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Area Mathematics - General concepts and linear algebra / Scalar and vector fields

IEV ref102-05-20

en
divergence
scalar div U associated at each point of a given space region with a vector U, equal to the limit of the flux of the vector which emerges from a closed surface S, divided by the volume of the interior of the surface when all its geometrical dimensions become infinitesimal

divU= lim V0 1 V S U e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGa amOvaiabgkziUkaaicdaaeqaaOWaaSaaaeaacaaIXaaabaGaamOvaa aadaWdwbqaaiaahwfacqGHflY1caWHLbWaaSbaaSqaaiaad6gaaeqa aOGaciizaiaadgeaaSqaaiaabofaaeqaniablkH7slabgUIiYlabgU IiYdaaaa@5082@

where endA is the vector surface element oriented outwards and V is the volume

Note 1 to entry: In orthonormal Cartesian coordinates, the divergence is:

divU= U x x + U y y + U z z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWcaaqaaiabgkGi2kaadwfadaWgaaWcbaGa amiEaaqabaaakeaacqGHciITcaWG4baaaiabgUcaRmaalaaabaGaey OaIyRaamyvamaaBaaaleaacaWG5baabeaaaOqaaiabgkGi2kaadMha aaGaey4kaSYaaSaaaeaacqGHciITcaWGvbWaaSbaaSqaaiaadQhaae qaaaGcbaGaeyOaIyRaamOEaaaaaaa@4D81@

Note 2 to entry: The divergence of the vector field U is denoted div U or U.


fr
divergence, f
scalaire div U associé en chaque point d'un domaine déterminé de l'espace à un vecteur U, égal à la limite du quotient du flux du vecteur sortant d'une surface fermée S par le volume de l'intérieur de la surface lorsque toutes ses dimensions géométriques tendent vers zéro

divU= lim V0 1 V S U e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGa amOvaiabgkziUkaaicdaaeqaaOWaaSaaaeaacaaIXaaabaGaamOvaa aadaWdwbqaaiaahwfacqGHflY1caWHLbWaaSbaaSqaaiaad6gaaeqa aOGaciizaiaadgeaaSqaaiaabofaaeqaniablkH7slabgUIiYlabgU IiYdaaaa@5082@

endA est l'élément vectoriel de surface orienté vers l'extérieur et V est le volume

Note 1 à l'article: En coordonnées cartésiennes orthonormées, la divergence est:

divU= U x x + U y y + U z z MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiGacsgacaGGPbGaai ODaiaahwfacqGH9aqpdaWcaaqaaiabgkGi2kaadwfadaWgaaWcbaGa amiEaaqabaaakeaacqGHciITcaWG4baaaiabgUcaRmaalaaabaGaey OaIyRaamyvamaaBaaaleaacaWG5baabeaaaOqaaiabgkGi2kaadMha aaGaey4kaSYaaSaaaeaacqGHciITcaWGvbWaaSbaaSqaaiaadQhaae qaaaGcbaGaeyOaIyRaamOEaaaaaaa@4D81@ .

Note 2 à l'article: La divergence du champ vectoriel U est notée div U ou U.


de
Divergenz, f

es
divergencia

ja
発散

pl
dywergencja

pt
divergência

sr
дивергенција, ж јд

sv
divergens

zh
散度

Publication date: 2017-07
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