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From: "Giuseppe Brunello" <gbrunello3@gatech.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Common tangent
Date: Mon, 11 Feb 2008 03:38:01 +0000 (UTC)
Organization: Georgia Tech
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Thank you for all replies and sorry I didn't reply earlier.

I agree that having a function, as opposed to a set of
points, would make the implementation much neater, but alas
the problem I had in mind is to obtain a phase diagram for a
binary mixture from the the Gibb's free energy. The material
system minimizes the energy, and if a binary mixture of the
two has a lower energy than a single phase then you'll get
two phases (the system's energy lies on the common tangent,
it being the weighted sum of the energy of the two phases).

Also the slope of the system approaches infinity as you
approach pure substances (i.e. the chemical potential of B
in pure A is infinite). 

For an implementation with discreet points I was thinking of
searching for the minimum of both curves, and then scan both
sides with a tangent. If the tangent is lower then the other
curves at all points I continue searching, if not I've
intersected the other curve (and have a close approximation
of the common tangent). 

Anyways thanks for all your help, I just thought this
problem was neat.