DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

dike
results. Because the particle mean free path λ
increases with energy, the ramp is steeper for
lower energies than for higher ones. In addition,
the intensity at the shock front is higher for
lower energies, reflecting the power-law spectrum.
In the study of particle events, the upstream
intensity increase is often used to determine
the scattering conditions upstream of the
shock.
4. Self-generated turbulence. A crucial parameter
for the acceleration time is the strength of the
interplanetary scattering, as can be seen from the
equation for the acceleration time. Downstream
of the shock turbulence is high because the disturbance
shock has just passed by. Thus upstream
scattering is the limiting factor. For typicalconditionsininterplanetaryspace,
theFermi
process would develop too slowly to reach MeV
energies during the time it takes the shock to
travel from the sun to Earth. Nonetheless, these
particles are observed. It is assumed that selfgenerated
turbulence allows for more efficient
scattering in the plasma upstream of the shock:
at first, particles are accelerated to low energies
only. Astheseparticlespropagateawayfromthe
shock, they generate and amplify Alfvén waves
in resonance with the field parallel motion of the
particles. These waves grow in response to the
intensity gradient of the energetic particles and
scatter particles back to the shock. These particles
therefore interact again with the shock,
gaining higher energy and, as they stream away
from the shock front, generating waves with
longer wavelength. This process repeats itself
with the faster particles, and as acceleration on
the shock continues, the particles acquire higher
and higher energies and a turbulent region develops
upstream of the shock. Such turbulent
foreshock regions have been observed at traveling
interplanetary shocks (proton energies up to
some 100 keV and the waves in resonance with
these particles) and at the quasi-parallel portion
of the terrestrial bow shock (proton energies up
to some 10 keV and waves in resonance with
these particles). See resonance scattering.
dike A crack through which magma flows,
the magma subsequently solidifying to form a
thin planar igneous body.
© 2001 by CRC Press LLC
dilatancy model A model to explain processes
of earthquake generation, connecting
with phenomena of anelastic volumetric expansion
of rocks (dilatancy). At the beginning of the
1970s, C.H. Scholz proposed the model, dividing
processes from strain accumulation to generation
of a large earthquake into five stages. According
to the dilatancy model, with increase of
underground stresses, many cracks are formed,
and pore water flows into the cracks. Then, pore
pressure decreases, causing dilatancy hardening.
Subsequently, the pore pressure gradually
increases due to water supply from the ambient
region, reaching main rupture. Land uplift preceding
a large earthquake, temporal change in
P-wave velocity, advent of seismic gap, and activity
of foreshocks might be better explained by
the model. However, since actual earthquakes
take place on planes with mechanical defects in
the crust, dilatancy does not necessarily develop
sufficiently to explain a large earthquake. Reliability
of observation for temporal change in
P-wave velocity is also suspect. Therefore, the
dilatancy model has attracted little attention in
recent years.
dilatation of time-Lorentz transformation
The increase in the time interval of an event
when measured in a uniformly moving reference
system rather than in the reference system
of the event, as calculated by the Lorentz Transformations
in the Special Theory of Relativity.
In special relativity time is not an absolute variable,
and it therefore varies for different reference
systems. See also coordinate transformation
in special relativity. See time dilatation.
dilaton A scalar component of gravity which
emerges in the low energy limit of string theory.
See dilaton gravity.
dilaton gravity In the framework of string
theory the field equations of general relativity
are obtained as an approximation which is
valid only for distances larger than the typical
(microscopic) string length (low energy). Further,
since string theory is a theory of extended
objects (including p-dimensional branes, with
p ≥ 2 and integer), one expects to have (nonlocal)
corrections to Einstein’s field equations.
The simplest corrections are extra fields, among