DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

the difference between the number of generators
ofG andH, 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:
√−γd2 S=−U ξ
where, the string being a one-dimensional object,
its history can be represented by a surface in
spacetime x µ (ξ a ) with internal worldsheet coordinates
ξ 0 =t, ξ 1 =ℓ. 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
surfacesandoftensynonymouswiththetermrift
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-
© 2001 by CRC Press LLC
gradual commencement storm
tonic forces. Divergent boundaries are usually
characterized by graben.
GRACE (Gravity Recovery and Climate
Experiment) AnapprovedEarthSystemScience
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−formconstructed
by
f,idx i .
See 1-form, partial derivative.
gradient drift See drift, gradient.
gradient Richardson number Ri The nondimensional
ratio Ri =N 2 /(∂u/∂z) 2 between
the stabilityN 2 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 conditionRi < 0.25. In natural systems (atmosphere,
oceans, lakes, etc.) the experimental
determination of Ri depends on the scale over
whichN 2 and(∂u/∂z) are determined. The rate
of mixing, generally increasing asRi 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.
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