vector field
Noun
Meaning
(mathematics) a function mapping a subset of
R
n
{\displaystyle \mathbb {R} ^{n}}
into a subset of
R
n
{\displaystyle \mathbb {R} ^{n}}
(differential geometry) a function which associates, to each point on a surface, a vector in the tangent plane of that point
Source: en.wiktionary.orgExamples
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration.
Conversely, a (continuous) conservative vector field is always the gradient of a function.
A vector field attaches to every point of the manifold a vector from the tangent space at that point, in a smooth manner.
Concretely, on R 3 this is given by: * 1-forms and 1-vector fields: the 1-form corresponds to the vector field * 1-forms and 2-forms: one replaces dx by the "dual" quantity (i.
Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density.
Field theory interpretation For an irrotational vector field in three-dimensional space, the inverse-square law corresponds to the property that the divergence is zero outside the source.