# 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. For simplifying the computation, the gradient modules are bound to (0, 1) by scaling the gradient field.
According to the literature [16-20], the effect of [B.sup.+.sub.1] encoding on the image quality and resolution as function of the variation in RF amplitude and nonuniformity in RF gradient field is comparable to that of [B.sub.0] gradient encoding.
The pixel shift magnitude and direction indicate the strength and direction, respectively, of the refractive index gradient field. The entire image is thus processed via the identification of unique background structures and their apparent change in location between the tare and flowfield images, providing refractive index gradient data throughout the available image area.
If f, M are as above, then there exists an approximate gradient field for f on the set regf of regular points of f.
The induced voltages caused by the pulsed gradient field in the MRI system can cause small voltages that can pace some hearts in some situations and not create much voltage in others.
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.
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.

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