翻訳と辞書
Words near each other
・ Divertimenti for ten winds (Mozart)
・ Divertimento
・ Divertimento (Penderecki)
・ Divertimento for chamber orchestra after keyboard pieces by Couperin
・ Divertimento for String Orchestra (Bartók)
・ Divertimento in E-flat (Mozart)
・ Divertimento in G major (Haydn)
・ Divertimento No. 11 (Mozart)
・ Diver rescue
・ Diver training organizations
・ Diver trim
・ Diver's pump
・ Diver-class rescue and salvage ship
・ Divercala
・ Divercia
Divergence
・ Divergence (album)
・ Divergence (computer science)
・ Divergence (disambiguation)
・ Divergence (film)
・ Divergence (linguistics)
・ Divergence (novel)
・ Divergence (statistics)
・ Divergence Eve
・ Divergence of the sum of the reciprocals of the primes
・ Divergence Peak
・ Divergence problem
・ Divergence theorem
・ Divergence-from-randomness model
・ Divergent (film)


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Divergence : ウィキペディア英語版
Divergence

In vector calculus, divergence is a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
For example:
consider air as it is heated or cooled. The relevant vector field for this example is the velocity of the moving air at a point. If air is heated in a region it will expand in all directions such that the velocity field points outward from that region. Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. If the air cools and contracts, the divergence has a negative value, as the region is a sink.
== Definition of divergence ==

In physical terms, the divergence of a three-dimensional vector field is the extent to which the vector field flow behaves like a source or a sink at a given point. It is a local measure of its "outgoingness"—the extent to which there is more exiting an infinitesimal region of space than entering it. If the divergence is nonzero at some point then there must be a source or sink at that position.〔(DIVERGENCE of a Vector Field )〕 (Note that we are imagining the vector field to be like the velocity vector field of a fluid (in motion) when we use the terms flow, sink and so on.)
More rigorously, the divergence of a vector field F at a point ''p'' is defined as the limit of the net flow of F across the smooth boundary of a three-dimensional region ''V'' divided by the volume of ''V'' as ''V'' shrinks to ''p''. Formally,
:\operatorname\,\mathbf(p) =
\lim_ \over |V| } \; dS
where |''V'' | is the volume of ''V'', ''S''(''V'') is the boundary of ''V'', and the integral is a surface integral with n being the outward unit normal to that surface. The result, div F, is a function of ''p''. From this definition it also becomes explicitly visible that div F can be seen as the ''source density'' of the flux of F.
In light of the physical interpretation, a vector field with constant zero divergence is called ''incompressible'' or ''solenoidal'' – in this case, no net flow can occur across any closed surface.
The intuition that the sum of all sources minus the sum of all sinks should give the net flow outwards of a region is made precise by the divergence theorem.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Divergence」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.