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Re: Re: soap films

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101214] Re: Re: [mg101103] soap films
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Sat, 27 Jun 2009 06:01:38 -0400 (EDT)

Hello, Dimitry, David, Jens-Peer/ /and all people who will discuss the soap film problem!


Dimitry, you can certainly simulate everything that can be expressed in
terms of mathematical equations. And most probably, Mathematica will
be able to realize your simulation.  Now, concerning equations of the
foam theory.  I worked several years in a very close field, the membrane
physics. For this reason I am pretty good aware also of results in
the area of fluid films. It was pioneered by lord Kelvin already, and
since that time practically every problem that can be somehow solved
analytically has been solved analytically, while others simulated.
There is a huge amount of literature on the problem including good
books, reviews and original papers.  So, mathematics of such a film
is well-known, and you can find it in literature for any statement
of problem.  There are basically two possibilities:

1. Your problem, Dimitry, is already solved, and all you need is to find
this result in literature. This is the most probable case. In some cases
you may even find a corresponding Mathematica notebook.

2. Your problem has some peculiarities, and is not solved yet. In this
case the peculiarities of your problem are most probable in boundary
conditions, rather than in equations. Then what you need is to understand
(also on the basis of literature), what equations and boundary conditions
correctly describe your case. Here no one of us can help you.  It is
your personal task, since it is you who is the one who knows the problem
in details best of all people.  After all, it is your job. Then we may
think together, how to simulate it, if you will still need help.

There is however, a third possibility, when it is easier to simulate
then to make a literature search, then have fun!

Best regards, and have a success, Alexei

(Comment for the moderator: sorry, it is again mainly about mathematics,
rather than about Mathematica. My answer however, is adequate to the
question, as I believe).



I don't know how we are to see the example you give below. Is that a web
address?

I'm certain it is possible to represent soap film surfaces with Mathematica.

Here is an example of a minimal surface parametrization (Enneper's minimal
surface) and a plot of it:

enneper[u_, v_] := {u - u^3/3 + u v^2, -v + v^3/3 - v u^2, u^2 - v^2}

ParametricPlot3D[enneper[u, v], {u, -3, 3}, {v, -3, 3}]

This is from an excellent book:

Alfred Gray, Modern Differential Geometry of Curves and Surfaces with
Mathematica, Second Edition, 1998, CRC Press.

Specifically with:
Chapter 30. Minimal Surfaces
Chapter 31. Minimal Surfaces and Complex Variables


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/ <http://home.comcast.net/%7Edjmpark/>  


From: Dimitry [mailto:dima.architekt at gmail.com] 


Hi All,

I'm an architect and I trying to apply complex geometry for buildings.
Now I'm engaged in simulating of soap films,
and my question is how it's possible to simulate soap films(see the
picture)/Users/dimitrydemin/Pictures/iPhoto Library/Originals/2009/
stadel/Picture 10.png

with mathematica?

Thank you very much and best Regards!
Dimitry

-- 
Alexei Boulbitch, Dr., habil.
Senior Scientist

IEE S.A.
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Luxembourg

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