3,610 research outputs found
Information entropy of classical versus explosive percolation
We study the Shannon entropy of the cluster size distribution in classical as
well as explosive percolation, in order to estimate the uncertainty in the
sizes of randomly chosen clusters. At the critical point the cluster size
distribution is a power-law, i.e. there are clusters of all sizes, so one
expects the information entropy to attain a maximum. As expected, our results
show that the entropy attains a maximum at this point for classical
percolation. Surprisingly, for explosive percolation the maximum entropy does
not match the critical point. Moreover, we show that it is possible determine
the critical point without using the conventional order parameter, just
analysing the entropy's derivatives.Comment: 6 pages, 6 figure
Characterization of the Noise in Secondary Ion Mass Spectrometry Depth Profiles
The noise in the depth profiles of secondary ion mass spectrometry (SIMS) is
studied using different samples under various experimental conditions. Despite
the noise contributions from various parts of the dynamic SIMS process, its
overall character agrees very well with the Poissonian rather than the Gaussian
distribution in all circumstances. The Poissonian relation between the measured
mean-square error (MSE) and mean can be used to describe our data in the range
of four orders. The departure from this relation at high counts is analyzed and
found to be due to the saturation of the channeltron used. Once saturated, the
detector was found to exhibit hysteresis between rising and falling input flux
and output counts.Comment: 14 pages, 4 postscript figures, to appear on J. Appl. Phy
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