“divergence”的概念、定义、翻译、参考文献-科学参考

divergence

Physics

The scalar product of the gradient operator ∇ with a vector. For a vector u that has components u₁, u₂, and u₃ in the x, y, and z directions, and is a function of x, y, and z, the divergence is given by:
$div u = \nabla . u = \partial u_{1} / \partial x + \partial u_{2} / \partial y + \partial u_{3} / \partial z .$

The divergence of a vector at a given point represents the flux of the vector per unit volume in the neighbourhood of that point. See also curl; Laplace equation.

Mathematics

For a vector function of position V(r) = V_xi + V_yj + V_zk, the divergence of V is the scalar product of the operator del with V giving

$div V = \nabla ∙ V = \frac{\partial V_{x}}{\partial x} + \frac{\partial V_{y}}{\partial y} + \frac{\partial V_{z}}{\partial z} .$

For a fluid with flow velocity u, then divu measures the rate of expansion of the fluid locally. Compare curl, gradient.

Biology

1. (in neuroanatomy) The branching of the terminal axon of a neuron so that it connects with numerous target cells. For example, each horizontal cell in the retina of the eye has a greatly branched axon ending that can transmit signals to many other cells in the retina.
2. Divergent evolution. See adaptive radiation. Compare convergence.

Geology and Earth Sciences

1. In meteorology, a situation in which, over a given time, more air flows out of a given area than flows in. Some subsiding motion can be expected to take place in the air over this region.
2. A horizontal flow of water in different directions away from a common centre or line. A particular example of divergence in the oceans is seen in areas of upwelling. Compare convergence.
3. Evolutionarily, genetic segregation and differentiation within a taxon to the extent that distinct derivative taxa result. The divergence may be at the species, genus, family, order, or higher level (see classification). Thus it is possible to refer for instance to the divergence of reptiles and mammals from a stem group, to the divergence of mammal orders, and to the divergence of a breeding population into two related species.

Geography

The spreading out of an air mass into paths of different directions, linked with the vertical shrinking of the atmosphere (see R. Barry and R. Chorley (1992) fig. 3.6). Upper-air divergence is associated with ground level depressions (Sutcliffe and Forsdyke (1950) Quart. J. RMS 76, 328), and closely related to vertical vorticity; see Chen and Bosart (1979) J. Atmos. Scis 36, 2.

单词	divergence
释义	divergence Physics The scalar product of the gradient operator ∇ with a vector. For a vector u that has components u₁, u₂, and u₃ in the x, y, and z directions, and is a function of x, y, and z, the divergence is given by: $div u = \nabla . u = \partial u_{1} / \partial x + \partial u_{2} / \partial y + \partial u_{3} / \partial z .$ The divergence of a vector at a given point represents the flux of the vector per unit volume in the neighbourhood of that point. See also curl; Laplace equation. Mathematics For a vector function of position V(r) = V_xi + V_yj + V_zk, the divergence of V is the scalar product of the operator del with V giving $div V = \nabla ∙ V = \frac{\partial V_{x}}{\partial x} + \frac{\partial V_{y}}{\partial y} + \frac{\partial V_{z}}{\partial z} .$ For a fluid with flow velocity u, then divu measures the rate of expansion of the fluid locally. Compare curl, gradient. Biology 1. (in neuroanatomy) The branching of the terminal axon of a neuron so that it connects with numerous target cells. For example, each horizontal cell in the retina of the eye has a greatly branched axon ending that can transmit signals to many other cells in the retina. 2. Divergent evolution. See adaptive radiation. Compare convergence. Geology and Earth Sciences 1. In meteorology, a situation in which, over a given time, more air flows out of a given area than flows in. Some subsiding motion can be expected to take place in the air over this region. 2. A horizontal flow of water in different directions away from a common centre or line. A particular example of divergence in the oceans is seen in areas of upwelling. Compare convergence. 3. Evolutionarily, genetic segregation and differentiation within a taxon to the extent that distinct derivative taxa result. The divergence may be at the species, genus, family, order, or higher level (see classification). Thus it is possible to refer for instance to the divergence of reptiles and mammals from a stem group, to the divergence of mammal orders, and to the divergence of a breeding population into two related species. Geography The spreading out of an air mass into paths of different directions, linked with the vertical shrinking of the atmosphere (see R. Barry and R. Chorley (1992) fig. 3.6). Upper-air divergence is associated with ground level depressions (Sutcliffe and Forsdyke (1950) Quart. J. RMS 76, 328), and closely related to vertical vorticity; see Chen and Bosart (1979) J. Atmos. Scis 36, 2.
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