Neumannn.1
/ˈnjuːmən/, /ˈnɔɪman/, U.S. /ˈnɔɪˌmɑn/ 1.
a. Neumann's formula n. an integral formula giving the mutual inductance between a pair of neighbouring closed circuits (see quot. 1922).
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1883 E. Atkinson tr. E. Mascart & J. Joubert Treat. Electr. & Magn. I. 337 (heading) Neumann's formula.
1922 R. Glazebrook Dict. Appl. Physics II. 384/1 Hence if dl, dl′ are line elements of A and B respectively, the mutual inductance between A and B is given by dldl′cos θ/ r... The above expression is known as Neumann's formula.
1976 B. I. Bleaney & B. Bleaney Electr. & Magn. (ed. 3) v. 136 We can derive a formula for the mutual inductance... This result is known as Neumann's formula.
b. Neumann's law n. a law relating the magnitude of an induced electromotive force to the rate of change of magnetic flux (see quot. 1990).
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1905 Science 29 Sept. 395/1 Prior to 1870 the famous law of Weber (1846) had gained wide recognition, containing as it did Coulomb's law, Ampère's law, Laplace's law, Neumann's law of induction, the conditions of electric oscillation and of electric convection.
1935 C. J. Smith Intermediate Physics (ed. 2) v. xlix. 840 From Neumann's law of electromagnetic induction we may derive a value for the induced E.M.F. in a circuit due to changes in the current through it.
1990 Conc. Oxf. Dict. Physics (rev. ed.) Neumann's law, the magnitude of an electromagnetically induced e.m.f. (E) is given by E = −dΦ/dt, where Φ is the magnetic flux. This is a quantitative statement of Faraday's second law of electromagnetic induction and is sometimes known as the Faraday–Neumann law.
2. Mathematics.
a. Neumann function n. (also Neumann's function) a function of a real variable x equal to ((cos nπ) Jn(x) − J−n(x))/sin nπ (where Jn is a Bessel function), which is a solution of Bessel's equation when n is not an integer.
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1899 Proc. Royal Soc. 66 33 If also Yn(z) denote Neumann's function of the nth order, [etc.].
1902 Science 25 July 127/2 In the corresponding two-dimensional problem, the starting-point is the undisturbed solution u = Y0(kr), where Y0 is the Neumann function.
1915 E. T. Whittaker & G. N. Watson Course Mod. Anal. (ed. 2) xvii. 366 Shew also that Neumann's function Y(n)(z) satisfies the recurrence formulae.
1964 E. A. Power Introd. Quantum Electrodynamics ii. 16 The careful reader will notice that for l = 0 the spherical Neumann function n0(kr) is not sufficiently singular for the integral (26) to diverge.
1989 Encycl. Brit. XIII. 508/2 Bessel functions of the second kind are sometimes called Neumann functions.
b. Neumann problem n. (also Neumann's problem) the problem of finding a solution to a partial differential equation within a bounded region, given the first partial derivative of the solution at the boundary in the direction normal to the boundary.
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the world > relative properties > number > calculus > [noun] > differential calculus > differentiation
differentiation1776
differentiating1813
Neumann problem1913
1913 Science 26 Dec. 905/1 In a third paper published in the Acta Mathematica in 1897 Poincaré deals with what he calls Neumann's problem.
1927 G. C. Evans Logarithmic Potential (Amer. Math. Soc. Colloquium Publ. No. 6) iv. 58 Equation (D) gives the solution of the Neumann problem for the class of functions (jj).
1959 G. James & R. C. James Math. Dict. (ed. 2) 265/2 The solution U(Q) of the Neumann problem can be represented in the form [etc.].
1976 Math. of Computation 30 73 (heading) Nonelliptic Approximation of Neumann's Problem.
1989 Encycl. Brit. XIII. 495/2 It turns out the Neumann problem cannot be solved for Laplace's equation uxx + uyy = 0 unless the prescribed function f satisfies the condition that the integral of f around the boundary equals zero.
This is a new entry (OED Third Edition, September 2003; most recently modified version published online March 2022).
Neumannn.2
/ˈnjuːmən/, /ˈnɔɪman/, U.S. /ˈnɔɪˌmɑn/ Metallurgy.
attributive. Designating narrow bands, lines, or lamellae parallel to crystallographic planes which can be seen in α-iron (ferrite) that has been subjected to sudden shock, and are usually attributed to twinning. Esp. in Neumann line, Neumann band.
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the world > matter > chemistry > crystallography (general) > crystal (general) > crystal types > [noun] > composite crystals > twin > Neumann bands
Neumann band1886
Neumann line1886
1886 Proc. Amer. Acad. Arts & Sci. 1885–6 21 498 On different sections of meteorites Widmanstättian figures and Neumann lines can be exhibited in every gradation, from the broadest bands to the finest markings.
1914 Jrnl. Soc. Chem. Industry 15 Aug. 791/2 The Neumann lamellæ occurring in any given grain are parallel to not more than 6 planes corresponding to the crystalline orientation of the grain itself.
1922 Chem. Abstr. 16 3845 (heading) Neumann bands as evidence of action of explosives upon metal.
1946 Jrnl. Iron & Steel Inst. 154 129 p/1 The Neumann band is primarily a shearing or faulting movement operating along the pre-existent planar disjunctions of the mosaic structure, and..as a secondary operation twinning may be completed, as is known to be possible in ferrite.
1966 C. R. Tottle Sci. Engin. Materials iii. 64 In alpha iron (b.c.c.) impact loading at room temperature can produce shear twins, called Neumann bands (which are found, incidentally, in metallic meteorites).
1986 J. G. Burke Cosmic Debris iv. 130 Scientists now accept that almost all Neumann bands [in meteorites] were formed by the shock of a long past cosmic event, though a few might have been the result of entry into the atmosphere.
1999 H. Y. McSween Meteorites (ed. 2) vi. 196 (caption) This cut shows Neumann lines formed by shock deformation, but is otherwise featureless.
This entry has been updated (OED Third Edition, September 2003; most recently modified version published online March 2022).
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