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The predicted power law behaviour is observed, and the predicted α(Df) relationship was seen to prevail in each case.
The mean square displacement of the segments displays a power law behaviour with respect to time 〈Δr2 t))〉∼(Dt)α.
Observed 1D samples may fail to show power law characteristics and, therefore, a lack of power law behaviour need not imply a non-power law parent population.
A model to validate this concept is presented in this paper; this analytical model is based on typical material law behaviour hypotheses of beam nonlinear mechanical behaviour.
The circuits exhibit Weber's law behaviour as in natural biological systems4, operate over a wide dynamic range of up to four orders of magnitude and can be designed to have tunable transfer functions.
Within the measured frequency ranges, power law behaviour for the dynamic modulus was observed at the gel point in all systems.
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The model explains the power-law behaviour seen in both conventional wars and terrorist attacks.
This power-law behaviour holds the potential to be established as a stylized fact of stock market indices in general.
It is shown that the temporal structure functions – in general – follow a 5/3 to 2/3 power-law behaviour.
A proper scaling of the activation energy is introduced, ensuring a proper degeneration towards the stress strain rate power-law behaviour.
As the complexity, and thus breadth, of the distribution increases, lognormal distributions begin to exhibit properties that are more commonly associated with power-law behaviour, providing a greater extent of overlap in which these two distributions are indistinguishable53 (Fig. 1c).
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