arXiv subjects

R. Piasecki

Publications and source records attributed to R. Piasecki.

23 records · Page 2Linked to original sources

arXiv2002

Effective conductivity in association with model structure and spatial inhomogeneity of polymer/carbon black composites

The relationship between effective conductivity and cell structure of polyethylene/carbon composites as well as between effective conductivity and spatial distribution of carbon black are discussed. Following Yoshida's model both structures can, in a way, be said to be intermediate between the well known Maxwell-Garnett (MG) and Bruggeman (BR) limiting structures. Using TEM photographs on composites with various carbon blacks we have observed that the larger is Garncarek's inhomogeneity measure H of two-dimensional (2D) representative distribution of the carbon black, the smaller is the effective conductivity of the composite.

cond-mat.mtrl-sci↗

arXiv2002

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.

cond-mat.stat-mech↗

arXiv2001

Application of relative configurational entropy as a measure of spatial inhomogeneity to Co/C film evolving along the temperature

Based on the digitized electron micrographs, we investigate a temperature evolution of Co/C film. The simple in usage quantitative characterization of the spatial disorder for systems of point objects has been employed. We show that a dominant increase of spatial inhomogeneity of cobalt phase is shifted towards the larger length scales along the sample heating temperature. The results allow the subtle differences of spatial inhomogeneity in thin metallic films to be explored.

cond-mat.mtrl-sci↗

arXiv2000

Coarsened Lattice Spatial Disorder in the Thermodynamic Limit

In this Rapid Research Note the application of recently introduced [Physica A 277 (2000) 157] entropic measure S_Delta of spatial disorder for systems of finite-sized objects is presented. In the thermodynamic limit the critical behaviour of coarsened lattice model of random two-phase systems is illustrated for certain grain size distributions (GSDs) and chosen parameters. Also the changes of spatial disorder, quantified by S_Delta, between the limit GSDs clearly show that the topological equivalence of the two phases is broken.

cond-mat.stat-mech↗

arXiv2000

What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?

A linear transformation f(S) of configurational entropy with length scale dependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangement of point objects the value of the measure is conserved. This property allows for computation of the measure at every length scale. Its remarkable sensitivity to the deviation (per cell) from a possible maximally uniform object distribution for the length scale considered is comparable to behaviour of strictly mathematical measure h introduced by Garncarek et al. in [2]. Computer generated object distributions reveal a correlation between the two measures at a given length scale for all configurations as well as at all length scales for a given configuration. Some examples of complementary behaviour of the two measures are indicated.

cond-mat.stat-mech↗