DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

interval, divided by that interval:
f(v)= 4π
M
2 πRT
3
2
v 2 e −Mv2
2RT
where M is the molar mass, R is the molar gas
constant, and T is the temperature.
The Maxwell–Boltzmann distribution is a
classical distribution; it does not take account
of quantum indistinguishability, which are described
by Bose–Einstein distribution for integer
spin quantum particles, and by the Fermi–
Dirac distribution for half-integer spin quantum
particles.
Maxwell material Also called a Maxwell
fluid or Maxwell solid. A viscoelastic material
that behaves as a linearly elastic solid in
response to high frequency loading but as an incompressible,
linearly viscous fluid in response
to low frequency loading. The strain rate for the
Maxwell material is a combination of the rate
of elastic strain according to Hooke’s law and
the rate of viscous strain according to Newtonian
flow law. The relation between volumetric
strain θ = εii and pressure p = σii/3 is
elastic: θ = p/K, where K is the bulk modulus.
The constitutive relation for the deviatoric
strain ε ′ ij = εij − θδij /3 and deviatoric stress
σ ′ ij = σij − pδij is
∂ε ′ ij
∂t
= 1
2G
∂σ ′
ij
∂t
1 ′
+ σ ij
2µ
where G is shear modulus, and µ is viscosity.
The quantity τM = µ/G is called the
Maxwell relaxation time, a time that roughly defines
the transition from predominantly elastic
to predominantly viscous behavior after a suddenly
imposed constant loading. In modeling
the rheology of the Earth or other planets, the
above constitutive relation is often modified by
replacing the Newtonian flow law with a nonlinear
flow law (such as the Power law). In geophysics,
such nonlinearly viscoelastic materials
are usually still referred to as the Maxwell materials.
mean anomaly, M Measured in degrees, the
ratio M/360 is equal to the ratio of the time
elapsed since last periapse to the orbital period.
Thus, at periapse, M = 0 , and at apoapse, M =
© 2001 by CRC Press LLC
mean field dynamo
180. For a circular orbit the mean anomaly and
the true anomaly are the same.
mean celestial equator The great circle on
the celestial sphere perpendicular to the mean
celestial pole. Its intersections with the ecliptic
define the mean vernal equinox, and the mean
autumnal equinox.
mean celestial pole The mean direction
of Earth’s north rotation pole when the short
timescale (days to decades) variations, called
nutation, are averaged out. This hypothetical
pole executes a circle of radius approximately
23.44 ◦ about the North Ecliptic Pole, in about
25,800 y. (There is a corresponding mean south
celestial pole, opposite to the north one.) The
precise derivation of the motion of this pole is
given by J.H. Lieske, T. Lederle, W. Fricke and
B. Morando in Astron. and Astrophys., 58, 1
(1977).
mean cosine of scattering angle The integral
over all directions of the volume scattering
function multiplied by the cosine of the scattering
angle, divided by the integral over all directions
of the volume scattering function; also
called the single-scattering asymmetry factor.
mean diameter, mean grain size The mean
particle size in a soil sample. Not as frequently
used as median grain size, d50.
mean field dynamo A mathematical simplification
of the physics governing the behavior
of magnetic field in a dynamo such as that
in the Earth’s core so that the evolution of the
magnetic field can be simulated. Essentially, the
system is considered to be axisymmetric; that is,
variations along lines of latitude are neglected.
However, it turns out that a purely axisymmetric
dynamo cannot exist (Cowling’s theorem),
as a vital part of the axisymmetric portion of
the magnetic field can only be generated from
longitudinal variations in the magnetic field. In
the mean field dynamo, such effects (which are
commonly assumed to be associated with fluid
turbulence) are parameterized. This simplification
of the equations allows dynamo solutions
to be found that satisfy both the equation governing
the evolution of the magnetic field and
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