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

Particle Dispersion on Rapidly Folding Random Hetero-Polymers

We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between the enhanced diffusion and the quenched disorder. The dispersion speed exhibits universal behavior independent of the folding statistics. On the other hand it is strongly affected by the structure of the disordered potential. The results may serve as a reference point for a number of translocation phenomena observed in biological cells, such as protein dynamics on DNA strands.Comment: 4 pages, 4 figure