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silent universe

same nonuniformities as are in apparent solar time, as well as a secular term due to precession of the equinoxes. Mean sidereal time is referred to the mean (not true) equinox and, hence, does not include the effects of nutation.

sidereal year

See year.

siderophile Element that displays a strong afﬁnity to associate with iron. Such elements are concentrated in iron meteorites and probably in the iron cores of the terrestrial planets.

sieve analysis A method for determination of sediment grain size distributions. Sediment is dried in an oven, placed into a stack of increasingly ﬁner sieves, and the entire assembly is shaken. Sediment falls through the stack of sieves, and is sorted by size. Each sieve is weighed before and after the test to determine percent ﬁner by weight.

Sievert The SI unit of radiation dose equivalent, equal to an absorbed energy of 1 Joule per kilogram.

sigma (σ ) coordinate In atmospheric physics, a nondimensional pressure coordinate. In atmospheric and oceanographic numerical studies, the Earth’s land surface and ocean bottom create problems in specifying the lower boundary condition in the conventional vertical coordinate system. The vertical coordinate z is replaced by σ so the coordinates are (x, y, σ ), where σ = p/ps (ps being the surface pressure) is a nondimensional, scaled, pressure coordinate which ranges from a value of unity at the earth’s surface (regardless of the terrain height) to zero at the top of the atmosphere in meteorology. In oceanography σ = z−η/(H +η) is a nondimensional, scaled, vertical coordinate which ranges from zero at the sea surface to −1 at the ocean bottom, where H is depth of the ocean, η is the sea surface height, and z is the upward coordinate variable.

signature The pattern of signs in the diagonal form of metric of a space or spacetime. Euclidean space has plus signs, and the signature of 3d Euclidean space is (+, +, +). Four-dimensional Euclidean space has signature

(+, +, +, +), while 4-dimensional Minkowski space has signature (−, +, +, +). For the purposes of doing tensor analysis, the overall sign is irrelevant, so Minkowski space equally has signature (+, −, −, −). In this dictionary we always use (−, +, +, +). Analysis must be carried out with a consistent use of signature and sign convention. See sign convention.

sign convention Geometrical tensors formed from the basis, the metric, and the connection require arbitrary choices of deﬁning signs, involving at least the signature of the space (or spacetime), the sign of the connection coefﬁcient, and the sign of the curvature tensor. A consistent set of such choices is a sign convention. This dictionary uses the sign convention of Misner, Thorne, and Wheeler, Gravitation (Freeman, 1973).

signiﬁcant ﬁgures A decimal number can have an arbitrarily long representation. In physics, the number of digits in a decimal number is adjusted to indicate the accuracy with which the number is believed known. For instance, 3 indicates a number known to be between 2.5 and 3.5, while 3.000 indicates a number between 2.995 and 3.005. For numbers not close to unity, the power-of-ten notation allows the indication of the number of signiﬁcant ﬁgures; for instance, 3 × 104 indicates a number known to be between 2.5 × 104 and 3.5 × 104,

while 3.000 × 104 indicates a number between 2.995 × 104 and 3.005 × 104.

signiﬁcant wave height (characteristic wave height) The average height of the one-third highest waves of a given wave group.

signiﬁcant wave period The average of the highest third of all measured wave periods. A collection of N waves are measured and sorted by height. Then the largest N/3 wave periods are averaged to determine the signiﬁcant wave period.

silent earthquake See slow earthquake.

silent universe In relativity, any dust spacetime whose velocity vector ﬁeld u is irrotational and such that the Weyl tensor is purely electrictype with respect to the velocity ﬁeld u. Such a

silicon burning

spacetime describes the evolution of an expanding or collapsing distribution of dust in which there is no exchange of information between different dust elements, either by sound waves or gravitational waves.

silicon burning The set of nuclear reactions that converts silicon (and adjacent elements) to iron-peak elements (especially 56Ni which later decays to 56Fe). It occurs very near the end of the lives of stars of more than about 10 solar masses. The reaction chain begins with the photodisintegration of some silicon nuclei to alpha particles (helium nuclei), which are then captured by other silicon nuclei to build up from 28 to 32, 36, 40, 44, 48, 52, and 56-particle nuclei of various elements.

silt Sediment in the size range between 0.0039 and 0.0626 mm.

Simon moments (1984) Multipole moments of electrically charged, stationary, and axisymmetric isolated sources in the theory of general relativity. They form two inﬁnite series, the gravitational and electromagnetic complex moments. The real parts of the two series begin with the mass and the electric charge and exist in the absence of currents. The imaginary parts are the current moments. See Geroch–Hansen moments.

simple harmonic motion Motion that is described by a displacement proportional to a sinusoidal function of time:

x = x0 sin(ωt + δ) ,

where x is a displacement, x0 is a constant parameter (the maximum of |x|), ω is an angular frequency, t is the time, and δ is a phase offset. The paradigm is 1-dimensional motion of a mass m on a perfect spring of force constant k (force per unit extension), in which case the frequency ω is

ω = (k/m) .

simple harmonic wave	A monochromatic,
sinusoidal wave.

simple pendulum A compact mass m on an essentially massless string of length L, in a gravitational ﬁeld of acceleration g, constrained to move in a plane. For small oscillations, the motion is simple harmonic with angular frequency

ω = (g/L) .

See simple harmonic motion.

simultaneity, in Newtonian mechanics See

Newtonian simultaneity.

sine-Gordon soliton The nonlinear equation ∂µ∂µα + m2 sin α = 0, µ = {t, x, y, z}. (Summation on double indices assumed.) The

sine-Gordon equation is mischievously named after the Klein–Gordon equation, which it resembles, with the mass term replaced with a sine term. This equation appears in many quantum ﬁeld theories, the function α usually having the meaning of a phase, hence the invariance of the equation under transformations where

α → α + 2π .

The sine-Gordon equation admits solutions where this phase rapidly varies from 0 to 2π in the form

α = 4 tan−1[exp(mx)] .

For these solutions, called solitons, the energy is very localized around x = 0, over a distance scale given by the Compton wavelength m−1. Seen in three-dimensional space, such a solution would appear as a domain wall. See axionic string, domain wall, hybrid topological defect, soliton, summation convention.

single scattering albedo For the scattering of light by a single particle, the ratio of scattered light to incident light.

single scattering phase function For the scattering of light by a particle, the fraction of light scattered into a given solid angle.

singularities In general relativity and in other ﬁeld theories, subsets of the spacetime on which some quantities (often curvature and matterdensity) become inﬁnite. Apparent singularities may be caused by the choice of the coordinate system; these are removed by a coordinate

skip zone

transformation. Examples of such apparent singularities occur at the poles on the Earth. At every other point on the surface of the Earth, the geographical longitude can be determined. However, at each pole the meridians converge to a point and the distance between points on two different meridians tends to zero. A coordinate system nonsingular at the pole can be easily constructed, for example, by placing the origin of a 2-d rectangular map at the pole. Genuine singularities signal the breakdown of the theory used to describe the process; a physical system emerging from a singularity has the initial values of some of its parameters undetermined, and some aspects of evolution of physical systems will be unpredictable. Consequently, for instance, the existence of the Big Bang implies that general relativity cannot completely predict the state of matter at very high densities. It is expected that the adequate theory to describe the universe in the vicinity of the Big Bang will be quantum gravity, a theory that combines classical relativity and quantum mechanics. In quantum gravity, the expectation goes, the state of inﬁnitely large density would be replaced with a very high, but ﬁnite density, through which the evolution of the universe can be calculated. Localized singularities are often discussed in the context of the cosmic censorship hypothesis, at present a vague conjecture that states that every generic singularity is hidden in a black hole and so no signal from it can propagate outside the surface of the black hole. See cosmic censorship.

singularity theorems A set of precise mathematical arguments that prove that a universe will contain a singularity in the past or future if a number of speciﬁc assumptions about its structure are true.

sinistral fault Another term for a left-lateral fault.

Sinope Moon of Jupiter, also designated JIX. Discovered by S. Nicholson in 1914, its orbit has an eccentricity of 0.275, an inclination of 153◦, and a semimajor axis of 2.37 × 107 km. Its radius is approximately 18 km, its mass 7.76 × 1016 kg, and its density 3.2 g cm−3. Its geometric albedo has not been well determined,

and it orbits Jupiter (retrograde) once every 758 Earth days.

sinusoidal wave A wave that has a proﬁle deﬁned by a simple sinusoid. Corresponds to linear or Airy wave theory.

Sirius -1.46 magnitude star of spectral type A1 at RA06h04m08.9s, dec −16◦42 58 .

SI (Systeme International) The system of units based on the meter, kilogram, and second.

skewness A measure of slant or preference for one side. The third moment of a statistical distribution about the mean.

skip fading When the operating frequency is close to the MUF and above the maximum observed overhead critical frequency, then skip fading (sometimes called MUF fading) may occur. Changes in the ionosphere may alter the MUF, taking it below the operating frequency resulting in a sharp drop in signal strength. It is possible that traveling ionospheric disturbances could cause skip fading, although the most common time it is observed is near dawn and dusk, when the MUF is changing more regularly. The distance from the receiver to the point where the transmitted frequency can ﬁrst be observed is the skip distance. See skip zone.

skip zone If the operating frequency of an HF transmitter is higher than the highest frequency that can be reﬂected from the overhead ionosphere, then there will be a region about the transmitter where signals cannot be received. This is called the skip zone. As the elevation angle for the radio waves drops from overhead, the obliquity factor increases until a point is reached when propagation is just possible. The distance from this point to the transmitter is called the skip distance. It is the minimum distance from the transmitter for which a sky wave will return to Earth when the operating frequency exceeds the vertical incidence critical frequency. The only way to reduce the skip distance is to lower the operating frequency. See ionospheric radio propagation path.

sky

sky The apparent dome over the Earth seen by an observer on the ground. Psychologically the sky is not a hemisphere but appears ﬂatter so that the overhead part is not perceived as being as far away as the horizon. The sky is blue in daytime because of scattered blue light from the sun; the sun and moon appear to lie in the surface of the sky. It is black at night, with bright stars, planets, occasional comets, and meteors visible. The clouds inhabit the sky and are sometimes said to obscure the sky.

Skylab The Skylab space station was launched May 14, 1973, from the NASA Kennedy Space Center. Skylab carried several solar experiments including a soft X-ray telescope which produced images of the sun in X- rays with wavelengths from 6 to 49 Å. Skylab reentered the atmosphere and crashed over Australia on July 11, 1979.

sky-wave propagation Describes radio waves reﬂected by the ionosphere in traveling between ground locations. While in the ionosphere, the radio wave experiences dispersion and changes in polarization that are controlled by the Earth’s magnetic ﬁeld, the ionospheric electron density and collisions (described by the collision frequency) between the electrons and the neutral atmosphere. See ionospheric radio propagation path.

slab model Model assumption about the properties of interplanetary magnetic ﬁeld ﬂuctuations and their importance for particle scattering. In the slab model, only waves with wave vectors parallel to the magnetic ﬁeld and axially symmetric transverse ﬂuctuating components are considered. Then the magnetic ﬁeld power spectrum f (k ) of these ﬂuctuations can be described by a power law

f k = C · k−q

with k being the wave number parallel to the ﬁeld, q the slope of the spectrum, and C the power at a certain frequency. The pitch-angle diffusion coefﬁcient κ(µ) is then related to the spectrum by

κ(µ) = A 1 − µ2 |µ|q−1

with µ being the pitch angle and A being a constant related to the level C of the turbulence.

From the above pitch-angle diffusion coefﬁcient a particle mean free path can be obtained as

	3		+1	1 − µ2	2
λ =		v				dµ
	8			κ(µ)
		−1

with v being the particle speed. Note that here the mean free path is not the average distance between two successive pitch-angle scatterings but the average distance traveled by a particle before its pitch-angle has been changed by 90◦, i.e., the direction of motion has been reversed. Thus, for the overall motion, the λ obtained from the above relation has a meaning comparable to the mean free path in spatial diffusion.

The method is falling from favor because mean free paths obtained from the magnetic ﬁeld ﬂuctuations under the assumption of the slab model in general are markedly smaller than the mean free paths obtained from ﬁts of a transport model on the observed intensity and anisotropy time proﬁles (discrepancy problem).

slab penetration In geophysics, there are some cases that an oceanic plate subducted from a trench (slab) penetrates into the lower mantle deeper than 660 km without becoming stagnant in the upper mantle. The phenomenon is referred to as slab penetration. The existence of subducting slabs can be identiﬁed from Wadati– Benioff zones in the upper mantle, whereas slab penetration into the lower mantle was previously not clear because deep earthquakes do not occur there. On and after the 1980s, it was shown that slabs penetrate into the lower mantle in some regions such as the Marianas subduction zone, through techniques of residual sphere and seismic tomography. On the other hand, there are some regions where slabs (like slabs beneath central Japan) are lying horizontally just above the 660-km seismic discontinuity. Such regionality of the fate of slabs (to penetrate or remain stagnant) is thought to be closely related to patterns of mantle convection.

slip system The combination of slip direction and slip plane for a given crystal system. Dislocation theory predicts that the slip direc-