On 3/25/2012 2:43 AM, Evgenii Rudnyi wrote:
Let us take Benard cells for example. It is a good idea. I guess that in this case the
incompressible Navier-Stokes equations with the Boussinesq approximation for free
convection should suffer.
If I understand correctly, bifurcation in this case arises when we increase the
temperature difference between two plates. That is, if we consider the stationary
Navier-Stokes equations on the top of thermal gradient Del T in the system, there is a
critical Del T after that we have several solutions.
To be back to my question. One could construct a system of equations from the stationary
Navier-Stokes equations + Del T(time). In this case we have a problem that at some time
when we reach a critical Del T, the system of equation has suddenly several solution and
the question would be which one will be chosen.
On the other hand, one could use the transient Navier-Stokes equations directly and it
seems that in this case the problem of bifurcation will not arise as such. Well, in this
case there are numerical problems.
And then one could use molecular dynamics directly - but this raises a different kind of
numerical problem: how to put in the initial conditions for 1e28 molecules. But nature
My question would be if physical laws allow for the first situation when at some point
during transient solution a mathematical model has several solutions. If yes, then I do
not understand how physics chose the one of possible solutions.
On 25.03.2012 05:50 Russell Standish said the following:
Look up the literature on catastrophe theory. There were many examples
of just these phenomena cooked up (particularly by Zimmerman IIRC)
some good, many not so good. I'm sure you should be able to find
something appropriate - maybe the appearance of Benard cells for
On Sat, Mar 24, 2012 at 10:05:00PM +0100, Evgenii Rudnyi wrote:
I am not sure if I completely understand you. My question was rather
what happens in Nature if we assume that its mathematical model
includes bifurcations and/or symmetry breaking.
Do you know a simple mathematical model with bifurcations and/or
symmetry breaking? It might be good to consider this on a simple
Say, I do not understand how do you apply statistics in this case.
Either it is unclear to me how infinite computational power will
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