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global thermohaline circulation

Pleistocene, about 2 million years ago, ending only about 10,000 years ago.

glacier A mass of moving ice formed by accumulation and compactiﬁcation of snow, and ﬂowing from an accumulation source to an edge where it is ablated. Glaciers are found on Earth and are suspected to have occurred on Mars in the past. Ground ice is present on both Earth and Mars. Some of the icy moons of the outer solar system show evidence of ice moving on top of liquid water oceans, either presently (such as Europa) or in the past (such as Ganymede). Glaciers contained within mountain valleys are called valley or alpine glaciers, while those spread out laterally over large areas are called continental glaciers, found in Greenland and Antarctica. Glaciers are very efﬁcient at eroding the underlying material and transporting this material to other locations where it is deposited as eskers, moraines, and drumlins. Ground ice also creates a number of geologic features, primarily thermokarst features produced by the collapse of overlying material as subterranean ice is removed by heating.

global loop oscillation Coronal loops act as high quality resonance cavities for hydromagnetic waves and, consequently, display a largescale frequency response sharply peaked at the global resonant frequency of the loop, deﬁned by vAlfvén = 2L/period. This global mode is crucial to wave heating models of the solar corona since, in order to be efﬁcient, the resonant absorption of waves requires a close matching to the length of the coronal loop through the condition of global-mode resonance.

globally hyperbolic space-time (Leray, 1952.) A space-time (M, g) is globally hyperbolic if

1.(M, g) is strongly causal.

2.For any two points p, q M, the intersection of the causal sets J +(p)∩J −(q) is compact where J +(p) is the causal future set of p, i.e.,

those points that can be inﬂuenced by p, and J −(q) is the causal past set of q. In a globally hyperbolic space-time, the wave equation with

source term δ(p) has a unique solution which vanishes outside the causal future set J +(p).

global positioning system (GPS) A U.S. Department of Defense system of 24 satellites used as timing standards and for navigation to monitor positions on the Earth’s surface. Satellites carrying precise cesium or rubidium atomic clocks which are synchronized with Coordinated Universal Time broadcast coded data streams giving their time and their position. By observing four satellites, all four parameters (x, y, z, time) describing the location and time at a near Earth receiver can be extracted. Precise mode (a military classiﬁed mode) allows locations to less than 1 m. Commercial devices are available that will provide a location of the device with an accuracy of 10s of meters using signals from these satellites. Differential GPS and interferometric applications can reduce errors to millimeters.

global seismology A research ﬁeld of seismology aimed at elucidation of the Earth’s deep structure, dynamics, and its driving forces through an international exchange of information and technique in seismology. In the 1980s, through analyses of digital data of global seismograph networks, three-dimensional velocity structural models of the Earth were proposed, and research on global seismology made remarkable progress. In order to know more about the structures and dynamics of the Earth, a seismograph network with broadband and high dynamic range was equipped, and many countries started to participate in a global seismograph network. As representative networks, there are GEOSCOPE (France), IRIS (U.S.), CANDIS (Canada), CDSN (China), FKPE (Germany), DRFEUS (Europe), and POSEIDON (Japan).

global thermohaline circulation A vertical overturning circulation in which cold water sinks in localized polar/subpolar regions, spreads to and rises to the surface in the rest of the world ocean. At low temperatures close to the freezing point, sea water density becomes less sensitive to temperature than to salinity differences. So the formation of deep water is determined by salinity differences among the oceans. Currently, most of the world ocean’s deep water sinks in the northern North Atlantic, and ﬂows southward along the western boundary into the Southern Ocean. Riding on the

by θ vac

global topological defect

Antarctic circumpolar current, the North Atlantic Deep Water spreads into the Indian and Paciﬁc basins, along with the Antarctic Bottom Water. Compensating the deep outﬂow, warm surface water ﬂows back into the North Atlantic. Because of a large temperature difference between the surface (10◦C) and deep (0◦C) waters, this overturning circulation transports a huge amount of heat into the North Atlantic, making winter much warmer in northern Europe than at the same latitudes in North America.

global topological defect Topological defects that may be important in early universe cosmology, formed from the breakdown of a rigid (or global) symmetry that does not have “compensating” gauge ﬁelds associated to it. Long-range interactions between the defects in the network and energy stored in gradients of the ﬁeld cannot be compensated far away from the defect; in general, these constitute divergentenergy conﬁgurations. A cutoff for the energy is physically given by other relevant scales of the problem under study, such as the mean distance between two arbitrary defects in the network, or the characteristic size of the loop (in the case of cosmic string loops), for example.

globular cluster A dense spherical cluster of stars of Population II, typically of low mass (≈ 0.5M ). Diameter of order 100 pc; containing up to 105 stars. Globular clusters are a component of the halo of the galaxy.

GMT See Universal Time (UT or UT1).

gnomon A vertical rod whose shadow in sunlight is studied to measure the angular position of the sun.

Goddard, Robert H. Rocket engineer (1882–1945). Designed the liquid-propellant rocket.

Goldberg–Sachs theorem (1962) A vacuum spacetime in general relativity is algebraically special if and only if it contains a shearfree geodesic null congruence. See congruence, Petrov types.

Goldstone boson See Goldstone model.

Goldstone model A quantum ﬁeld model of a scalar ﬁeld with a nonlinear self-interaction (Goldstone, 1961). A theory in which the symmetry of the Lagrangian is not shared by the ground state (the vacuum, i.e., the lowest energy) solution. The Lagrangian density reads

L = (∂µφ) (∂µφ) − V (φ)

with φ a complex scalar ﬁeld ( means complex conjugate) and the symmetry breaking potential V (φ) has the “Mexican hat” form V = 41 λ(φ φ −η2)2, with λ and η positive constants.

Lis invariant under the global transformation

φ→ ei<φ, with < a constant in spacetime. This model has a local potential maximum at

φ= 0 and the minima occur when the absolute

value of φ equals η. Hence, the minima can be expressed as φ = ηeiθ and the phase θ can take any of the equivalent values between zero and

2π. Once one of these phases is chosen (and we have, say, φvac = ηeiθ vac as our vacuum state) the original symmetry possessed by the model

is lost (broken). To see this, the original U(1) transformation φ → ei<φ will now change θvac

+ <: the model is no longer invariant under the original symmetry.

By further analyzing this model in the vicinity of the new vacuum state, one deduces that the original Lagrangian can be written in terms of massive and massless scalar ﬁelds, plus other uninteresting interaction terms. It is the particle associated with this massless ﬁeld (whose degree of freedom is related to motion around the equal energy circle of minima of the potential V ) that became known as the Goldstone boson.

In cosmology, global strings may arise from conﬁgurations of the Goldstone ﬁeld; these can have important implications for the structure of the universe. See Goldstone theorem, Higgs mechanism.

Goldstone theorem Any spontaneous breaking of a continuous symmetry leads to the existence of a massless particle. This theorem shows that when the Lagrangian of the theory is invariant under a group of symmetries G, but the ground state is only invariant under a subgroup H , there will be a number of massless (Goldstone) particles equal to the dimension of the quotient space M G/H , and hence equal to

gradual commencement storm

the difference between the number of generators of G and H , or said otherwise, to the number of generators of G that are not generators of H . Actually, the theorem is more general, also applying in the case the symmetry is broken, but not spontaneously.

A particularly simple example is the Goldstone model. There we have a breaking scheme U(1) → {1} and the production of one Goldstone particle. See Goldstone model, spontaneous symmetry breaking.

Gondwanaland Continent in existence prior to the opening of the South Atlantic Ocean, consisting of South America, Africa, and Australia.

Goto–Nambu string Structureless vacuum vortex defects that can be macroscopically described by a simple cosmic string equation of state T = U = const., where U is the string energy per unit length and T is its tension.

The motion is derived by ﬁnding ξ0 and ξ1 that minimize the action:

S = −U √−γ d2ξ

where, the string being a one-dimensional object, its history can be represented by a surface in spacetime xµ(ξa) with internal worldsheet coordinates ξ0 = t, ξ1 = >. γ is the determinant of the induced metric on the two-dimensional worldsheet of the string evolving in time. The integrand essentially represents the element of surface area swept out by the string in spacetime.

One can then say that the string evolves in such a way as to extremize the area of its spacetime worldsheet. See cosmic string, cusp (cosmic string), energy per unit length (cosmic string), fundamental tensors of a worldsheet, Higgs mechanism.

GPS See global positioning system.

graben Common features on most planetary surfaces and often synonymous with the term rift valley. They are long, narrow troughs bounded by two (sometimes more) parallel normal faults, giving rise to a downdropped valley surrounded by high plateaus. Graben are created when two blocks of rock are pulled apart by tensional tec-

tonic forces. Divergent boundaries are usually characterized by graben.

GRACE (Gravity Recovery and Climate Experiment) An approved Earth System Science Pathﬁnder NASA space mission which will employ a satellite-to-satellite microwave tracking system between two spacecraft to measure the Earth’s gravity ﬁeld and its time variability. The mission is scheduled to be launched in 2001 and will operate over ﬁve years.

gradient For a scalar function f of coordinates, the collection of partial derivatives with respect to the coordinates: {f,i} (the ,i indicating partial derivative with respect to coordinate i). Or, more formally, the 1−f orm constructed by

@f,idxi .

See 1-form, partial derivative.

gradient drift See drift, gradient.

gradient Richardson number Ri						The non-
ratio Ri		=	N2	/(∂u/∂z)	2	between
dimensional 2
the stability N	and the vertical shear ∂u/∂z of a

stably stratiﬁed water column, which is subject to vertical gradients of the horizontal currents u. A necessary condition for turbulence to occur (typically Kelvin–Helmholtz instabilities) is the condition Ri < 0.25. In natural systems (at- mosphere, oceans, lakes, etc.) the experimental determination of Ri depends on the scale over which N2 and (∂u/∂z) are determined. The rate of mixing, generally increasing as Ri decreases, is not a unique function of Ri.

gradual commencement storm Geomagnetic storms may commence gradually, the storm having no well-deﬁned onset time. These storms may persist for many days, geomagnetic activity increasing irregularly, sometimes to major storm levels. Geomagnetic activity associated with gradual commencement storms may recur every 27 days, consistent with the solar rotation. They are thought to be due to highspeed solar wind streams arising in long-lived coronal hole regions on the sun. See geomagnetic storm.

gradual ﬂare

gradual ﬂare Solar ﬂare with long-lasting electromagnetic radiation, originating high in the corona. In more detail, the properties of gradual ﬂares are: (a) the soft X-ray emission lasts for more than 1 h, (b) the decay constant of the soft X-ray emission is larger than 10 min,

(c) the duration in hard X-rays is at least 10 min, (d) the duration in microwaves is at least 5 min, (e) gradual ﬂares are always accompanied by metric type II and metric type IV bursts, metric type III bursts are observed in half of the gradual ﬂares, (f) the height in the corona is about 5 ·104 km, (g) the ﬂare volume is between 1028 cm3 and 1029 cm3, (h) the energy density is low, (i) the size in Hα is large, and (j) gradual ﬂares are always accompanied by coronal mass ejections.

If a gradual ﬂare gives rise to an energetic particle event observed in interplanetary space, this event has properties different from particle events caused by impulsive ﬂares. Many of these differences can be attributed to the interplanetary shock caused by the coronal mass ejection in gradual ﬂares. In detail, the properties of a particle event originating in a gradual ﬂare are: (a) the event is proton-rich with H/He being about 100, (b) the 3He/4He ratio is about 0.0005 which is the ratio observed in the solar wind, (c) the Fe/O ratio is 0.155, which is also close to the ratio in the solar wind, (d) the charge state of iron is about 14, which suggests rather low temperatures in the acceleration region and therefore acceleration out of the corona or the solar wind, (e) the particle event in interplanetary space at the orbit of Earth lasts for some days,

(f) particles can be observed over a longitude cone of about 180◦, and (g) an interplanetary shock is observed. Occurrence of such events is about 10 per year.

The distinct feature of the gradual ﬂare is the coronal mass ejection and consequently the interplanetary shock. Some instability below a ﬁlament causes reconnection at the anchoring ﬁeld lines which leads to heating and the generation of electromagnetic radiation (the ﬂare) and to a disconnection and expulsion of the ﬁlament (the coronal mass ejection).

gradually varied ﬂow A description of ﬂow in an open channel (such as a canal or river) which assumes that the rate of change of depth

is small (i.e., Dh/L is small, where Dh is the change in depth, and L is the distance over which the depth changes).

Grad–Vasyliunas theorem An equation used in the study of guiding center plasmas in the Earth’s magnetic ﬁeld, an equivalent formulation of force balance. It assumes that under the inﬂuence of convection electric ﬁelds, the plasma of each ﬂux tube moves together, from one tube to another, that its particle motion has no preferred direction (isotropy), that a scalar (rather than tensor) pressure p can be used, and that Euler potentials (α, β) of the magnetic ﬁeld are given. Under those assumptions, it relates the ﬁeld aligned current density j|| with the distributions of pressure p(α, β) and of speciﬁc volume V(α, β), as j|| = | V (α , β) × p(α, β)|. Since the above assumptions are best met in the Earth’s plasma sheet, it has been widely used to deal with plasma convection there. Also known as Vasyliunas theorem.

grain-boundary migration To help minimize the energy of the solid materials in response to changing P-T conditions, the atoms forming the contacts between individual grains self rearrange to a more stable conﬁguration. To a large extent this is achieved by the process of grain-boundary migration. This involves movement at a high angle to the plane of the grain boundary. Such a process usually produces regular interfaces and a polygonal aggregate of grain.

grain-boundary sliding Movement of grains is limited within the plane of the grain boundary. Grain-boundary sliding can be envisaged in terms of the physical movement of individual grains past each other under an applied shear stress. Grain-boundary sliding is recognized as one of the most important deformation mechanisms in ﬁne-grained polycrystalline aggregates, and is considered one of the main deformation mechanisms responsible for superplasticity of polycrystalline materials.

grain chemistry: dense interstellar In dense interstellar media (i.e., visual extinction Av ≥ 5 magnitudes, or nH ≥ 104 cm−3), where the radiation ﬁeld is attenuated and the average