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 theincompressible Navier-Stokes equations with the Boussinesq approximation for freeconvection should suffer.## Advertising

If I understand correctly, bifurcation in this case arises when we increase thetemperature difference between two plates. That is, if we consider the stationaryNavier-Stokes equations on the top of thermal gradient Del T in the system, there is acritical Del T after that we have several solutions.To be back to my question. One could construct a system of equations from the stationaryNavier-Stokes equations + Del T(time). In this case we have a problem that at some timewhen we reach a critical Del T, the system of equation has suddenly several solution andthe question would be which one will be chosen.On the other hand, one could use the transient Navier-Stokes equations directly and itseems that in this case the problem of bifurcation will not arise as such. Well, in thiscase 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`

`manages.`

Brent

My question would be if physical laws allow for the first situation when at some pointduring transient solution a mathematical model has several solutions. If yes, then I donot understand how physics chose the one of possible solutions.Evgenii 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 instance. Cheers On Sat, Mar 24, 2012 at 10:05:00PM +0100, Evgenii Rudnyi wrote:Hi Stephen, 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 example. Say, I do not understand how do you apply statistics in this case. Either it is unclear to me how infinite computational power will help. Evgenii

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