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Homogeneous regions have spatial gradient vector norm equal to zero. When evaluated over vertical position (altitude or depth), it is called vertical derivative or vertical gradient; the remainder is called horizontal gradient component, the vector projection of the full gradient onto the horizontal plane. Examples: Biology
The gradient of a function is called a gradient field. A (continuous) gradient field is always a conservative vector field: its line integral along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous) conservative ...
Biogeography is the study of the distribution of species and ecosystems in geographic space and through geological time.Organisms and biological communities often vary in a regular fashion along geographic gradients of latitude, elevation, isolation and habitat area. [1]
Elevational diversity gradient (EDG) is an ecological pattern where biodiversity changes with elevation. The EDG states that species richness tends to decrease as elevation increases, up to a certain point, creating a "diversity bulge" at middle elevations.
These gradients are critical for cellular identity and cell relocation. Similarly, the gradients produced by cells may influence cellular fate by their temporal and spatial characteristics. In certain organisms, the choice of cell fate can be determined by a gradient, a binary choice, or through a relay of molecules released by a cell. [1]
Download as PDF; Printable version; ... the gradient is the vector field: ... as in the following example which uses the algebraic identity C⋅(A ...
Species richness, or biodiversity, increases from the poles to the tropics for a wide variety of terrestrial and marine organisms, often referred to as the latitudinal diversity gradient. [1] The latitudinal diversity gradient is one of the most widely recognized patterns in ecology. [1] It has been observed to varying degrees in Earth's past. [2]
The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).