Spectral density inversely proportional

The value of an is inversely proportional to the square root of the integration time, so in terms of spectral density (one-sided) it has a white amplitude ... 

The virial expansion of the time correlation functions is possible for times smaller than the mean time x between collisions. Accordingly, the spectral profiles may be expanded in powers of density, for angular frequencies much greater than the reciprocal mean time between collisions, co 1/r. Since at low density the mean time between collisions is inversely proportional to density, lower densities permit a meaningful virial expansion for a greater portion of the spectral profiles. 

Noise with a spectral density that is inversely proportional to frequency over a wide frequency range is a well-known phenomenon found in a great number of quite different objects that include biological membranes and other ionic systems. Extensive reviews of earlier works relevant to membrane biophysics can be found in the literature (3, 6, 56). 

Johnson noise [11-13], which occurs on the seal, i.e., in the junction between the pipette and the membrane. The spectral density of this noise is inversely proportional to the seal resistance. Therefore, it is important to have a very tight seal, the so-called gigaseal, which should significantly improve the noise characteristics of the patch-clamp record. 

It may be shown (e.g., Aki and Richards 2002 Havskov and AlguacU 2010) that this noise is proportional (Eq. 14) to the mechanical damping coefficient h (not included the feedback effect) and inversely proportional to the suspended mass. The power spectral density (PSD) of the mass acceleration noise (the PSD integrated between two frequencies gives the noise variance in this band) is... 

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