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MathGroup Archive 2003

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Re: Re: Fluid dynamics

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44475] Re: [mg44454] Re: Fluid dynamics
  • From: Anton Antonov <antonov at wolfram.com>
  • Date: Wed, 12 Nov 2003 08:01:25 -0500 (EST)
  • References: <boif5j$oau$1@smc.vnet.net> <200311110055.TAA25144@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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. 
>>    
>>
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.

>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
>>>
>>>      
>>>
>
>  
>



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