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Re: Re: Fluid dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44477] Re: [mg44454] Re: Fluid dynamics
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 12 Nov 2003 08:01:27 -0500 (EST)
  • References: <boif5j$oau$1@smc.vnet.net> <200311110055.TAA25144@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Cellular automata are indeed discretizations of differntial equations: 
see Ablowits and Clarkson, "Solitons, Non-Linear Evolution Equations 
and Inverse Scattering", p. 152 for a nice account in connection with 
solitons.   But Paul is right, Wolfram's point is quite different.

Andrzej Kozlowski

On 11 Nov 2003, at 09:55, Paul Abbott 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.
>
> 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
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/


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