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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.
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).
The rarefaction curve, is defined as: = [] = () ... Despite being defined at discrete values of n, these curves are most frequently displayed as continuous functions.
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.
The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform.
The Riemann problem is very useful for the understanding of equations like Euler conservation equations because all properties, such as shocks and rarefaction waves, appear as characteristics in the solution. It also gives an exact solution to some complex nonlinear equations, such as the Euler equations.
For electromagnetic waves in vacuum, the angular frequency is proportional to the wavenumber: =. This is a linear dispersion relation, in which case the waves are said to be non-dispersive. [1]
The Pull of the Recent (POR) describes a phenomenon in which a combination of factors causes palaeontologists to overestimate diversity towards the present day. Biased preservation and sampling in the fossil record results in past biodiversity estimates to be lower with modern taxa being considered more diverse because present biodiversity is the best sampled. [1]