Chaos = Order: WUSTL physicists make baffling discovery

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From http://news-info.wustl.edu/tips/page/normal/6845.html

Pandemoniumm on demand

By Douglas M. Main


April 3, 2006 -- "Da police are not here to create disorder; dere here to preserve disorder."
 
EsoQuest said:
From http://news-info.wustl.edu/tips/page/normal/6845.html

Pandemoniumm on demand

While other research has shown that disorder can create order, these studies often involved manipulating parameters within the systems such as changing pendulum length. The researchers say that their work is novel because it involves changing externally applied forces. Thus, they believe, their findings might have potential in the real world, where it would be more difficult to change parameters within the system — neurons, for example — but relatively simple to apply an external forcing.

"This is of course basic research," said Brandt. "But what you can learn from this is that complex systems ... sometimes behave in a very unexpected way, completely opposite to your intuition or expectation. It will be interesting to see if the mechanism that we have found can actually be put to some use."
That external randomness helps is indeed not new. The idea is rather simple: the sytem has a tendency to set in low-energy valleys, which may be chaotic. Applying an external random force may help the system to skip these valleys and to create/find other valleys, not chaotic ones. This is sometimes called "simulated annealing". From Wikipaedia:
The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one.

By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods.
The new (as it seems) thing is that in the pendulum experiment the external random force needs to be applied continuously. But we know that for self-organizing chemical reactions some heating (thus randomness) is needed. The reactions stop when the system is cooled down. A well known example of a self-organizing chemical reaction is Belousov-Zhabotinsky (BZ) reaction

Examples of randomness creating order can also be seen in "quantum fractals" - see my new paper: Quantum Fractals. Geometric modeling of quantum jumps with conformal maps

ark
 
Ark said:
That external randomness helps is indeed not new. The idea is rather simple: the sytem has a tendency to set in low-energy valleys, which may be chaotic. Applying an external random force may help the system to skip these valleys and to create/find other valleys, not chaotic ones. This is sometimes called "simulated annealing".
This brings to mind the order that can result in a person's life from receiving an outside shock, as well
 
Ark said:
Examples of randomness creating order can also be seen in "quantum fractals" - see my new paper: Quantum Fractals. Geometric modeling of quantum jumps with conformal maps
I was sure I recongized the effect as nothing really new. Thank's for clarifying this, and for the reference.
 
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