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Laplace Laplace Fr.: Laplace The French great mathematician, physicist, and astronomer Pierre-Simon Marquis de Laplace (1749-1827). → Laplace operator; → Laplace plane; → Laplace resonance; → Laplace transform; → Laplace's demon ; → Laplace's equation ; → Kant-Laplace hypothesis |
Laplace operator âpârgar-e Laplace Fr.: opérateur de Laplace Same as → Laplacian. |
Laplace plane hâmon-e Laplace Fr.: plan de Laplace The plane normal to the axis about which the pole of a satellite's orbit → precesses. In his study of Jupiter's satellites, Laplace (1805) recognized that the combined effects of the solar tide and the planet's oblateness induced a "proper" inclination in satellite orbits with respect to Jupiter's equator. He remarked that this proper inclination increases with the distance to the planet, and defined an orbital plane (currently called Laplace plane) for circular orbits that lies between the orbital plane of the planet's motion around the Sun and its equator plane (Tremaine et al., 2009, AJ, 137, 3706). |
Laplace resonance bâzâvâyi-ye Laplace Fr.: résonance de Laplace An → orbital resonance that makes a 4:2:1 period ratio among three bodies in orbit. The → Galilean satellites → Io, → Europa, → Ganymede are in the Laplace resonance that keeps their orbits elliptical. This interaction prevents the orbits of the satellites from becoming perfectly circular (due to tidal interactions with Jupiter), and therefore permits → tidal heating of Io and Europa. For every four orbits of Io, Europa orbits twice and Ganymede orbits once. Io cannot keep one side exactly facing Jupiter and with the varying strengths of the tides because of its elliptical orbit, Io is stretched and twisted over short time periods. This commensurability was first pointed out by Pierre-Simon Laplace, → Laplace; → resonance. |
Laplace transform tarâdis-e Laplace (#) Fr.: transformée de Laplace An integral transform of a function obtained by multiplying the given function f(t) by e^{-pt}, where p is a new variable, and integrating with respect to t from t = 0 to t = ∞. |
Laplace's demon pari-ye Laplace Fr.: démon de Laplace An imaginary super-intelligent being who knows all the laws of nature and all the parameters describing the state of the Universe at a given moment can predict all subsequent events by virtue of using physical laws. In the introduction to his 1814 Essai philosophique sur les probabilités, Pierre-Simon Laplace puts forward this concept to uphold → determinism, namely the belief that the past completely determines the future. The relevance of this statement, however, has been called into question by quantum physics laws and the discovery of → chaotic systems. |
Laplace's equation hamugeš-e Laplace Fr.: équation de Laplace A → linear differential equation of the second order the solutions of which are important in many fields of science, mainly in electromagnetism, fluid dynamics, and is often used in astronomy. It is expressed by: ∂^{2}V/ ∂x^{2} + ∂^{2}V/ ∂y^{2} + ∂^{2}V/ ∂z^{2} = 0. Laplace's equation can more concisely expressed by: ∇^{2}V = 0. The function V may, for example, be the potential at any point in the electric field where there is no free charge. The general theory of solutions to Laplace's equation is known as potential theory. |
Laplacian lâplâsi (#) Fr.: laplacien A differential → operator, denoted ∇^{2} = ∇.∇, which is the sum of all second partial derivatives of a dependant variable: ∇^{2}≡ ∂^{2}/∂x^{2} + ∂^{2}/∂y^{2} + ∂^{2}/∂z^{2}, in Cartesian coordinates. It has numerous applications in several fields of physics and mathematics. Also called Laplace operator. Named after → Laplace. |
large bozorg (#) Fr.: grand Of more than average size, quantity, degree, etc.; of great scope or range. From O.Fr. large "broad, wide," from L. largus "abundant, copious, plentiful," of unknown origin. Bozorg "great, large, immense, grand, magnificient;" Mid.Pers. vazurg "great, big, high, lofty;" O.Pers. vazarka- "great;" Av. vazra- "club, mace" (Mod.Pers. gorz "mace"); cf. Skt. vájra- "(Indra's) thunderbolt," vaja- "strength, speed;" L. vigere "be lively, thrive," velox "fast, lively," vegere "to enliven," vigil "watchful, awake;" P.Gmc. *waken (Du. waken; O.H.G. wahhen; Ger. wachen "to be awake;" E. wake); PIE base *weg- "to be strong, be lively." |
Large Magellanic Cloud (LMC) Abr-e Bozorg-e Magellan (#) Fr.: Grand Nuage de Magellan The larger of the two Magellanic Clouds dwarf irregular galaxies visible in the southern hemisphere in constellations → Dorado and → Mensa. The LMC spans 8° on the sky, which corresponds to about 20,000 → light-years in diameter, for a distance of some 170,000 light-years. It has a visible mass of about one-tenth that of our own Galaxy. The LMC and its twin, the → Small Magellanic Cloud, are two of our most prominent Galactic neighbours. → large; Magellanic named in honor of Ferdinand Magellan, the Portuguese navigator (c 1480-1521), who undertook the first voyage around the world. The two Clouds were first described by Magellan's chronicler Pigafetta, after leaving the Strait of Magellan in 1520; → cloud. |
large number adad-e bozorg Fr.: grand nombre A → dimensionless number representing the ratio of
various → physical constants. For example: |
large number hypothesis engâre-ye adadhâ-ye bozorg Fr.: hypothèse des grands nombres The idea whereby the coincidence of various → large numbers would bear a profound sense as to the nature of physical laws and the Universe. Dirac suggested that the coincidence seen among various large numbers of different nature is not accidental but must point to a hitherto unknown theory linking the quantum mechanical origin of the Universe to the various cosmological parameters. As a consequence, some of the → fundamental constants cannot remain unchanged for ever. According to Dirac's hypothesis, atomic parameters cannot change with time and hence the → gravitational constant should vary inversely with time (G∝ 1/t). Dirac, P. A. M., 1937, Nature 139, 323; 1938, Proc. R. Soc. A165, 199. → large; → number; → hypothesis. |
large Reynolds number flow tacân bâ adad-e bozorg-e Reynolds Fr.: écoulement à grand nombre de Reynolds A turbulent flow in which viscous forces are negligible compared to nonlinear advection terms, which characterize the variation of fluid quantities. The dynamics becomes generally turbulent when the Reynolds number is high enough. However, the critical Reynolds number for that is not universal, and depends in particular on boundary conditions. → large; → Reynolds number; → flow. |
large scale bozorg-marpel Fr.: grande échelle 1) A scale representing measures that significantly override the usual ones of
the same kind. |
Large Synoptic Survey Telescope (LSST) teleskop-e bozorg-e hanvini barâye bardid Fr.: Grand Télescope d'étude synoptique A new kind of optical telescope with a 6.7-m diameter → primary mirror, currently under construction in Chile. It will have a large → field of view almost 10 square degrees of sky, or 40 times the size of the full moon. The LSST will move quickly between images to rapidly → survey the sky. From its mountain top site in the Andes (Cerro Pachon, a 2,682-m high mountain in Coquimbo Region), the LSST will take more than 800 panoramic images each night with its 3.2 billion-pixel camera, recording the entire visible sky twice each week. Each patch of sky it images will be visited 1000 times during the survey, each of its 30-second observations will be able to detect objects 10 million times fainter than visible with the human eye. The LSST's combination of telescope, mirror, camera, → data processing, and survey will capture changes in billions of faint objects. Hence, the data it provides will be used to create an animated, three-dimensional cosmic map with unprecedented depth and detail. This map will serve many purposes, from locating the → dark matter and characterizing the properties of the → dark energy, to tracking transient objects, to studying our own Milky Way Galaxy in depth. It will even be used to detect and track → potentially hazardous asteroids that might impact the Earth. |
large-scale structure sâxtâr-e bozorg-marpel Fr.: structure à grandes échelles The distribution of galaxies and other forms of mass on large distance scales, covering hundreds of millions of → light-years. |
Larissa Larissa (#) Fr.: Larissa The fifth of Neptune's known satellites. It orbits 73,600 km from Neptune and is a non spherical object about 208 x 178 km in size. It was discovered using NASA's Voyager 2 mission in 1989. In Gk. mythology, Larissa is a princess of Argos (in central Greece) who, according to some, bore Poseidon three sons: Akhaios, Pelasgos and Pythios (though others gave these eponymous heroes different parents). |
Larmor frequency basâmad-e Larmor (#), feregi-ye ~ (#) Fr.: fréquence de Larmor The frequency of precession of a charged particle describing a circular motion in a plane perpendicular to the magnetic induction in a uniform magnetic field. Named after Joseph Larmor (1857-1942), an Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field; → frequency. |
Larmor radius šoâ'-e Larmor (#) Fr.: rayon de Larmor The radius of the circular motion of a → charged particle moving in a → uniform magnetic field. Same as → gyroradius, → radius of gyration, → cyclotron radius. The Larmor radius (r_{L}) is obtained by equating the → Lorentz force with the → centripetal force: qvB = mv^{2}/r_{L}, which leads to r_{L} = p/(ZeB), where p is → momentum, Z is → atomic number, e is the → electron charge, and B is → magnetic induction. The frequency of this circular motion is known as the → gyrofrequency. → Larmor frequency; → radius. |
Larmor's theorem farbin-e Larmor Fr.: théorème de Larmor If a system of → charged particles, all having the same ratio of charge to mass (q/m), acted on by their mutual forces, and by a central force toward a common center, is subject in addition to a weak uniform magnetic field (B), its possible motions will be the same as the motions it could perform without the magnetic field, superposed upon a slow → precession of the entire system about the center of force with angular velocity ω = -(q/2mc)B. → Larmor frequency; → theorem. |
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