Talk:Universality (dynamical systems)

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[edit] Universality and SOC in piles of sand

(This comment also applies to the notes on universality in the scale invariance article.)

Avalanches in piles of sand are not examples of self-organized criticality, or not in general at any rate. You're mixing up a metaphor used to visualise a theoretical model with a real system (to be fair, you're far from the only ones:-).

More urgently, I don't think the sandpile model per se is an "example" of universality. Universality is about systems with diverse details sharing the same common dynamics at heart. To give an example, with the sandpile model, you can drive it continuously (all sites being continuously increased until one breaks threshold), or you can have the toppling consist of resetting to zero and equally sharing all the energy among the neighbours (this needs a continuous "sand" value of course). These two alternative dynamics have the same exponents, they belong to the same universality class as the original sandpile model. But ... change it so that both the driving is continuous and the toppling consists of resetting to zero and evenly redistributing among neighbours, and you are in a different universality class, that of the Olami-Feder-Christensen model.

See what I'm getting at? Examples of universality are not given by single systems, they're given by different systems that can be shown to be equivalent at heart. —WebDrake 01:46, 29 December 2006 (UTC)