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

**Follow-Ups**:**Re: Re: Fluid dynamics***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: Fluid dynamics***From:*Anton Antonov <antonov@wolfram.com>