# Vector Field

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## vector field

[′vek·tər ‚fēld]
(mathematics)
The field of vectors arising from considering a system of differential equations on a differentiable manifold.
A function whose range is in a vector space.
(physics)
A field which is characterized by a vector function.

## Vector Field

a region, at each point P of which a vector a(P) is assigned. Mathematically, a vector field can be defined in a given region G by the vector function a(P) of the variable point P of this region. A whole series of physical phenomena and processes (for example, the vectors of the velocities of a moving fluid’s particles at each moment of time form a vector field) lead to the concept of a vector field. Vector-field theory has been extensively developed and has diverse applications in various branches of natural science.

### REFERENCE

Budak, B. M., and S. V. Fomin. Kratnye integraly i riady, 2nd ed.Moscow, 1967.

E. G. POZNIAK

References in periodicals archive ?
For each point in the image, three components of gradient are computed by filtering the volume data with three Sobel kernels to construct the 3D gradient field.
The pixel shift magnitude and direction indicate the strength and direction, respectively, of the refractive index gradient field.
If f, M are as above, then there exists an approximate gradient field for f on the set regf of regular points of f.
Coating defects are identified by locating the epicenter of the DC voltage gradient field created as the CP current travels to a coating anomaly.
These poor results are primarily because the velocity gradient field calculated from the velocity field obtained via the finite element method near the two singular corners where the barrel surface and the screw flight meet is worse in its accuracy than the data obtained in the other regions.
0 Tesla magnet with a gantry opening of at least 70 cm as well as a gradient field strength of at least 45 mT / m per room axis and a nominal one is required Slewrate of at least 200 mT / m / ms.
This method is useful because the velocity gradient field is calculated based on the local coordinate system from the filling analysis, and the flowability constants in Eq.
With its cryogenless superconducting magnet design, unique gradient field technology, and the industry's best slew rate, Ultra is one of the most powerful whole-body open-MRI systems available today.
The spatial location of the particles via a static gradient field, the so-called selection field achieved which a slowly varying field, the focus area, is superimposed to the selected scan the imaging volume.

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