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.org

Examples

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. Source: Internet

Conversely, a (continuous) conservative vector field is always the gradient of a function. Source: Internet

A vector field attaches to every point of the manifold a vector from the tangent space at that point, in a smooth manner. Source: Internet

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. Source: Internet

Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density. Source: Internet

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. Source: Internet

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