pâyâ-ye Kolmogorov (#)
Fr.: constante de Kolmogorov
The proportionality constant C in Kolmogorov's mathematical analysis of → turbulence which states that the spectral energy E(k) in the range of turbulent scales is E(k) =C ε2/3 k-5/3, where k represents the → wave number (inversely proportional to the wavelength or → eddy size), and ε is the average energy dissipation per unit mass in the fluid. Experimental measurements give C close to 1.5.
Andrei Nikolaevich Kolmogorov (1903-1987), a prominent Soviet mathematician, who made major advances in different scientific fields, mainly probability theory, topology, turbulence, classical mechanics, and computational complexity; → constant.
Fr.: échelle de Kolmogorov
Fr.: spectre de Kolmogorov
The distribution of energy over different scales in a → turbulent flow where → energy cascade occurs. Let E be the energy per unit → wave number (k) and ε the energy → dissipation parameter, E = E(k,ε). → Dimensional analysis yields: E = Cε2/3k-5/3, where C is the → Kolmogorov constant.
A. N. Kolmogorov, 1941, Local structure of turbulence in an incompressible fluid for very large Reynolds numbers, Doklady Acad Sci. USSR 31, 301; → spectrum.
Fr.: mécanisme de Kozai-Lidov
In the → three-body problem, the → perturbation of the orbit of a → secondary body by the garvity of a third body located at a distance much larger than the separation between the → primary body and the secondary. The secondary's orbit oscillates about a constant value involving a periodic exchange between the extreme values of its → inclination and orbital → eccentricity. The Kozai-Lidov mechanism results from the conservation of the quantity (1 - e2)1/2.cos i for each component, where e is eccentricity and i is inclination. The total → angular momentum of the system remains constant while the angular momentum is exchanged betwwen the components. It has been suggested that the Kozai mechanism is responsible for the high eccentricities observed in the orbits of → extrasolar planets. If the parent star has a massive yet unseen substellar companion, orbiting at a great distance, and in an orbit highly inclined to the plane of the planets' orbits, the mechanism should induce high eccentricities into the orbits of the planets. Similarly, this mechanism may be responsible for the high eccentricities observed in the orbits of many → Kuiper Belt Objects such as 2003 UB313.
Named for the japanese Yoshihide Kozai (1962, Astronomical J. 67, 591), and the Russian Michael Lidov (1962, Planetary & Space Science 9, 719).
qânun-e Kramers (#)
Fr.: loi de Kramers
An approximate expression for deriving the → opacity that depends upon temperature with a power law: κ ∝ ρT-3.5, where ρ represents the density. In → partial ionization zones, a part of the energy released during a layer's compression can be used for further ionization, rather than raising the temperature of the gas. As the temperature of the compressed layer has not substantially increased, the increase in density produces a corresponding increase in the opacity of the layer. Likewise, during the expansion phase, the temperature does not decrease significantly since the ions release energy when they recombine with electrons.
Derived in 1923 by the Dutch physicist Henrik Kramers (1894-1952); → law.
Kramers' opacity law
qânun-e kederi-ye Kramers (#)
Fr.: loi de l'opacité de Kramers
Same as → Kramers' law.
Named after Henrik Kramers (1894-1952); → law.
deltâ-ye Kronecker (#)
Fr.: delta de Kronecker
The function δik of two variables i and j defined by δik = 1 if i = j, and δik = 0 if i ≠ j.
Leopold Kronecker (1823-1891), a German mathematician; delta, Gk. letter of alphabet.
Fr.: diagramme de Kruskal
A diagram used to plot trajectories in → space-time near a → black hole. The vertical and horizontal axes are two complicated functions of time and distance from the black hole. Lines of constant time radiate from the origin of the diagram, with steeper slopes corresponding to later times. Lines of constant distance are hyperbolas, lines of constant time pass through the origin; photons always travel along diagonal lines at ±45° to the vertical. The trajectory of an object falling into the black hole is shown as a curving line moving upward on the diagram at less than 45° to the vertical.
Named after the American physicist Martin David Kruskal (1925-2006); → diagram.
A colorless, odorless, highly un-reactive gaseous chemical element and a member of the inert gas family. Symbol Kr; atomic number 36; atomic weight 83.80; melting point -156.6°C; boiling point -152.3°C.
Krypton, from Gk. kryptos "concealed, hidden". It was discovered in liquefied atmospheric air by the Scottish chemist William Ramsay and the English chemist Morris William Travers in 1898.
kamarband-e Kuiper (#)
Fr.: ceinture de Kuiper
A region of the → Solar System extending roughly from the orbit of → Neptune, or 30 → astronomical units (AU), to 50 AU from the Sun that contains many small icy bodies. The Kuiper belt is now considered to be the source of the → short-period comets.
Named after Gerard Peter Kuiper (1905-1973), a Dutch-born American astronomer, who predicted the belt in 1951. He is also considered the father of modern planetary science for his contributions to the study of our solar system; → belt.
Kuiper belt object (KBO)
barâxt-e kamarband-e Kuiper
Fr.: objet de la ceinture de Kuiper
The measure of "peakedness" of the curve describing a frequency distribution in the region about its mode. The kurtosis of the normal distribution is 0.
From Gk. kurtosis "bulging, curvature," from kurtos "convex," kirkos "a ring;" cf. Av. skarəna- "round;" L. circus "circle, ring;" PIE base *sker- "to turn, bend."
Afrâštegi condition, state adj. of afrâšté "elevated, erect, upright," p.p. of afrâštan "to raise, exalt, extole," from Mid.Pers. abrâstan, abrâz- "to lift, raise," from ab-, from O.Pers./Av. abiy-/aiwi- "to, upon, against;" cf. Skt. abhi-, Gk. amphi- + râst "straight, direct, true;" from O.Pers. rāsta- "straight, true," rās- "to be right, straight, true;" Av. rāz- "to direct, put in line, set," razan- "order;" cf. Skt. raj- "to direct, stretch," rjuyant- "walking straight;" Gk. orektos "stretched out;" L. regere "to lead straight, guide, rule," p.p. rectus "right, straight;" Ger. recht; E. right; PIE base *reg- "move in a straight line," hence, "to direct, rule."