This page was last edited on 9 September 2017, at 02:26. 1, the usual exponential function is recovered. In phenomenological applications, it is often not clear whether the stretched exponential function should apply to the differential or to the integral distribution function—or to neither. In each case one gets gradshteyn and ryzhik pdf same asymptotic decay, but a different power law prefactor, which makes fits more ambiguous than for simple exponentials.
In physics, attempts have been made to explain stretched exponential behaviour as a linear superposition of simple exponential decays. 1, corresponding to the simple exponential function. To describe results from spectroscopy or inelastic scattering, the sine or cosine Fourier transform of the stretched exponential is needed. It must be calculated either by numeric integration, or from a series expansion. Kohlrausch-Williams-Watts function in the frequency domain. Rudolf, to describe torsional relaxation. 1949 as the fluorescence decay law of electronic energy donors.
MRI signal in the brain. Non-Symmetrical Dielectric Relaxation Behavior Arising from a Simple Empirical Decay Function”. Asymptotic evaluation of certain Markov process expectations for large time”. Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature”. Translated by Scripta Technica, Inc. Detailed comparison of the Williams-Watts and Cole-Davidson functions”.
Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Logarithmic moments of relaxation time distributions”. Debye susceptibilities in glassy systems”. Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions”. Characterization of Continuously Distributed Water Diffusion Rates in Cerebral Cortex with a Stretched Exponential Model”. Theoretical estimation of maximum human lifespan”. This page was last edited on 16 September 2017, at 16:45.