Emergence model via reductionism

[Evgenii Rudnyi]

I would like to thank Chris and Dick for the references on emergence.

From a simulation viewpoint, the phase field theory came to my mind.
Let us consider dendrites during crystallization, for example see a
picture in Wikipedia

http://en.wikipedia.org/wiki/Dendrite_%28crystal%29

Can one refer to this as emergence? There was a liquid and then after
the temperature goes down one obtains such nice structures.

Nowadays the phase field theory is used to simulate such a phenomena.
The idea here is to introduce a unified Gibbs energy equation for both
phases, liquid and solid. Then one internal parameter can have values
from 0 to 1, 0 corresponding to crystal and 1 to liquid. Other values
between 0 and 1 corresponds to a transition state. So when at the
beginning the values of the internal parameter for all coordinates are
equal to 1, we have just liquid. Then eventually there are some regions
where the internal parameter is equal to 0 and thus dendrite growths.

Some short description of the phase field theory is in

http://evgenii.rudnyi.ru/doc/papers2/07multiscale.pdf

see section Phase Field Theory.

So the question is whether this is emergence or not. I myself do not see
any reason why it is not. But then a reductionism theory can nicely
describe this.

Evgenii