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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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