820 research outputs found
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
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