Statistics – Applications
Scientific paper
Jan 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977natur.265..128m&link_type=abstract
Nature, Volume 265, Issue 5590, pp. 128-129 (1977).
Statistics
Applications
19
Scientific paper
A PROBLEM of practical importance in a wide variety of situations is that of calculating the permittivity (or equivalently, the conductivity) of simple cubic arrays of spheres embedded in another material. Applications occur in, for example, the analysis of optical properties of inhomogeneous films1, dielectric dispersion in mixtures2, the behaviour of artificial dielectrics3, the study of lunar soil samples4 and in vision research5. Although the problem is an old one, and has attracted the attention of some of the great names of physics (for example, J. C. Maxwell6 and Lord Rayleigh7) it seems that a completely satisfactory theory has not existed until the present time. This is shown by the fact that in the most critical case, that of perfectly conducting spheres, none of the existing theories give the expected divergence at the critical volume fraction (fc = π/6) at which the spheres touch. We have extended Lord Rayleigh's treatment and present a theory which gives the correct behaviour for all volume fractions.
McKenzie David R.
McPhedran Ross C.
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