active fault

achronal set (semispacelike set) A set of points S of a causal space such that there are no two points in S with timelike separation.

acoustic tomography An inverse method which infers the state of an ocean region from measurements of the properties of sound waves passing through it. The properties of sound in the ocean are functions of temperature, water velocity, and salinity, and thus each can be exploited for acoustic tomography. The ocean is nearly transparent to low-frequency sound waves, which allows signals to be transmitted over hundreds to thousands of kilometers.

actinides The elements of atomic number 89 through 103, i.e., Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr.

action In mechanics the integral of the Lagrangian along a path through endpoint events with given endpoint conditions:

	tb,xbj
I	= ta ,xaj	,C
			L xi, dxi/dt, t	dt

(or, if appropriate, the Lagrangian may contain higher time derivatives of the pointcoordinates). Extremization of the action over paths with the same endpoint conditions leads to a differential equation. If the Lagrangian is a simple L = T − V , where T is quadratic in the velocity and V is a function of coordinates of the point particle, then this variation leads to Newton’s second law:

d2xi		∂V
	= −		, i = 1, 2, 3 .
dt2		∂xi

By extension, the word action is also applied to field theories, where it is defined:

I = tb,xbj L |g|dnx ,

ta ,xaj

where L is a function of the fields (which depend on the spacetime coordinates), and of the gradients of these fields. Here n is the dimension of spacetime. See Lagrangian, variational principle.

activation energy (Ha ) That energy required before a given reaction or process can

proceed. It is usually defined as the difference between the internal energy (or enthalpy) of the transition state and the initial state.

activation entropy ( Sa ) The activation entropy is defined as the difference between the entropy of the activated state and initial state, or the entropy change. From the statistical definition of entropy, it can be expressed as

*Sa = R ln ωa ωI

where ωa is the number of “complexions” associated with the activated state, and ωI is the number of “complexions” associated with the initial state. R is gas constant. The activation entropy therefore includes changes in the configuration, electronic, and vibration entropy.

activation volume ( V ) The activation volume is defined as the volume difference between initial and final state in an activation process, which is expressed as

*V = ∂*G ∂P

where *G is the Gibbs energy of the activation process and P is the pressure. The activation volume reflects the dependence of process on pressure between the volume of the activated state and initial state, or entropy change.

active continental margin A continental margin where an oceanic plate is subducting beneath the continent.

active fault A fault that has repeated displacements in Quaternary or late Quaternary period. Its fault trace appears on the Earth’s surface, and the fault has a potential to reactivate in the future. Hence, naturally, a fault which had displacements associated with a large earthquake in recent years is an active fault. The degree of activity of an active fault is represented by average displacement rate, which is deduced from geology, topography, and trench excavation. The higher the activity, the shorter the recurrence time of large earthquakes. There are some cases where large earthquakes take place on an active fault with low activity.

© 2001 by CRC Press LLC

active front

active front An active anafront or an active katafront. An active anafront is a warm front at which there is upward movement of the warm sector air. This is due to the velocity component crossing the frontal line of the warm air being larger than the velocity component of the cold air. This upward movement of the warm air usually produces clouds and precipitation. In general, most warm fronts and stationary fronts are active anafronts. An active katafront is a weak cold frontal condition, in which the warm sector air sinks relative to the colder air. The upper trough of active katafront locates the frontal line or prefrontal line. An active katafront moves faster than a general cold front.

active galactic nuclei (AGN) Luminous nuclei of galaxies in which emission of radiation ranges from radio frequencies to hard-X or, in the case of blazars, to γ rays and is most likely due to non-stellar processes related to accretion of matter onto a supermassive black hole. Active galactic nuclei cover a large range in luminosity ( 1042 −1047 ergs s−1) and include, at the low luminosity end, LINERs and Seyfert-2 galaxies, and at the high luminosity end, the most energetic sources known in the universe, like quasi-stellar objects and the most powerful radio galaxies. Nearby AGN can be distinguished from normal galaxies because of their bright nucleus; their identification, however, requires the detection of strong emission lines in the optical and UV spectrum. Radio-loud AGN, a minority (10 to 15%) of all AGN, have comparable optical and radio luminosity; radio quiet AGN are not radio silent, but the power they emit in the radio is a tiny fraction of the optical luminosity. The reason for the existence of such dichotomy is as yet unclear. Currently debated explanations involve the spin of the supermassive black hole (i.e., a rapidly spinning black hole could help form a relativistic jet) or the morphology of the active nucleus host galaxy, since in spiral galaxies the interstellar medium would quench a relativistic jet. See black hole, QSO, Seyfert galaxies.

active margins The boundaries between the oceans and the continents are of two types, active and passive. Active margins are also plate boundaries, usually subduction zones. Active

margins have major earthquakes and volcanism; examples include the “ring of fire” around the Pacific.

active region A localized volume of the solar atmosphere in which the magnetic fields are extremely strong. Active regions are characterized as bright complexes of loops at ultraviolet and X-ray wavelengths. The solar gas is confined by the strong magnetic fields forming loop-like structures and is heated to millions of degrees Kelvin, and are typically the locations of several solar phenomena such as plages, sunspots, faculae, and flares. The structures evolve and change during the lifetime of the active region. Active regions may last for more than one solar rotation and there is some evidence of them recurring in common locations on the sun. Active regions, like sunspots, vary in frequency during the solar cycle, there being more near solar maximum and none visible at solar minimum. The photospheric component of active regions are more familiar as sunspots, which form at the center of active regions.

adiabat Temperature vs. pressure in a system isolated from addition or removal of thermal energy. The temperature may change, however, because of compression. The temperature in the convecting mantle of the Earth is closely approximated by an adiabat.

adiabatic atmosphere A simplified atmosphere model with no radiation process, water phase changing process, or turbulent heat transfer. All processes in adiabatic atmosphere are isentropic processes. It is a good approximation for short-term, large scale atmospheric motions. In an adiabatic atmosphere, the relation between temperature and pressure is

T0	=	p0		AR
T			p	Cp

where T is temperature, p is pressure, T0 and p0 are the original states of T and p before adiabatic processes, A is the mechanical equivalent of heat, R is the gas constant, and Cp is the specific heat at constant pressure.

adiabatic condensation point The height point at which air becomes saturated when it

© 2001 by CRC Press LLC

ADM form of the Einstein–Hilbert action

is lifted adiabatically. It can be determined by the adiabatic chart.

adiabatic cooling In an adiabatic atmosphere, when an air parcel ascends to upper lower pressure height level, it undergoes expansion and requires the expenditure of energy and consequently leading to a depletion of internal heat.

adiabatic deceleration Deceleration of energetic particles during the solar wind expansion: energetic particles are scattered at magnetic field fluctuations frozen into the solar wind plasma. During the expansion of the solar wind, this “cosmic ray gas” also expands, resulting in a cooling of the gas which is equivalent to a deceleration of the energetic particles. In a transport equation, adiabatic deceleration is described by a term

· vsowi ∂

(αT U)

3 ∂T

with T being the particle’s energy, To its rest energy, U the phase space density, vsowi the solar wind speed, and α = (T + 2T o)/(T + T o).

Adiabatic deceleration formally is also equivalent to a betatron effect due to the reduction of the interplanetary magnetic field strength with increasing radial distance.

adiabatic dislocation Displacement of a virtual fluid parcel without exchange of heat with the ambient fluid. See potential temperature.

adiabatic equilibrium An equilibrium status when a system has no heat flux across its boundary, or the incoming heat equals the outgoing heat. That is, dU = −dW, from the first law of thermodynamics without the heat term, in which dU is variation of the internal energy, dW is work. Adiabatic equilibrium can be found, for instance, in dry adiabatic ascending movements of air parcels; and in the closed systems in which two or three phases of water exist together and reach an equilibrium state.

adiabatic index Ratio of specific heats: Cp/CV where Cp is the specific heat at constant pressure, and CV is the specific heat at constant volume. For ideal gases, equal to

(2+degrees of freedom )/(degrees of freedom).

adiabatic invariant A quantity in a mechanical or field system that changes arbitrarily little even when the system parameter changes substantially but arbitrarily slowly. Examples include the magnetic flux included in a cyclotron orbit of a plasma particle. Thus, in a variable magnetic field, the size of the orbit changes as the particle dufts along a guiding flux line. Another example is the angular momentum of an orbit in a spherical system, which is changed if the spherical force law is slowly changed. Adiabatic invariants can be expressed as the surface area of a closed orbit in phase space. They are the objects that are quantized (=mh) in the Bohr model of the atom.

adiabatic lapse rate Temperature vertical change rate when an air parcel moves vertically with no exchange of heat with surroundings. In the special case of an ideal atmosphere, the adiabatic lapse rate is 10◦ per km.

ADM form of the Einstein–Hilbert action

In general relativity, by introducing the ADM (Arnowitt, Deser, Misner) decomposition of the metric, the Einstein–Hilbert action for pure gravity takes the general form

SEH =		1
		16 π G
	d4x α γ 1/2 Kij Kij − K2 + (3)R
−8 π G		a	ta		d3x γ 1/2 K + 8 π G
	1				1

dt d2x γ 1/2 K βi − γ ij α,j ,

xi b b

where the first term on the r.h.s. is the volume contribution, the second comes from possible space-like boundaries 4ta of the spacetime manifold parametrized by t = ta, and the third contains contributions from time-like boundaries xi = xbi . The surface terms must be included in order to obtain the correct equations of motion upon variation of the variables γij which vanish on the borders but have nonvanishing normal derivatives therein.

In the above,

Kij = 1 βi|j + βj|i − γij,0

2 α

© 2001 by CRC Press LLC

ADM mass

is the extrinsic curvature tensor of the surfaces of constant time 4t , | denotes covariant differentiation with respect to the three-dimensional metric γ , K = Kij γ ij , and (3)R is the intrinsic scalar curvature of 4t . From the above form of the action, it is apparent that α and βi are not dynamical variables (no time derivatives of the lapse and shifts functions appear). Further, the extrinsic curvature of 4t enters in the action to build a sort of kinematical term, while the intrinsic curvature plays the role of a potential. See Arnowitt–Deser–Misner (ADM) decomposition of the metric.

ADM mass According to general relativity, the motion of a particle of mass m located in a region of weak gravitational field, that is far away from any gravitational source, is well approximated by Newton’s law with a force

F = G m MADM ,

r2

where r is a radial coordinate such that the metric tensor g approaches the usual flat Minkowski metric for large values of r. The effective ADM mass MADM is obtained by expanding the timetime component of g in powers of 1/r,

gtt = −1 +	r	+ O	r2 .
	2 MADM		1

Intuitively, one can think of the ADM mass as the total (matter plus gravity) energy contained in the interior of space. As such it generally differs from the volume integral of the energymomentum density of matter. It is conserved if no radial energy flow is present at large r.

More formally, M can be obtained by integrating a surface term at large r in the ADM form of the Einstein–Hilbert action, which then adds to the canonical Hamiltonian. This derivation justifies the terminology. In the same way one can define other (conserved or not) asymptotical physical quantities like total electric charge and gauge charges. See ADM form of the Einstein– Hilbert action, asymptotic flatness.

Adrastea Moon of Jupiter, also designated JXV. Discovered by Jewitt, Danielson, and Synnott in 1979, its orbit lies very close to that of Metis, with an eccentricity and inclination

that are very nearly 0 and a semimajor axis of 1.29 × 105 km. Its size is 12.5 × 10 × 7.5 km, its mass, 1.90 ×1016 kg, and its density roughly 4 gcm−3. It has a geometric albedo of 0.05 and orbits Jupiter once every 0.298 Earth days.

ADV (Acoustic Doppler Velocimeter) A device that measures fluid velocity by making use of the Doppler Effect. Sound is emitted at a specific frequency, is reflected off of particles in the fluid, and returns to the instrument with a frequency shift if the fluid is moving. Speed of the fluid (along the sound travel path) may be determined from the frequency shift. Multiple sender-receiver pairs are used to allow 3-D flow measurements.

advance of the perihelion In unperturbed Newtonian dynamics, planetary orbits around a spherical sun are ellipses fixed in space. Many perturbations in more realistic situations, for instance perturbations from other planets, contribute to a secular shift in orbits, including a rotation of the orbit in its plane, a precession of the perihelion. General relativity predicts a specific advance of the perihelion of planets, equal to 43 sec of arc per century for Mercury, and this is observationally verified. Other planets have substantially smaller advance of their perihelion: for Venus the general relativity prediction is 8.6 sec of arc per century, and for Earth the prediction is 3.8 sec of arc per century. These are currently unmeasurable.

The binary pulsar (PSR 1913+16) has an observable periastron advance of 4.227◦/year, consistent with the general relativity prediction. See binary pulsar.

advection The transport of a physical property by entrainment in a moving medium. Wind advects water vapor entrained in the air, for instance.

advection dominated accretion disks Accretion disks in which the radial transport of heat becomes relevant to the disk structure. The advection-dominated disk differs from the standard geometrically thin accretion disk model because the energy released by viscous dissipation is not radiated locally, but rather advected toward the central star or black hole. As a conse-

© 2001 by CRC Press LLC