Re: LOGO-L> brownian motion

[George Mills <mills@softronix.com>]

When someone mentions this type of problem the first thing that
comes to mind is a finite element analysis solution.

The "Heat Plate" example I posted a while back is a crude 2
dimensional finite element analysis solution to statically applying
different temperatures to an "Ideal" 2D plate. It can be extended to
3d pretty easily.

However it's compute intensive problems like this that something like
Logo breaks down on rather quickly.  This is what Cray's and Connection
machines are built and sold for (Weather forecasting, Combustion Chamber
simulation etc.). A exploding Water balloon is similarly complex.
FORTRAN or a Parallel FORTRAN is probably the most common language
for this stuff.

However the great thing about finite element analysis is that it's
very scaleable. That is you can use a very course grid or simulate
just a small portion (interesting portion or representative portion)
of the problem. This allows you to develop your algorithm on a small
data set.  But to get slick pictures you need a fast processor and
a fast language.

You might be able to also break the problem down into a 2D one to
make the problem more manageable for Logo. Even the simple 2D
heat plate example is an OVERNIGHT run on Pentium 133 in Logo.
It would probably be a few seconds if written in C. And a 3D
version would run in hours.

I'm not familiar with Brownian motion but a quick search on
www.altavista.com
of "brownian motion" on the web produced 2000 hits, many of which were
java
scripts you could play with.  Most everything I saw simulated only a
single
particle which may be all you need to create an interesting project in
Logo.
Brownian motion to me looked like a Chaos/Fractal path of some sort.

Basically you could place "water" in the center of a 3d Element Cube (3d
Array)
in a solid sphere shape.  Then surround that sphere with a layer of
balloon
followed by air. You would place a puncture in the balloon (a cancer
cell if you
will) and let the cancer seek out and destroy neighboring balloon
"elements" (cells). The water would then travel (Bleed, seek out to
consume) the
air "elements".  MSWLogo/UCBLogo supports fast native 1D arrays. 
MultiDimentional
arrays are simulated and slow down a lot (it would be cool if
MSWLogo/UCBLogo
did MultiDimensional arrays natively hint hint).  But still an order of
magnitude faster
than doing something like this with lists (hold on, I have to get my
hands to stop
shaking at just the thought of it).  And forget recursive techniques
while your at it too.

The actual formulas used between the elements could be over simplified.
The proper ones probably require you read a few dozen books which would
get into velocities etc.

I don't mean to scare you from attacking such a problem. You should be
able to bite off a small enough piece of the problem to keep it
interesting
and challenging enough and still be achievable.

There are very likely other techniques to solving such a complex
problem.  But like I said FEA is very common.  Try a search on
"Finite Element Analysis" on altavista as well.

Good luck.


prkosuth wrote:
> 
> Hi all:
> 
>         As i gear up for the start of the new semester (it seems like last
> semester just finished !!) I have done some thinking regarding some of the
> problems that I want my physical science students to be tackling. The first
> 3 week module, I am going to explore what kinds of forces a water balloon
> can tolerate (via dropping and  by pressure) and then how we can extend
> this tolerance limit via some creative design. As I think about pressure I
> am then hit with some brownian motion within a boundary (the water hitting
> up against the balloon) and how to model this.
> 
> I seem to recall some discussion on the list about brownian motion and some
> programs with respect to this. I ran through the archeives but came up
> short. Can anyone help me out on this ?
> 
> Thanks a bunch ( in advance)
> 
> Paul
> 
> prkosuth@mychoice.net
> OPINIONS ARE MY  OWN
> Brehm Preparatory School
> Carbondale IL
> 
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-- 
===============================================================
George Mills
email: mills@softronix.com
http://www.softronix.com
The www page contains some very powerful educational software.
Our single most important investment is our kids.

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