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## Re: mean.m (a question of mathematics, not programming)

 From: David Doolin Subject: Re: mean.m (a question of mathematics, not programming) Date: Wed, 21 Mar 2001 13:09:04 -0500 (EST)

```On Wed, 21 Mar 2001, Joshua Rigler wrote:

> Risking ridcule by numericists and mathematicians alike, I bravely put
> forth what may very well be a dumb (and perhaps inappropriate for this
> mailing list) question...
>
> Would somebody be willing to tell me what the "geometric" and "harmonic"

In physical processes, such as groundwater flow or wave propagation,
harmonic means appear because the global behavior is controlled by the
part with the least magnitude.  For example, consider 2 thick beds of
gravel separated by a layer clay.  The gravel conducts flow very well,
the clay does not.  It deosn't take very much clay to stop flow across
the entire domain, a very thin layer will suffice.  Heat flow works
exactly the same way.  The way to see it appear is to assume mass
continuity (div q = 0), then derive the global flow assuming mass balance.
The harmonic mean pops out as a resultant global conductivity.

Disclaimer: This is a grossly simplified model for groundwater flow!
I know that!

Dave Doolin

> options are in the mean.m function?  Actually, I can see "what" they are
> in the source code, but I'd like to know what practical significance
> they might have.  References would be greatly appreciated.
>
> -EJR
>
>
>
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