Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-27 Thread Evgenii Rudnyi
Stephen, Nature computes itself by evolving in time Let me put then my question this way. When Nature computes itself does the next state is uniquely determined the previous steps? Or, to make the next state, does Nature play a dice? I would appreciate if you explain how bifurcations and

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-25 Thread Evgenii Rudnyi
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

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-25 Thread Evgenii Rudnyi
I have found Logistic Map http://mathworld.wolfram.com/LogisticMap.html Here the system has very different outcomes depending from initial conditions (now I understand your use of statistics). Yet, each trajectory is deterministic. Hence, this was not my question. Sorry for being unclear.

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-25 Thread meekerdb
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

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-25 Thread Stephen P. King
On 3/25/2012 2:46 PM, meekerdb wrote: 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

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-24 Thread Evgenii Rudnyi
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

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-24 Thread Russell Standish
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

Re: Determinism in the case of bifurcations and symmetry breaking

2012-03-23 Thread Stephen P. King
On 3/23/2012 3:08 PM, Evgenii Rudnyi wrote: In physics there are bifurcations and symmetry breaking. What happens then if I solve some transient problem for a system where a bifurcation or symmetry breaking happens. How the choice will be made? Evgenii Hi! We would use statistics to