# Is there any physics behind flocking?

There are many articles published in physics journals about flocking. Is there a physical reason for these phenomena or is it just because physics methods are being used to study collective motion?

It seems there is no true mechanics in models of flocking, there are no Hamiltonians defined and so on, only rules of motion, like alignment rule and constant velocity of self-propelled particles. Yet physicists debate the validity of Mermin-Wagner theorem in simple flocking models. Isn't this fundamentally problematic because of absence of real dynamics in these systems?

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I read the wiki link, and there seems to be no physics in the concept, just game rules. If I were thinking from scratch certainly for birds I would introduce physics: wind resistance and shadowing allowing partial gliding for the birds behind the leader, like the wake of a boat. I do not know about the theorem, sounds esoteric at this level. – anna v May 30 '11 at 16:09
All physics must be studied in terms of hamiltonians? This is going to be upsetting news to a lot of physicists! – Colin K May 30 '11 at 16:48
@anna v: I agree. Self-propelled particles model and its simplest form, Vicsek model, is just an agent based model with simplest possible behavior rules that are able to reproduce collective motion, e.g. build up of velocity correlations in a system of many particles, moving at constant velocity without any other interaction but that defined by the rule. There is no physical interaction here at all, it's a rule based model. I suppose one could say there is no real physics behind this model. – liberias Jul 2 '11 at 22:02
But some have coarse-grained this model with hydrodynamical approach [ Toner, Tu ]. Within this continuum theory they discuss the reason for non-applicability of the Mermin-Wagner theorem. My question was, what is the reason, to even discuss this theorem, although we haven't got a Hamiltonian defined as in case of the Heisenberg model. I would expect a similar reasoning as is done here. But i guess this comparison is done very nonspecifically. – liberias Jul 2 '11 at 22:03
@Colin K: I think you misinterpreted my question. I never wanted to upset anyone with such a great idea ;) – liberias Jul 2 '11 at 22:04

For your first question: Yes, there is a physical reason for this phenomenon as is (or should be) for every observable phenomenon.

For your second part: Depends on who is debating the validity or applicability of that theorem. Can you please add a reference, then perhaps someone may be able to answer it.

For your third question: Yes there is a lot of "real" dynamics involved here. In fact, because a lot of objects are interacting with each other, it is highly involved as well. Different models to explain/simulate flocking behavior use almost the same physical phenomena in their calculations --gravitational pull from earth, fluid mechanics, wing flapping. What they debate is usually one or more of the following:

• What is a bird's comfort level of independence? Meaning, how far will a bird on the edge will go away from the flock before it senses danger. This has nothing* to do with physics and has everything to do with such factors as the predators around, the evolutionary history of the birds, etc.
• How close do birds like flying to each other? At what distance they sense an impending collision? Again, nothing to do with physics really.
• How perfectly do birds prefer to align to the group? Is there a single leader or multiple?
• Does a change in the wind's direction change the leader's course?
• etc...

One can of course abstract out the biology and social behaviour out of this model and empirically define a force and construct laws (similar to Newton's laws of gravity, Maxwell's equations etc.) for that force. Perhaps then that person may be able to reuse some of the results that physicists have derived for other problems (note: this depends a lot on how your force laws are defined). Basic physical laws that apply universally shall still be applicable.

### Footnotes

*You can say everything is physics deep deep down but that is not the point here obviously.

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For Mermin-Wagner theorem I meant this reference. A system of a large number of interacting birds, which are very complex physical manifestations, interact physically through vision mostly i guess and through hydrodynamic effects made on the surrounding medium, air. There was an interesting empirical study of this interaction made in Rome. – liberias Jul 2 '11 at 21:58

Depends what do you understand by 'physics'. If in narrow sense only first-principle theory and experiment, then - no. Obviously birds are not particles. But hey, modeling folding of proteins (or even - orbitals of atoms) you consider an effective model, nowhere near to the particle physics.

But when you by 'physics' understands mathematical description of real phenomena, then surely analysis of 'collective behavior' (or 'flocking' to be more specific) is physics.

As many mathematical tools came from statistical mechanics (or is related), it is very natural they publish in physical journals.

But of course, the motion need not to obey any fundamental laws (e.g. conservation principles, Hamiltonian dynamics, ...) - it is only an effective description.

For the reference see e.g.

• Tamás Vicsek, Anna Zafiris, Collective motion, arXiv:1010.5017v1 [cond-mat.stat-mech]
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I think that this Order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays is a result of a collective hidrodynamic behaviour somehow similar to a flock of birds (it's physics as anna v. noted)

The V formation greatly boosts the efficiency and range of flying birds

It is also likely that fish benefit from shoal membership through increased hydrodynamic efficiency.

The whole issue of colective behaviour is very interesting because the result is more than the sum of the components and we learn how to solve complex problems, like increasing the efficiency of motion or lowering the collective risk, using simple 'inteligent' agents that cooperate. The package MASON Multiagent based simulation (IA) is very interesting.
A system of Rules can be translated to a system of equations, if it makes you feel more comfortable.
The theorem you mention, related to statistics (and QM), has nothing to do with 'flocking', imo .

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