| 释义 |
divergence|dɪˈvɜːdʒəns, daɪ-|
[ad. mod.L. dīvergentia (f. dīvergĕre) or a. F. divergence (17th c. in Hatz.-Darm.): see divergent and -ence.]
1. The action of diverging: moving off in different directions from the same point (called the point of divergence), so that the intervening distance continually increases. The opposite of convergence.
1656Hobbes Six Less. iii. Wks. 1845 VII. 252 That angle which is generated by the divergence of two straight lines. 1657Wallis Corr. of Hobbes ix. 81 Doth it remain the same angle, the same quantity of divergence? 1713Derham Phys. Theol. iv. ii. (Seager) The convergences and divergences of the rays. 1870R. M. Ferguson Electr. 34 This divergence from the true north.
b. ellipt. for amount or degree of divergence.
1880Gray Struct. Bot. iv. §i. 121 This angular divergence (i.e. the angular distance of any two successive leaves). 1882Vines Sachs' Bot. 608 The stamens stand in one or two turns with the divergence 8/21 or 13/34.
2. transf. and fig. The departure from each other of two paths, courses, modes of action, or processes; continuous departure or deviation from a standard or norm.
1839Alison Hist. Europe (1849–50) VII. xliv. §84. 370 Augereau's divergence had been occasioned by something more than the snow-storm. 1858Gladstone Homer II. 140 The natural divergence of the two traditions. 1871L. Stephen Playgr. Eur. iv. iii. 232 There was the widest divergence of opinion as to our probable fate. 1888Bryce Amer. Commw. II. ii. xl. 88 note, An illustration of the divergences between countries both highly democratic.
3. Math.
a. Of a series: the action of diverging (diverge v. 1 c), or fact of being divergent.
b. In fluid motion, the decrement of density at any point. In quaternions, the negative of the scalar part of the result of operating with the Hamiltonian operator upon a vector function (which serves to measure such decrement).
1858Todhunter Algebra xl. heading, Convergence and Divergence of Series.
Restrict Math. to senses 3 a, b in Dict. [3.] [b.] Substitute for def.: The scalar product (written div F or ∇· F ) of the operator ∇ (see del n.) and some given vector F ; it gives a measure of the quantity of flux emanating from any point of the vector field or the rate of loss of mass, heat, etc., from it. Abbrev. div n.2 (Examples.)
[1871J. C. Maxwell in Proc. London Math. Soc. III. 231, I propose to call the scalar part the Convergence of σ... I think..that the convergence of a vector function is a very good name for the effect of that vector function in carrying its subject inwards towards a point.] 1878W. K. Clifford Elements of Dynamic iii. ii. 209 Prof. Clerk Maxwell calls the quantity -E the convergence of σ. We might perhaps therefore call E itself the divergence of σ. 1950H. Lass Vector & Tensor Analysis ii. 46 The divergence of a curl is zero. 1973J. Yarwood Electr. & Magnetism 638 The divergence of a vector is concerned with the net outflow of some physical entity, such as heat or electric flux, through the surface area of a unit volume in a vector field.
c. The horizontal movement of air or ocean currents away from a region, a process accompanied by a vertical movement into it; a mathematical measure of this, such as the divergence (sense 3 b) of the velocity vector.
1906Shaw & Lempfert Life Hist. Surface Air Currents i. 18 A position of ascent is indicated by the trajectories where there is a convergence of the lines and a position of descent where there is divergence... These terms must be understood in a generalised or mathematical sense. 1919N. Shaw Man. Meteorol. IV. 105 The mapping of a large area for air motion will generally disclose a series of lines or points of convergence or divergence of the instantaneous lines of flow with which must be associated instantaneous upward or downward flow. 1944Jrnl. Meteorol. I. 3/1 In a qualitative sense we may visualize positive horizontal divergence as a horizontal spreading of air, and negative divergence (i.e. convergence) as a horizontal crowding of air. 1967R. W. Fairbridge Encycl. Atmospheric Sci. 250/2 The large-scale motions of the atmosphere..are characterized by very small values of the divergence (∼10-6 sec-1) . 1984A. C. & A. Duxbury Introd. World's Oceans vii. 226 (caption) The major surface currents of the world's oceans, with principal zones of surface convergence and divergence shown.
d. A region where there is a divergence of air or ocean currents.
1942H. Sverdrup Oceanogr. for Meteorologists v. 85 Ascending motion occurs in regions of diverging currents (divergences). 1959H. Wexler in B. Bolin Atmosphere & Sea in Motion 113/2 It appears difficult to find a strictly internal explanation for such a sharp fixed line as the Antarctic Divergence. 1984A. C. & A. Duxbury Introd. World's Oceans vi. 186 Water from below is upwelled at a divergence. |