Sectorfield

Sectorfield is a term used in geometry and theoretical physics to describe a field defined on a sector-shaped region of a larger domain. In two dimensions, a sector is the region between two rays emanating from a common origin, restricted in angle. A sectorfield assigns either a scalar or vector value to each point in that region, and may satisfy specified boundary conditions on the two bounding rays or on the circular arc that limits the sector.

In mathematical practice, a sectorfield F may be expressed in polar coordinates (r,θ) as F(r,θ) = r^k G(θ) for some degree k and angular profile G. Such fields are used to study how solutions to partial differential equations, such as Laplace's equation, behave near wedge-like boundaries. Sectorfields can be extended to larger domains by symmetry, reflection, or by stitching together multiple sectors.

Applications include potential theory in wedge domains, elasticity problems with wedge-shaped inclusions, and simplified models of anisotropic media. They also appear in expository discussions about boundary effects and singularities, where the angular dependence controls the strength of singularities at the apex.

The term is not widely standardized in mainstream mathematics or physics and appears mainly in pedagogical or exploratory contexts rather than formal theory. When used, it typically denotes a contextual construct rather than a universal object.

See also: vector field, scalar field, sector (geometry), wedge problem, polar coordinates.