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MathGroup Archive 2003

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Re: Fluid dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44454] Re: Fluid dynamics
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Mon, 10 Nov 2003 19:55:39 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <boif5j$oau$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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. 

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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