What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?
Institute of Mathematics, University of Opole, Oleska 48, 45052 Opole, Poland
2 Institute of Chemistry, University of Opole, Oleska 48, 45052 Opole, Poland
Corresponding author: firstname.lastname@example.org
Revised: 7 October 1998
Accepted: 16 December 1998
Published online: 15 March 1999
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 . 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.
PACS: 05.90.+m – Other topics in statistical physics, thermodynamics and nonlinear dynamical systems / 68.55.-a – Thin film structure and morphology
© EDP Sciences, 1999