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
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
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.
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
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
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
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
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
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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
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