Path: news.mathworks.com!not-for-mail
From: "matias nordin" <matias.nordin@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: particle interaction
Date: Tue, 12 Feb 2008 09:02:02 +0000 (UTC)
Organization: The MathWorks, Inc.
Lines: 64
Message-ID: <fornaa$e3h$1@fred.mathworks.com>
References: <fo6o84$mcu$1@fred.mathworks.com> <fohsjn$4pu$1@fred.mathworks.com> <foi3vv$ai6$1@fred.mathworks.com> <fopbv1$7p$1@fred.mathworks.com> <foqbqr$h35$1@canopus.cc.umanitoba.ca>
Reply-To: "matias nordin" <matias.nordin@gmail.com>
NNTP-Posting-Host: webapp-05-blr.mathworks.com
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1202806922 14449 172.30.248.35 (12 Feb 2008 09:02:02 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Tue, 12 Feb 2008 09:02:02 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 1269242
Xref: news.mathworks.com comp.soft-sys.matlab:450737


roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in
message <foqbqr$h35$1@canopus.cc.umanitoba.ca>...
> In article <fopbv1$7p$1@fred.mathworks.com>,
> matias nordin <matias.nordin@gmail.com> wrote:
> 
> >As a physicist I would like to treat the problem as follows:
> 
> >The particles are connected by springs all with the equal
> >spring force so that in absence of f(x), they are equally
> >distributed. And f(x) is introduced as a external potential
> > distorting the equal spacing. The dynamics is not of
> >importance, only to find equilibrium.
> 
> Is the potential associated with the position (i.e., a field),
> or is the potential associated with the particle (e.g.,
> by varying the spring forces) ?
> 
> Should we read that "springs" as implying that (in the
> absence of the external force) the dynamic potential between
> any two adjacent particles is proportional to the square
of the
> distance between them?
> 
> If the density is inversely proportional to the function,
> then adjusting the function by a constant (to avoid negative
> numbers) introduces non-linear distortions and the value of
> the constant would become crucial in determining the
distribution.
> -- 
>    "I was very young in those days, but I was also rather
dim."
>    -- Christopher Priest

Thanks for the attention Walter!


Yes, the potential is an external field. So we do not change
the internal forces of the springs.

And yes, the potential rising from the springs is
proportional to the square of distance between them.

Total potential from the springs:
U_s=Sum_i(  (X_i-X_(i+1))^2 )

note: the last particle is connected to the first, so we
adjust the summation for that chriteria.


external potential:

U_e=g(X)

..gives the total potential

U_tot(X_1,X_2,...,X_N)=Us_+U_e


for what choordinates, X_1...X_N, is U_tot minimized?
How is this treated in MATLAB?


  Matias