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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 ...
In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux .
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. [1] A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the ...
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse:
Developmental bioelectricity is a sub-discipline of biology, related to, but distinct from, neurophysiology and bioelectromagnetics.Developmental bioelectricity refers to the endogenous ion fluxes, transmembrane and transepithelial voltage gradients, and electric currents and fields produced and sustained in living cells and tissues.
In contrast, a signal can act in a gradient, which induces a specific cell fate as a function of the concentration of the molecule in the gradient. These types of molecules are known as morphogens. An example of this phenomenon is observed in the neural tube with varying concentrations of the Sonic Hedgehog protein. [1]
A selection gradient describes the relationship between a character trait and a species' relative fitness. [1] A trait may be a physical characteristic, such as height or eye color, or behavioral, such as flying or vocalizing. Changes in a trait, such as the amount of seeds a plant produces or the length of a bird's beak, may improve or reduce ...