Regularization of vector fields by surgery
Excising neighborhood of singularity from manifold with vector field definition, making possible regularization of two and three body problems
Easton, R.↗
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Results for “vector fields”
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Geometric Representations of Condition Queries on Three-Dimensional Vector Fields
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.
Henze, Chris↗
A median filter approach for correcting errors in a vector field
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.
Schultz, H.↗
DC-magnetic field vector measurement
A magnetometer experiment was designed to determine the local magnetic field by measuring the total of the Earth's magnetic field and that of an unknown spacecraft. The measured field vector components are available to all onboard experiments via the Spacelab command and data management system. The experiment consists of two parts, an electronic box and the magnetic field sensor. The sensor includes three independent measuring flux-gate magnetometers, each measuring one component. The physical background is the nonlinearity of the B-H curve of a ferrite material. Two coils wound around a ferrite rod are necessary. One of them, a tank coil, pumps the ferrite rod at approximately 20 kilohertz. As a consequence of the nonlinearity, many harmonics can be produced. The second coil (i.e., the detection coil) resonates to the first harmonic. If an unknown dc or low-frequency magnetic field exists, the amplitude of the first harmonic is a measure for the unknown magnetic field. The voltages detected by the sensors are to be digitized and transferred to the command and data management system.
Schmidt, R.↗
The magnetic states of a van der Waals ferromagnet CrGeTe 3 probed by vector-field magnetic force microscopy
Here, we present a study on the magnetic domain configuration in the van der Waals ferromagnet CrGeTe 3 using a vector-field cryogenic magnetic force microscopy. Our investigation demonstrates the influence of magnetic fields strength and angle on the magnetic domain configuration, showing the coexistence of striped and spike-like magnetic domains. This study contributes to understanding the impact of uniaxial magnetic anisotropy on the domain configuration of van der Waals ferromagnets, offering insights into stabilizing different domain patterns.
36 MATERIALS SCIENCE↗
The Vector Field Proton Magnetometer for IGY Satellite Ground Stations
The application of homogeneous-bias fields to a proton precessional magnetometer allows the measurement of the vector field by measuring the absolute scalar field F, declination variations (Delta)D, and inclination variations (Delta)I. The absolute scalar field can be measured to an accuracy of +/- 1 gamma and absolute declination and inclination to an accuracy of +/- 2 minutes. This paper describes a vector proton magnetometer that has been in operation at nine Minitrack stations since the spring of 1958.
Shapiro, I. R.↗
Plasma flows and magnetic field vectors in the plasma sheet during substorms
A detailed study of the plasma flow and the magnetic field vector in the plasma sheet during magnetospheric substorms is made to determine whether plasma flows are field-aligned or crossfield. It is shown that there is generally a large magnetic field-aligned component in the rapid plasma flow observed in the plasma sheet during substorms. In particular, the larger the observed flow speed, the closer the observed flow direction is aligned with the magnetic field line. There is no clear association between the plasma flow direction and the sign of the Bz component of the magnetic field during plasma sheet thinnings at substorms. The rapid plasma flows observed in the magnetotail are predominantly magnetic field-aligned.
Lui, A. T. Y.↗
The development of Gibbs's dyadic and implications for the gradient of a vector field
In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.
97 MATHEMATICS AND COMPUTING↗
Multiresolution and Explicit Methods for Vector Field Analysis and Visualization
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.
Nielson, Gregory M.↗
Implementation of a Doppler-Free Saturation Spectroscopy (DFSS) Diagnostic for Helicon Wave Electric Field Vector Measurement in Edge Plasma in DIII-D
A laser-based technique known as Doppler-free saturation spectroscopy (DFSS) has been designed, fabricated, and installed on the DIII-D National Fusion Facility to measure the helicon wave electric field vector in the edge plasma. These experimental measurements quantify phenomena resulting in decreased current drive efficiency due to wave/edge plasma interactions. This implementation of DFSS on DIII-D is the first of its kind on a tokamak and thus presents unique engineering challenges, including integration of the system onto an existing multidiagnostic port flange without impacts to system serviceability, as well as maintaining precise laser alignment over a 2-m distance during disruptions and thermal drift of the vessel. Further, these challenges were resolved using innovative design approaches such as a novel decoupled shutter system to facilitate serviceability of the in-vessel mirror assemblies without the need for personnel vessel entry, as well as an ex-vessel piezo-mirror-based optical system for laser beam shaping and real-time steering of the measurement location. The solutions to these engineering challenges were demonstrated during the successful installation and operation of these diagnostic components during the 2022 DIII-D vent and subsequent experimental campaign.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Achieving Consistent Doppler Measurements from SDO/HMI Vector Field Inversions
NASA's Solar Dynamics Observatory is delivering vector magnetic field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geosynchronous orbit. The relative spacecraft-Sun velocity varies by +/-3 kms−1 over a day, which introduces major orbital artifacts in the Helioseismic Magnetic Imager (HMI) data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly developed three-stage procedure for mitigating these artifacts in the Doppler data obtained from the Milne-Eddington inversions in the HMI pipeline. The procedure ultimately uses 32 velocity-dependent coefficients to adjust 10 million pixels-a remarkably sparse correction model given the complexity of the orbital artifacts. This procedure was applied to full-disk images of AR 11084 to produce consistent Dopplergrams. The data adjustments reduce the power in the orbital artifacts by 31 dB. Furthermore, we analyze in detail the corrected images and show that our procedure greatly improves the temporal and spectral properties of the data without adding any new artifacts. We conclude that this new procedure makes a dramatic improvement in the consistency of the HMI data and in its usefulness for precision scientific studies.
Schuck, Peter W.↗
Multiresolution and Explicit Methods for Vector Field Analysis and Visualization
We first report on our current progress in the area of explicit methods for tangent curve computation. The basic idea of this method is to decompose the domain into a collection of triangles (or tetrahedra) and assume linear variation of the vector field over each cell. With this assumption, the equations which define a tangent curve become a system of linear, constant coefficient ODE's which can be solved explicitly. There are five different representation of the solution depending on the eigenvalues of the Jacobian. The analysis of these five cases is somewhat similar to the phase plane analysis often associate with critical point classification within the context of topological methods, but it is not exactly the same. There are some critical differences. Moving from one cell to the next as a tangent curve is tracked, requires the computation of the exit point which is an intersection of the solution of the constant coefficient ODE and the edge of a triangle. There are two possible approaches to this root computation problem. We can express the tangent curve into parametric form and substitute into an implicit form for the edge or we can express the edge in parametric form and substitute in an implicit form of the tangent curve. Normally the solution of a system of ODE's is given in parametric form and so the first approach is the most accessible and straightforward. The second approach requires the 'implicitization' of these parametric curves. The implicitization of parametric curves can often be rather difficult, but in this case we have been successful and have been able to develop algorithms and subsequent computer programs for both approaches. We will give these details along with some comparisons in a forthcoming research paper on this topic.
Source record↗
The role of excitation vector fields and all-polarisation state control in cavity magnonics
Recently the field of cavity magnonics, a field focused on controlling the interaction between magnons and photons confined within microwave resonators, has drawn significant attention as it offers a platform for enabling advancements in quantum- and spin-based technologies. Here, we introduce excitation vector fields, whose polarisation and profile can be easily tuned in a two-port cavity setup, thus acting as an effective experimental dial to explore the coupled dynamics of cavity magnon-polaritons. Moreover, we develop theoretical models that accurately predict and reproduce the experimental results for any polarisation state and field profile within the cavity resonator. This versatile experimental platform offers a new avenue for controlling spin-photon interactions by manipulating the polarisation of excitation fields. By introducing real-time tunable parameters that control the polarisation state, our experiment delivers a mechanism to readily control the exchange of information between hybrid systems.
condensed-matter physics↗
Velocity Vector Field Visualization of Flow in Liquid Acquisition Device Channel
A capillary flow liquid acquisition device (LAD) for cryogenic propellants has been developed and tested in NASA Glenn Research Center to meet the requirements of transferring cryogenic liquid propellants from storage tanks to an engine in reduced gravity environments. The prototypical mesh screen channel LAD was fabricated with a mesh screen, covering a rectangular flow channel with a cylindrical outlet tube, and was tested with liquid oxygen (LOX). In order to better understand the performance in various gravity environments and orientations at different liquid submersion depths of the screen channel LAD, a series of computational fluid dynamics (CFD) simulations of LOX flow through the LAD screen channel was undertaken. The resulting velocity vector field visualization for the flow in the channel has been used to reveal the gravity effects on the flow in the screen channel.
McQuillen, John B.↗
Solar magnetic field studies using the 12 micron emission lines. II - Stokes profiles and vector field samples in sunspots
Polarimetric observations at 12 microns of two sunpots are reported. The horizontal distribution of parameters such as magnetic field strength, inclination, azimuth, and magnetic field filling factors are presented along with information about the height dependence of the magnetic field strength. Comparisons with contemporary magnetostatic sunspot models are made. The magnetic data are used to estimate the height of 12 micron line formation. From the data, it is concluded that within a stable sunspot there are no regions that are magnetically filamentary, in the sense of containing both strong-field and field-free regions.
Hewagama, Tilak↗
Multiscale vector fields for image pattern recognition
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.
Low, Kah-Chan↗
Von Neumann Stability Analysis of DG-Like and PNPM-Like Schemes for PDEs with Globally Curl-Preserving Evolution of Vector Fields
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Dinshaw S. Balsara↗