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MathGroup Archive 2003

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Re: Fluid dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44532] Re: Fluid dynamics
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Thu, 13 Nov 2003 05:57:50 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <boif5j$oau$1@smc.vnet.net> <200311110055.TAA25144@smc.vnet.net> <botblj$cdu$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <botblj$cdu$1 at smc.vnet.net>,
 Anton Antonov <antonov at wolfram.com> wrote:

>In article <boif5j$oau$1 at smc.vnet.net>,
> Nathan Moore <nmoore at physics.umn.edu> wrote:
>
>Cellular automa has always looked like a discretization of continuous 
>differential equations (ever looked closely at the Runge-Kutta DEQ 
>solver?  A cursory glance shows that any x(i+1) comes from x(i) and 
>maybe also x(i-1) with statistical weights coming from taylor 
>expansions.  This means that any differential equation can be 
>discretized and expressed as a "cellular automa system"
>
>There's nothing new and fabulous about that - its the standard approach 
>in Numerical methods. 
>>    
>>
> I was doing research in large scale air pollutioning for some time. In 
> this area are usually considered 5 different physical processes with 
> very different time scales. From the mathematical modeling one gets, 
> say, 30-70 equations. The system cannot be treated directly with 
> classical PDE or ODE methods.  These methods are used together with a  
> procedure called "splitting". E.g. one simulates separately  first the 
> advection, then the chemistry; then again the advection, then the 
> chemistry, and so on. Now I find the idea to use the cellular automata 
> to skip the splitting as fabulous and exciting, :) but probably I like  
> mathematics too much. And at least in this researh area cellular 
> automata are not standard Numerical methods.

And this _is_ the point of NKS! At the NKS conference I had an 
interesting conversation with Brian Vick <bvick at vt.edu> on this very topic.

Paul Abbott wrote:
 
> >But this is _not_ the point of A New Kind of Science (NKS): Of course 
> >you can discretize the Navier-Stokes equations but, instead of starting 
> >with a differential equation and discretizing, why not _start_ with a 
> >cellular automata, modeling the microscopic behavior of fluid molecules, 
> >having properties directly related to the physics at hand (by satisfying 
> >a set of simple collsion rules). See NKS pp 376-382 and 996-997.
> >
> >Cheers,
> >Paul
> >
> > 
> >>On Friday, November 7, 2003, at 04:16 AM, martinro at carleton.edu wrote:
> >>
> >>    
> >>
> >>>Hi,
> >>>A partner and I are working on a project that describes fluid dynamic
> >>>behavior in systems such as hurricanes and galaxy formation, for a 
> >>>college
> >>>cellular automata physics seminar.  It seems that research about the 
> >>>models
> >>>to create these simulations are extremely hard to find, has anyone done
> >>>this type of research on Mathematica or would know the form to write 
> >>>the
> >>>programs? I know that the galaxy formation has been done on Fortran, 
> >>>but
> >>>hurricanes and similar systems yield almost no results on a literature
> >>>search.  Dr. Wolfram says in his book A New Kind of Science that these 
> >>>type
> >>>of weather related systems can be described by cellular automata in a
> >>>similar manner to fluid dynamics, but gives no examples of the 
> >>>programs,
> >>>can anyone help us?
> >>>
> >>>Thanks
> >>>Ross Martin
> >>>Carleton College
> >>>
> >>>      
> >>>
> >
> >  
> >
> 
>

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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