Duality and spatial inhomogeneity

Within the framework on non-extensive thermostatistics we revisit the recently advanced q-duality concept. We focus our attention here on a modified q-entropic measure of the spatial inhomogeneity for binary patterns. At a fixed length-scale this measure exhibits a generalised duality that links appropriate pairs of q and q' values. The simplest q q' invariant function, without any free parameters, is deduced here. Within an adequate interval q < qo < q', in which the function reaches its maximum value at qo, this invariant function accurately approximates the investigated q-measure, nitidly evidencing the duality phenomenon. In the close vicinity of qo, the approximate meaningful relation q + q' = 2qo holds.Comment: Contribution to International School and Conference on "Non Extensive Thermodynamics and physical applications", Villasimius-Capo Boi (Cagliari), Italy, 23-30 May 2001, 6 pages, 2 figures, replaced with published versio

Entropic descriptor of a complex behaviour

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.Comment: 14 pages, 7 figures, extended versio

Detecting self-similarity in surface microstructures

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend on the kind of the carpet. These peaks point to the presence of self-similarity even for randomly perturbed initial fractal sets. This is also demonstrated for the model population of particles diffusing over the surface considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the subtle self-similarity traces to be explored.Comment: 9 pages, 4 figures, presented at ECOSS18 (Vienna) Sept. 199

Apparatus and method for control of a solid fueled rocket vehicle Patent

Solid propellant rocket vehicle thrust control method and apparatu

Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Recently, entropic descriptors based the Monte Carlo hybrid reconstruction of the microstructure of a binary/greyscale pattern has been proposed (Piasecki 2011 Proc. R. Soc. A 467 806). We try to speed up this method applied in this instance to the reconstruction of a binary labyrinth target. Instead of a random configuration, we propose to start with a suitable synthetic pattern created by cellular automaton. The occurrence of the characteristic attributes of the target is the key factor for reducing the computational cost that can be measured by the total number of MC steps required. For the same set of basic parameters, we investigated the following simulation scenarios: the biased/random alternately mixed #2m approach, the strictly biased #2b and the random/partially biased #2rp one. The series of 25 runs were performed for each scenario. To maintain comparable accuracy of the reconstructions, during the final stages the only selection procedure we used was the biased one. This allowed us to make the consistent comparison of the first three scenarios. The purely random #2r approach of low efficiency was included only for completeness of the approaches. Finally, for the conditions established, the best single reconstruction and the best average tolerance value among all the scenarios were given by the mixed #2m method, which was also the fastest one. The slightly slower the alternative #2b and #2rp variants provided comparable but less satisfactory results.Comment: 11 pages, 3 figures, 2 tables, published versio