DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

period The amount of time for some motion
to return to its original state and to repeat its
motion.
period-luminosity relation The relation between
the luminosity of Cepheid variable stars
and the variability period of these stars. The
basic trend is that those stars with longer periods
are brighter. By measuring the period of
Cepheid variables, astronomers can use this relationship
to deduce the intrinsic luminosity of
these stars. Combined with a measurement of
the apparent luminosity, the distance of Cepheid
variables can be estimated. The Hubble Space
Telescope has been used to detect Cepheid variables
out to the Virgo cluster, measuring the distance
of the Virgo cluster to roughly a 10% accuracy.
See Cepheid variable.
permafrost Soil or subsoil that is permanently
frozen for two or more years, typical of
arctic regions, or in other arctic climates (such
as high altitude) where the temperature remains
below 0 ◦ C for two or more years.
permeability In electromagnetism, the relation
between the microscopic magnetic field B
and the macroscopic field (counting material polarizability)
H. In fluid flow, permeability, also
called the intrinsic permeability, characterizes
the ease with which fluids flow through a porous
medium. Theoretically, permeability is the intrinsic
property of a porous medium, independent
of the fluids involved. In reality, the permeabilitiesofsomerocksorsoilsareaffectedbythe
fluid. Permeability in fluid flow has the dimension
of area. For an anisotropic porous medium,
the permeability is a tensor. See Darcy’s law.
permeability coefficient In electromagnetism,
the coefficientµ in the relation B =µH
between the microscopic magnetic field B and
the macroscopic field H. In general, µ may be
a3× 3 linear function of position, with time
hysteresis, though it is often taken to be a scalar
constant. In fluid flow, the coefficient measuring
how easily water molecules can cross the surface
film. For clear water (Davies and Rideal, 1963),
it is equal to 5 ms −1 .
© 2001 by CRC Press LLC
perturbative solution
persistent current See current generation
(cosmic string).
perturbation theory A tool that can be applied
to questions ranging from classical mechanics
to quantum theory. Independent of the
actual question, the basic idea is to find an approximate
solution of the equations for a complex
system by first solving the equations of
a physically similar system chosen so that its
solution is relatively easy. Then the effects of
small changes or perturbations on this solution
are studied. In classical mechanics, for instance,
the motion of a planet around the sun is studied
first and the influences of the other planets are
added later.
Formally, a complex system is described by
a set of coupled non-linear partial differential
equations. If only small-amplitude disturbances
are considered, such a system can be simplified
by linearization of the equations: whenever two
oscillating quantities are multiplied, since both
are small, their product is a higher order term
and can be ignored. If these results are to be
applied to a real situation, however, one always
has to take one step back and justify whether
the amplitudes calculated in the real situation
are small enough so that the non-linear terms
actually are negligible compared with the linear
ones.
perturbative solution An approximate solution,
usually found to a problem that is too
difficult to be solved by an exact calculation. In
a perturbative solution there exists at least one
small dimensionless parameter (ε) that must be
distinctly smaller than 1. Then, ε 2 ≪ ε. The
equations to be solved are expanded in power
series with respect to ε and in the first step all
terms proportional to ε n where n>1 are assumed
to be equal to zero. In the next step, the
already found first approximation is substituted
for the terms proportional to ε, the terms proportional
to ε n where n>2 are assumed equal to
zero both in the equation and in the solution,
and the coefficient of ε 2 is determined. The
procedure can, in principle, go to an arbitrarily
high degree of approximation, but in practice
the calculations often become prohibitively
complicated in the second step (this happens,
e.g., with Einstein’s equations in almost every
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