# Divergence

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Related to Divergence: Divergence theorem

## divergence

[də′vər·jəns]
(electronics)
The spreading of a cathode-ray stream due to repulsion of like charges (electrons).
(fluid mechanics)
The ratio of the area of any section of fluid emerging from a nozzle to the area of the throat of the nozzle.
(mathematics)
For a vector-valued function, the sum of the diagonal entries of the Jacobian matrix; it is the scalar product of the del operator and the vector.
(meteorology)
The two-dimensional horizontal divergence of the velocity field.
(nucleonics)
In a nuclear reactor, the condition wherein the number of neutrons produced increases in each succeeding generation.
(oceanography)
A horizontal flow of water, in different directions, from a common center or zone.
(physics)
The spreading apart of a beam of particles of light.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Divergence

in biology, the divergence of characters of organisms in the process of evolution.

The concept of divergence was proposed by C. Darwin to explain the appearance of diverse varieties of cultivated plants, breeds of domestic animals, and biological species in nature. In artificial selection divergence within each group of cultivated plants and domestic animals depends on the needs of man. Darwin used the principle of divergence to explain species formation in nature. If a species has a broad distribution and adapts to various ecological conditions, divergence takes place. Divergence is expressed in the appearance of differences in populations that were originally similar and is caused by the inevitably slightly different direction of natural selection in various parts of a species’ range. Divergence leads to the appearance of organisms that vary in structure and function; this in turn assures more complete use of environmental conditions, since, according to Darwin, the greatest “sum of life” is realized by the broadest variety of structures. Divergence is supported by the struggle for existence: usually even slightly specialized forms have selective advantages, which brings about more rapid extinction of intermediate forms and development of various types of isolation. The principle of divergence also explains the process of formation of larger (supraspecies) systematic groups and the rise of gaps between them.

A. V. IABLOKOV

## Divergence

[of a vector field a(M) at a point (x, y, z)], the scalar quantity

div a = σPx + σQy + σRR/σZ

where P, Q, and R are components of the vector a. The divergence is the limit of the ratio of the flux of a vector field through a closed surface surrounding the given point, to the volume delimited by it when the surface contracts toward the point. Divergence plays an important role in the applications of mathematics to physics. For example, if the vector field a(M) is considered to be a velocity field in a steady flow of an incompressible fluid, then div a at a point designates the intensity of the source (div a > 0) or of the flow (div a < 0) located at this point, or the absence of source and flow (div a = 0). The properties of divergence are:

div (a + b) = div a + div b

div (φa) = φ div a + a grad φ div rot a =0

where Δ is a Laplace operator.

## divergence

Directional divergence or divergence due to diffluent flow.
i. A static instability due to the aerodynamic loads which deform the control surface or body being greater than the elastic restoring forces.
ii. A situation in which a control application by the pilot results in uncommanded and/or undesirable behavior of the aircraft that is unintended by the pilot, such as a steepening spiral descent, spin, pitch-up, etc. Divergence may result in severe deformation or even breakup of the aircraft.
iii. A condition that exists when the distribution of winds within a given area results in a net horizontal flow of air outward from the region.

## digital divergence

(1) See technology gap.

(2) Using digital technologies, the capability of creating infinite product variations that were far more difficult by mechanical methods. See Long Tail and digital convergence.
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References in periodicals archive ?
A function D : NS(U) x NS(U) [right arrow] R is a divergence measure of neutrosophic sets if it satisfies the following conditions:
So we simulated the photovoltaic characteristics of triple-junction cells under the illumination of light sources with different divergence angles.
Furthermore, it possesses enough sequence divergence required for species discrimination (Hebert et al., 2003 b).
"The outcome is likely to be increased divergence between those economies that have built up resilience, like the US and India, and those that are vulnerable to negative shocks, like Brazil, South Africa and Turkey."
The quality of received signal and BER is analysed for various transmitter beam divergence angles.
In terms of what Allianz-owned PIMCO is thinking about its portfolio holdings, El-Erian says dealing with divergence is the name of the game for the bond shop, as well as for others managing money.
At least a half-dozen cases of linguistic divergence can be found around the world, often resulting from the desire of a national or ethnic group to assert a separate identity.
Divergence soils in geotechnical engineering are among the most problematic soils and monuments as one of the causes of soil degradation are the hydraulic structures - dirt and water channels have been the source of many injuries [8].
Once a divergence develops, it is important to monitor the following.
But experts said that while borrowing for house purchases looks set to lift further in the next few months, the latest figures also showed a "striking divergence" between the pick-up in lending to households and borrowing by businesses.
Kidapawan City - "Convergence, not divergence." This was the message of former peace adviser Jesus Dureza to elusive Moro leader Professor Nur Misuari now that the talks between the government and another Moro rebel group are already yielding "good results."

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