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

Published online by Cambridge University Press:  15 March 1999

Z. Garncarek  and
R. Piasecki
Z. Garncarek
Affiliation:
Institute of Mathematics, University of Opole, Oleska 48, 45052 Opole, Poland
R. Piasecki*
Affiliation:
Institute of Chemistry, University of Opole, Oleska 48, 45052 Opole, Poland
*
[email protected]
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Abstract

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.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 5 , Issue 3 , March 1999 , pp. 243 - 249
Copyright
© EDP Sciences, 1999

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References

R. Hilfer, Adv. Chem. Phys. XCII, 299 (1996).
Garncarek, Z., Idzik, J., Int. J. Heat Mass Transf. 35, 2769 (1992). CrossRef
Czainski, A., Garncarek, Z., Piasecki, R., J. Phys. D: Appl. Phys. 27, 616 (1994). CrossRef
Z. Garncarek, T. Majcherczyk, R. Piasecki, D. Potoczna-Petru (to be published).
Garncarek, Z., Piasecki, R., Borecki, J., Maj, A., Sudol, M., J. Phys. D: Appl. Phys. 29, 1360 (1996). CrossRef
Rose, D., Durose, K., Palosz, W., Szczerbakow, A., Grasza, K., J. Phys. D: Appl. Phys. 31, 1009 (1998). CrossRef
Missiaen, J.M., Thomas, G., J. Phys.-Cond. 7, 2937 (1995).
D. Stoyan, H. Stoyan, Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics (John Wiley & Sons Ltd, 1994), Part III.
van Siclen, C.DeW., Phys. Rev. E 56, 5211 (1997). CrossRef
Broger, F., Feder, J., Jøssang, T., Hilfer, R., Physica A 187, 55 (1992). CrossRef
Andraud, C., Beghdadi, A., Lafait, J., Physica A 207, 208 (1994). CrossRef
Andraud, C., Beghdadi, A., Haslund, E., Hilfer, R., Lafait, J., Virgin, B., Physica A 235, 307 (1997). CrossRef
Z. Garncarek, Ph.D. thesis, Jagellonian University, 1980 and discussion on International School of Cosmology, Cracow (1986).
Frieden, B.R., J. Opt. Soc. Am. 62, 511 (1972). CrossRef
Daniell, G.J., Gull, S.F., IEE Proc. E 127, 170 (1980).
Skilling, J., Int. Spectrosc. Lab. 2, 5 (1992).
Z. Garncarek, Constructions of the Measures of Distribution Features for Finite Point Sets with Examples of Applications in Natural and Technical Sciences (Pedagogical University Press, in Polish, Opole 1993), Vol. 203.