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behaves like an incompressible fluid, that is for an observer moving with the flow, the phase space density is constant. Liouville’s theorem is a consequence of the equation of continuity (see equation of continuity) in phase space


+ 6


= 0



with f being the phase space density, C the speed in phase space, and 6 the divergence in phase space. If there are collisions,

df/dt = f,t + F i f,pi + pif,xi = Coll ,

where Coll represents the collision of particles located at the same position in physical space, which diminish or replenish particles of momentum pi, and the subscript commas denote partial differentiation.

liquefaction When loosely accumulated alluvial sandy ground is shaken by strong earthquake motion, friction acting among sand particles decreases due to increase of pore water pressure, and the ground loses shear resistance, causing loss of the supporting force. This phenomenon is referred to as liquefaction. To generate liquefaction, necessary conditions are: the ground is saturated with water; the sand is loosely accumulated; the average diameter of sand particles ranges from about 0.02 to 2 mm. At the time of liquefaction, a large amount of underground water sometimes springs up with sand.

LISA (Laser Interferometric Space Antenna)

A proposal to put an array of several laser devices forming an interferometric gravitational wave detector on a heliocentric orbit. The sensitivity of gravitational wave amplitude h 1023 will be achieved in the frequency range 102 to 103 Hz. See GEO, LIGO, Virgo.

lithophile Elements that display a strong affinity to combine with oxygen. Such elements are concentrated in the crusts of the terrestrial planets and in stony meteorites.

lithosphere The outermost rigid layer of a terrestrial planet is called the lithosphere. The Earth’s lithosphere is comprised of the crust and

the upper part of the mantle. It is the region of a planet where stress and strain result in fracturing of the brittle rocks. The lithosphere is the portion of the Earth that is broken up into plates (see plate tectonics) and the motions of these plates give rise to most of the earthquake and volcanic activity on our planet. On Earth the lower boundary of the lithosphere is defined by the temperature below which rocks behave rigidly, typically 1400 K. The typical thickness of the lithosphere is 100 km although it will be much thinner in zones of active volcanism such as ocean ridges. On other planets, such as Venus and Mars, the lithosphere is not apparently broken up into plates, but extensive fracturing indicates that these surfaces also experience tectonic processes.

lithostatic pressure The lithostatic pressure pl(y) is the pressure within the earth as a function of depth y taking into account the variation of local gravitational acceleration and density ρ as a function of depth.

little ice age A period between about 1550 and 1860 during which the climate of the middle latitudes became generally colder and there was a world-wide expansion of glaciers. However, it was not always colder during this period. There were three cold subperiods. At 55N Europe, they are 1541–1680, 1741–1770, 1801–1890. In China, they are 1470–1520, 1620–1720, and 1840–1890. An explanation for the little ice age is very low solar activity during the Maunder Minimum period. Little ice age effects have been recorded in the Alps, Norway, and Iceland, where farm land and buildings were destroyed. There were times of especial severity during the early 1600s when glaciers were particularly active in Chamonix valley, in the French Alps.

littoral A term used to refer to the coastal region that is affected by wind and wave-driven sediment transport.

littoral barrier A physical barrier to longshore sediment transport. A groin, placed to try to stabilize a shoreline, represents such a barrier.

littoral cell A littoral region that does not receive or lose sediment to adjoining upcoast

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local topological defect

and downcoast areas. Sediment is transported within the littoral cell, and may enter it via a source such as a river, or leave via a submarine canyon or other sink.

littoral current A mean flow of water within the littoral zone, in the longshore direction. See longshore current.

littoral drift A term used to denote the sediment transport along a coast by wave action. See longshore sediment transport. Often measured in units of yd3/y or m3/y.

littoral drift rose A polar graph that illustrates the potential longshore sediment transport rate at a site as a function of incident wave energy.

littoral transport Transport of sediment within the littoral zone. Generally used to refer to sediment transport in the longshore direction. See longshore sediment transport.

lobe In general, a roundish division or projection of an object. See lobe dominated quasars, lobes, high latitude.

lobe dominated quasars High luminosity, radio-loud active galactic nuclei whose radio emission is dominated by extended lobe emission. Lobe dominated quasars have radio power and morphologies similar to those of Fanaroff– Riley class II radio galaxies. In quasars, the jet appears one-sided, and both core and jet have higher luminosity than in Fanaroff–Riley II galaxies. See Fanaroff–Riley radio galaxies.

lobes, high latitude (also known as tail lobes) Two regions extending into the tail of the magnetosphere (the magnetotail), located north and south of the plasma sheet. Each tail lobe contains a bundle of magnetic field lines connected to one of the Earth’s polar caps: the lines of the northern lobe lead into the region around the north magnetic pole, while those of the southern lobe come out of the region near the southern pole.

The magnetic field of the tail lobes is relatively strong and nearly uniform — about 20 to 30 nano Tesla (nT) near Earth, diminishing to 9

to 10 nT in the distant tail. Their ion density is very low, around 0.01 ion/cm3, and they seem to stretch well past 100 to 200 RE, at which distance they become infiltrated by plasma sharing the flow of the solar wind (possibly originating in the plasma mantle). The magnetic energy stored in the lobes is considerable and is widely believed to be the main energy source of substorms.

local acceleration of gravity The force per unit mass of gravitational attraction toward the Earth or other large local concentration of matter, Fgrav/m. For distance r from a spherical “Earth” of mass M the local acceleration of

gravity is

g = −zGMˆ /r2 , where zˆ is a vertical unit vector.

Local Group A group of approximately 30 galaxies, which includes the galaxy and its closest neighbor galaxies within a distance 1 Mpc. Most members are thought to form a gravitationally bound system; the Local Group is therefore the closest example of a cluster of galaxies. The brightest members are our galaxy, the spiral galaxy Messier 31 (the Andromeda galaxy), and the Sc spiral M33, although the majority of galaxies belonging to the Local Group are dwarf galaxies, either dwarf spheroidal or irregular galaxies. With present-day instruments, several galaxies of the Local Group can be resolved into stars.

local thermodynamic equilibrium (LTE)

The assumption that a localized volume of emitting gas is in thermodynamic equilibrium such that the source function for the emitted radiation is given by the Planck function at the local temperature. LTE can be assumed to apply to plasma which is sufficiently dense that most of the photons are absorbed and thermalized before they travel a distance over which the temperature changes considerably.

local topological defect In cosmic topological defects formed as the result of the breakdown of a gauge (or local) symmetry, an important role is played by the gauge fields. In fact, these help to compensate the growing energy gradients of the Higgs field far away from

© 2001 by CRC Press LLC


the defect. In this way they achieve the confinement of the energy of the configuration to a small radius given by the Compton wavelengths of the Higgs field ( mH1) and the gauge field

( mgauge1 ), which form the core of the defect. See Abelian Higgs model, Nielsen–Olesen vor-

tex, t’Hooft–Polyakov monopole.

loess An unstratified windblown deposit composed of loosely arranged silt-sized particles (1/256 to 1/16 mm in diameter). Loess deposits occur primarily in semiarid and temperate zones, never being found in tropical regions or areas covered by ice in the last ice age. Loess deposits provide excellent soil for agriculture and some of the most productive grain-raising areas (such as the Great Plains of the U.S.) are located in loess deposits. Most experts consider loess to be windblown sediment associated with glacial activity — glacial and accompanying fluvial activity produced the small particles, which are then moved by wind to their current location. Loess usually occurs as plains, although some is also found as mantling deposits on mountains and hills. Loess is found on Earth primarily in the 2455N and 3040S latitude ranges, and has been suggested to occur on Mars as well.

Long Duration Event (LDE) A solar flare with a long gradual phase mostly associated with coronal mass ejections. When seen in soft X- rays, such flares are composed of a small number of prominent loops of order 105 km in length.

longitude, terrestrial The longitude of a terrestrial point P is an angle between a meridian through P and the Greenwich meridian, measured positive eastward and negative westward. Longitudes meet at the ±180meridian, where the longitude is discontinuous. The International Date Line runs close to this meridian, but does not always coincide, zigzagging a bit in the interest of keeping civil time zones continuous within certain political domains. Longitude is defined on other planetary bodies by choosing a prime meridian.

longitudinal invariant An adiabatic invariant associated with the bounce motion of trapped particles, equal to I = p||ds, where p|| is the momentum component parallel to the field

line, ds is the element of length along the field line, and the integration is usually between mirror points.

The value of I determines onto which of the neighboring field lines a particle trapped along a given line will drift, averaged over its motion along the given line: namely, to that of the neighboring lines, for which the integral I between the particle’s mirror points has the same value as before (the mirror points are determined by the magnetic moment, which is also an adiabatic invariant).

longitudinal wave In mechanical systems, a propagation of a signal in which the microscopic motion is in the direction of the wave motion. Sound propagating in ordinary isotropic fluids (e.g., air, water) constitutes a longitudinal wave.

long period variables Long period variable stars (LPVs) are either in the red giant stage or the asymptotic giant branch stage of stellar evolution. The variation of light, with typical periods of 400 days or longer, is caused by pulsations of the star’s atmosphere due to a pumping mechanism just below the photosphere, where partial ionization of H or He causes changes in opacity, trapping radiation and then releasing it, like a steam engine. LPVs are classified as SR (semiregular, with periods of typically 200 days and light variations less than 2.5 magnitudes in the visible band), Miras (regular pulsators with generally longer periods than the SRs and deep amplitudes of pulsation causing light variations of greater than 2.5 magnitudes and often as much as 4 or 5 magnitudes), and Lb (irregular variables). The conditions for this type of pulsation require low surface gravity (low density in the atmosphere) and cool temperatures, thus limiting the LPVs to cold red giants or asymptotic giant branch stars. Most are of spectral type M, N, R, or S.

longshore bar A bump or rise in the seafloor in the vicinity of a wave breakpoint. A beach profile may have several longshore bars. They run generally parallel to the coastline.

longshore current A mean flow of water, in or near the vicinity of the surf zone, in a direction parallel to the coast.

© 2001 by CRC Press LLC

Lorentz transformation

longshore sediment transport Transport of sediment in a direction parallel to the trend of the coast. See littoral transport.

long slit spectroscopy A technique employed to obtain spectra of extended objects, such as galaxies or planetary nebulae. The spectrograph aperture on the focal plane of the telescope is limited by a slit, whose width is typically a few seconds of arcs or less, and whose height may cover an angular size of several minutes of arc. Only light coming from the narrow strip defined by the slit is allowed to enter the spectrograph to avoid contamination by adjacent strips: nearby sources could produce spectra that would overlap spatially on the detector. Long slit spectroscopy has been employed in the measurement of continuum, absorption, and emission lines from every extended object. An example is the construction of radial velocity and rotation curves of galaxies. See velocity curve.

look-back time The finite speed of light means that objects are seen as they were at some time prior to the observer’s time of observation. Thus T , the look-back time, is T = d/c, where d is the distance to the observed object, and c is the speed of light.

Lorentz boost Lorentz transformation of space-time coordinates from one system of reference to another moving at a constant velocity with respect to each other. These transformations distinguish themselves from general Lorentz transformations in that they do not include rotation of spatial coordinates. Named after Hendrik Lorentz (1853–1928). See Lorentz transformation.

Lorentz factor, γ

The quantity


γ =

1 vc22

where v is the speed and c is the speed of light. γ is an indicator of special relativistic effects and enters into length contraction and time dilitation, for instance.

Lorentz–Fitzgerald contraction The decrease of the length of a physical body when

measured in a uniformly moving reference system rather than in the reference system of the body, as calculated by the Lorentz Transformations in the Special Theory of Relativity. Named after Hendrik Lorentz and George Francis FitzGerald. See coordinate transformation in special relativity.

Lorentz force equation Equation describing the force on a charged particle moving in specified electric (E) and magnetic (B) field, with velocity v:

F = q(E + v × B) ,

where this is a vector equation; the charge is in coulombs, the electric field has units of Voltmeters, and the magnetic field is measured in Tesla. The presence of the cross product × indicates that the magnetic force is orthogonal to both the direction of the magnetic field, and to the direction of motion of the charged particle.

Lorentzian metric The metric of a fourdimensional manifold with one negative and three positive eigenvalues, thus of signature (, +, +, +) (or one negative and three positive). An example is Minkowski space-time, having the metric ds2 = −c2dt2 +dx2 +dy2 + dz2 written in Cartesian coordinates, where c is the speed of light. The space-time model of general relativity is also one with a Lorentzian metric.

Lorentz invariance The invariance of physical expressions under Lorentz transformations from one coordinate system to another coordinate system moving uniformly with respect to the first. In special relativity all physical laws must be Lorentz invariant. Named after Hendrik Lorentz (1853–1928). See coordinate transformation in special relativity.

Lorentz transformation In special relativity, the coordinate transformations relating distance and time measurements in two reference systems (“frames”) in relative motion. If writ-








t, x, y, z

} =







, x


, x

, x }

the relation



© 2001 by CRC Press LLC

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