Langevinn.

/ˈlɒnʒəvã/

Etymology: < the name of Paul Langevin (1872–1946), French physicist.

Mathematics and Physics.

Used attributively and in the possessive to designate concepts invented by Langevin or arising out of his work, as Langevin equation n. (also Langevin's equation) (a) the general differential equation governing the Brownian motion of a free particle; (b) any of several expressions for magnetic susceptibility formulated by Langevin. Langevin equation n. (also Langevin's formula) = Langevin equation n. Langevin function n. the function coth x − 1/x, usually denoted by ℒ(x).

ΘΚΠ

the world > matter > physics > electromagnetic radiation > magnetism > [noun] > expressions of magnetic susceptibility

Langevin equation1943

the world > relative properties > number > algebra > [noun] > expression > formula

binomial theorem1755

formula1794

Rankine's formula1868

proportionality1882

Hero's formula1886

Rutherford's law1913

Mellin transform1927

Langevin equation1943

the world > relative properties > number > algebra > [noun] > expression > equation

equation1570

cardanic equation1684

binomial equation1814

simultaneous equation1816

characteristic equation1828

characteristic equation1841

characteristic equation1849

intrinsic equation of a curve1849

complete primitive1859

primitive1862

Poisson's equation1873

Jacobi equation1882

formulaic equation1884

adjoint1889

recursion formula1895

characteristic equation1899

characteristic equation1900

Pell equation1910

Lotka–Volterra equations1937

Langevin equation1943

the world > matter > physics > mechanics > types of motion > [noun] > irregular oscillation of free particles > specific formula or equation

Langevin equation1943

the world > relative properties > number > algebra > [noun] > expression > function

function1758

exponential1784

potential function1828

syzygy1850

permutant1852

Green function1863

theta-function1871

Greenian1876

Gudermannian1876

discriminoid1877

Weierstrassian function1878

gradient1887

beta function1888

distribution function1889

Riemann zeta function1899

Airy integral1903

Poisson bracket1904

Stirling approximation1908

functional1915

metric1921

Fourier transform1923

recursive function1934

utility function1934

Airy function1939

transfer function1948

objective function1949

restriction1949

multifunction1954

restriction mapping1956

scalar function1956

Langevin function1960

mass function1961

1937 F. Bitter Introd. Ferromagnetism ii. 31 The function (coth a−1/a) is sometimes written L(a), after Langevin, who first performed the derivation that led to it.]

1943 Rev. Mod. Physics 15 20 The modern theory of the Brownian motion of a free particle (i.e. in the absence of an external field of force) generally starts with Langevin's equation du/dt = − βu + A(t), where u denotes the velocity of the particle.

1951 R. M. Bozorth Ferromagnetism x. 458 The foregoing equation, known as Langevin's equation of diamagnetism, is applicable to all atoms.

1960 Reitz & Milford Found. Electromagn. Theory v. 100 Equation (5–19) then yields: 〈p₀ cos θ〉 = p₀ [coth y − 1/y], which is known as the Langevin formula.

1960 Reitz & Milford Found. Electromagn. Theory xi. 222 For a material composed entirely of one molecular species, each molecule having magnetic moment m₀, the fractional orientation is given approximately by the Langevin function.

1962 D. R. Corson & P. Lorrain Introd. Electromagn. Fields iii. 109 The Langevin equation..was first derived by Langevin in 1905 for magnetic dipoles.

1974 Jrnl. Chem. Physics 61 4242/2 To reduce the atom-chain scattering to a two-body collision process involving the incident atom and an effective single harmonic oscillator..we first develop a generalized Langevin equation governing the motion of the effective oscillator.

1985 J. J. Becker in R. M. Besançon Encycl. Physics (ed. 3) 684/1 In the classical theory of paramagnetism, the orientations of the moments are considered to be initially thermally randomized in space. An applied field produces a net magnetic moment in its direction, as described by the classical Langevin function.

1988 Nature 9 June 496/3 ‘Langevin’ equations..model the fluctuations of the polarization..and the laser electric field about their mean values.

This entry has not yet been fully updated (first published 1997; most recently modified version published online September 2018).

单词	langevin
释义	Langevinn. /ˈlɒnʒəvã/ Etymology: < the name of Paul Langevin (1872–1946), French physicist. Mathematics and Physics. Used attributively and in the possessive to designate concepts invented by Langevin or arising out of his work, as Langevin equation n. (also Langevin's equation) (a) the general differential equation governing the Brownian motion of a free particle; (b) any of several expressions for magnetic susceptibility formulated by Langevin. Langevin equation n. (also Langevin's formula) = Langevin equation n. Langevin function n. the function coth x − 1/x, usually denoted by ℒ(x). ΘΚΠ the world > matter > physics > electromagnetic radiation > magnetism > [noun] > expressions of magnetic susceptibility Langevin equation1943 the world > relative properties > number > algebra > [noun] > expression > formula binomial theorem1755 formula1794 Rankine's formula1868 proportionality1882 Hero's formula1886 Rutherford's law1913 Mellin transform1927 Langevin equation1943 the world > relative properties > number > algebra > [noun] > expression > equation equation1570 cardanic equation1684 binomial equation1814 simultaneous equation1816 characteristic equation1828 characteristic equation1841 characteristic equation1849 intrinsic equation of a curve1849 complete primitive1859 primitive1862 Poisson's equation1873 Jacobi equation1882 formulaic equation1884 adjoint1889 recursion formula1895 characteristic equation1899 characteristic equation1900 Pell equation1910 Lotka–Volterra equations1937 Langevin equation1943 the world > matter > physics > mechanics > types of motion > [noun] > irregular oscillation of free particles > specific formula or equation Langevin equation1943 the world > relative properties > number > algebra > [noun] > expression > function function1758 exponential1784 potential function1828 syzygy1850 permutant1852 Green function1863 theta-function1871 Greenian1876 Gudermannian1876 discriminoid1877 Weierstrassian function1878 gradient1887 beta function1888 distribution function1889 Riemann zeta function1899 Airy integral1903 Poisson bracket1904 Stirling approximation1908 functional1915 metric1921 Fourier transform1923 recursive function1934 utility function1934 Airy function1939 transfer function1948 objective function1949 restriction1949 multifunction1954 restriction mapping1956 scalar function1956 Langevin function1960 mass function1961 1937 F. Bitter Introd. Ferromagnetism ii. 31 The function (coth a−1/a) is sometimes written L(a), after Langevin, who first performed the derivation that led to it.] 1943 Rev. Mod. Physics 15 20 The modern theory of the Brownian motion of a free particle (i.e. in the absence of an external field of force) generally starts with Langevin's equation du/dt = − βu + A(t), where u denotes the velocity of the particle. 1951 R. M. Bozorth Ferromagnetism x. 458 The foregoing equation, known as Langevin's equation of diamagnetism, is applicable to all atoms. 1960 Reitz & Milford Found. Electromagn. Theory v. 100 Equation (5–19) then yields: 〈p₀ cos θ〉 = p₀ [coth y − 1/y], which is known as the Langevin formula. 1960 Reitz & Milford Found. Electromagn. Theory xi. 222 For a material composed entirely of one molecular species, each molecule having magnetic moment m₀, the fractional orientation is given approximately by the Langevin function. 1962 D. R. Corson & P. Lorrain Introd. Electromagn. Fields iii. 109 The Langevin equation..was first derived by Langevin in 1905 for magnetic dipoles. 1974 Jrnl. Chem. Physics 61 4242/2 To reduce the atom-chain scattering to a two-body collision process involving the incident atom and an effective single harmonic oscillator..we first develop a generalized Langevin equation governing the motion of the effective oscillator. 1985 J. J. Becker in R. M. Besançon Encycl. Physics (ed. 3) 684/1 In the classical theory of paramagnetism, the orientations of the moments are considered to be initially thermally randomized in space. An applied field produces a net magnetic moment in its direction, as described by the classical Langevin function. 1988 Nature 9 June 496/3 ‘Langevin’ equations..model the fluctuations of the polarization..and the laser electric field about their mean values. This entry has not yet been fully updated (first published 1997; most recently modified version published online September 2018). < n.1943
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