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For example, the gradient of the function (,,) = + is (,,) = + (). or (,,) = []. In some applications it is customary to represent the gradient as a row vector or column vector of its components in a rectangular coordinate system; this article follows the convention of the gradient being a column vector, while the derivative is a row ...
For example, species abundance usually changes along environmental gradients in a more or less predictable way. However, the species abundance along an environmental gradient is not only determined by the abiotic factor associated with the gradient but, also by the change in the biotic interactions , like competition and predation, along the ...
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature spatial gradient is a vector quantity with dimension of temperature difference per unit length. The SI unit is kelvin per meter (K/m).
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).
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
A diffusion gradient is a gradient in the rates of diffusion of multiple groups of molecules through a medium or substrate.The groups of molecules may constitute multiple substances, portions of the same substance that have different temperatures, or other differentiable groupings.
Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter , but can apply to any quantity whose density can be measured .
In other words, the surface gradient is the orthographic projection of the gradient onto the surface. The surface gradient arises whenever the gradient of a quantity over a surface is important. In the study of capillary surfaces for example, the gradient of spatially varying surface tension doesn't make much sense, however the surface gradient ...