Re: question about output file

On Mon, 14 Aug 2006, [email protected] wrote:
> I have question about output file contents
> epsilon:1-1.96, mean 1.74389, harm. mean 1.63197, 86.4136% > 1, 77.489% 
> "fill"
> what is meaning of harm and latter thing ?

The output line you quoted means that the dielectric function (epsilon):

 	* ranges from epsilon=1 to epsilon=1.96
 	* has a mean <epsilon> = 1.74389
 	* has a harmonic mean 1/<1/epsilon> (the inverse of the mean
           of the inverse of epsilon) = 1.63917
 	* is > 1 over 86.4136% of the volume
 	* fill fraction = 77.489%
 		= fraction of volume that would have to be occupied
 		  by max epsilon to give the same mean <epsilon>

The reason that the fill fraction is smaller than the fraction > 1, in a 
structure with only two materials where it might seem that they should be 
identical, is due to the pixellization.  Basically, pixels that intersect a 
fraction of the high-index material are assigned an "effective" index slightly 
> 1.  This causes the volume fraction > 1 to expand.  The two numbers should 
approach one another as you increase the resolution.

Both the ordinary mean and the harmonic mean are significant in homogenization 
(effective medium) theory because they give the Wiener bounds [ Aspnes, Am. J. 
Phys. 50, 704-709 (1982) ].

Cordially,
Steven G. Johnson