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 ?
The vector field X naturally induces a meromorphic vector field Y on B such that [[PI].
1), we obtain easily that for a Yamabe soliton the vector field V is a conformal vector field, that is,
The key point of proposed MA-R algorithm is to compute the motion vector field of the to-be-reconstructed frame by using the neighboring reconstructed key frames.
g]) admitting an ACV vector field which also satisfies the evolution equation (6) of an ARS vector field.
As another example, consider a vector field V, with components [V.
Note: Determinism Test of the approximated vector field for the attractor of DJIA, which is embedded in a three-dimensional manifold, with the pertaining determinism factor L = 0.
Section 3 deals with the classification of the integral curves of a linear vector field on [E.
Hence, there is no logical reason why the standard 3D Navier-Stokes equations must always have solutions, even when the initial velocity vector field is smooth; if they do always have solutions, it is due to probability (see [6]) and not logic, just like the Collatz 3n + 1 Conjecture and the Riemann Hypothesis (see [3,4]).
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Swarm's core instrument -- the Vector Field Magnetometer -- was provided by the Technical University of Denmark.