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/

**References**:**Re: Fluid dynamics***From:*Paul Abbott <paul@physics.uwa.edu.au>