[Swarm-Modelling] Mean Field Theory

[Russell Standish]

Actually, a panmictic model is spatially homogenous if there is a
spatial dimension. Also, mean field models are also spatially
homogenous. See Ashcroft & Mermin "Solid State Physics" for a
technical discussion of the term "mean field" in it original
application.

Panmictic and mean field approximations are only equivalent when the
effect of interactions with the other agents  can
be replaced by the average effect, multiplied by the interaction
rate. When this condition is true, the phenomenon in question is
called "resultant".

People using "mean field" to mean "panmictic" are mistaken,
misleading and downright obfuscatory...

					Cheers

Doug Donalson wrote:
> 
> I disagree.  mean fierld is used as an alternate term for well-mixed models,
> not just spatially homogeneous models.  For example, implicit in ODE models
> are both homogeneous space and the well-mixed (your soup) assumptions.  ODEs
> are often refered to as mean field models for both those reason.  Then
> again, it is not uncommon to find different uses of terms from different
> groups of researchers.
> 
> Cheers
> ----- Original Message -----
> From: "Russell Standish" <R.Standish@unsw.edu.au>
> To: <modelling@swarm.org>
> Sent: Tuesday, May 27, 2003 4:23 PM
> Subject: Re: [Swarm-Modelling] Re: [Swarm-Support] Re: Agent communication
> and grid models
> 
> 
> > No! Mean field means that agents interact solely with an average
> > background property, not with individual agents. A panmictic model
> > (dubbed "soup" model here) has each agent having equal probability of
> > interacting with the other agents (or simply interacting with all
> > other agents). A mean field approximation is really only valid when
> > the effect of all agents is equivalent to the sum (or average) of the
> > agents - pretty much when there is no complex emergence in the system.
> >
> > Cheers
> >
> > Doug Donalson wrote:
> > >
> > > Just for reference.  The more common term for "soup" models is  "mean
> > > field".
> > >
> > > Cheers,
> > >
> > > D4
> > >
> >
> >
> > --------------------------------------------------------------------------
> --
> > A/Prof Russell Standish            Director
> > High Performance Computing Support Unit, Phone 9385 6967, 8308 3119
> (mobile)
> > UNSW SYDNEY 2052                     Fax   9385 6965, 0425 253119 (")
> > Australia            R.Standish@unsw.edu.au
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> http://parallel.hpc.unsw.edu.au/rks
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> 
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----------------------------------------------------------------------------
A/Prof Russell Standish            	 Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052                     	 Fax   9385 6965, 0425 253119 (")
Australia            			 R.Standish@unsw.edu.au             
Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02
----------------------------------------------------------------------------