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Rarefaction is the reduction of an item's density, the opposite of compression. [1] Like compression, which can travel in waves ( sound waves , for instance), rarefaction waves also exist in nature. A common rarefaction wave is the area of low relative pressure following a shock wave (see picture).
In ecology, rarefaction is a technique to assess species richness from the results of sampling. Rarefaction allows the calculation of species richness for a given number of individual samples, based on the construction of so-called rarefaction curves. This curve is a plot of the number of species as a function of the number of samples.
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
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Characteristics may fail to cover part of the domain of the PDE. This is called a rarefaction, and indicates the solution typically exists only in a weak, i.e. integral equation, sense. The direction of the characteristic lines indicates the flow of values through the solution, as the example above demonstrates.
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates. Hearing protectors help reduce acoustic flux from flowing into the ears.
Diagram showing displacement of the Sun's image at sunrise and sunset Comparison of inferior and superior mirages due to differing air refractive indices, n. Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. [1]
The curve represents a plot of equation with p 1, v 1, c 0, and s known. If p 1 = 0, the curve will intersect the specific volume axis at the point v 1. Hugoniot elastic limit in the p-v plane for a shock in an elastic-plastic material. For shocks in solids, a closed form expression such as equation cannot be derived from first principles.