstly, the duct structure in a robot vacuum cleaner is taken as a research object, with the computational fluid dynamics (CFD theories adopted; a three-dimensional fluid model of the duct is established by means of the FLUENT solver of the CFD software. Secondly, with the k-∊ turbulence model of three-dimensional incompressible fluid considered and the PRISO pressure modification algorithm employed, the flow field numerical simulations inside the duct of the robot vacuum cleaner are carried out. Then, the velocity vector plots on the arbitrary plane of the duct flow field are obtained. Finally, an investigation of the dynamic characteristics of the duct flow field is done and defects of the original duct flow field are analysed, the optimisation of the original flow field has then been conducted. Experimental results show that the duct flow field after optimisation can effectively reduce pressure drop, the feasibility as well as the correctness of the theoretical modelling and optimisation approaches are validated.

Research on Duct Flow Field Optimisation of a Robot Vacuum Cleaner

Directory of Open Access Journals (Sweden)

Xiao-bo Lai

2011-11-01

Full Text Available The duct of a robot vacuum cleaner is the length of the flow channel between the inlet of the rolling brush blower and the outlet of the vacuum blower. To cope with the pressure drop problem of the duct flow field in a robot vacuum cleaner, a method based on Pressure Implicit with Splitting of Operators (PRISO algorithm is introduced and the optimisation design of the duct flow field is implemented. Firstly, the duct structure in a robot vacuum cleaner is taken as a research object, with the computational fluid dynamics (CFD theories adopted; a three‐dimensional fluid model of the duct is established by means of the FLUENT solver of the CFD software. Secondly, with the k‐ε turbulence model of three‐ dimensional incompressible fluid considered and the PRISO pressure modification algorithm employed, the flow field numerical simulations inside the duct of the robot vacuum cleaner are carried out. Then, the velocity vector plots on the arbitrary plane of the duct flow field are obtained. Finally, an investigation of the dynamic characteristics of the duct flow field is done and defects of the original duct flow field are analysed, the optimisation of the original flow field has then been conducted. Experimental results show that the duct flow field after optimisation can effectively reduce pressure drop, the feasibility as well as the correctness of the theoretical modelling and optimisation approaches are validated.

Three-dimensional flow field measurements in a radial inflow turbine scroll using LDV

Science.gov (United States)

Malak, M. F.; Hamed, A.; Tabakoff, W.

1986-01-01

The results of an experimental study of the three-dimensional flow field in a radial inflow turbine scroll are presented. A two-color LDV system was used in the measurement of three orthogonal velocity components at 758 points located throughout the scroll and the unvaned portion of the nozzle. The cold flow experimental results are presented for through-flow velocity contours and the cross velocity vectors.

Vector flow mapping in obstructive hypertrophic cardiomyopathy to assess the relationship of early systolic left ventricular flow and the mitral valve.

Science.gov (United States)

Ro, Richard; Halpern, Dan; Sahn, David J; Homel, Peter; Arabadjian, Milla; Lopresto, Charles; Sherrid, Mark V

2014-11-11

The hydrodynamic cause of systolic anterior motion of the mitral valve (SAM) is unresolved. This study hypothesized that echocardiographic vector flow mapping, a new echocardiographic technique, would provide insights into the cause of early SAM in obstructive hypertrophic cardiomyopathy (HCM). We analyzed the spatial relationship of left ventricular (LV) flow and the mitral valve leaflets (MVL) on 3-chamber vector flow mapping frames, and performed mitral valve measurements on 2-dimensional frames in patients with obstructive and nonobstructive HCM and in normal patients. We compared 82 patients (22 obstructive HCM, 23 nonobstructive HCM, and 37 normal) by measuring 164 LV pre- and post-SAM velocity vector flow maps, 82 maximum isovolumic vortices, and 328 2-dimensional frames. We observed color flow and velocity vector flow posterior to the MVL impacting them in the early systolic frames of 95% of obstructive HCM, 22% of nonobstructive HCM, and 11% of normal patients (p 60° of local vector flow onto the posterior surface of the leaflets whether the flow was ejection (59%) or the early systolic isovolumic vortex (41%). Ricochet of vector flow, rebounding off the leaflet into the cul-de-sac, was noted in 82% of the obstructed HCM, 9% of nonobstructive HCM, and none (0%) of the control patients (p Flow velocities in the LV outflow tract on the pre-SAM frame 1 and 2 mm from the tip of the anterior leaflet were low: 39 and 43 cm/s, respectively. Early systolic flow impacts the posterior surfaces of protruding MVL initiating SAM in obstructive HCM. Copyright © 2014 American College of Cardiology Foundation. Published by Elsevier Inc. All rights reserved.

3-D Vector Flow Estimation With Row-Column-Addressed Arrays.

Science.gov (United States)

Holbek, Simon; Christiansen, Thomas Lehrmann; Stuart, Matthias Bo; Beers, Christopher; Thomsen, Erik Vilain; Jensen, Jorgen Arendt

2016-11-01

Simulation and experimental results from 3-D vector flow estimations for a 62 + 62 2-D row-column (RC) array with integrated apodization are presented. A method for implementing a 3-D transverse oscillation (TO) velocity estimator on a 3-MHz RC array is developed and validated. First, a parametric simulation study is conducted, where flow direction, ensemble length, number of pulse cycles, steering angles, transmit/receive apodization, and TO apodization profiles and spacing are varied, to find the optimal parameter configuration. The performance of the estimator is evaluated with respect to relative mean bias ~B and mean standard deviation ~σ . Second, the optimal parameter configuration is implemented on the prototype RC probe connected to the experimental ultrasound scanner SARUS. Results from measurements conducted in a flow-rig system containing a constant laminar flow and a straight-vessel phantom with a pulsating flow are presented. Both an M-mode and a steered transmit sequence are applied. The 3-D vector flow is estimated in the flow rig for four representative flow directions. In the setup with 90° beam-to-flow angle, the relative mean bias across the entire velocity profile is (-4.7, -0.9, 0.4)% with a relative standard deviation of (8.7, 5.1, 0.8)% for ( v x , v y , v z ). The estimated peak velocity is 48.5 ± 3 cm/s giving a -3% bias. The out-of-plane velocity component perpendicular to the cross section is used to estimate volumetric flow rates in the flow rig at a 90° beam-to-flow angle. The estimated mean flow rate in this setup is 91.2 ± 3.1 L/h corresponding to a bias of -11.1%. In a pulsating flow setup, flow rate measured during five cycles is 2.3 ± 0.1 mL/stroke giving a negative 9.7% bias. It is concluded that accurate 3-D vector flow estimation can be obtained using a 2-D RC-addressed array.

The significance of vector magnetic field measurements

Science.gov (United States)

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.

Vector fields on nonorientable surfaces

Directory of Open Access Journals (Sweden)

Ilie Barza

2003-01-01

X, and the space of vector fields on X are proved by using a symmetrisation process. An example related to the normal derivative on the border of the Möbius strip supports the nontriviality of the concepts introduced in this paper.

The index of a vector field under blow ups

International Nuclear Information System (INIS)

Seade, J.

1991-08-01

A useful technique when studying the behaviour of holomorphic vector fields around their isolated singularities is that of blowing up the singular points. On the other hand, the most basic invariant of a vector field with isolated singularities is its local index, as defined by Poincare and Hopf. It is thus natural to ask how does the index of a vector field behaves under blowing ups? The purpose of this work is to study and answer this question, by taking a rather general point of view and bearing in mind that complex manifolds have a powerful birational invariant, the Todd genus. 20 refs

Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

International Nuclear Information System (INIS)

Anco, Stephen C.

2003-01-01

A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

Vector condensate and AdS soliton instability induced by a magnetic field

International Nuclear Information System (INIS)

Cai, Rong-Gen; Li, Li; Li, Li-Fang; Wu, You

2014-01-01

We continue to study the holographic p-wave superconductor model in the Einstein-Maxwell-complex vector field theory with a non-minimal coupling between the complex vector field and the Maxwell field. In this paper we work in the AdS soliton background which describes a conformal field theory in the confined phase and focus on the probe approximation. We find that an applied magnetic field can lead to the condensate of the vector field and the AdS soliton instability. As a result, a vortex lattice structure forms in the spatial directions perpendicular to the applied magnetic field. As a comparison, we also discuss the vector condensate in the Einstein-SU(2) Yang-Mills theory and find that in the setup of the present paper, the Einstein-Maxwell-complex vector field model is a generalization of the SU(2) model in the sense that the vector field has a general mass and gyromagnetic ratio

Stable solutions of inflation driven by vector fields

Energy Technology Data Exchange (ETDEWEB)

Emami, Razieh [Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Mukohyama, Shinji [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto (Japan); Namba, Ryo [Department of Physics, McGill University, Montréal, QC, H3A 2T8 (Canada); Zhang, Ying-li, E-mail: iasraziehm@ust.hk, E-mail: shinji.mukohyama@yukawa.kyoto-u.ac.jp, E-mail: namba@physics.mcgill.ca, E-mail: yingli@bao.ac.cn [National Astronomy Observatories, Chinese Academy of Science, Beijing 100012 (China)

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.

Stable solutions of inflation driven by vector fields

International Nuclear Information System (INIS)

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

2017-01-01

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.

Avoiding ergodicity and turbulence in R3 vector fields

International Nuclear Information System (INIS)

Ancochea, J.M.; Campoamor-Stursberg, R.; Gonzalez-Gascon, F.

2003-01-01

We show that analytic R 3 vector fields having the property of being transversal to either analytic functions or foliations F 2 , or parallel to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via induced vector fields is also proven

Discovering and understanding the vector field using simulation in android app

Science.gov (United States)

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.

Real-Time GPU Implementation of Transverse Oscillation Vector Velocity Flow Imaging

DEFF Research Database (Denmark)

Bradway, David; Pihl, Michael Johannes; Krebs, Andreas

2014-01-01

Rapid estimation of blood velocity and visualization of complex flow patterns are important for clinical use of diagnostic ultrasound. This paper presents real-time processing for two-dimensional (2-D) vector flow imaging which utilizes an off-the-shelf graphics processing unit (GPU). In this work...... vector flow acquisition takes 2.3 milliseconds seconds on an Advanced Micro Devices Radeon HD 7850 GPU card. The detected velocities are accurate to within the precision limit of the output format of the display routine. Because this tool was developed as a module external to the scanner’s built...

Perturbations of ultralight vector field dark matter

Energy Technology Data Exchange (ETDEWEB)

Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

2017-02-13

We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

Topological invariants and the dynamics of an axial vector torsion field

International Nuclear Information System (INIS)

Drechsler, W.

1983-01-01

A generalized throry of gravitation is discussed which is based on a Riemann-Cartan space-time, U 4 , with an axial vector torsion field. Besides Einstein's equations determining the metric of the U 4 a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for the U 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic. (author)

[Quantitative Measurements on the Blood Flow Fields of Left Atrial Appendage using Vector Flow Mapping in Patients with Nonvalvular Atrial Fibrillation].

Science.gov (United States)

Cai, Yu-Yan; Wei, Xin; Zhang, Xiao-Ling; Liu, Gu-Yue; Li, Xi; Tang, Hong

2018-01-01

To quantify the hemodynamic characteristics of patients with nonvalvular atrial fibrillation. Twenty patients with paroxysmal atrial fibrillation and 15 patients with persistent atrial fibrillation enrolled in this study,while 12 patients with sinus rhythms served as controls. The hemodynamic characteristics of the patients in left atrial appendage were measured by transesophageal echocardiography (TEE) and vector flow mapping (VFM) using indicators such as vectors,vortex and energy loss (EL). ① Significant differences appeared between the patients with atrial fibrillation and the controls in heart rate,size of left atrium,size of left atrial appendage (LAA),and velocities of LAA filling and emptying. ② Regular vectors in LAA in early systole and late diastole were found in the patients with paroxysmal atrial fibrillation and the controls; whereas,irregular vectors with direction alternating were visualized in the whole cardiac cycle in the patients with persistent atrial fibrillation. ③ Small vortexes were observed at the opening of the left atrial appendage in late diastole in the patients with paroxysmal atrial fibrillation and the controls. ④ Peak EL values occurred in early systole and late diastole in the patients with paroxysmal atrial fibrillation and the controls. But the patients with persistent atrial fibrillation had increased EL values over the whole cardiac cycle. VFM can visualize and quantify the hemodynamics of LAA in patients with different heart rhythms. It may provide a new method for assessing atrial fibrillation. CopyrightCopyright© by Editorial Board of Journal of Sichuan University (Medical Science Edition).

VECTOR TOMOGRAPHY FOR THE CORONAL MAGNETIC FIELD. II. HANLE EFFECT MEASUREMENTS

International Nuclear Information System (INIS)

Kramar, M.; Inhester, B.; Lin, H.; Davila, J.

2013-01-01

In this paper, we investigate the feasibility of saturated coronal Hanle effect vector tomography or the application of vector tomographic inversion techniques to reconstruct the three-dimensional magnetic field configuration of the solar corona using linear polarization measurements of coronal emission lines. We applied Hanle effect vector tomographic inversion to artificial data produced from analytical coronal magnetic field models with equatorial and meridional currents and global coronal magnetic field models constructed by extrapolation of real photospheric magnetic field measurements. We tested tomographic inversion with only Stokes Q, U, electron density, and temperature inputs to simulate observations over large limb distances where the Stokes I parameters are difficult to obtain with ground-based coronagraphs. We synthesized the coronal linear polarization maps by inputting realistic noise appropriate for ground-based observations over a period of two weeks into the inversion algorithm. We found that our Hanle effect vector tomographic inversion can partially recover the coronal field with a poloidal field configuration, but that it is insensitive to a corona with a toroidal field. This result demonstrates that Hanle effect vector tomography is an effective tool for studying the solar corona and that it is complementary to Zeeman effect vector tomography for the reconstruction of the coronal magnetic field

Vector field statistical analysis of kinematic and force trajectories.

Science.gov (United States)

Pataky, Todd C; Robinson, Mark A; Vanrenterghem, Jos

2013-09-27

When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of 'non-directed' hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called 'statistical parametric mapping' (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems. © 2013 Published by Elsevier Ltd. All rights reserved.

Vector supersymmetry in topological field theories

International Nuclear Information System (INIS)

Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.

2000-01-01

We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)

The Curl of a Vector Field: Beyond the Formula

Science.gov (United States)

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…

Polynomial Vector Fields in One Complex Variable

DEFF Research Database (Denmark)

Branner, Bodil

In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....

Numerical analysis of flow fields generated by accelerating flames

Energy Technology Data Exchange (ETDEWEB)

Kurylo, J.

1977-12-01

Presented here is a numerical technique for the analysis of non-steady flow fields generated by accelerating flames in gaseous media. Of particular interest in the study is the evaluation of the non-steady effects on the flow field and the possible transition of the combustion process to detonation caused by an abrupt change in the burning speed of an initially steady flame propagating in an unconfined combustible gas mixture. Optically recorded observations of accelerating flames established that the flow field can be considered to consist of non-steady flow fields associated with an assembly of interacting shock waves, contact discontinuities, deflagration and detonation fronts. In the analysis, these flow fields are treated as spatially one-dimensional, the influence of transport phenomena is considered to be negligible, and unburned and burned substances are assumed to behave as perfect gases with constant, but different, specific heats. The basis of the numerical technique is an explicit, two step, second order accurate, finite difference scheme employed to integrate the flow field equations expressed in divergence form. The burning speed, governing the motion of the deflagration, is expressed in the form of a power law dependence on pressure and temperature immediately ahead of its front. The steady wave solution is obtained by the vector polar interaction technique, that is, by determining the point of intersection between the loci of end states in the plane of the two interaction invariants, pressure and particle velocity. The technique is illustrated by a numerical example in which a steady flame experiences an abrupt change in its burning speed. Solutions correspond either to the eventual reestablishment of a steady state flow field commensurate with the burning speed or to the transition to detonation. The results are in satisfactory agreement with experimental observations.

Vector velocity volume flow estimation: Sources of error and corrections applied for arteriovenous fistulas

DEFF Research Database (Denmark)

Jensen, Jonas; Olesen, Jacob Bjerring; Stuart, Matthias Bo

2016-01-01

radius. The error sources were also studied in vivo under realistic clinical conditions, and the theoretical results were applied for correcting the volume flow errors. Twenty dialysis patients with arteriovenous fistulas were scanned to obtain vector flow maps of fistulas. When fitting an ellipsis......A method for vector velocity volume flow estimation is presented, along with an investigation of its sources of error and correction of actual volume flow measurements. Volume flow errors are quantified theoretically by numerical modeling, through flow phantom measurements, and studied in vivo...

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

Science.gov (United States)

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.

Determination of key parameters of vector multifractal vector fields

Science.gov (United States)

Schertzer, D. J. M.; Tchiguirinskaia, I.

2017-12-01

For too long time, multifractal analyses and simulations have been restricted to scalar-valued fields (Schertzer and Tchiguirinskaia, 2017a,b). For instance, the wind velocity multifractality has been mostly analysed in terms of scalar structure functions and with the scalar energy flux. This restriction has had the unfortunate consequences that multifractals were applicable to their full extent in geophysics, whereas it has inspired them. Indeed a key question in geophysics is the complexity of the interactions between various fields or they components. Nevertheless, sophisticated methods have been developed to determine the key parameters of scalar valued fields. In this communication, we first present the vector extensions of the universal multifractal analysis techniques to multifractals whose generator belong to a Levy-Clifford algebra (Schertzer and Tchiguirinskaia, 2015). We point out further extensions noting the increased complexity. For instance, the (scalar) index of multifractality becomes a matrice. Schertzer, D. and Tchiguirinskaia, I. (2015) `Multifractal vector fields and stochastic Clifford algebra', Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(12), p. 123127. doi: 10.1063/1.4937364. Schertzer, D. and Tchiguirinskaia, I. (2017) `An Introduction to Multifractals and Scale Symmetry Groups', in Ghanbarian, B. and Hunt, A. (eds) Fractals: Concepts and Applications in Geosciences. CRC Press, p. (in press). Schertzer, D. and Tchiguirinskaia, I. (2017b) `Pandora Box of Multifractals: Barely Open ?', in Tsonis, A. A. (ed.) 30 Years of Nonlinear Dynamics in Geophysics. Berlin: Springer, p. (in press).

Space-times carrying a quasirecurrent pairing of vector fields

International Nuclear Information System (INIS)

Rosca, R.; Ianus, S.

1977-01-01

A quasirecurrent pairing of vector fields(X 1 ,X 2 ,) defined previously by Rosca (C.R. Acad. Sci. 282 (1976)) is investigated on a space-time in two cases: (1) X 1 is spacelike and X 2 is timelike; (2) X 1 is null and X 2 is spacelike. The physical interpretation of these vector fields is given. (author)

The principal part of plane vector fields with fixed Newton diagram

International Nuclear Information System (INIS)

Berezovskaya, F.

1991-09-01

Considering the main part of a plane vector field in a neighbourhood of a singular point 0(0,0) it is well known that if the singularity real parts of eigenvalues are non-zero, the linear part of the vector field provides the topological normal form and tangents of all the o-curves. The problem is to find the main part of a plane vector field which would provide the topological orbital normal form in a neighbourhood of singular point and asymptotics of all characteristics trajectories. In this work the solution to the problem for the generic ease of so-called nondegenerate vector fields, using Newton diagram is given. 13 refs, 5 figs

A vector field method on the distorted Fourier side and decay for wave equations with potentials

CERN Document Server

Donninger, Roland

2016-01-01

The authors study the Cauchy problem for the one-dimensional wave equation \\partial_t^2 u(t,x)-\\partial_x^2 u(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)\\sim -\\tfrac14 |x|^{-2}\\mbox{ as } |x|\\to \\infty. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t\\partial_t+x\\partial_x, where the latter are obtained by employing a vector field method on the âeoedistortedâe Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, âeoeCodimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski spaceâe, preprint arXiv:1310.5606 (2013).

Generalized Proca action for an Abelian vector field

International Nuclear Information System (INIS)

Allys, Erwan; Peter, Patrick; Rodríguez, Yeinzon

2016-01-01

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature

On the non-Gaussian correlation of the primordial curvature perturbation with vector fields

DEFF Research Database (Denmark)

Kumar Jain, Rajeev; Sloth, Martin Snoager

2013-01-01

We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified...... with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit...

Research on external flow field of a car based on reverse engineering

Science.gov (United States)

Hu, Shushan; Liu, Ronge

2018-05-01

In this paper, the point cloud data of FAW-VOLKSWAGEN car body shape is obtained by three coordinate measuring instrument and laser scanning method. The accurate three dimensional model of the car is obtained using CATIA software reverse modelling technology. The car body is gridded, the calculation field and boundary condition type of the car flow field are determined, and the numerical simulation is carried out in Hyper Mesh software. The pressure cloud diagram, velocity vector diagram, air resistance coefficient and lift coefficient of the car are obtained. The calculation results reflect the aerodynamic characteristics of the car's external flow field. The motion of the separation flow on the surface of the vehicle body is well simulated, and the area where the vortex motion is relatively intense has been determined. The results provide a theoretical basis for improving and optimizing the body shape.

An example of a vector field with the oriented shadowing property

OpenAIRE

Tikhomirov, Sergey

2014-01-01

We consider shadowing properties for vector fields corresponding to different type of reparametrisations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property.

A vector model for off-axis hysteresis loops using anisotropy field

Energy Technology Data Exchange (ETDEWEB)

Jamali, Ali, E-mail: alijamal@gwu.edu [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States); Torre, Edward Della [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States); Cardelli, Ermanno [Department of Engineering, University of Perugia, Perugia (Italy); ElBidweihy, Hatem [Electrical and Computer Engineering Department, United States Naval Academy, Annapolis, MD 21402 (United States); Bennett, Lawrence H. [Electrical and Computer Engineering Department, The George Washington University, Washington, D.C. 20052 (United States)

2016-11-15

A model for the off-axis vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. In this paper, to account for anisotropy, the direction of the reversible magnetization component is specified by the vector sum of the applied field and an effective anisotropy field. The formulation of the new anisotropy field (AF) model is derived and its results are discussed considering (i) oscillation and rotational modes, (ii) lag angle, and (iii) unitary magnetization. The advantages of the AF model are outlined by comparing its results to the results of the classical Stoner–Wohlfarth model.

A vector model for off-axis hysteresis loops using anisotropy field

International Nuclear Information System (INIS)

Jamali, Ali; Torre, Edward Della; Cardelli, Ermanno; ElBidweihy, Hatem; Bennett, Lawrence H.

2016-01-01

A model for the off-axis vector magnetization of a distribution of uniaxial particles is presented. Recent work by the authors decomposed the magnetization into two components and modeled the total vector magnetization as their vector sum. In this paper, to account for anisotropy, the direction of the reversible magnetization component is specified by the vector sum of the applied field and an effective anisotropy field. The formulation of the new anisotropy field (AF) model is derived and its results are discussed considering (i) oscillation and rotational modes, (ii) lag angle, and (iii) unitary magnetization. The advantages of the AF model are outlined by comparing its results to the results of the classical Stoner–Wohlfarth model.

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

Science.gov (United States)

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.

Creation of a new vector field and focusing engineering

OpenAIRE

Wang, Xi-Lin; Chen, Jing; Li, Yongnan; Ding, Jianping; Guo, Cheng-Shan; Wang, Hui-Tian

2009-01-01

Recently many methods have been proposed to create the vector fields, due to the academic interest and a variety of attractive applications such as for particle acceleration, optical trapping, particle manipulation, and fluorescence imaging. For the most of the created vector fields, the spatial distribution in states of polarization (SoPs) is dependent of azimuthal angle only. It is very interesting and crucial that if we can introduce the radial controlling freedom, which undoubtedly opens ...

MHD thrust vectoring of a rocket engine

Science.gov (United States)

Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic

2016-09-01

In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.

Symbolic computer vector analysis

Science.gov (United States)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Validation of SplitVectors Encoding for Quantitative Visualization of Large-Magnitude-Range Vector Fields.

Science.gov (United States)

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.

Energy Based Clutter Filtering for Vector Flow Imaging

DEFF Research Database (Denmark)

Villagómez Hoyos, Carlos Armando; Jensen, Jonas; Ewertsen, Caroline

2017-01-01

for obtaining vector flow measurements, since the spectra overlaps at high beam-to-flow angles. In this work a distinct approach is proposed, where the energy of the velocity spectrum is used to differentiate among the two signals. The energy based method is applied by limiting the amplitude of the velocity...... spectrum function to a predetermined threshold. The effect of the clutter filtering is evaluated on a plane wave (PW) scan sequence in combination with transverse oscillation (TO) and directional beamforming (DB) for velocity estimation. The performance of the filter is assessed by comparison...

Non-Gaussianity and statistical anisotropy from vector field populated inflationary models

CERN Document Server

Dimastrogiovanni, Emanuela; Matarrese, Sabino; Riotto, Antonio

2010-01-01

We present a review of vector field models of inflation and, in particular, of the statistical anisotropy and non-Gaussianity predictions of models with SU(2) vector multiplets. Non-Abelian gauge groups introduce a richer amount of predictions compared to the Abelian ones, mostly because of the presence of vector fields self-interactions. Primordial vector fields can violate isotropy leaving their imprint in the comoving curvature fluctuations zeta at late times. We provide the analytic expressions of the correlation functions of zeta up to fourth order and an analysis of their amplitudes and shapes. The statistical anisotropy signatures expected in these models are important and, potentially, the anisotropic contributions to the bispectrum and the trispectrum can overcome the isotropic parts.

Interstellar Gas Flow Vector and Temperature Determination over 5 Years of IBEX Observations

International Nuclear Information System (INIS)

Möbius, E; Heirtzler, D; Kucharek, H; Lee, M A; Leonard, T; Schwadron, N; Bzowski, M; Kubiak, M A; Sokół, J M; Fuselier, S A; McComas, D J; Wurz, P

2015-01-01

The Interstellar Boundary Explorer (IBEX) observes the interstellar neutral gas flow trajectories at their perihelion in Earth's orbit every year from December through early April, when the Earth's orbital motion is into the oncoming flow. These observations have defined a narrow region of possible, but very tightly coupled interstellar neutral flow parameters, with inflow speed, latitude, and temperature as well-defined functions of inflow longitude. The best- fit flow vector is different by ≈ 3° and lower by ≈ 3 km/s than obtained previously with Ulysses GAS, but the temperature is comparable. The possible coupled parameter space reaches to the previous flow vector, but only for a substantially higher temperature (by ≈ 2000 K). Along with recent pickup ion observations and including historical observations of the interstellar gas, these findings have led to a discussion, whether the interstellar gas flow into the solar system has been stable or variable over time. These intriguing possibilities call for more detailed analysis and a longer database. IBEX has accumulated observations over six interstellar flow seasons. We review key observations and refinements in the analysis, in particular, towards narrowing the uncertainties in the temperature determination. We also address ongoing attempts to optimize the flow vector determination through varying the IBEX spacecraft pointing and discuss related implications for the local interstellar cloud and its interaction with the heliosphere

VECTOR MAGNETIC FIELDS AND ELECTRIC CURRENTS FROM THE IMAGING VECTOR MAGNETOGRAPH

International Nuclear Information System (INIS)

Li Jing; Mickey, Don; Van Ballegooijen, A. A.

2009-01-01

First, we describe a general procedure to produce high-quality vector magnetograms using the Imaging Vector Magnetograph (IVM) at Mees Solar Observatory. Two IVM effects are newly discussed and taken into account: (1) the central wavelength of the Fabry-Perot is found to drift with time as a result of undiagnosed thermal or mechanical instabilities in the instrument; (2) the Stokes V-sign convention built into the IVM is found to be opposite to the conventional definition used in the study of radiative transfer of polarized radiation. At the spatial resolution 2'' x 2'', the Stokes Q, U, V uncertainty reaches ∼1 x 10 -3 to 5 x 10 -4 in time-averaged data over 1 hr in the quiet Sun. When vector magnetic fields are inferred from the time-averaged Stokes spectral images of FeI 6302.5 A, the resulting uncertainties are on the order of 10 G for the longitudinal fields (B || ), 40 G for the transverse field strength (B perpendicular ) and ∼9 0 for the magnetic azimuth (φ). The magnetic field inversion used in this work is the 'Triplet' code, which was developed and implemented in the IVM software package by the late B. J. LaBonte. The inversion code is described in detail in the Appendix. Second, we solve for the absolute value of the vertical electric current density, |J z |, accounting for the above IVM problems, for two different active regions. One is a single sunspot region (NOAA 10001 observed on 2002 June 20) while the other is a more complex, quadrupolar region (NOAA10030 observed on 2002 July 15). We use a calculation that does not require disambiguation of 180 0 in the transverse field directions. The |J z | uncertainty is on the order of ∼7.0 mA m -2 . The vertical current density increases with increasing vertical magnetic field. The rate of increase is about 1-2 times as large in the quadrupolar NOAA 10030 region as in the simple NOAA 10001, and it is more spatially variable over NOAA 10030 than over NOAA 10001.

Invariant hyperplanes and Darboux integrability of polynomial vector fields

International Nuclear Information System (INIS)

Zhang Xiang

2002-01-01

This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in n variables. This result generalizes those given in Artes et al (1998 Pac. J. Math. 184 207-30) and Llibre and Rodriguez (2000 Bull. Sci. Math. 124 599-619). The second part gives an extension of the Darboux theory of integrability to polynomial vector fields on algebraic varieties

Normal equivariant forms of vector fields

International Nuclear Information System (INIS)

Sanchez Bringas, F.

1992-07-01

We prove a theorem of linearization of type Siegel and a theorem of normal forms of type Poincare-Dulac for germs of holomorphic vector fields in the origin of C 2 , Γ -equivariants, where Γ is a finite subgroup of GL (2,C). (author). 5 refs

Dynamic effects on the stretching of the magnetic field by a plasma flow

Energy Technology Data Exchange (ETDEWEB)

Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)

2003-08-22

A key mechanism in the growth of magnetic energy in kinematic dynamos is the stretching of the magnetic field vector by making it point in an unstable direction of the strain matrix. Our objective is to study whether this feature may be maintained in an ideal plasma when also considering the back reaction of the magnetic field upon the flow through the Lorentz force. Several effects occur: in addition to the nonlocal ones exerted by the total pressure, a complex geometry of magnetic field lines decreases the rate of growth of magnetic energy, rotation of the flow enhances it and above all the rate of growth decreases with minus the square of the eigenvalue associated with the magnetic field direction. Thus local dynamics tend to rapidly quench the stretching of the field.

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

Science.gov (United States)

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.

Initial geomagnetic field model from Magsat vector data

Science.gov (United States)

Langel, R. A.; Mead, G. D.; Lancaster, E. R.; Estes, R. H.; Fabiano, E. B.

1980-01-01

Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.

Managing focal fields of vector beams with multiple polarization singularities.

Science.gov (United States)

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.

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

Science.gov (United States)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-04-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

On the existence of polynomial Lyapunov functions for rationally stable vector fields

DEFF Research Database (Denmark)

Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer

2018-01-01

This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....

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

Science.gov (United States)

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.

Propulsion efficiency and imposed flow fields of a copepod jump.

Science.gov (United States)

Jiang, Houshuo; Kiørboe, Thomas

2011-02-01

Pelagic copepods jump to relocate, to attack prey and to escape predators. However, there is a price to be paid for these jumps in terms of their energy costs and the hydrodynamic signals they generate to rheotactic predators. Using observed kinematics of various types of jumps, we computed the imposed flow fields and associated energetics of jumps by means of computational fluid dynamics simulations by modeling the copepod as a self-propelled body. The computational fluid dynamics simulation was validated by particle image velocimetry data. The flow field generated by a repositioning jump quickly evolves into two counter-rotating viscous vortex rings that are near mirror image of one another, one in the wake and one around the body of the copepod; this near symmetrical flow may provide hydrodynamic camouflage because it contains no information about the position of the copepod prey within the flow structure. The flow field associated with an escape jump sequence also includes two dominant vortex structures: one leading wake vortex generated as a result of the first jump and one around the body, but between these two vortex structures is an elongated, long-lasting flow trail with flow velocity vectors pointing towards the copepod; such a flow field may inform the predator of the whereabouts of the escaping copepod prey. High Froude propulsion efficiency (0.94-0.98) was obtained for individual power stroke durations of all simulated jumps. This is unusual for small aquatic organisms but is caused by the rapidity and impulsiveness of the jump that allows only a low-cost viscous wake vortex to travel backwards.

Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization

International Nuclear Information System (INIS)

Chen, Rui-Pin; Zhao, Ting-Yu; Zhang, Xiaobo; Zhong, Li-Xin; Chew, Khian-Hooi

2015-01-01

Based on a pair of coupled 2D nonlinear Schrödinger equations, the collapse dynamics of a vector field with hybrid states of polarization (SoP) in a Kerr medium is demonstrated. The critical power for an optical field to collapse is present, and the full vectorial numerical simulations provide detailed information about the evolution and partial collapse of the vector field in a Kerr medium. Our results reveal that the optical field prefers to collapse in linearly-polarization, as a result of the self-focusing effect difference in linearly, elliptically and circularly polarized components. The SoP in the field cross-section changes and propagates with a spiral trajectory when the vector beams are imposed with a vortex. The vectorial effect on the collapse of a vector optical field can prevail over the noise even though it reaches 10% amplitude of the optical field. The unique feature of these structured collapses of a vector optical field may lead to new phenomena in the interaction of light with matter. (paper)

The local structure of a Liouville vector field

International Nuclear Information System (INIS)

Ciriza, E.

1990-05-01

In this work we investigate the local structure of a Liouville vector field ξ of a Kaehler manifold (P,Ω) which vanishes on an isotropic submanifold Q of P. Some of the eigenvalues of its linear part at the singular points are zero and the remaining ones are in resonance. We show that there is a C 1 -smooth linearizing conjugation between the Liouville vector field ξ and its linear part. To do this we construct Darboux coordinates adapted to the unstable foliation which is provided by the Centre Manifold Theorem. We then apply recent linearization results due to G. Sell. (author). 11 refs

Cardiovascular fluid dynamics. Methods for flow and pressure field analysis from magnetic resonance imaging

International Nuclear Information System (INIS)

Ebbers, T.

2001-01-01

Cardiovascular blood flow is highly complex and incompletely understood. Blood flow patterns are expected to influence the opening and closing of normal and prosthetic heart valves, the efficiency of cardiac filling and ejection, and the resistance to thrombus formation within the heart. Conventional diagnostic techniques are poorly suited to the study of the three-dimensional (3D) blood flow patterns in the heart chambers and large vessels. Noninvasive methods have also been inadequate in studying intracardiac pressure differences, which are the driving force of flow and are critical in the evaluation of many cardiovascular abnormalities. This thesis focuses on the development of non-invasive methods for analysis of 3D cardiovascular blood flow. Simultaneous study of cardiovascular fluid dynamics allowed knowledge exchange across the two disciplines, facilitating the development process and broadening the applicability of the methods. A time-resolved 3D phase-contrast Magnetic Resonance Imaging (MRI) technique was used to acquire the velocity vector field in a 3D volume encompassing the entire heart or a large vessel. Cardiovascular blood flow patterns were visualized by use of particle traces, which revealed, for instance, vortical flow patterns in the left atrium. By applying the Navier-Stokes equation along a user-defined line in the 3D velocity vector field, the relative pressure could be obtained as an excellent supplement to the flow pattern visualization. Using a delineation of the blood pool, the time-varying 3D relative pressure field in the human left ventricle was obtained from the velocity field by use of the pressure Poisson equation. A delineation of the heart muscle, a task that is almost impossible to perform on 3D MRI either automatically or manually, was also achieved by usage of particle traces. This segmentation allows automatic calculation of the 3D relative pressure field, as well as calculation of well-established parameters such as

Cardiovascular fluid dynamics. Methods for flow and pressure field analysis from magnetic resonance imaging

Energy Technology Data Exchange (ETDEWEB)

Ebbers, T

2001-05-01

Cardiovascular blood flow is highly complex and incompletely understood. Blood flow patterns are expected to influence the opening and closing of normal and prosthetic heart valves, the efficiency of cardiac filling and ejection, and the resistance to thrombus formation within the heart. Conventional diagnostic techniques are poorly suited to the study of the three-dimensional (3D) blood flow patterns in the heart chambers and large vessels. Noninvasive methods have also been inadequate in studying intracardiac pressure differences, which are the driving force of flow and are critical in the evaluation of many cardiovascular abnormalities. This thesis focuses on the development of non-invasive methods for analysis of 3D cardiovascular blood flow. Simultaneous study of cardiovascular fluid dynamics allowed knowledge exchange across the two disciplines, facilitating the development process and broadening the applicability of the methods. A time-resolved 3D phase-contrast Magnetic Resonance Imaging (MRI) technique was used to acquire the velocity vector field in a 3D volume encompassing the entire heart or a large vessel. Cardiovascular blood flow patterns were visualized by use of particle traces, which revealed, for instance, vortical flow patterns in the left atrium. By applying the Navier-Stokes equation along a user-defined line in the 3D velocity vector field, the relative pressure could be obtained as an excellent supplement to the flow pattern visualization. Using a delineation of the blood pool, the time-varying 3D relative pressure field in the human left ventricle was obtained from the velocity field by use of the pressure Poisson equation. A delineation of the heart muscle, a task that is almost impossible to perform on 3D MRI either automatically or manually, was also achieved by usage of particle traces. This segmentation allows automatic calculation of the 3D relative pressure field, as well as calculation of well-established parameters such as

Enumeration of Combinatorial Classes of Single Variable Complex Polynomial Vector Fields

DEFF Research Database (Denmark)

Dias, Kealey

A vector field in the space of degree d monic, centered single variable complex polynomial vector fields has a combinatorial structure which can be fully described by a combinatorial data set consisting of an equivalence relation and a marked subset on the integers mod 2d-2, satisfying certain...

Cobordism Obstructions to Vector Fields and a Generalization of Lin's Theorem

DEFF Research Database (Denmark)

Svane, Anne Marie

Atiyah and Dupont have studied the existence of linearly independent vector fields on manifolds by means of K-theory. They obtained the complete conditions for up to three independent vector fields. In the thesis, we try to copy their approach using certain spectra related to cobordism theory. We...

Antenna diagnostics for power flow in extreme near-field of a standard gain horn

DEFF Research Database (Denmark)

Popa, Paula Irina; Breinbjerg, Olav

2016-01-01

The plane wave spectrum of an aperture antenna can be calculated from a complex measurement of the radiated near- or far-field and it facilitates antenna diagnostics for the extreme near-field of the antenna. While antenna diagnostics often concerns the magnitude of the co-polar field, the plane...... wave spectrum actually allows for determination of both magnitude and phase of all three components of the electric as well as the magnetic field - and thus also the Poynting vector. In this work we focus on the Poynting vector and thus the power flow in the extreme near-field; as an example we employ...... that these oscillations are not merely a “Gibbs-like” phenomenon due to the availability of only the visible region of the plane wave spectrum and they are not caused by multiple reflections between the horn and the near-field probe - but resulted from the interference between the direct field and the edge...

Combinatorial vector fields and the valley structure of fitness landscapes.

Science.gov (United States)

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.

Center type performance of differentiable vector fields in R2

International Nuclear Information System (INIS)

Rabanal, Roland

2007-08-01

Let X : R 2 / D → R 2 be a differentiable vector field, where D is compact. If the eigenvalues of the jacobian matrix DX z are (nonzero) purely imaginary, for all z element of R 2 / D . Then, X + v has a center type performance at infinity, for some v element of R 2 . More precisely, X + v has a periodic trajectory Γ subset of R2/ D which is surrounding D such that in the unbounded component of (R 2 / D )/ Γ all the trajectories of X + v are nontrivial cycles. In the case of global vector fields Y : R 2 → R 2 with Y (0) = 0, we prove that such eigenvalue condition implies the topological equivalency of Y with the linear vector field (x, y) → (-y, x). (author)

Ultrasonic 3-D Vector Flow Method for Quantitative In Vivo Peak Velocity and Flow Rate Estimation

DEFF Research Database (Denmark)

Holbek, Simon; Ewertsen, Caroline; Bouzari, Hamed

2017-01-01

Current clinical ultrasound (US) systems are limited to show blood flow movement in either 1-D or 2-D. In this paper, a method for estimating 3-D vector velocities in a plane using the transverse oscillation method, a 32×32 element matrix array, and the experimental US scanner SARUS is presented...... is validated in two phantom studies, where flow rates are measured in a flow-rig, providing a constant parabolic flow, and in a straight-vessel phantom ( ∅=8 mm) connected to a flow pump capable of generating time varying waveforms. Flow rates are estimated to be 82.1 ± 2.8 L/min in the flow-rig compared...

Vector models and generalized SYK models

Energy Technology Data Exchange (ETDEWEB)

Peng, Cheng [Department of Physics, Brown University,Providence RI 02912 (United States)

2017-05-23

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. 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.

Accuracy and Precision of a Plane Wave Vector Flow Imaging Method in the Healthy Carotid Artery

DEFF Research Database (Denmark)

Jensen, Jonas; Villagómez Hoyos, Carlos Armando; Traberg, Marie Sand

2018-01-01

The objective of the study described here was to investigate the accuracy and precision of a plane wave 2-D vector flow imaging (VFI) method in laminar and complex blood flow conditions in the healthy carotid artery. The approach was to study (i) the accuracy for complex flow by comparing...... of laminar flow in vivo. The precision in vivo was calculated as the mean standard deviation (SD) of estimates aligned to the heart cycle and was highest in the center of the common carotid artery (SD = 3.6% for velocity magnitudes and 4.5° for angles) and lowest in the external branch and for vortices (SD...... the velocity field from a computational fluid dynamics (CFD) simulation to VFI estimates obtained from the scan of an anthropomorphic flow phantom and from an in vivo scan; (ii) the accuracy for laminar unidirectional flow in vivo by comparing peak systolic velocities from VFI with magnetic resonance...

The vector structure of active magnetic fields

Science.gov (United States)

Parker, E. N.

1985-01-01

Observations are needed to show the form of the strains introduced into the fields above the surface of the Sun. The longitudinal component alone does not provide the basic information, so that it has been necessary in the past to use the filamentary structure observed in H sub alpha to supplement the longitudinal information. Vector measurements provide the additional essential information to determine the strains, with the filamentary structure available as a check for consistency. It is to be expected, then, that vector measurements will permit a direct mapping of the strains imposed on the magnetic fields of active regions. It will be interesting to study the relation of those strains to the emergence of magnetic flux, flares, eruptive prominences, etc. In particular we may hope to study the relaxation of the strains via the dynamical nonequilibrium.

Flow behind an exponential shock wave in a rotational axisymmetric perfect gas with magnetic field and variable density.

Science.gov (United States)

Nath, G; Sahu, P K

2016-01-01

A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.

Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations

Science.gov (United States)

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?

The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

Directory of Open Access Journals (Sweden)

František FOJTÍK

2014-06-01

Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

Development of software-hardware complex for investigation of the vector field of speeds in the cyclone-separator

Science.gov (United States)

Borisov, A.

2018-05-01

The current issue of studying the vector velocity field in a cyclone-separator with a screw insert is considered in the article. Modeling of the velocity vector field in SolidWorks was carried out, tangential, axial and radial velocities were investigated. Also, a software and hardware complex was developed that makes it possible to obtain data on the speed inside a cyclone separator. The results of the experiment showed that on flour dusts the efficiency of the cyclone separator in question was more than 99.5%, with an air flow rate of 376 m3 / h, 472 m3 / h and 516 m3 / h, and ΔP less than 600 Pa. The velocity in the inlet branch of the screw insert was 18-20 m / s, and at the exit of the screw insert the airflow velocity is 50-70 m / s.

A dynamic counterpart of Lamb vector in viscous compressible aerodynamics

International Nuclear Information System (INIS)

Liu, L Q; Wu, J Z; Shi, Y P; Zhu, J Y

2014-01-01

The Lamb vector is known to play a key role in incompressible fluid dynamics and vortex dynamics. In particular, in low-speed steady aerodynamics it is solely responsible for the total force acting on a moving body, known as the vortex force, with the classic two-dimensional (exact) Kutta–Joukowski theorem and three-dimensional (linearized) lifting-line theory as the most famous special applications. In this paper we identify an innovative dynamic counterpart of the Lamb vector in viscous compressible aerodynamics, which we call the compressible Lamb vector. Mathematically, we present a theorem on the dynamic far-field decay law of the vorticity and dilatation fields, and thereby prove that the generalized Lamb vector enjoys exactly the same integral properties as the Lamb vector does in incompressible flow, and hence the vortex-force theory can be generalized to compressible flow with exactly the same general formulation. Moreover, for steady flow of polytropic gas, we show that physically the force exerted on a moving body by the gas consists of a transverse force produced by the original Lamb vector and a new longitudinal force that reflects the effects of compression and irreversible thermodynamics. (paper)

Determination of Coronal Magnetic Fields from Vector Magnetograms

Science.gov (United States)

Mikic, Zoran

1997-01-01

During the course of the present contract we developed an 'evolutionary technique' for the determination of force-free coronal magnetic fields from vector magnetograph observations. The method can successfully generate nonlinear force- free fields (with non-constant-a) that match vector magnetograms. We demonstrated that it is possible to determine coronal magnetic fields from photospheric measurements, and we applied it to vector magnetograms of active regions. We have also studied theoretical models of coronal fields that lead to disruptions. Specifically, we have demonstrated that the determination of force-free fields from exact boundary data is a well-posed mathematical problem, by verifying that the computed coronal field agrees with an analytic force-free field when boundary data for the analytic field are used; demonstrated that it is possible to determine active-region coronal magnetic fields from photospheric measurements, by computing the coronal field above active region 5747 on 20 October 1989, AR6919 on 15 November 1991, and AR7260 on 18 August 1992, from data taken with the Stokes Polarimeter at Mees Solar Observatory, University of Hawaii; started to analyze active region 7201 on 19 June 1992 using measurements made with the Advanced Stokes Polarimeter at NSO/Sac Peak; investigated the effects of imperfections in the photospheric data on the computed coronal magnetic field; documented the coronal field structure of AR5747 and compared it to the morphology of footpoint emission in a flare, showing that the 'high- pressure' H-alpha footpoints are connected by coronal field lines; shown that the variation of magnetic field strength along current-carrying field lines is significantly different from the variation in a potential field, and that the resulting near-constant area of elementary flux tubes is consistent with observations; begun to develop realistic models of coronal fields which can be used to study flare trigger mechanisms; demonstrated that

The Lie Bracket of Adapted Vector Fields on Wiener Spaces

International Nuclear Information System (INIS)

Driver, B. K.

1999-01-01

Let W(M) be the based (at o element of M) path space of a compact Riemannian manifold M equipped with Wiener measure ν . This paper is devoted to considering vector fields on W(M) of the form X s h (σ )=P s (σ)h s (σ ) where P s (σ ) denotes stochastic parallel translation up to time s along a Wiener path σ element of W(M) and {h s } i sanelementof [0,1] is an adapted T o M -valued process on W(M). It is shown that there is a large class of processes h (called adapted vector fields) for which we may view X h as first-order differential operators acting on functions on W(M) . Moreover, if h and k are two such processes, then the commutator of X h with X k is again a vector field on W(M) of the same form

ON A PROLONGATION CONSTRUCTION FOR LOCAL NON-DIVERGENT VECTOR FIELDS ON Rn

Directory of Open Access Journals (Sweden)

A. M. Lukatsky

2015-01-01

Full Text Available The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.

On the interpretation of different flow vectors of different ion species in the magnetospheric boundary layer

International Nuclear Information System (INIS)

Lundin, R.; Stasiewicz, K.; Hultqvist, B.

1986-05-01

Recent measurements of the ion composition in the magnetospheric boundary layer indicate that the boundary layer may contain clouds of magnetosheath plasma which are gradually becoming mixed with the magnetospheric plasma. A significant difference between flow vectors of different ion species (ca50-100 km/s) implies that an ideal MHD equation E+VxB=0, does not describe the macroscopic plasma flow inside such inhomogeneities. An analysis based on the first order drift theory indicates that gradients of the partial ion pressure and of the magnetic field could induce differential ion drifts comparable in magnitude to the electric drift velocity. We discuss some implications of these results on the physics of solar wind-magnetosphere interactions. (authors)

Localization of vector field on dynamical domain wall

Directory of Open Access Journals (Sweden)

Masafumi Higuchi

2017-03-01

Full Text Available In the previous works (arXiv:1202.5375 and arXiv:1402.1346, the dynamical domain wall, where the four dimensional FRW universe is embedded in the five dimensional space–time, has been realized by using two scalar fields. In this paper, we consider the localization of vector field in three formulations. The first formulation was investigated in the previous paper (arXiv:1510.01099 for the U(1 gauge field. In the second formulation, we investigate the Dvali–Shifman mechanism (arXiv:hep-th/9612128, where the non-abelian gauge field is confined in the bulk but the gauge symmetry is spontaneously broken on the domain wall. In the third formulation, we investigate the Kaluza–Klein modes coming from the five dimensional graviton. In the Randall–Sundrum model, the graviton was localized on the brane. We show that the (5,μ components (μ=0,1,2,3 of the graviton are also localized on the domain wall and can be regarded as the vector field on the domain wall. There are, however, some corrections coming from the bulk extra dimension if the domain wall universe is expanding.

Reproduction of pressure field in ultrasonic-measurement-integrated simulation of blood flow.

Science.gov (United States)

Funamoto, Kenichi; Hayase, Toshiyuki

2013-07-01

Ultrasonic-measurement-integrated (UMI) simulation of blood flow is used to analyze the velocity and pressure fields by applying feedback signals of artificial body forces based on differences of Doppler velocities between ultrasonic measurement and numerical simulation. Previous studies have revealed that UMI simulation accurately reproduces the velocity field of a target blood flow, but that the reproducibility of the pressure field is not necessarily satisfactory. In the present study, the reproduction of the pressure field by UMI simulation was investigated. The effect of feedback on the pressure field was first examined by theoretical analysis, and a pressure compensation method was devised. When the divergence of the feedback force vector was not zero, it influenced the pressure field in the UMI simulation while improving the computational accuracy of the velocity field. Hence, the correct pressure was estimated by adding pressure compensation to remove the deteriorating effect of the feedback. A numerical experiment was conducted dealing with the reproduction of a synthetic three-dimensional steady flow in a thoracic aneurysm to validate results of the theoretical analysis and the proposed pressure compensation method. The ability of the UMI simulation to reproduce the pressure field deteriorated with a large feedback gain. However, by properly compensating the effects of the feedback signals on the pressure, the error in the pressure field was reduced, exhibiting improvement of the computational accuracy. It is thus concluded that the UMI simulation with pressure compensation allows for the reproduction of both velocity and pressure fields of blood flow. Copyright © 2012 John Wiley & Sons, Ltd.

Computation of Surface Integrals of Curl Vector Fields

Science.gov (United States)

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…

Experimental study of flow field characteristics on bed configurations in the pebble bed reactor

International Nuclear Information System (INIS)

Jia, Xinlong; Gui, Nan; Yang, Xingtuan; Tu, Jiyuan; Jia, Haijun; Jiang, Shengyao

2017-01-01

Highlights: • PTV study of flow fields of pebble bed reactor with different configurations are carried out. • Some criteria are proposed to quantify vertical velocity field and flow uniformity. • The effect of different pebble bed configurations is also compared by the proposed criteria. • The displacement thickness is used analogically to analyze flow field characteristics. • The effect of mass flow variation in the stagnated region of the funnel flow is measured. - Abstract: The flow field characteristics are of fundamental importance in the design work of the pebble bed high temperature gas cooled reactor (HTGR). The different effects of bed configurations on the flow characteristics of pebble bed are studied through the PTV (Particle Tracking Velocimetry) experiment. Some criteria, e.g. flow uniformity (σ) and mass flow level (α), are proposed to estimate vertical velocity field and compare the bed configurations. The distribution of the Δθ (angle difference between the individual particle velocity and the velocity vector sum of all particles) is also used to estimate the resultant motion consistency level. Moreover, for each bed configuration, the thickness of displacement is analyzed to measure the effect of the funnel flow zone based on the boundary layer theory. Detailed information shows the quantified characteristics of bed configuration effects on flow uniformity and other characteristics; and the sequence of levels of each estimation criterion is obtained for all bed configurations. In addition, a good design of the pebble bed configuration is suggested and these estimation criteria can be also applied and adopted in testing other geometry designs of pebble bed.

A late time accelerated FRW model with scalar and vector fields via Noether symmetry

Directory of Open Access Journals (Sweden)

Babak Vakili

2014-11-01

Full Text Available We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW model, a scalar field with potential function V(ϕ with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(ϕ. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion. Keywords: Noether symmetry, Scalar field cosmology, Vector field cosmology

In-Flight spacecraft magnetic field monitoring using scalar/vector gradiometry

DEFF Research Database (Denmark)

Primdahl, Fritz; Risbo, Torben; Merayo, José M.G.

2006-01-01

Earth magnetic field mapping from planetary orbiting satellites requires a spacecraft magnetic field environment control program combined with the deployment of the magnetic sensors on a boom in order to reduce the measurement error caused by the local spacecraft field. Magnetic mapping missions...... (Magsat, Oersted, CHAMP, SAC-C MMP and the planned ESA Swarm project) carry a vector magnetometer and an absolute scalar magnetometer for in-flight calibration of the vector magnetometer scale values and for monitoring of the inter-axes angles and offsets over time intervals from months to years...... sensors onboard the Oersted satellite. For Oersted, a large difference between the pre-flight determined spacecraft magnetic field and the in-flight estimate exists causing some concern about the general applicability of the dual sensors technique....

Screening vector field modifications of general relativity

International Nuclear Information System (INIS)

Beltrán Jiménez, Jose; Delvas Fróes, André Luís; Mota, David F.

2013-01-01

A screening mechanism for conformal vector–tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a non-null value in low density environments. Such process occurs due to a spontaneous symmetry breaking mechanism and gives rise to both the screening of fifth forces as well as Lorentz violations. The cosmology and local constraints are also computed

Near-field/far-field array manifold of an acoustic vector-sensor near a reflecting boundary.

Science.gov (United States)

Wu, Yue Ivan; Lau, Siu-Kit; Wong, Kainam Thomas

2016-06-01

The acoustic vector-sensor (a.k.a. the vector hydrophone) is a practical and versatile sound-measurement device, with applications in-room, open-air, or underwater. It consists of three identical uni-axial velocity-sensors in orthogonal orientations, plus a pressure-sensor-all in spatial collocation. Its far-field array manifold [Nehorai and Paldi (1994). IEEE Trans. Signal Process. 42, 2481-2491; Hawkes and Nehorai (2000). IEEE Trans. Signal Process. 48, 2981-2993] has been introduced into the technical field of signal processing about 2 decades ago, and many direction-finding algorithms have since been developed for this acoustic vector-sensor. The above array manifold is subsequently generalized for outside the far field in Wu, Wong, and Lau [(2010). IEEE Trans. Signal Process. 58, 3946-3951], but only if no reflection-boundary is to lie near the acoustic vector-sensor. As for the near-boundary array manifold for the general case of an emitter in the geometric near field, the far field, or anywhere in between-this paper derives and presents that array manifold in terms of signal-processing mathematics. Also derived here is the corresponding Cramér-Rao bound for azimuth-elevation-distance localization of an incident emitter, with the reflected wave shown to play a critical role on account of its constructive or destructive summation with the line-of-sight wave. The implications on source localization are explored, especially with respect to measurement model mismatch in maximum-likelihood direction finding and with regard to the spatial resolution between coexisting emitters.

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

Science.gov (United States)

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.

Inflationary buildup of a vector field condensate and its cosmological consequences

International Nuclear Information System (INIS)

Sanchez, Juan C. Bueno; Dimopoulos, Konstantinos

2014-01-01

Light vector fields during inflation obtain a superhorizon perturbation spectrum when their conformal invariance is appropriately broken. Such perturbations, by means of some suitable mechanism (e.g. the vector curvaton mechanism), can contribute to the curvatue perturbation in the Universe and produce characteristic signals, such as statistical anisotropy, on the microwave sky, most recently surveyed by the Planck satellite mission. The magnitude of such characteristic features crucially depends on the magnitude of the vector condensate generated during inflation. However, in the vast majority of the literature the expectation value of this condensate has so-far been taken as a free parameter, lacking a definite prediction or a physically motivated estimate. In this paper, we study the stochastic evolution of the vector condensate and obtain an estimate for its magnitude. Our study is mainly focused in the supergravity inspired case when the kinetic function and mass of the vector boson is time-varying during inflation, but other cases are also explored such as a parity violating axial theory or a non-minimal coupling between the vector field and gravity. As an example, we apply our findings in the context of the vector curvaton mechanism and contrast our results with current observations

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Limit sets and global dynamic for 2-D divergence-free vector fields

International Nuclear Information System (INIS)

Marzougui, H.

2004-08-01

T. Ma and S. Wang studied the global structure of regular divergence-free vector fields on compact surfaces with or without boundary. This paper extends their study to the general case of divergence-free vector fields (regular or not) on closed surfaces and gives as a consequence a simple proof of their results. (author)

Derivatives, forms and vector fields on the κ-deformed Euclidean space

International Nuclear Information System (INIS)

Dimitrijevic, Marija; Moeller, Lutz; Tsouchnika, Efrossini

2004-01-01

The model of κ-deformed space is an interesting example of a noncommutative space, since it allows a deformed symmetry. In this paper, we present new results concerning different sets of derivatives on the coordinate algebra of κ-deformed Euclidean space. We introduce a differential calculus with two interesting sets of one-forms and higher-order forms. The transformation law of vector fields is constructed in accordance with the transformation behaviour of derivatives. The crucial property of the different derivatives, forms and vector fields is that in an n-dimensional spacetime there are always n of them. This is the key difference with respect to conventional approaches, in which the differential calculus is (n + 1)-dimensional. This work shows that derivative-valued quantities such as derivative-valued vector fields appear in a generic way on noncommutative spaces

Linearization of germs of hyperbolic vector fields

NARCIS (Netherlands)

Bonckaert, P; Naudot, [No Value; Yang, JZ

2003-01-01

We develop a normal form to express asymptotically a conjugacy between a germ of resonant vector field and its linear part. We show that such an asymptotic expression can be written in terms of functions of the Logarithmic Mourtada type. To cite this article: P Bonckaert et al., C. R. Acad. Sci.

Electric field vector measurements in a surface ionization wave discharge

International Nuclear Information System (INIS)

Goldberg, Benjamin M; Adamovich, Igor V; Lempert, Walter R; Böhm, Patrick S; Czarnetzki, Uwe

2015-01-01

This work presents the results of time-resolved electric field vector measurements in a short pulse duration (60 ns full width at half maximum), surface ionization wave discharge in hydrogen using a picosecond four-wave mixing technique. Electric field vector components are measured separately, using pump and Stokes beams linearly polarized in the horizontal and vertical planes, and a polarizer placed in front of the infrared detector. The time-resolved electric field vector is measured at three different locations across the discharge gap, and for three different heights above the alumina ceramic dielectric surface, ∼100, 600, and 1100 μm (total of nine different locations). The results show that after breakdown, the discharge develops as an ionization wave propagating along the dielectric surface at an average speed of 1 mm ns −1 . The surface ionization wave forms near the high voltage electrode, close to the dielectric surface (∼100 μm). The wave front is characterized by significant overshoot of both vertical and horizontal electric field vector components. Behind the wave front, the vertical field component is rapidly reduced. As the wave propagates along the dielectric surface, it also extends further away from the dielectric surface, up to ∼1 mm near the grounded electrode. The horizontal field component behind the wave front remains quite significant, to sustain the electron current toward the high voltage electrode. After the wave reaches the grounded electrode, the horizontal field component experiences a secondary rise in the quasi-dc discharge, where it sustains the current along the near-surface plasma sheet. The measurement results indicate presence of a cathode layer formed near the grounded electrode with significant cathode voltage fall, ≈3 kV, due to high current density in the discharge. The peak reduced electric field in the surface ionization wave is 85–95 Td, consistent with dc breakdown field estimated from the Paschen

Null vectors in superconformal quantum field theory

International Nuclear Information System (INIS)

Huang Chaoshang

1993-01-01

The superspace formulation of the N=1 superconformal field theory and superconformal Ward identities are used to give a precise definition of fusion. Using the fusion procedure, superconformally covariant differential equations are derived and consequently a complete and straightforward algorithm for finding null vectors in Verma modules of the Neveu-Schwarz algebra is given. (orig.)

On a class of vector fields

Directory of Open Access Journals (Sweden)

Galimzian G. Islamov

2015-12-01

Full Text Available It is shown that a simple postulate “The displacement field of the vacuum is a normalized electric field”, is equivalent to three parametric representation of the displacement field of the vacuum: $$ u(x;t = P(x \\cos k(xt + Q(x \\sin k(xt. $$ Here $t$ — time; $k(x$ — frequency vibrations at the point of three-dimensional Euclidean space; $P(x, Q(x$ — a pair of stationary orthonormal vector fields; $(k,P, Q$ — parameter list of the displacement field. In this case, the normalization factor has dimension $T^{-2}$. The speed of the displacement field $$ v(x;t = \\frac{\\partial u(x;t}{\\partial t} = k(x(Q(x \\cos k(xt - P(x \\sin k(xt. $$ The electric field corresponding to this distribution of the displacement field of vacuum, is given by the formula $$ E(x;t = -\\frac{\\partial v(x;t}{\\partial t} = k^2(xu(x;t. $$ Moreover, the magnetic induction $$ B(x;t = \\mathop{\\mathrm{rot }} v(x; t. $$ These constructions are used in the determination of local and global solutions of Maxwell's equations describing the dynamics of electromagnetic fields.

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

Science.gov (United States)

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.

Motion Vector field improvement for picture rate conversion with reduced Halo

NARCIS (Netherlands)

Mertens, M.J.W.; Haan, de G.; Girod, B.; Bouman, C.A.; Steinbach, E.G.

2001-01-01

The quality of the interpolated images in picture rate upconversion is predominantly dependent on the accuracy of the motion vector fields. Block based MEs typically yield incorrect vectors in occlusion areas, which leads to an annoying halo in the upconverted video sequences. In the past we have

Vector blood velocity estimation in medical ultrasound

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt; Gran, Fredrik; Udesen, Jesper

2006-01-01

Two methods for making vector velocity estimation in medical ultrasound are presented. All of the techniques can find both the axial and transverse velocity in the image and can be used for displaying both the correct velocity magnitude and direction. The first method uses a transverse oscillation...... in the ultrasound field to find the transverse velocity. In-vivo examples from the carotid artery are shown, where complex turbulent flow is found in certain parts of the cardiac cycle. The second approach uses directional beam forming along the flow direction to estimate the velocity magnitude. Using a correlation...... search can also yield the direction, and the full velocity vector is thereby found. An examples from a flow rig is shown....

On the use of the Kodama vector field in spherically symmetric dynamical problems

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan [MTA KFKI, Reszecske- es Magfizikai Kutatointezet, H-1121 Budapest, Konkoly Thege Miklos ut 29-33, (Hungary)

2006-01-07

It is shown that by making use of the Kodama vector field, as a preferred time evolution vector field, in spherically symmetric dynamical systems unexpected simplifications arise. In particular, the evolution equations relevant for the case of a massless scalar field minimally coupled to gravity are investigated. The simplest form of these equations in the 'canonical gauge' is known to possess the character of a mixed first-order elliptic-hyperbolic system. The advantages related to the use of the Kodama vector field are twofold although they show up simultaneously. First, it is found that the true degrees of freedom separate. Second, a subset of the field equations possessing the form of a first-order symmetric hyperbolic system for these preferred degrees of freedom is singled out. It is also demonstrated, in the appendix, that the above results generalize straightforwardly to the case of a generic self-interacting scalar field.

Vector-field statistics for the analysis of time varying clinical gait data.

Science.gov (United States)

Donnelly, C J; Alexander, C; Pataky, T C; Stannage, K; Reid, S; Robinson, M A

2017-01-01

In clinical settings, the time varying analysis of gait data relies heavily on the experience of the individual(s) assessing these biological signals. Though three dimensional kinematics are recognised as time varying waveforms (1D), exploratory statistical analysis of these data are commonly carried out with multiple discrete or 0D dependent variables. In the absence of an a priori 0D hypothesis, clinicians are at risk of making type I and II errors in their analyis of time varying gait signatures in the event statistics are used in concert with prefered subjective clinical assesment methods. The aim of this communication was to determine if vector field waveform statistics were capable of providing quantitative corroboration to practically significant differences in time varying gait signatures as determined by two clinically trained gait experts. The case study was a left hemiplegic Cerebral Palsy (GMFCS I) gait patient following a botulinum toxin (BoNT-A) injection to their left gastrocnemius muscle. When comparing subjective clinical gait assessments between two testers, they were in agreement with each other for 61% of the joint degrees of freedom and phases of motion analysed. For tester 1 and tester 2, they were in agreement with the vector-field analysis for 78% and 53% of the kinematic variables analysed. When the subjective analyses of tester 1 and tester 2 were pooled together and then compared to the vector-field analysis, they were in agreement for 83% of the time varying kinematic variables analysed. These outcomes demonstrate that in principle, vector-field statistics corroborates with what a team of clinical gait experts would classify as practically meaningful pre- versus post time varying kinematic differences. The potential for vector-field statistics to be used as a useful clinical tool for the objective analysis of time varying clinical gait data is established. Future research is recommended to assess the usefulness of vector-field analyses

Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation

Directory of Open Access Journals (Sweden)

Mitsuo Kato

2018-01-01

Full Text Available A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.

Oscillatory regime in the multidimensional homogeneous cosmological models induced by a vector field

International Nuclear Information System (INIS)

Benini, R; Kirillov, A A; Montani, Giovanni

2005-01-01

We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analysing the Hamiltonian equations we derive the Poincare return map associated with the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a four-dimensional spacetime, the oscillatory regime here constructed overlaps the usual Belinski-Khalatnikov-Liftshitz one

Signed zeros of Gaussian vector fields - density, correlation functions and curvature

CERN Document Server

Foltin, G

2003-01-01

We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one- and two-point functions. The zeros of a two-dimensional Gaussian vector field model the distribution of topological defects in the high-temperature phase of two-dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.

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

International Nuclear Information System (INIS)

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

1975-01-01

We present the results of an extensive analysis of plasma and magnetic field data from Pioneer 7 taken in the geomagnetic tail approximately 1000 R/sub E/ 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

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

Science.gov (United States)

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.

Identification method for gas-liquid two-phase flow regime based on singular value decomposition and least square support vector machine

International Nuclear Information System (INIS)

Sun Bin; Zhou Yunlong; Zhao Peng; Guan Yuebo

2007-01-01

Aiming at the non-stationary characteristics of differential pressure fluctuation signals of gas-liquid two-phase flow, and the slow convergence of learning and liability of dropping into local minima for BP neural networks, flow regime identification method based on Singular Value Decomposition (SVD) and Least Square Support Vector Machine (LS-SVM) is presented. First of all, the Empirical Mode Decomposition (EMD) method is used to decompose the differential pressure fluctuation signals of gas-liquid two-phase flow into a number of stationary Intrinsic Mode Functions (IMFs) components from which the initial feature vector matrix is formed. By applying the singular vale decomposition technique to the initial feature vector matrixes, the singular values are obtained. Finally, the singular values serve as the flow regime characteristic vector to be LS-SVM classifier and flow regimes are identified by the output of the classifier. The identification result of four typical flow regimes of air-water two-phase flow in horizontal pipe has shown that this method achieves a higher identification rate. (authors)

The Vector Electric Field Instrument on the C/NOFS Satellite

Science.gov (United States)

Pfaff, R.; Kujawski, J.; Uribe, P.; Bromund, K.; Fourre, R.; Acuna, M.; Le, G.; Farrell, W.; Holzworth, R.; McCarthy, M.;

Performance of a vanadium redox flow battery with and without flow fields

International Nuclear Information System (INIS)

Xu, Q.; Zhao, T.S.; Zhang, C.

2014-01-01

Highlights: • The performances of a VRFB with/without flow fields are compared. • The respective maximum power efficiency occurs at different flow rates. • The battery with flow fields Exhibits 5% higher energy efficiency. - Abstract: A flow field is an indispensable component for fuel cells to macroscopically distribute reactants onto electrodes. However, it is still unknown whether flow fields are also required in all-vanadium redox flow batteries (VRFBs). In this work, the performance of a VRFB with flow fields is analyzed and compared with the performance of a VRFB without flow fields. It is demonstrated that the battery with flow fields has a higher discharge voltage at higher flow rates, but exhibits a larger pressure drop. The maximum power-based efficiency occurs at different flow rates for the both batteries with and without flow fields. It is found that the battery with flow fields Exhibits 5% higher energy efficiency than the battery without flow fields, when operating at the flow rates corresponding to each battery's maximum power-based efficiency. Therefore, the inclusion of flow fields in VRFBs can be an effective approach for improving system efficiency

Interactive exploratory visualization of 2D vector fields

NARCIS (Netherlands)

Isenberg, Tobias; Everts, Maarten H.; Grubert, Jens; Carpendale, Sheelagh

In this paper we present several techniques to interactively explore representations of 2D vector fields. Through a set of simple hand postures used on large, touch-sensitive displays, our approach allows individuals to custom design glyphs (arrows, lines, etc.) that best reveal patterns of the

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

Science.gov (United States)

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.

Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11

International Nuclear Information System (INIS)

Wang, S.; Yu, P.

2006-01-01

In this article, a systematic procedure has been explored to studying general Z q -equivariant planar polynomial Hamiltonian vector fields for the maximal number of closed orbits and the maximal number of limit cycles after perturbation. Following the procedure by taking special consideration of Z 12 -equivariant vector fields of degree 11, the maximal of 99 closed orbits are obtained under a well-defined coefficient group. Consequently, perturbation parameter control in limit cycle computation leads to the existence of 121 limit cycles in the perturbed Hamiltonian vector field, which gives rise to the lower bound of Hilbert number of 11th-order systems as H(11) ≥ 11 2 . Two conjectures are proposed regarding the maximal number of closed orbits for equivariant polynomial Hamiltonian vector fields and the maximal number of limit cycles bifurcated from the well defined Hamiltonian vector fields after perturbation

Anomalous scaling of a passive vector advected by the Navier-Stokes velocity field

International Nuclear Information System (INIS)

Jurcisinova, E; Jurcisin, M; Remecky, R

2009-01-01

Using the field theoretic renormalization group and the operator-product expansion, the model of a passive vector field (a weak magnetic field in the framework of the kinematic MHD) advected by the velocity field which is governed by the stochastic Navier-Stokes equation with the Gaussian random stirring force δ-correlated in time and with the correlator proportional to k 4-d-2ε is investigated to the first order in ε (one-loop approximation). It is shown that the single-time correlation functions of the advected vector field have anomalous scaling behavior and the corresponding exponents are calculated in the isotropic case, as well as in the case with the presence of large-scale anisotropy. The hierarchy of the anisotropic critical dimensions is briefly discussed and the persistence of the anisotropy inside the inertial range is demonstrated on the behavior of the skewness and hyperskewness (dimensionless ratios of correlation functions) as functions of the Reynolds number Re. It is shown that even though the present model of a passive vector field advected by the realistic velocity field is mathematically more complicated than, on one hand, the corresponding models of a passive vector field advected by 'synthetic' Gaussian velocity fields and, on the other hand, than the corresponding model of a passive scalar quantity advected by the velocity field driven by the stochastic Navier-Stokes equation, the final one-loop approximate asymptotic scaling behavior of the single-time correlation or structure functions of the advected fields of all models are defined by the same anomalous dimensions (up to normalization)

Liquid metal flow measurement by neutron radiography

International Nuclear Information System (INIS)

Takenaka, N.; Ono, A.; Matsubayashi, M.; Tsuruno, A.

1996-01-01

Visualization of a liquid metal flow and image processing methods to measure the vector field are carried out by real-time neutron radiography. The JRR-3M real-time thermal neutron radiography facility in the Japan Atomic Energy Research Institute was used. Lead-bismuth eutectic was used as a working fluid. Particles made from a gold-cadmium intermetallic compound (AuCd 3 ) were used as the tracer for the visualization. The flow vector field was obtained by image processing methods. It was shown that the liquid metal flow vector field was obtainable by real-time neutron radiography when the attenuation of neutron rays due to the liquid metal was less than l/e and the particle size of the tracer was larger than one image element size digitized for the image processing. (orig.)

Non-existence of limit cycles for planar vector fields

Directory of Open Access Journals (Sweden)

Jaume Gine

2014-03-01

Full Text Available This article presents sufficient conditions for the non-existence of limit cycles for planar vector fields. Classical methods for the nonexistence of limit cycles are connected with the theory developed here.

The Local Stellar Velocity Field via Vector Spherical Harmonics

Science.gov (United States)

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

Energy-momentum tensor of intermediate vector bosons in an external electromagnetic field

International Nuclear Information System (INIS)

Mostepanenko, V.M.; Sokolov, I.Yu.

1988-01-01

Expressions are obtained for the canonical and metric energy-momentum tensors of the vector field of intermediate bosons in an external electromagnetic field. It is shown that in the case of a gyromagnetic ratio not equal to unity the energy-momentum tensor cannot be symmetrized on its indices, and an additional term proportional to the anomalous magnetic moment appears in the conservation laws. A modification of the canonical formalism for scalar and vector fields in an external field is proposed in accordance with which the Hamiltonian density is equal to the 00 component of the energy-momentum tensor. An expression for the energy-momentum tensor of a closed system containing a gauge field of intermediate bosons and an electromagnetic field is obtained

Comments on conformal Killing vector fields and quantum field theory

International Nuclear Information System (INIS)

Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.

1982-01-01

We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space

Achievement of needle-like focus by engineering radial-variant vector fields.

Science.gov (United States)

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.

Numerical investigation of renormalization group equations in a model of vector field advected by anisotropic stochastic environment

International Nuclear Information System (INIS)

Busa, J.; Ajryan, Eh.A.; Jurcisinova, E.; Jurcisin, M.; Remecky, R.

2009-01-01

Using the field-theoretic renormalization group, the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passive transverse vector field advected by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and the borderline spatial dimension d e (1,3] below which the stability of the scaling regime is not present is found as a function of anisotropy parameters

3-D Vector Flow Estimation With Row–Column-Addressed Arrays

DEFF Research Database (Denmark)

Holbek, Simon; Christiansen, Thomas Lehrmann; Stuart, Matthias Bo

2016-01-01

Simulation and experimental results from 3-D vector flow estimations for a 62 + 62 2-D row–column (RC) array with integrated apodization are presented. A method for implementing a 3-D transverse oscillation (TO) velocity estimator on a 3-MHz RC array is developed and validated. First, a parametric...... mean bias B˜ and mean standard deviation σ˜ . Second, the optimal parameter configuration is implemented on the prototype RC probe connected to the experimental ultrasound scanner SARUS. Results from measurements conducted in a flow-rig system containing a constant laminar flow and a straight.......7, −0.9, 0.4)% with a relative standard deviation of (8.7, 5.1, 0.8)% for (vx , vy, vz). The estimated peak velocity is 48.5 ± 3 cm/s giving a −3% bias. The out-of-plane velocity component perpendicular to the cross section is used to estimate volumetric flow rates in the flow rig at a 90° beam...

Transitive Lie algebras of vector fields: an overview

NARCIS (Netherlands)

Draisma, J.

2011-01-01

This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on

Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory of Gravitation

International Nuclear Information System (INIS)

Shabbir, Ghulam; Khan, Suhail

2010-01-01

In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)

The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads

International Nuclear Information System (INIS)

Dai, H.L.; Wang, X.

2006-01-01

In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed

Apparatus and method for transfer of information by means of a curl-free magnetic vector potential field

International Nuclear Information System (INIS)

Gelinas, R.C.

1984-01-01

A system for transmission of information using a curl-free magnetic vector potential radiation field. The system includes current-carrying apparatus for generating a magnetic vector potential field with a curl-free component coupled to apparatus for modulating the current applied to the field generating apparatus. Receiving apparatus includes a detector with observable properties that vary with the application of an applied curl-free magnetic vector potential field. Analyzing apparatus for determining the information content of modulation imposed on the curl-free vector potential field can be established in materials that are not capable of transmitting more common electromagnetic radiation

Geometric Representations of Condition Queries on Three-Dimensional Vector Fields

Science.gov (United States)

Henze, Chris

1999-01-01

Condition queries on distributed data ask where particular conditions are satisfied. It is possible to represent condition queries as geometric objects by plotting field data in various spaces derived from the data, and by selecting loci within these derived spaces which signify the desired conditions. Rather simple geometric partitions of derived spaces can represent complex condition queries because much complexity can be encapsulated in the derived space mapping itself A geometric view of condition queries provides a useful conceptual unification, allowing one to intuitively understand many existing vector field feature detection algorithms -- and to design new ones -- as variations on a common theme. A geometric representation of condition queries also provides a simple and coherent basis for computer implementation, reducing a wide variety of existing and potential vector field feature detection techniques to a few simple geometric operations.

Nonparaxial propagation and focusing properties of azimuthal-variant vector fields diffracted by an annular aperture.

Science.gov (United States)

Gu, Bing; Xu, Danfeng; Pan, Yang; Cui, Yiping

2014-07-01

Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.

Three ways to show 3D fluid flow

NARCIS (Netherlands)

Wijk, van J.J.; Hin, A.J.S.; Leeuw, de W.C.; Post, F.H.

1994-01-01

Visualizing 3D fluid flow fields presents a challenge to scientific visualization, mainly because no natural visual representation of 3D vector fields exists. We can readily recognize geometric objects, color, and texture: unfortunately for computational fluid dynamics (CFD) researchers, vector

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

Science.gov (United States)

Eppard, W. M.; Grossman, B.

1993-01-01

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

Algebraic structure of general electromagnetic fields and energy flow

International Nuclear Information System (INIS)

Hacyan, Shahen

2011-01-01

Highlights: → Algebraic structure of general electromagnetic fields in stationary spacetime. → Eigenvalues and eigenvectors of the electomagnetic field tensor. → Energy-momentum in terms of eigenvectors and Killing vector. → Explicit form of reference frame with vanishing Poynting vector. → Application of formalism to Bessel beams. - Abstract: The algebraic structures of a general electromagnetic field and its energy-momentum tensor in a stationary space-time are analyzed. The explicit form of the reference frame in which the energy of the field appears at rest is obtained in terms of the eigenvectors of the electromagnetic tensor and the existing Killing vector. The case of a stationary electromagnetic field is also studied and a comparison is made with the standard short-wave approximation. The results can be applied to the general case of a structured light beams, in flat or curved spaces. Bessel beams are worked out as example.

Infrared Dual-Line Hanle Diagnostic of the Coronal Vector Magnetic Field

Energy Technology Data Exchange (ETDEWEB)

Dima, Gabriel I.; Kuhn, Jeffrey R. [Institute for Astronomy, University of Hawaii, Pukalani, HI (United States); Berdyugina, Svetlana V., E-mail: gdima@hawaii.edu [Institute for Astronomy, University of Hawaii, Pukalani, HI (United States); Kiepenheuer Institut fuer Sonnenphysik, Freiburg (Germany); Predictive Science Inc., San Diego, CA (United States)

2016-04-20

Measuring the coronal vector magnetic field is still a major challenge in solar physics. This is due to the intrinsic weakness of the field (e.g., ~4G at a height of 0.1R⊙ above an active region) and the large thermal broadening of coronal emission lines. We propose using concurrent linear polarization measurements of near-infrared forbidden and permitted lines together with Hanle effect models to calculate the coronal vector magnetic field. In the unsaturated Hanle regime both the direction and strength of the magnetic field affect the linear polarization, while in the saturated regime the polarization is insensitive to the strength of the field. The relatively long radiative lifetimes of coronal forbidden atomic transitions implies that the emission lines are formed in the saturated Hanle regime and the linear polarization is insensitive to the strength of the field. By combining measurements of both forbidden and permitted lines, the direction and strength of the field can be obtained. For example, the SiX 1.4301 μm line shows strong linear polarization and has been observed in emission over a large field-of-view (out to elongations of 0.5 R⊙). Here we describe an algorithm that combines linear polarization measurements of the SiX 1.4301 μm forbidden line with linear polarization observations of the HeI 1.0830 μm permitted coronal line to obtain the vector magnetic field. To illustrate the concept we assume that the emitting gas for both atomic transitions is located in the plane of the sky. The further development of this method and associated tools will be a critical step toward interpreting the high spectral, spatial and temporal infrared spectro-polarimetric measurements that will be possible when the Daniel K. Inouye Solar Telescope (DKIST) is completed in 2019.

Improvement of vector compensation method for vehicle magnetic distortion field

Energy Technology Data Exchange (ETDEWEB)

Pang, Hongfeng, E-mail: panghongfeng@126.com; Zhang, Qi; Li, Ji; Luo, Shitu; Chen, Dixiang; Pan, Mengchun; Luo, Feilu

2014-03-15

Magnetic distortions such as eddy-current field and low frequency magnetic field have not been considered in vector compensation methods. A new compensation method is proposed to suppress these magnetic distortions and improve compensation performance, in which the magnetic distortions related to measurement vectors and time are considered. The experimental system mainly consists of a three-axis fluxgate magnetometer (DM-050), an underwater vehicle and a proton magnetometer, in which the scalar value of magnetic field is obtained with the proton magnetometer and considered to be the true value. Comparing with traditional compensation methods, experimental results show that the magnetic distortions can be further reduced by two times. After compensation, error intensity and RMS error are reduced from 11684.013 nT and 7794.604 nT to 16.219 nT and 5.907 nT respectively. It suggests an effective way to improve the compensation performance of magnetic distortions. - Highlights: • A new vector compensation method is proposed for vehicle magnetic distortion. • The proposed model not only includes magnetometer error but also considers magnetic distortion. • Compensation parameters are computed directly by solving nonlinear equations. • Compared with traditional methods, the proposed method is not related with rotation angle rate. • Error intensity and RMS error can be reduced to 1/2 of the error with traditional methods.

Improvement of vector compensation method for vehicle magnetic distortion field

International Nuclear Information System (INIS)

Pang, Hongfeng; Zhang, Qi; Li, Ji; Luo, Shitu; Chen, Dixiang; Pan, Mengchun; Luo, Feilu

2014-01-01

Magnetic distortions such as eddy-current field and low frequency magnetic field have not been considered in vector compensation methods. A new compensation method is proposed to suppress these magnetic distortions and improve compensation performance, in which the magnetic distortions related to measurement vectors and time are considered. The experimental system mainly consists of a three-axis fluxgate magnetometer (DM-050), an underwater vehicle and a proton magnetometer, in which the scalar value of magnetic field is obtained with the proton magnetometer and considered to be the true value. Comparing with traditional compensation methods, experimental results show that the magnetic distortions can be further reduced by two times. After compensation, error intensity and RMS error are reduced from 11684.013 nT and 7794.604 nT to 16.219 nT and 5.907 nT respectively. It suggests an effective way to improve the compensation performance of magnetic distortions. - Highlights: • A new vector compensation method is proposed for vehicle magnetic distortion. • The proposed model not only includes magnetometer error but also considers magnetic distortion. • Compensation parameters are computed directly by solving nonlinear equations. • Compared with traditional methods, the proposed method is not related with rotation angle rate. • Error intensity and RMS error can be reduced to 1/2 of the error with traditional methods

HEIGHT VARIATION OF THE VECTOR MAGNETIC FIELD IN SOLAR SPICULES

Energy Technology Data Exchange (ETDEWEB)

Suárez, D. Orozco; Ramos, A. Asensio; Bueno, J. Trujillo, E-mail: dorozco@iac.es [Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife (Spain)

2015-04-20

Proving the magnetic configuration of solar spicules has hitherto been difficult due to the lack of spatial resolution and image stability during off-limb ground-based observations. We report spectropolarimetric observations of spicules taken in the He i 1083 nm spectral region with the Tenerife Infrared Polarimeter II at the German Vacuum Tower Telescope of the Observatorio del Teide (Tenerife, Canary Islands, Spain). The data provide the variation with geometrical height of the Stokes I, Q, U, and V profiles, whose encoded information allows the determination of the magnetic field vector by means of the HAZEL inversion code. The inferred results show that the average magnetic field strength at the base of solar spicules is about 80 gauss, and then it decreases rapidly with height to about 30 gauss at a height of 3000 km above the visible solar surface. Moreover, the magnetic field vector is close to vertical at the base of the chromosphere and has mid-inclinations (about 50°) above 2 Mm height.

Lipschitz estimates for convex functions with respect to vector fields

Directory of Open Access Journals (Sweden)

Valentino Magnani

2012-12-01

Full Text Available We present Lipschitz continuity estimates for a class of convex functions with respect to Hörmander vector fields. These results have been recently obtained in collaboration with M. Scienza, [22].

Magnetic monopole and vector field of the spin 0

International Nuclear Information System (INIS)

Pantyushin, A.A.

2001-01-01

The motion of electrically charged particles in uniform magnetic field by time is considered. It is found out that additional force acting on eclectically charged particle from the spin 0 vector field side is proportional to the magnetic field. Proportion coefficient is equal to eg/4π (g - unknown parameter, determining of the rate and character of source non-preservation) - the analogue of constant thin structure α=e 2 /4π. Obtained results give evidence to suppose that for explanation of indicated experiments the monopole introduction is not essential

Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces

International Nuclear Information System (INIS)

Chu, Chong-Sun; Zumino, B.

1995-01-01

The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail

Migration transformation of two-dimensional magnetic vector and tensor fields

DEFF Research Database (Denmark)

Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

2012-01-01

We introduce a new method of rapid interpretation of magnetic vector and tensor field data, based on ideas of potential field migration which extends the general principles of seismic and electromagnetic migration to potential fields. 2-D potential field migration represents a direct integral...... to the downward continuation of a well-behaved analytical function. We present case studies for imaging of SQUID-based magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from magnetic tensor field migration agree very well with both Euler deconvolution and the known...

Vectorization on the star computer of several numerical methods for a fluid flow problem

Science.gov (United States)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

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

Science.gov (United States)

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.

Rotation invariants of vector fields from orthogonal moments

Czech Academy of Sciences Publication Activity Database

Yang, B.; Kostková, Jitka; Flusser, Jan; Suk, Tomáš; Bujack, R.

2018-01-01

Roč. 74, č. 1 (2018), s. 110-121 ISSN 0031-3203 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Vector field * Total rotation * Invariants * Gaussian–Hermite moments * Zernike moments * Numerical stability Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.582, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0478329.pdf

A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers

Directory of Open Access Journals (Sweden)

Jaume Llibre

2012-06-01

Full Text Available We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields which are volume preserving and possess nontrivial normalizers. Our approach is geometric and coordinate-free and hence it works on any smooth orientable manifold.

Off disk-center potential field calculations using vector magnetograms

Science.gov (United States)

Venkatakrishnan, P.; Gary, G. Allen

1989-01-01

A potential field calculation for off disk-center vector magnetograms that uses all the three components of the measured field is investigated. There is neither any need for interpolation of grid points between the image plane and the heliographic plane nor for an extension or a truncation to a heliographic rectangle. Hence, the method provides the maximum information content from the photospheric field as well as the most consistent potential field independent of the viewing angle. The introduction of polarimetric noise produces a less tolerant extrapolation procedure than using the line-of-sight extrapolation, but the resultant standard deviation is still small enough for the practical utility of this method.

In-Vivo High Dynamic Range Vector Flow Imaging

DEFF Research Database (Denmark)

Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo; Jensen, Jørgen Arendt

2015-01-01

example with a high dynamic velocity range. Velocities with an order of magnitude apart are detected on the femoral artery of a 41 years old healthy individual. Three distinct heart cycles are captured during a 3 secs acquisition. The estimated vector velocities are compared against each other within...... the heart cycle. The relative standard deviation of the measured velocity magnitude between the three peak systoles was found to be 5.11% with a standard deviation on the detected angle of 1.06◦ . In the diastole, it was 1.46% and 6.18◦ , respectively. Results proves that the method is able to estimate flow...

Double gauge invariance and covariantly-constant vector fields in Weyl geometry

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

2014-08-01

The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".

Lovelock vacua with a recurrent null vector field

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello

2018-01-01

Roč. 97, č. 4 (2018), č. článku 044051. ISSN 2470-0010 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Lovelock gravity * recurrent null vector field Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.044051

Lovelock vacua with a recurrent null vector field

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello

2018-01-01

Roč. 97, č. 4 (2018), č. článku 044051. ISSN 2470-0010 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Lovelock gravity * recurrent null vector field Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.97.044051

Flow visualization of a low density hypersonic flow field

International Nuclear Information System (INIS)

Masson, B.S.; Jumper, E.J.; Walters, E.; Segalman, T.Y.; Founds, N.D.

1989-01-01

Characteristics of laser induced iodine fluorescence (LIIF) in low density hypersonic flows are being investigated for use as a diagnostic technique. At low pressures, doppler broadening dominates the iodine absorption profile producing a fluorescence signal that is primarily temperature and velocity dependent. From this dependency, a low pressure flow field has the potential to be mapped for its velocity and temperature fields. The theory for relating iodine emission to the velocity and temperature fields of a hypersonic flow is discussed in this paper. Experimental observations are made of a fluorescencing free expansion and qualitatively related to the theory. 7 refs

Classification of Kantowski-Sachs and Bianchi Type III Space-Times According to Their Killing Vector Fields in Teleparallel Theory of Gravitation

International Nuclear Information System (INIS)

Shabbir, Ghulam; Khan, Suhail

2010-01-01

In this paper we classify Kantowski-Sachs and Bianchi type III space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. (general)

Improved Vector Velocity Estimation using Directional Transverse Oscillation

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt

2015-01-01

A method for estimating vector velocities using transverse oscillation (TO) combined with directional beamforming is presented. Directional Transverse Oscillation (DTO) is selfcalibrating, which increase the estimation accuracy and finds the lateral oscillation period automatically. A normal...... focused field is emitted and the received signals are beamformed in the lateral direction transverse to the ultrasound beam. A lateral oscillation is obtained by having a receive apodization waveform with two separate peaks. The IQ data are obtained by making a Hilbert transform of the directional signal...... transducer with a focal point at 105.6 mm (F#=5) for Vector Flow Imaging (VFI). A 6 mm radius tube in a circulating flow rig was scanned and the parabolic volume flow of 112.7 l/h (peak velocity 0.55 m/s) measured by a Danfoss Magnetic flow meter for reference. Velocity estimates for DTO are found for 32...

Merging of magnetic fields with field-aligned plasma flow components

International Nuclear Information System (INIS)

Mitchell, H.G. Jr.; Kan, J.R.

1978-01-01

The Sonnerup merging model for an incompressible plasma is extended to allow a flow component along the field lines in the inflow regions. Solutions are found to exist as long as the difference between the quantities B. V for the two inflow regions does not exceed a critical magnitude dependent on the inflow field magnitudes and plasma densities. All such solutions satisfy Vasyliunas' definition of merging, but some classes of solution have radically altered geometries, i.e. geometries in which the inflow regions are much smaller than the outflow regions. The necessary but not sufficient condition for these unusual geometries is that the field-aligned flow component in at least one inflow region be super-Alfvenic. A solution for the case of a vacuum field in one inflow region is obtained in which any flow velocity is allowed in the non-vacuum inflow region, although super-Alfvenic flow can still result in an unusual geometry. For symmetric configurations, the usual geometry, that of Petschek and Sonnerup, is retained as long as both field-aligned flow components in the inflow regions are less than twice the inflow Alfven speed. For the case of a vacuum field on one side and fields approximating the boundary between the solar wind and the earth's dayside magnetosphere, the usual geometry is retained for flow less than about 2.5 times the local Alfven speed. (author)

An introduction to vectors, vector operators and vector analysis

CERN Document Server

Joag, Pramod S

2016-01-01

Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.

Surface representations of two- and three-dimensional fluid flow topology

Science.gov (United States)

Helman, James L.; Hesselink, Lambertus

1990-01-01

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

Vectorization of a particle code used in the simulation of rarefied hypersonic flow

Science.gov (United States)

Baganoff, D.

1990-01-01

A limitation of the direct simulation Monte Carlo (DSMC) method is that it does not allow efficient use of vector architectures that predominate in current supercomputers. Consequently, the problems that can be handled are limited to those of one- and two-dimensional flows. This work focuses on a reformulation of the DSMC method with the objective of designing a procedure that is optimized to the vector architectures found on machines such as the Cray-2. In addition, it focuses on finding a better balance between algorithmic complexity and the total number of particles employed in a simulation so that the overall performance of a particle simulation scheme can be greatly improved. Simulations of the flow about a 3D blunt body are performed with 10 to the 7th particles and 4 x 10 to the 5th mesh cells. Good statistics are obtained with time averaging over 800 time steps using 4.5 h of Cray-2 single-processor CPU time.

Numerical simulation using vorticity-vector potential formulation

Science.gov (United States)

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

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

Science.gov (United States)

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.

Investigation of optical currents in coherent and partially coherent vector fields

DEFF Research Database (Denmark)

Angelsky, O. V.; Gorsky, M. P.; Maksimyak, P. P.

2011-01-01

We present the computer simulation results of the spatial distri-bution of the Poynting vector and illustrate motion of micro and nanopar-ticles in spatially inhomogeneously polarized fields. The influence of phase relations and the degree of mutual coherence of superimposing waves...... by polarization characteristics of an optical field alone, using nanoscale me-tallic particles has been shown experimentally....

Cryogenic STM in 3D vector magnetic fields realized through a rotatable insert.

Science.gov (United States)

Trainer, C; Yim, C M; McLaren, M; Wahl, P

2017-09-01

Spin-polarized scanning tunneling microscopy (SP-STM) performed in vector magnetic fields promises atomic scale imaging of magnetic structure, providing complete information on the local spin texture of a sample in three dimensions. Here, we have designed and constructed a turntable system for a low temperature STM which in combination with a 2D vector magnet provides magnetic fields of up to 5 T in any direction relative to the tip-sample geometry. This enables STM imaging and spectroscopy to be performed at the same atomic-scale location and field-of-view on the sample, and most importantly, without experiencing any change on the tip apex before and after field switching. Combined with a ferromagnetic tip, this enables us to study the magnetization of complex magnetic orders in all three spatial directions.

Optical cage generated by azimuthal- and radial-variant vector beams.

Science.gov (United States)

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

2018-05-01

We propose a method to generate an optical cage using azimuthal- and radial-variant vector beams in a high numerical aperture optical system. A new kind of vector beam that has azimuthal- and radial-variant polarization states is proposed and demonstrated theoretically. Then, an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input azimuthal- and radial-variant vector beams is derived and built based on the vector diffraction theory of Richards and Wolf. From calculations, a full polarization-controlled optical cage is obtained by simply tailoring the radial index of the polarization, the uniformity U of which is up to 0.7748, and the cleanness C is zero. Additionally, a perfect optical cage can be achieved with U=1, and C=0 by introducing an amplitude modulation; its magnetic field and energy flow are also demonstrated in detail. Such optical cages may be helpful in applications such as optical trapping and high-resolution imaging.

Increasing the Dynamic Range of Synthetic Aperture Vector Flow Imaging

DEFF Research Database (Denmark)

Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo; Jensen, Jørgen Arendt

2014-01-01

images. The emissions for the two imaging modes are interleaved 1-to-1 ratio, providing a high frame rate equal to the effective pulse repetition frequency of each imaging mode. The direction of the flow is estimated, and the velocity is then determined in that direction. This method Works for all angles...... standard deviations are 1.59% and 6.12%, respectively. The presented method can improve the estimates by synthesizing a lower pulse repetition frequency, thereby increasing the dynamic range of the vector velocity imaging....

Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction

Directory of Open Access Journals (Sweden)

Andrea Bonfiglioli

2014-12-01

Full Text Available The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic Lie groups defined on RN (with its usual differentiable structure. We show that such a characterization amounts to asking that: (i g is N-dimensional; (ii g admits a set of Lie generators which are complete vector fields; (iii g satisfies Hörmander’s rank condition. These conditions are necessary, sufficient and mutually independent. Our approach is constructive, in that for any such g we show how to construct a Lie group G = (RN, * whose Lie algebra is g. We do not make use of Lie’s Third Theorem, but we only exploit the Campbell-Baker-Hausdorff-Dynkin Theorem for ODE’s.

Comparative Visualization of Vector Field Ensembles Based on Longest Common Subsequence

Energy Technology Data Exchange (ETDEWEB)

Liu, Richen; Guo, Hanqi; Zhang, Jiang; Yuan, Xiaoru

2016-04-19

We propose a longest common subsequence (LCS) based approach to compute the distance among vector field ensembles. By measuring how many common blocks the ensemble pathlines passing through, the LCS distance defines the similarity among vector field ensembles by counting the number of sharing domain data blocks. Compared to the traditional methods (e.g. point-wise Euclidean distance or dynamic time warping distance), the proposed approach is robust to outlier, data missing, and sampling rate of pathline timestep. Taking the advantages of smaller and reusable intermediate output, visualization based on the proposed LCS approach revealing temporal trends in the data at low storage cost, and avoiding tracing pathlines repeatedly. Finally, we evaluate our method on both synthetic data and simulation data, which demonstrate the robustness of the proposed approach.

A Note on Classification of Spatially Homogeneous Rotating Space-Times According to Their Teleparallel Killing Vector Fields in Teleparallel Theory of Gravitation

International Nuclear Information System (INIS)

Shabbir, Ghulam; Khan, Suhail; Ali, Amjad

2011-01-01

In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields. (general)

3D Vector Velocity Estimation using a 2D Phased Array

DEFF Research Database (Denmark)

Pihl, Michael Johannes; Jensen, Jørgen Arendt

2011-01-01

of using the TO method for estimation 3D velocity vectors, and the proposed decoupling is demonstrated. A 64x64 and a 32x32 elements transducer are emulated using Field II. Plug flow with a speed of 1 m/s in a small region is rotated in the XY -plane. A binary flow example with [vx,vy]=[1,0] and [0,1] m......A method to estimate the three dimensional (3D) velocity vector is presented is this paper. 3D velocity vector techniques are needed to measure the full velocity and characterize the complicated flow patterns in the human body. The Transverse Oscillation (TO) method introduces oscillations...... matrix transducer. For the 32x32 transducer, the mean and standard deviation for the speed are 0.94 0.11 m/s and for the angle bias -0.487.7. The simulation study clearly demonstrates, that the new method can be used to estimate the 3D velocity vector using a 2D phased matrix array, and that the velocity...

A median filter approach for correcting errors in a vector field

Science.gov (United States)

Schultz, H.

1985-01-01

Techniques are presented for detecting and correcting errors in a vector field. These methods employ median filters which are frequently used in image processing to enhance edges and remove noise. A detailed example is given for wind field maps produced by a spaceborne scatterometer. The error detection and replacement algorithm was tested with simulation data from the NASA Scatterometer (NSCAT) project.

Relativistic gravitation from massless systems of scalar and vector fields

International Nuclear Information System (INIS)

Fonseca Teixeira, A.F. da.

1979-01-01

Under the laws of Einstein's gravitational theory, a massless system consisting of the diffuse sources of two fields is discussed. One fields is scalar, of long range, the other is a vector field of short range. A proportionality between the sources is assumed. Both fields are minimally coupled to gravitation, and contribute positive definitely to the time component of the energy momentum tensor. A class of static, spherically symmetric solutions of the equations is obtained, in the weak field limit. The solutions are regular everywhere, stable, and can represent large or small physical systems. The gravitational field presents a Schwarzschild-type asymptotic behavior. The dependence of the energy on the various parameters characterizing the system is discussed in some detail. (Author) [pt

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

Science.gov (United States)

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.

Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields

KAUST Repository

Wang, B.

2013-06-01

Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.

Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields

KAUST Repository

Wang, B.; Rosen, P.; Skraba, P.; Bhatia, H.; Pascucci, V.

2013-01-01

Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time-varying 2D vector fields. This framework allows the end-users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.

On scalar and vector fields coupled to the energy-momentum tensor

Science.gov (United States)

Jiménez, Jose Beltrán; Cembranos, Jose A. R.; Sánchez Velázquez, Jose M.

2018-05-01

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge-and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.

Numerical simulation of turbulent flow and heat transfer in a parallel channel. Verification of the field synergy principle

International Nuclear Information System (INIS)

Tian Wenxi; Su, G.H.; Qiu Suizheng; Jia Dounan

2004-01-01

The field synergy principle was proposed by Guo(1998) which is based on 2-D boundary laminar flow and it resulted from a second look at the mechanism of convective heat transfer. Numerical verification of this principle's validity for turbulent flow has been carried out by very few researchers, and mostly commercial software such as FLUENT, CFX etc. were used in their study. In this paper, numerical simulation of turbulent flow with recirculation was developed using SIMPLE algorithm with two-equation k-ε model. Extension of computational region method and wall function method were quoted to regulate the whole computational region geometrically. Given the inlet Reynold number keeps constant: 10000, by changing the height of the solid obstacle, simulation was conducted and the result showed that the wall heat flux decreased with the angle between the velocity vector and the temperature gradient. Thus it is validated that the field synergy principle based on 2-D boundary laminar flow can also be applied to complex turbulent flow even with recirculation. (author)

Flow-synchronous field motion refrigeration

Science.gov (United States)

Hassen, Charles N.

2017-08-22

An improved method to manage the flow of heat in an active regenerator in a magnetocaloric or an electrocaloric heat-pump refrigeration system, in which heat exchange fluid moves synchronously with the motion of a magnetic or electric field. Only a portion of the length of the active regenerator bed is introduced to or removed from the field at one time, and the heat exchange fluid flows from the cold side toward the hot side while the magnetic or electric field moves along the active regenerator bed.

2-D blood vector velocity estimation using a phase shift estimator

DEFF Research Database (Denmark)

Udesen, Jesper

are presented. Here the TO method is tested both in simulations using the Field II program and in flow phantom experiments using the RASMUS scanner. Both simulations and flow phantom experiments indicate that the TO method can estimate the 2-D vector velocity with an acceptable low bias and standard deviation...... velocity estimation is discussed. The TO method is introduced, and the basic theory behind the method is explained. This includes the creation of the acoustic fields, beamforming, echo-canceling and the velocity estimator. In the second part of the thesis the eight papers produced during this PhD project...... when the angle between the blood and the ultrasound beam is above $50^\\circ$. Furthermore, the TO method is tested in-vivo where the scannings are performed by skilled sonographers. The in-vivo scannings resulted in a sequence of 2-D vector CFM images which showed 2-D flow patterns in the bifurcation...

SOLAR FLARE PREDICTION USING SDO/HMI VECTOR MAGNETIC FIELD DATA WITH A MACHINE-LEARNING ALGORITHM

International Nuclear Information System (INIS)

Bobra, M. G.; Couvidat, S.

2015-01-01

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 database 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

Vectorization of nuclear codes for atmospheric transport and exposure calculation of radioactive materials

International Nuclear Information System (INIS)

Asai, Kiyoshi; Shinozawa, Naohisa; Ishikawa, Hirohiko; Chino, Masamichi; Hayashi, Takashi

1983-02-01

Three computer codes MATHEW, ADPIC of LLNL and GAMPUL of JAERI for prediction of wind field, concentration and external exposure rate of airborne radioactive materials are vectorized and the results are presented. Using the continuous equation of incompressible flow as a constraint, the MATHEW calculates the three dimensional wind field by a variational method. Using the particle-in -cell method, the ADPIC calculates the advection and diffusion of radioactive materials in three dimensional wind field and terrain, and gives the concentration of the materials in each cell of the domain. The GAMPUL calculates the external exposure rate assuming Gaussian plume type distribution of concentration. The vectorized code MATHEW attained 7.8 times speedup by a vector processor FACOM230-75 APU. The ADPIC and GAMPUL are estimated to attain 1.5 and 4 times speedup respectively on CRAY-1 type vector processor. (author)

Stability of the line preserving flows

Science.gov (United States)

Figura, Przemysław

2017-11-01

We examine the equations that are used to describe flows which preserve field lines. We study what happens if we introduce perturbations to the governing equations. The stability of the line preserving flows in the case of the magneto-fluids permeated by magnetic fields is strictly connected to the non-null magnetic reconnection processes. In most of our study we use the Euler potential representation of the external magnetic field. We provide general expressions for the perturbations of the Euler potentials that describe the magnetic field. Similarly, we provide expressions for the case of steady flow as well as we obtain certain conditions required for the stability of the flow. In addition, for steady flows we formulate conditions under which the perturbations of the external field are negligible and the field may be described by its initial unperturbed form. Then we consider the flow equation that transforms quantities from the laboratory coordinate system to the related external field coordinate system. We introduce perturbations to the equation and obtain its simplified versions for the case of a steady flow. For a given system, use of this method allows us to simplify the considerations provided that some part of the system may be described as a perturbation. Next, to study regions favourable for the magnetic reconnection to occur we introduce a deviation vector to the basic line preserving flows condition equation. We provide expressions of the vector for some simplifying cases. This method allows us to examine if given perturbations either stabilise the system or induce magnetic reconnection. To illustrate some of our results we study two examples, namely a simple laboratory plasma flow and a simple planetary magnetosphere model.

Supergravity inspired vector curvaton

International Nuclear Information System (INIS)

Dimopoulos, Konstantinos

2007-01-01

It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied

Multiscale vector fields for image pattern recognition

Science.gov (United States)

Low, Kah-Chan; Coggins, James M.

1990-01-01

A uniform processing framework for low-level vision computing in which a bank of spatial filters maps the image intensity structure at each pixel into an abstract feature space is proposed. Some properties of the filters and the feature space are described. Local orientation is measured by a vector sum in the feature space as follows: each filter's preferred orientation along with the strength of the filter's output determine the orientation and the length of a vector in the feature space; the vectors for all filters are summed to yield a resultant vector for a particular pixel and scale. The orientation of the resultant vector indicates the local orientation, and the magnitude of the vector indicates the strength of the local orientation preference. Limitations of the vector sum method are discussed. Investigations show that the processing framework provides a useful, redundant representation of image structure across orientation and scale.

Different elution modes and field programming in gravitational field-flow fractionation. III. Field programming by flow-rate gradient generated by a programmable pump.

Science.gov (United States)

Plocková, J; Chmelík, J

2001-05-25

Gravitational field-flow fractionation (GFFF) utilizes the Earth's gravitational field as an external force that causes the settlement of particles towards the channel accumulation wall. Hydrodynamic lift forces oppose this action by elevating particles away from the channel accumulation wall. These two counteracting forces enable modulation of the resulting force field acting on particles in GFFF. In this work, force-field programming based on modulating the magnitude of hydrodynamic lift forces was implemented via changes of flow-rate, which was accomplished by a programmable pump. Several flow-rate gradients (step gradients, linear gradients, parabolic, and combined gradients) were tested and evaluated as tools for optimization of the separation of a silica gel particle mixture. The influence of increasing amount of sample injected on the peak resolution under flow-rate gradient conditions was also investigated. This is the first time that flow-rate gradients have been implemented for programming of the resulting force field acting on particles in GFFF.

Spherical cap modelling of Orsted magnetic field vectors over southern Africa

CSIR Research Space (South Africa)

Kotze, PB

2001-01-01

Full Text Available Vector magnetic field observations by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000, have been employed to derive a spherical cap harmonic model (Haines, 1985) over the southern African region between 10 degrees...

Estimation of 3-D conduction velocity vector fields from cardiac mapping data.

Science.gov (United States)

Barnette, A R; Bayly, P V; Zhang, S; Walcott, G P; Ideker, R E; Smith, W M

2000-08-01

A method to estimate three-dimensional (3-D) conduction velocity vector fields in cardiac tissue is presented. The speed and direction of propagation are found from polynomial "surfaces" fitted to space-time (x, y, z, t) coordinates of cardiac activity. The technique is applied to sinus rhythm and paced rhythm mapped with plunge needles at 396-466 sites in the canine myocardium. The method was validated on simulated 3-D plane and spherical waves. For simulated data, conduction velocities were estimated with an accuracy of 1%-2%. In experimental data, estimates of conduction speeds during paced rhythm were slower than those found during normal sinus rhythm. Vector directions were also found to differ between different types of beats. The technique was able to distinguish between premature ventricular contractions and sinus beats and between sinus and paced beats. The proposed approach to computing velocity vector fields provides an automated, physiological, and quantitative description of local electrical activity in 3-D tissue. This method may provide insight into abnormal conduction associated with fatal ventricular arrhythmias.

Internal and external potential-field estimation from regional vector data at varying satellite altitude

Science.gov (United States)

Plattner, Alain; Simons, Frederik J.

2017-10-01

When modelling satellite data to recover a global planetary magnetic or gravitational potential field, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g. by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the source) while balancing the conflicting demands for spatial concentration and spectral limitation. The `altitude-cognizant' gradient vector Slepian functions (AC-GVSF) enjoy a noise tolerance under downward continuation that is much improved relative to the `classical' gradient vector Slepian functions (CL-GVSF), which do not factor satellite altitude into their construction. Furthermore, venturing beyond the realm of their first application, published in a preceding paper, in the present article we extend the theory to being able to handle both internal and external potential-field estimation. Solving simultaneously for internal and external fields under the limitation of regional data availability reduces internal-field artefacts introduced by downward-continuing unmodelled external fields, as we show with numerical examples. We explain our solution strategies on the basis of analytic expressions for the behaviour of the estimation bias and variance of models for which signal and noise are uncorrelated, (essentially) space- and band-limited, and spectrally (almost) white. The AC-GVSF are optimal linear combinations of vector spherical harmonics

Instantaneous flow field above the free end of finite-height cylinders and prisms

International Nuclear Information System (INIS)

Rostamy, N.; Sumner, D.; Bergstrom, D.J.; Bugg, J.D.

2013-01-01

Highlights: • PIV measurements of the flow above the free end of finite-height bodies. • Effect of cross-sectional shape of the models on the instantaneous flow. • Small-scale structures generated by the separated shear layer were revealed. • Effect of aspect ratio on the reattachment of the separated flow on the free end. -- Abstract: The flow above the free ends of surface-mounted finite-height circular cylinders and square prisms was studied experimentally using particle image velocimetry (PIV). Cylinders and prisms with aspect ratios of AR = 9, 7, 5, and 3 were tested at a Reynolds number of Re = 4.2 × 10 4 . The bodies were mounted normal to a ground plane and were partially immersed in a turbulent zero-pressure-gradient boundary layer, where the boundary layer thickness relative to the body width was δ/D = 1.6. PIV measurements were made above the free ends of the bodies in a vertical plane aligned with the flow centreline. The present PIV results provide insight into the effects of aspect ratio and body shape on the instantaneous flow field. The recirculation zone under the separated shear layer is larger for the square prism of AR = 3 compared to the more slender prism of AR = 9. Also, for a square prism with low aspect ratio (AR = 3), the influence of the reverse flow over the free end surface becomes more significant compared to that for a higher aspect ratio (AR = 9). For the circular cylinder, a cross-stream vortex forms within the recirculation zone. As the aspect ratio of the cylinder decreases, the reattachment point of the separated flow on the free end surface moves closer to the trailing edge. For both the square prism and circular cylinder cases, the instantaneous velocity vector field and associated in-plane vorticity field revealed small-scale structures mostly generated by the separated shear layer

Vector velocimeter

DEFF Research Database (Denmark)

2012-01-01

The present invention relates to a compact, reliable and low-cost vector velocimeter for example for determining velocities of particles suspended in a gas or fluid flow, or for determining velocity, displacement, rotation, or vibration of a solid surface, the vector velocimeter comprising a laser...

Non-Gaussianity at tree and one-loop levels from vector field perturbations

International Nuclear Information System (INIS)

Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon; Lyth, David H.

2009-01-01

We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in P ζ and (or) in B ζ ] and vice versa. The level of non-Gaussianity in the bispectrum, f NL , is calculated and related to the level of statistical anisotropy in the power spectrum, g ζ . For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.

Visualization of Flow Field: Application of PLIF Technique

Directory of Open Access Journals (Sweden)

Jiang Bo Peng

2018-01-01

Full Text Available The objective of this paper is to apply planar laser-induced fluorescence (PLIF technology to flow field visualization. This experiment was carried out in a one-meter wind tunnel to study the wake flow field around a circular cylinder. This experiment studied the method of injecting tracer into the flow field; the frequency of the vortex in the wake field and the vortex speed are quantitatively analyzed. This paper gives the correspondence between the speed of the flow field and the frequency of the laser, which could be used as a rough reference standard for future wind tunnel visualization experiments. The result shows that PLIF diagnostic technology has great potential in visualization of flow field.

ARE INTERNATIONAL TRADE FLOWS A VECTOR OF GLOBALIZATION?

Directory of Open Access Journals (Sweden)

Sebastian-Florian ENEA

2015-10-01

Full Text Available International commerce and regional integration have long been considered key determinants of national development. The purpose of the present paper is to answer the question whether international trade flows are a vector of globalization and economic growth. In order to achieve this, we have conducted panel data analysis on a sample consisting of members from regional economic structures, such as the E.U., NAFTA, MERCOSUR and ASEAN, and covering a time span of 24 years, from 1990 to 2013. The results of the study underline the fact that, on average and taking into account the heterogeneity of the sample, international commerce counts from around 50 % of the annual economic growth. The future research direction will aim to conduct a more thorough analysis, by focusing more on the regional perspective.

Lagrangian analysis of vector and tensor fields: Algorithmic foundations and applications in medical imaging and computational fluid dynamics

OpenAIRE

Ding, Zi'ang

2016-01-01

Both vector and tensor fields are important mathematical tools used to describe the physics of many phenomena in science and engineering. Effective vector and tensor field visualization techniques are therefore needed to interpret and analyze the corresponding data and achieve new insight into the considered problem. This dissertation is concerned with the extraction of important structural properties from vector and tensor datasets. Specifically, we present a unified approach for the charact...

Plasma Flows in Crossed Magnetic and Electric Fields

International Nuclear Information System (INIS)

Belikov, A.G.

2005-01-01

The effect of the magnitude and direction of an external electric field on the plasma flowing through a magnetic barrier is studied by numerically solving two-fluid MHD equations. The drift velocity of the plasma flow and the distribution of the flow electrons over transverse velocities are found to depend on the magnitude and direction of the electric field. It is shown that the direction of the induced longitudinal electric field is determined by the direction of the external field and that the electric current generated by the plasma flow significantly disturbs the barrier field

The Vector Electric Field Investigation on the C/NOFS Satellite

Science.gov (United States)

Pfaff, R.; Acuna, M.; Kujawski, J.; Fourre, R.; Uribe, P.; Hunsaker, F.; Rowland, D.; Le, G.; Farrell, W.; Maynard, N.;

Flavor-singlet axial-vector current in quark model within background field

International Nuclear Information System (INIS)

Chen Kun; Yan Mulin

1993-01-01

The flavor-singlet axial-vector current is calculated in a quark model within pseudoscalar background-field through the Seeley-DeWitt coefficients. This current is responsible for the quark spin content of proton and is of O(1) in the large-N e expansion

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

Love, J.J.; Constable, C.G.

2003-01-01

formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

Love, J. J.; Constable, C. G.

2003-03-01

formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)

International Nuclear Information System (INIS)

Banyaga, A.; Landa, Alain Musesa

2004-03-01

We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)

Hawking radiation of a vector field and gravitational anomalies

International Nuclear Information System (INIS)

Murata, Keiju; Miyamoto, Umpei

2007-01-01

Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with the Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed

A Quantized Boundary Representation of 2D Flows

KAUST Repository

Levine, J. A.

2012-06-01

Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations.

DIRECT OBSERVATION OF SOLAR CORONAL MAGNETIC FIELDS BY VECTOR TOMOGRAPHY OF THE CORONAL EMISSION LINE POLARIZATIONS

International Nuclear Information System (INIS)

Kramar, M.; Lin, H.; Tomczyk, S.

2016-01-01

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, we 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

Algebraic characterization of vector supersymmetry in topological field theories

International Nuclear Information System (INIS)

Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G.; Sorella, S.P.

1997-01-01

An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author)

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

Science.gov (United States)

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.

Simulation-Based Optimization of a Vector Showerhead System for the Control of Flow Field Profile in a Vertical Reactor Chamber

Directory of Open Access Journals (Sweden)

Huanxiong Xia

2014-03-01

Full Text Available Optimization of a vector showerhead in a vertical reactor involves thousands of holes on the showerhead face plate and the spatial distribution of physical fields, so parameterizing the geometry configuration of the holes in high resolution is very difficult, which makes the conventional optimization methods hard to deal with. To solve this problem, a profile error feedback (PEF optimization solution was proposed to optimize a vector showerhead gas delivery system for the control of mass transport. The gas velocity profile in the reactor and the continuous-feature impedance distribution profile on the showerhead face plate are defined as design objective and variables, respectively. A cyclic iterative approximation idea was implemented in this solution. The algorithm was started from a guessed initial design model and then cyclically adjusted the design variables by the constructed PEF iterative formula to generate a better model and to make the gas velocity profile in the critical domain of the new model continually approximate to the expected profile, until it could be accepted. Finally, the optimized impedance profile was mapped to the holes geometry configuration through the established equivalent impedance model for the showerhead face plate.

Taylor-Couette flow stability with toroidal magnetic field

International Nuclear Information System (INIS)

Shalybkov, D

2005-01-01

The linear stability of the dissipative Taylor-Couette flow with imposed azimuthal magnetic field is considered. Unlike to ideal flow, the magnetic field is fixed function of radius with two parameters only: a ratio of inner to outer cylinder radii and a ratio of the magnetic field values on outer and inner cylinders. The magnetic field with boundary values ratio greater than zero and smaller than inverse radii ratio always stabilizes the flow and called stable magnetic field below. The current free magnetic field is the stable magnetic field. The unstable magnetic field destabilizes every flow if the magnetic field (or Hartmann number) exceeds some critical value. This instability survives even without rotation (for zero Reynolds number). For the stable without the magnetic field flow, the unstable modes are located into some interval of the vertical wave numbers. The interval length is zero for critical Hartmann number and increases with increasing Hartmann number. The critical Hartmann numbers and the length of the unstable vertical wave numbers interval is the same for every rotation law. There are the critical Hartmann numbers for m = 0 sausage and m = 1 kink modes only. The critical Hartmann numbers are smaller for kink mode and this mode is the most unstable mode like to the pinch instability case. The flow stability do not depend on the magnetic Prandtl number for m = 0 mode. The same is true for critical Hartmann numbers for m = 0 and m = 1 modes. The typical value of the magnetic field destabilizing the liquid metal Taylor-Couette flow is order of 100 Gauss

Stokes profile analysis and vector magnetic fields. I. Inversion of photospheric lines

International Nuclear Information System (INIS)

Skumanich, A.; Lites, B.W.

1987-01-01

Improvements are proposed for the Auer et al. (1977) method for the analytic inversion of Stokes profiles via nonlinear least squares. The introduction of additional physics into the Mueller absorption matrix (by including damping wings and magnetooptical birefringence, and by decoupling the intensity profile from the three-vector polarization profile in the analysis) is found to result in a more robust inversion method, providing more reliable and accurate estimates of sunspot vector magnetic fields without significant loss of economy. The method is applied to sunspot observations obtained with the High Altitude Observatory polarimeter. 29 references

Thrust Vectoring of a Continuous Rotating Detonation Engine by Changing the Local Injection Pressure

International Nuclear Information System (INIS)

Liu Shi-Jie; Lin Zhi-Yong; Sun Ming-Bo; Liu Wei-Dong

2011-01-01

The thrust vectoring ability of a continuous rotating detonation engine is numerically investigated, which is realized via increasing local injection stagnation pressure of half of the simulation domain compared to the other half. Under the homogeneous injection condition, both the flow-field structure and the detonation wave propagation process are analyzed. Due to the same injection condition along the inlet boundary, the outlines of fresh gas zones at different moments are similar to each other. The main flow-field features under thrust vectoring cases are similar to that under the baseline condition. However, due to the heterogeneous injection system, both the height of the fresh gas zone and the pressure value of the fresh gas in the high injection pressure zone are larger than that in the low injection pressure zone. Thus the average pressure in half of the engine is larger than that in the other half and the thrust vectoring adjustment is realized. (fundamental areas of phenomenology(including applications))

Helicons in uniform fields. II. Poynting vector and angular momenta

Science.gov (United States)

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

2018-03-01

The orbital and spin angular momenta of helicon modes have been determined quantitatively from laboratory experiments. The current density is obtained unambiguously from three dimensional magnetic field measurements. The only approximation made is to obtain the electric field from Hall Ohm's law which is usually the case for low frequency whistler modes. This allows the evaluation of the Poynting vector from which the angular momentum is obtained. Comparing two helicon modes (m = 0 and m = 1), one can separate the contribution of angular momentum of a rotating and non-rotating wave field. The orbital angular momentum is important to assess the wave-particle interaction by the transverse Doppler shift of rotating waves which has not been considered so far.

An MHD Simulation of Solar Active Region 11158 Driven with a Time-dependent Electric Field Determined from HMI Vector Magnetic Field Measurement Data

Science.gov (United States)

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.

High frame rate synthetic aperture vector flow imaging for transthoracic echocardiography

Science.gov (United States)

Villagómez-Hoyos, Carlos A.; Stuart, Matthias B.; Bechsgaard, Thor; Nielsen, Michael Bachmann; Jensen, Jørgen Arendt

2016-04-01

This work presents the first in vivo results of 2-D high frame rate vector velocity imaging for transthoracic cardiac imaging. Measurements are made on a healthy volunteer using the SARUS experimental ultrasound scanner connected to an intercostal phased-array probe. Two parasternal long-axis view (PLAX) are obtained, one centred at the aortic valve and another centred at the left ventricle. The acquisition sequence was composed of 3 diverging waves for high frame rate synthetic aperture flow imaging. For verification a phantom measurement is performed on a transverse straight 5 mm diameter vessel at a depth of 100 mm in a tissue-mimicking phantom. A flow pump produced a 2 ml/s constant flow with a peak velocity of 0.2 m/s. The average estimated flow angle in the ROI was 86.22° +/- 6.66° with a true flow angle of 90°. A relative velocity bias of -39% with a standard deviation of 13% was found. In-vivo acquisitions show complex flow patterns in the heart. In the aortic valve view, blood is seen exiting the left ventricle cavity through the aortic valve into the aorta during the systolic phase of the cardiac cycle. In the left ventricle view, blood flow is seen entering the left ventricle cavity through the mitral valve and splitting in two ways when approximating the left ventricle wall. The work presents 2-D velocity estimates on the heart from a non-invasive transthoracic scan. The ability of the method detecting flow regardless of the beam angle could potentially reveal a more complete view of the flow patterns presented on the heart.

Strong-field non-sequential ionization: The vector momentum distribution of multiply charged Ne ions

International Nuclear Information System (INIS)

Rottke, H.; Trump, C.; Wittmann, M.; Korn, G.; Becker, W.; Hoffmann, K.; Sandner, W.; Moshammer, R.; Feuerstein, B.; Dorn, A.; Schroeter, C.D.; Ullrich, J.; Schmitt, W.

2000-01-01

COLTRIMS (COLd Target Recoil-Ion Momentum Spectroscopy) was used to measure the vector momentum distribution of Ne n+ (n=1,2,3) ions formed in ultrashort (30 fsec) high-intensity (≅10 15 W/cm 2 ) laser pulses with center wavelength at 795 nm. To a high degree of accuracy the length of the Ne n+ ion momentum vector is equal to the length of the total momentum vector of the n photoelectrons released, with both vectors pointing into opposite directions. At a light intensity where non-sequential ionization of the atom dominates the Ne 2+ and Ne 3+ momentum distributions show distinct maxima at 4.0 a.u. and 7.5 a.u. along the polarization axis of the linearly polarized light beam. First, this is a clear signature of non-sequential multiple ionization. Second, it indicates that instantaneous emission of two (or more) electrons at electric field strength maxima of the light wave can be ruled out as main mechanism of non-sequential strong-field multiple ionization. In contrast, this experimental result is in accordance with the kinematical constraints of the 'rescattering model'

Numerical approach of multi-field two-phase flow models in the OVAP code

International Nuclear Information System (INIS)

Anela Kumbaro

2005-01-01

use full Eigen-structure information. Basic comparisons in terms of numerical results and physical modeling will be provided and interpreted. The intent is to provide guidelines for future development of such methods and models. References: [1] Lahey, R.T. Jr., Drew D.A. An Analysis of Two-Phase Flow and Heat Transfer using a Multidimensional, Multi-Field, Two-Fluid Computational Fluid Dynamics (CFD) Model, Japan/US Seminar on Two-Phase Flow Dynamics, California, June 5-8, 2000. [2] Lo S., Some recent developments and applications of CFD to multiphase flows in stirred reactors, AMIF-ESF Workshop, Computing two-phase flows, Aussois, 2000. [3] Roe P.L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comp. Phys., 43(2), 1981. [4] Toumi and A. Kumbaro, An Approximate Linearized Riemann Solver for a Two-Fluid Model, J. Comput. Phys., 124, 286-300, 1996. [5] A. Kumbaro, I. Toumi and V. Seignole, Numerical Modeling of Two-Phase Flows Using Advanced Two Fluid Systems, Tenth International Conference on Nuclear Engineering, April 14-18 2002, Arlington, Virginia, USA. (author)

Algebraic characterization of vector supersymmetry in topological field theories

Energy Technology Data Exchange (ETDEWEB)

Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica. Dept. de Fisica Teorica

1997-01-01

An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author). 32 refs., 5 tabs.

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

Science.gov (United States)

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.

Internal Flow of a High Specific-Speed Diagonal-Flow Fan (Rotor Outlet Flow Fields with Rotating Stall

Directory of Open Access Journals (Sweden)

Norimasa Shiomi

2003-01-01

Full Text Available We carried out investigations for the purpose of clarifying the rotor outlet flow fields with rotating stall cell in a diagonal-flow fan. The test fan was a high–specific-speed (ns=1620 type of diagonal-flow fan that had 6 rotor blades and 11 stator blades. It has been shown that the number of the stall cell is 1, and its propagating speed is approximately 80% of its rotor speed, although little has been known about the behavior of the stall cell because a flow field with a rotating stall cell is essentially unsteady. In order to capture the behavior of the stall cell at the rotor outlet flow fields, hot-wire surveys were performed using a single-slant hotwire probe. The data obtained by these surveys were processed by means of a double phase-locked averaging technique, which enabled us to capture the flow field with the rotating stall cell in the reference coordinate system fixed to the rotor. As a result, time-dependent ensemble averages of the three-dimensional velocity components at the rotor outlet flow fields were obtained. The behavior of the stall cell was shown for each velocity component, and the flow patterns on the meridional planes were illustrated.

A Comparison Study of Vector Velocity, Spectral Doppler and Magnetic Resonance of Blood Flow in the Common Carotid Artery

DEFF Research Database (Denmark)

Brandt, Andreas Hjelm; Hansen, Kristoffer Lindskov; Ewertsen, Caroline

2018-01-01

Magnetic resonance phase contrast angiography (MRA) is the gold standard for blood flow evaluation. Spectral Doppler ultrasound (SDU) is the first clinical choice, although the method is angle dependent. Vector flow imaging (VFI) is an angle-independent ultrasound method. The aim of the study...

Derivative self-interactions for a massive vector field

Energy Technology Data Exchange (ETDEWEB)

Beltrán Jiménez, Jose, E-mail: jose.beltran@cpt.univ-mrs.fr [CPT, Aix Marseille Université, UMR 7332, 13288 Marseille (France); Heisenberg, Lavinia, E-mail: lavinia.heisenberg@eth-its.ethz.ch [Institute for Theoretical Studies, ETH Zurich, Clausiusstrasse 47, 8092 Zurich (Switzerland)

2016-06-10

In this work we revisit the construction of theories for a massive vector field with derivative self-interactions such that only the 3 desired polarizations corresponding to a Proca field propagate. We start from the decoupling limit by constructing healthy interactions containing second derivatives of the Stueckelberg field with itself and also with the transverse modes. The resulting interactions can then be straightforwardly generalized beyond the decoupling limit. We then proceed to a systematic construction of the interactions by using the Levi–Civita tensors. Both approaches lead to a finite family of allowed derivative self-interactions for the Proca field. This construction allows us to show that some higher order terms recently introduced as new interactions trivialize in 4 dimensions by virtue of the Cayley–Hamilton theorem. Moreover, we discuss how the resulting derivative interactions can be written in a compact determinantal form, which can also be regarded as a generalization of the Born-Infeld lagrangian for electromagnetism. Finally, we generalize our results for a curved background and give the necessary non-minimal couplings guaranteeing that no additional polarizations propagate even in the presence of gravity.

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

Science.gov (United States)

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.

An improved estimation and focusing scheme for vector velocity estimation

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt; Munk, Peter

1999-01-01

to reduce spatial velocity dispersion. Examples of different velocity vector conditions are shown using the Field II simulation program. A relative accuracy of 10.1 % is obtained for the lateral velocity estimates for a parabolic velocity profile for a flow perpendicular to the ultrasound beam and a signal...

Vector electric field measurement via position-modulated Kelvin probe force microscopy

Science.gov (United States)

Dwyer, Ryan P.; Smieska, Louisa M.; Tirmzi, Ali Moeed; Marohn, John A.

2017-10-01

High-quality spatially resolved measurements of electric fields are critical to understanding charge injection, charge transport, and charge trapping in semiconducting materials. Here, we report a variation of frequency-modulated Kelvin probe force microscopy that enables spatially resolved measurements of the electric field. We measure electric field components along multiple directions simultaneously by employing position modulation and lock-in detection in addition to numeric differentiation of the surface potential. We demonstrate the technique by recording linescans of the in-plane electric field vector in the vicinity of a patch of trapped charge in a 2,7-diphenyl[1]benzothieno[3,2-b][1]benzothiophene (DPh-BTBT) organic field-effect transistor. This technique is simple to implement and should be especially useful for studying electric fields in spatially inhomogeneous samples like organic transistors and photovoltaic blends.

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

Science.gov (United States)

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

Fast Blood Vector Velocity Imaging using ultrasound: In-vivo examples of complex blood flow in the vascular system

DEFF Research Database (Denmark)

Hansen, Kristoffer Lindskov; Udesen, Jesper; Gran, Fredrik

2008-01-01

Conventional ultrasound methods for acquiring color flow images of the blood motion are restricted by a relatively low frame rate and angle dependent velocity estimates. The Plane Wave Excitation (PWE) method has been proposed to solve these limitations. The frame rate can be increased, and the 2-D...... vector velocity of the blood motion can be estimated. The transmitted pulse is not focused, and a full speckle image of the blood can be acquired for each emission. A 13 bit Barker code is transmitted simultaneously from each transducer element. The 2-D vector velocity of the blood is found using 2-D...... speckle tracking between segments in consecutive speckle images. The flow patterns of six bifurcations and two veins were investigated in-vivo. It was shown: 1) that a stable vortex in the carotid bulb was present opposed to other examined bifurcations, 2) that retrograde flow was present...

The intermittency of vector fields and random-number generators

Science.gov (United States)

Kalinin, A. O.; Sokoloff, D. D.; Tutubalin, V. N.

2017-09-01

We examine how well natural random-number generators can reproduce the intermittency phenomena that arise in the transfer of vector fields in random media. A generator based on the analysis of financial indices is suggested as the most promising random-number generator. Is it shown that even this generator, however, fails to reproduce the phenomenon long enough to confidently detect intermittency, while the C++ generator successfully solves this problem. We discuss the prospects of using shell models of turbulence as the desired generator.

Spectral Analysis of Vector Magnetic Field Profiles

Science.gov (United States)

Parker, Robert L.; OBrien, Michael S.

1997-01-01

We investigate the power spectra and cross spectra derived from the three components of the vector magnetic field measured on a straight horizontal path above a statistically stationary source. All of these spectra, which can be estimated from the recorded time series, are related to a single two-dimensional power spectral density via integrals that run in the across-track direction in the wavenumber domain. Thus the measured spectra must obey a number of strong constraints: for example, the sum of the two power spectral densities of the two horizontal field components equals the power spectral density of the vertical component at every wavenumber and the phase spectrum between the vertical and along-track components is always pi/2. These constraints provide powerful checks on the quality of the measured data; if they are violated, measurement or environmental noise should be suspected. The noise due to errors of orientation has a clear characteristic; both the power and phase spectra of the components differ from those of crustal signals, which makes orientation noise easy to detect and to quantify. The spectra of the crustal signals can be inverted to obtain information about the cross-track structure of the field. We illustrate these ideas using a high-altitude Project Magnet profile flown in the southeastern Pacific Ocean.

Vectorization of a particle simulation method for hypersonic rarefied flow

Science.gov (United States)

Mcdonald, Jeffrey D.; Baganoff, Donald

1988-01-01

An efficient particle simulation technique for hypersonic rarefied flows is presented at an algorithmic and implementation level. The implementation is for a vector computer architecture, specifically the Cray-2. The method models an ideal diatomic Maxwell molecule with three translational and two rotational degrees of freedom. Algorithms are designed specifically for compatibility with fine grain parallelism by reducing the number of data dependencies in the computation. By insisting on this compatibility, the method is capable of performing simulation on a much larger scale than previously possible. A two-dimensional simulation of supersonic flow over a wedge is carried out for the near-continuum limit where the gas is in equilibrium and the ideal solution can be used as a check on the accuracy of the gas model employed in the method. Also, a three-dimensional, Mach 8, rarefied flow about a finite-span flat plate at a 45 degree angle of attack was simulated. It utilized over 10 to the 7th particles carried through 400 discrete time steps in less than one hour of Cray-2 CPU time. This problem was chosen to exhibit the capability of the method in handling a large number of particles and a true three-dimensional geometry.

Vectorization of a particle simulation method for hypersonic rarefied flow

International Nuclear Information System (INIS)

Mcdonald, J.D.; Baganoff, D.

1988-01-01

An efficient particle simulation technique for hypersonic rarefied flows is presented at an algorithmic and implementation level. The implementation is for a vector computer architecture, specifically the Cray-2. The method models an ideal diatomic Maxwell molecule with three translational and two rotational degrees of freedom. Algorithms are designed specifically for compatibility with fine grain parallelism by reducing the number of data dependencies in the computation. By insisting on this compatibility, the method is capable of performing simulation on a much larger scale than previously possible. A two-dimensional simulation of supersonic flow over a wedge is carried out for the near-continuum limit where the gas is in equilibrium and the ideal solution can be used as a check on the accuracy of the gas model employed in the method. Also, a three-dimensional, Mach 8, rarefied flow about a finite-span flat plate at a 45 degree angle of attack was simulated. It utilized over 10 to the 7th particles carried through 400 discrete time steps in less than one hour of Cray-2 CPU time. This problem was chosen to exhibit the capability of the method in handling a large number of particles and a true three-dimensional geometry. 14 references

On particle creation by black holes. [Quantum mechanical state vector, gravitational collapse, Hermition scalar field, density matrix

Energy Technology Data Exchange (ETDEWEB)

Wald, R M [Chicago Univ., Ill. (USA). Lab. for Astrophysics and Space Research

1975-11-01

Hawking's analysis of particle creation by black holes is extended by explicity obtaining the expression for the quantum mechanical state vector PSI which results from particle creation starting from the vacuum during gravitational collapse. We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail with black body emission (orig./BJ).

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

International Nuclear Information System (INIS)

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-01-01

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), and (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.

Different elution modes and field programming in gravitational field-flow fractionation. III. Field programming by flow-rate gradient generated by a programmable pump

Czech Academy of Sciences Publication Activity Database

Plocková, Jana; Chmelík, Josef

2001-01-01

Roč. 918, č. 2 (2001), s. 361-370 ISSN 0021-9673 R&D Projects: GA AV ČR IAA4031805 Institutional research plan: CEZ:AV0Z4031919 Keywords : field-flow fractionation * field programming * flow-rate gradients Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 2.793, year: 2001

Short-term traffic flow prediction model using particle swarm optimization–based combined kernel function-least squares support vector machine combined with chaos theory

Directory of Open Access Journals (Sweden)

Qiang Shang

2016-08-01

Full Text Available Short-term traffic flow prediction is an important part of intelligent transportation systems research and applications. For further improving the accuracy of short-time traffic flow prediction, a novel hybrid prediction model (multivariate phase space reconstruction–combined kernel function-least squares support vector machine based on multivariate phase space reconstruction and combined kernel function-least squares support vector machine is proposed. The C-C method is used to determine the optimal time delay and the optimal embedding dimension of traffic variables’ (flow, speed, and occupancy time series for phase space reconstruction. The G-P method is selected to calculate the correlation dimension of attractor which is an important index for judging chaotic characteristics of the traffic variables’ series. The optimal input form of combined kernel function-least squares support vector machine model is determined by multivariate phase space reconstruction, and the model’s parameters are optimized by particle swarm optimization algorithm. Finally, case validation is carried out using the measured data of an expressway in Xiamen, China. The experimental results suggest that the new proposed model yields better predictions compared with similar models (combined kernel function-least squares support vector machine, multivariate phase space reconstruction–generalized kernel function-least squares support vector machine, and phase space reconstruction–combined kernel function-least squares support vector machine, which indicates that the new proposed model exhibits stronger prediction ability and robustness.

An effective parameter optimization technique for vibration flow field characterization of PP melts via LS-SVM combined with SALS in an electromagnetism dynamic extruder

Science.gov (United States)

Xian, Guangming

2018-03-01

A method for predicting the optimal vibration field parameters by least square support vector machine (LS-SVM) is presented in this paper. One convenient and commonly used technique for characterizing the the vibration flow field of polymer melts films is small angle light scattering (SALS) in a visualized slit die of the electromagnetism dynamic extruder. The optimal value of vibration vibration frequency, vibration amplitude, and the maximum light intensity projection area can be obtained by using LS-SVM for prediction. For illustrating this method and show its validity, the flowing material is used with polypropylene (PP) and fifteen samples are tested at the rotation speed of screw at 36rpm. This paper first describes the apparatus of SALS to perform the experiments, then gives the theoretical basis of this new method, and detail the experimental results for parameter prediction of vibration flow field. It is demonstrated that it is possible to use the method of SALS and obtain detailed information on optimal parameter of vibration flow field of PP melts by LS-SVM.

Resolving the 180-degree ambiguity in vector magnetic field measurements: The 'minimum' energy solution

Science.gov (United States)

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.

TH-CD-207A-05: Lung Surface Deformation Vector Fields Prediction by Monitoring Respiratory Surrogate Signals

International Nuclear Information System (INIS)

Nasehi Tehrani, J; Wang, J; McEwan, A

2016-01-01

Purpose: In this study, we developed and evaluated a method for predicting lung surface deformation vector fields (SDVFs) based on surrogate signals such as chest and abdomen motion at selected locations and spirometry measurements. Methods: A Patient-specific 3D triangular surface mesh of the lung region at end-expiration (EE) phase was obtained by threshold-based segmentation method. For each patient, a spirometer recorded the flow volume changes of the lungs; and 192 selected points at a regular spacing of 2cm X 2cm matrix points over a total area of 34cm X 24cm on the surface of chest and abdomen was used to detect chest wall motions. Preprocessing techniques such as QR factorization with column pivoting (QRCP) were employed to remove redundant observations of the chest and abdominal area. To create a statistical model between the lung surface and the corresponding surrogate signals, we developed a predictive model based on canonical ridge regression (CRR). Two unique weighting vectors were selected for each vertex on the surface of the lung, and they were optimized during the training process using the all other phases of 4D-CT except the end-inspiration (EI) phase. These parameters were employed to predict the vertices locations of a testing data set, which was the EI phase of 4D-CT. Results: For ten lung cancer patients, the deformation vector field of each vertex of lung surface mesh was estimated from the external motion at selected positions on the chest wall surface plus spirometry measurements. The average estimation of 98th percentile of error was less than 1 mm (AP= 0.85, RL= 0.61, and SI= 0.82). Conclusion: The developed predictive model provides a non-invasive approach to derive lung boundary condition. Together with personalized biomechanical respiration modelling, the proposed model can be used to derive the lung tumor motion during radiation therapy accurately from non-invasive measurements.

TH-CD-207A-05: Lung Surface Deformation Vector Fields Prediction by Monitoring Respiratory Surrogate Signals

Energy Technology Data Exchange (ETDEWEB)

Nasehi Tehrani, J; Wang, J [UT Southwestern Medical Center, Dallas, TX (United States); McEwan, A [The University of Sydney, Sydney, New South Wales (Australia)

2016-06-15

Purpose: In this study, we developed and evaluated a method for predicting lung surface deformation vector fields (SDVFs) based on surrogate signals such as chest and abdomen motion at selected locations and spirometry measurements. Methods: A Patient-specific 3D triangular surface mesh of the lung region at end-expiration (EE) phase was obtained by threshold-based segmentation method. For each patient, a spirometer recorded the flow volume changes of the lungs; and 192 selected points at a regular spacing of 2cm X 2cm matrix points over a total area of 34cm X 24cm on the surface of chest and abdomen was used to detect chest wall motions. Preprocessing techniques such as QR factorization with column pivoting (QRCP) were employed to remove redundant observations of the chest and abdominal area. To create a statistical model between the lung surface and the corresponding surrogate signals, we developed a predictive model based on canonical ridge regression (CRR). Two unique weighting vectors were selected for each vertex on the surface of the lung, and they were optimized during the training process using the all other phases of 4D-CT except the end-inspiration (EI) phase. These parameters were employed to predict the vertices locations of a testing data set, which was the EI phase of 4D-CT. Results: For ten lung cancer patients, the deformation vector field of each vertex of lung surface mesh was estimated from the external motion at selected positions on the chest wall surface plus spirometry measurements. The average estimation of 98th percentile of error was less than 1 mm (AP= 0.85, RL= 0.61, and SI= 0.82). Conclusion: The developed predictive model provides a non-invasive approach to derive lung boundary condition. Together with personalized biomechanical respiration modelling, the proposed model can be used to derive the lung tumor motion during radiation therapy accurately from non-invasive measurements.

The morphology and evolution of the Stromboli 2002-2003 lava flow field--An example of a basaltic flow field emplaced on a steep slope

Science.gov (United States)

Lodato, Luigi; Harris, A.; Spampinato, L.; Calvari, Sonia; Dehn, J.; Patrick, M.

2007-01-01

The use of a hand-held thermal camera during the 2002–2003 Stromboli effusive eruption proved essential in tracking the development of flow field structures and in measuring related eruption parameters, such as the number of active vents and flow lengths. The steep underlying slope on which the flow field was emplaced resulted in a characteristic flow field morphology. This comprised a proximal shield, where flow stacking and inflation caused piling up of lava on the relatively flat ground of the vent zone, that fed a medial–distal lava flow field. This zone was characterized by the formation of lava tubes and tumuli forming a complex network of tumuli and flows linked by tubes. Most of the flow field was emplaced on extremely steep slopes and this had two effects. It caused flows to slide, as well as flow, and flow fronts to fail frequently, persistent flow front crumbling resulted in the production of an extensive debris field. Channel-fed flows were also characterized by development of excavated debris levees in this zone (Calvari et al. 2005). Collapse of lava flow fronts and inflation of the upper proximal lava shield made volume calculation very difficult. Comparison of the final field volume with that expecta by integrating the lava effusion rates through time suggests a loss of ~70% erupted lava by flow front crumbling and accumulation as debris flows below sea level. Derived relationships between effusion rate, flow length, and number of active vents showed systematic and correlated variations with time where spreading of volume between numerous flows caused an otherwise good correlation between effusion rate, flow length to break down. Observations collected during this eruption are useful in helping to understand lava flow processes on steep slopes, as well as in interpreting old lava–debris sequences found in other steep-sided volcanoes subject to effusive activity.

Modeling two-phase flow in three-dimensional complex flow-fields of proton exchange membrane fuel cells

Science.gov (United States)

Kim, Jinyong; Luo, Gang; Wang, Chao-Yang

2017-10-01

3D fine-mesh flow-fields recently developed by Toyota Mirai improved water management and mass transport in proton exchange membrane (PEM) fuel cell stacks, suggesting their potential value for robust and high-power PEM fuel cell stack performance. In such complex flow-fields, Forchheimer's inertial effect is dominant at high current density. In this work, a two-phase flow model of 3D complex flow-fields of PEMFCs is developed by accounting for Forchheimer's inertial effect, for the first time, to elucidate the underlying mechanism of liquid water behavior and mass transport inside 3D complex flow-fields and their adjacent gas diffusion layers (GDL). It is found that Forchheimer's inertial effect enhances liquid water removal from flow-fields and adds additional flow resistance around baffles, which improves interfacial liquid water and mass transport. As a result, substantial improvements in high current density cell performance and operational stability are expected in PEMFCs with 3D complex flow-fields, compared to PEMFCs with conventional flow-fields. Higher current density operation required to further reduce PEMFC stack cost per kW in the future will necessitate optimizing complex flow-field designs using the present model, in order to efficiently remove a large amount of product water and hence minimize the mass transport voltage loss.

Field Equations for Abelian Vector Fields in the Bianchi Type I Metric in the Framework of Teleparallel Gravity

International Nuclear Information System (INIS)

Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.

2010-01-01

Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.

Phase portraits of cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2

International Nuclear Information System (INIS)

Cairo, Laurent; Llibre, Jaume

2007-01-01

We classify all the global phase portraits of the cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2. For such vector fields there are exactly 28 different global phase portraits in the Poincare disc up to a reversal of sense of all orbits

Shear-free flows of a perfect fluid

International Nuclear Information System (INIS)

Barnes, A.

1984-01-01

Previous results on shear-free fluid flows are reviewed. Attention is then restricted to flows which satisfy the additional condition that the Weyl tensor is purely electric: Hsub(ac)=*Csub(abcd)usup(b)usup(d)=O where usup(a) is the velocity vector of the fluid. The analysis is also applied to Einstein spaces admitting a shear-free timelike vector field usup(a). If the Weyl tensor is purely electric or purely magnetic, it is shown that usup(a) is necessarily irrotational unless the spacetime has constant curvature. (author)

Geology of the Tyrrhenus Mons Lava Flow Field, Mars

Science.gov (United States)

Crown, David A.; Mest, Scott C.

2014-11-01

The ancient, eroded Martian volcano Tyrrhenus Mons exhibits a central caldera complex, layered flank deposits dissected by radial valleys, and a 1000+ km-long flow field extending to the southwest toward Hellas Planitia. Past studies suggested an early phase of volcanism dominated by large explosive eruptions followed by subsequent effusive activity at the summit and to the southwest. As part of a new geologic mapping study of northeast Hellas, we are examining the volcanic landforms and geologic evolution of the Tyrrhenus Mons flow field, including the timing and nature of fluvial activity and effects on volcanic units. New digital geologic mapping incorporates THEMIS IR (100 m/pixel) and CTX (5 m/pixel) images as well as constraints from MOLA topography.Mapping results to-date include delineation of the boundaries of the flow field, identification and mapping of volcanic and erosional channels within the flow field, and mapping and analysis of lava flow lobes. THEMIS IR and CTX images allow improved discrimination of the numerous flow lobes that are observed in the flow field, including refinement of the margins of previously known flows and identification of additional and smaller lobes. A prominent sinuous rille extending from Tyrrhenus Mons’ summit caldera is a major feature that supplied lava to the flow field. Smaller volcanic channels are common throughout the flow field; some occur in segments along crests of local topographic highs and may delineate lava tubes. In addition to volcanic channels, the flow field surface is characterized by several types of erosional channels, including wide troughs with scour marks, elongate sinuous channels, and discontinuous chains of elongate pits and troughs. High-resolution images reveal the widespread and significant effects of fluvial activity in the region, and further mapping studies will examine spatial and temporal interactions between volcanism and fluvial processes.

Fast calculation of microphone array steering vectors with shear flow

NARCIS (Netherlands)

Sijtsma, P.

2018-01-01

This paper proposes a fast method for calculating the acoustic time delay between an observer and a receiver in a shear flow. This method is applied to an outdoor microphone array measurement on a large-scale wind turbine. In such a set-up, a shear flow represents the actual wind field better than a

Robust point matching via vector field consensus.

Science.gov (United States)

Jiayi Ma; Ji Zhao; Jinwen Tian; Yuille, Alan L; Zhuowen Tu

2014-04-01

In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set.

CFD Numerical Simulation of the Complex Turbulent Flow Field in an Axial-Flow Water Pump

Directory of Open Access Journals (Sweden)

Wan-You Li

2014-09-01

Full Text Available Further optimal design of an axial-flow water pump calls for a thorough recognition of the characteristics of the complex turbulent flow field in the pump, which is however extremely difficult to be measured using the up-to-date experimental techniques. In this study, a numerical simulation procedure based on computational fluid dynamics (CFD was elaborated in order to obtain the fully three-dimensional unsteady turbulent flow field in an axial-flow water pump. The shear stress transport (SST k-ω model was employed in the CFD calculation to study the unsteady internal flow of the axial-flow pump. Upon the numerical simulation results, the characteristics of the velocity field and pressure field inside the impeller region were discussed in detail. The established model procedure in this study may provide guidance to the numerical simulations of turbomachines during the design phase or the investigation of flow and pressure field characteristics and performance. The presented information can be of reference value in further optimal design of the axial-flow pump.

Involutive distributions of operator-valued evolutionary vector fields and their affine geometry

NARCIS (Netherlands)

Kiselev, A.V.; van de Leur, J.W.

2010-01-01

We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to collective commutation closure. The linear space of such

Flow field of flexible flapping wings

Science.gov (United States)

Sallstrom, Erik

The agility and maneuverability of natural fliers would be desirable to incorporate into engineered micro air vehicles (MAVs). However, there is still much for engineers to learn about flapping flight in order to understand how such vehicles can be built for efficient flying. The goal of this study is to develop a methodology for capturing high quality flow field data around flexible flapping wings in a hover environment and to interpret it to gain a better understanding of how aerodynamic forces are generated. The flow field data was captured using particle image velocimetry (PIV) and required that measurements be taken around a repeatable flapping motion to obtain phase-averaged data that could be studied throughout the flapping cycle. Therefore, the study includes the development of flapping devices with a simple repeatable single degree of freedom flapping motion. The acquired flow field data has been examined qualitatively and quantitatively to investigate the mechanisms behind force production in hovering flight and to relate it to observations in previous research. Specifically, the flow fields have been investigated around a rigid wing and several carbon fiber reinforced flexible membrane wings. Throughout the whole study the wings were actuated with either a sinusoidal or a semi-linear flapping motion. The semi-linear flapping motion holds the commanded angular velocity nearly constant through half of each half-stroke while the sinusoidal motion is always either accelerating or decelerating. The flow fields were investigated by examining vorticity and vortex structures, using the Q criterion as the definition for the latter, in two and three dimensions. The measurements were combined with wing deflection measurements to demonstrate some of the key links in how the fluid-structure interactions generated aerodynamic forces. The flow fields were also used to calculate the forces generated by the flapping wings using momentum balance methods which yielded

Observations of vector magnetic fields in flaring active regions

Science.gov (United States)

Chen, Jimin; Wang, Haimin; Zirin, Harold; Ai, Guoxiang

1994-01-01

We present vector magnetograph data of 6 active regions, all of which produced major flares. Of the 20 M-class (or above) flares, 7 satisfy the flare conditions prescribed by Hagyard (high shear and strong transverse fields). Strong photospheric shear, however, is not necessarily a condition for a flare. We find an increase in the shear for two flares, a 6-deg shear increase along the neutral line after a X-2 flare and a 13-deg increase after a M-1.9 flare. For other flares, we did not detect substantial shear changes.

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

Science.gov (United States)

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.

Changes in measured vector magnetic fields when transformed into heliographic coordinates

Science.gov (United States)

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.

Normal forms of invariant vector fields under a finite group action

International Nuclear Information System (INIS)

Sanchez Bringas, F.

1992-07-01

Let Γ be a finite subgroup of GL(n,C). This subgroup acts on the space of germs of holomorphic vector fields vanishing at the origin in C n . We prove a theorem of invariant conjugation to a normal form and linearization for the subspace of invariant elements and we give a description of these normal forms in dimension n=2. (author)

On parasupersymmetric oscillators and relativistic vector mesons in constant magnetic fields

Science.gov (United States)

Debergh, Nathalie; Beckers, Jules

1995-01-01

Johnson-Lippmann considerations on oscillators and their connection with the minimal coupling schemes are visited in order to introduce a new Sakata-Taketani equation describing vector mesons in interaction with a constant magnetic field. This new proposal, based on a specific parasupersymmetric oscillator-like system, is characterized by real energies as opposed to previously pointed out relativistic equations corresponding to this interacting context.

Combined tangential-normal vector elements for computing electric and magnetic fields

International Nuclear Information System (INIS)

Sachdev, S.; Cendes, Z.J.

1993-01-01

A direct method for computing electric and magnetic fields in two dimensions is developed. This method determines both the fields and fluxes directly from Maxwell's curl and divergence equations without introducing potential functions. This allows both the curl and the divergence of the field to be set independently in all elements. The technique is based on a new type of vector finite element that simultaneously interpolates to the tangential component of the electric or the magnetic field and the normal component of the electric or magnetic flux. Continuity conditions are imposed across element edges simply by setting like variables to be the same across element edges. This guarantees the continuity of the field and flux at the mid-point of each edge and that for all edges the average value of the tangential component of the field and of the normal component of the flux is identical

Lovelock vacua with a recurrent null vector field

Science.gov (United States)

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.

Instabilities in the flow past localized magnetic fields

International Nuclear Information System (INIS)

Beltran, Alberto; Cuevas, Sergio; Smolentsev, Sergey

2007-01-01

The flow in a shallow layer of an electrically conducting fluid past a localized magnetic field is analyzed numerically. The field occupies only a small fraction of the total flow domain and resemblances the magnetic field created by a permanent magnet located close to the fluid layer. Two different physical cases are considered. In the first one, the fluid layer is free from externally injected electric currents, therefore, only induced currents are present. In the second case, an external electric current is injected to the fluid layer, transversally to the main flow direction. It is shown that the Lorentz force created by the interaction of the electric currents with the non-uniform magnetic field acts as an obstacle for the flow and creates different flow patterns similar to those observed in the flow past bluff bodies. A quasi-two-dimensional model that takes into account the existence of the bottom wall through a linear Hartmann-Rayleigh friction term is considered. When inertial and magnetic forces are strong enough, the wake formed behind the zone of high magnetic field is destabilized and a periodic vortex shedding similar to the classical von Karman street is found. The effect of Hartmann-Rayleigh friction in the emergence of the instability is analyzed

Quantization of the minimal and non-minimal vector field in curved space

OpenAIRE

Toms, David J.

2015-01-01

The local momentum space method is used to study the quantized massive vector field (the Proca field) with the possible addition of non-minimal terms. Heat kernel coefficients are calculated and used to evaluate the divergent part of the one-loop effective action. It is shown that the naive expression for the effective action that one would write down based on the minimal coupling case needs modification. We adopt a Faddeev-Jackiw method of quantization and consider the case of an ultrastatic...

Vector network analyzer ferromagnetic resonance spectrometer with field differential detection

Science.gov (United States)

Tamaru, S.; Tsunegi, S.; Kubota, H.; Yuasa, S.

2018-05-01

This work presents a vector network analyzer ferromagnetic resonance (VNA-FMR) spectrometer with field differential detection. This technique differentiates the S-parameter by applying a small binary modulation field in addition to the DC bias field to the sample. By setting the modulation frequency sufficiently high, slow sensitivity fluctuations of the VNA, i.e., low-frequency components of the trace noise, which limit the signal-to-noise ratio of the conventional VNA-FMR spectrometer, can be effectively removed, resulting in a very clean FMR signal. This paper presents the details of the hardware implementation and measurement sequence as well as the data processing and analysis algorithms tailored for the FMR spectrum obtained with this technique. Because the VNA measures a complex S-parameter, it is possible to estimate the Gilbert damping parameter from the slope of the phase variation of the S-parameter with respect to the bias field. We show that this algorithm is more robust against noise than the conventional algorithm based on the linewidth.

MHD shear flows with non-constant transverse magnetic field

International Nuclear Information System (INIS)

Núñez, Manuel

2012-01-01

Viscous conducting flows parallel to a fixed plate are studied. In contrast with the Hartmann setting, the problem is not linearized near a fixed transverse magnetic field, although the field tends to be transversal far from the wall. While general solutions may be formally obtained for all cases, their behavior is far more clear when the magnetic Prandtl number equals one. We consider two different instances: a fixed magnetic field at the wall, or an insulating sheet. The evolution of the flow and the magnetic field both near the plate and far from it are detailed, analyzing the possibility of reverse flow and instability of the solutions. -- Highlights: ► A conducting shear flow does not leave a transverse magnetic field invariant. ► Solutions are found for all cases, but these are more useful when kinetic and magnetic diffusivities coincide. ► Dirichlet and Neumann conditions on the magnetic field are studied. ► Reverse flow, and eventual instability, are possible.