Chaos theory just got alot more confussing

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Discussion Overview

The discussion revolves around the concept of chaos theory, particularly focusing on a computational study that suggests introducing disorder can lead to order in certain systems. Participants explore the implications of this finding, relating it to phenomena like stochastic resonance, and express confusion and curiosity about the underlying principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants reference a study indicating that a network of oscillators behaves chaotically under ordered forces but becomes synchronized when disorder is introduced.
  • One participant draws a parallel between the study's findings and the concept of stochastic resonance, suggesting a potential commonality in how chaos can lead to order.
  • Another participant provides a detailed explanation of stochastic resonance, discussing its implications in signal processing and the effects of randomization on measurement accuracy.
  • There is a mix of confusion and intrigue regarding the implications of the study, with some participants expressing a desire for further understanding.
  • Participants also engage in light-hearted commentary about spelling and thread management, which may detract from the technical focus.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and interest in the topic, with no clear consensus on the implications of the findings or their relationship to stochastic resonance. The discussion remains open-ended, with multiple viewpoints presented.

Contextual Notes

Some participants mention the complexity of the concepts involved, indicating that the relationship between chaos and order may depend on specific conditions and definitions that are not fully resolved in the discussion.

Who May Find This Useful

This discussion may be of interest to those studying chaos theory, signal processing, and related phenomena in physics and engineering.

scott1
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According to a computational study conducted by a group of physicists at Washington University in St. Louis, one may create order by introducing disorder.
http://news-info.wustl.edu/tips/page/normal/6845.html"
(sorry for the misleading title for this thread)
:confused:
Is there anyone who read the article understand this.If there isn't we might consider cloning einstein...
 
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Physics news on Phys.org
Oh, God, please learn how to spell 'thread.' Please.

- Warren
 
Your, Dog, does not answer prayers. Please hold. ......
 
http://www.physorg.com/news63381025.html

While working on their model – a network of interconnected pendulums, or "oscillators" – the researchers noticed that when driven by ordered forces the various pendulums behaved chaotically and swung out of sync like a group of intoxicated synchronized swimmers. This was unexpected – shouldn't synchronized forces yield synchronized pendulums?

But then came the real surprise: When they introduced disorder – forces were applied at random to each oscillator – the system became ordered and synchronized.

And here is the paper:

http://hbar.wustl.edu/~sbrandt/papers/couposc.pdf
 
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A remarkable article!
This somewhat reminds me of a phenomenon in advanced signal analysis which involves the introduction of "noise" to actually increase signal identity.
Called "stochastic resonance" the effect is also counter-intuitive but is now better understood.
I would be interested to find if there is some underlying comonality between stochastic resonance and the effect described in your link.
Since both appear to create order through the introduction of chaos, I suspect there is.
 
chroot said:
Oh, God, please learn how to spell 'thread.' Please.

- Warren
I edited it:approve:
 
I have been interested in the phenomenon of "stochastic resonance" for many years and have always worked at the technonlogical limits of analogue and digital processing. Let me try to explain what is going on simply. Let us assume that you are trying to digitise an analogue signal with a rather poor resolution a/d converter. If you do this precisely on time and voltage levels this introduces narrow band harmonic artefacts in the signal you have digitised. These harmonic artefacts severely limit the information that you can detect from the original signal, If however you randomise slightly the timing and/or the voltage levels of your a/d converter. The spectrum of the digitisation noise that you get is not a series of harmonic peaks but spread all over the band. This allows you to detect far more detail in the signal that you are digitising particularly if this detail is much more slowly varying than the speed of your digital conversion. All measurement and stimulation systems are subject to various sorts of errors. If you make your measurement or stimulation system very precise these errors can also be very precise and mess up the results more than if you had a less precise measurement.

Biological sensors seem to make very good use of this principle but many mathematicians do not like it because it is not clearly analytic. This is one of the many cases where the physics has it over the maths in my book! :-)
 
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