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From: "matias nordin" <matias.nordin@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: particle interaction
Date: Mon, 11 Feb 2008 11:36:01 +0000 (UTC)
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"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid>
wrote in message <foi3vv$ai6$1@fred.mathworks.com>...
> "matias nordin" <matias.nordin@gmail.com> wrote in message
<fohsjn$4pu
> $1@fred.mathworks.com>...
> > 
> > Sorry, what I mean is the following.
> > 
> > Assume you have N particles.
> > Spread the particles equally on a line (with symmetrical
> > boundaries).
> > 
> > Then apply a function (some well defined function) that
> > distorts the distance between the particles. The function is
> > scaled so that particles don't come too close or too far
> > apart. So you can choose that "in that area  the particles
> > are at this distance from each other". So I want this:
> > 
> > equally spread on [1 25] as [1  5  10 15 20]
> > 
> > apply a function --->
> > 
> > not equally spread on [1 25] as for example [1 2 3 15 20].
> > 
> >   Matias
> ---------
>   Matias, you haven't yet told us precisely in what way
your f(x) relates to the 
> condition that "a small value gives a small spatial
distances while a large 
> value gives a big spatial distance".  In my previous
article in this thread I 
> speculated that in a sense the density of spacing of the
particles is to be 
> inversely proportional to f(x).  This leads to a problem
that can be solved in a 
> case such as your f(x) = sin(x).  The question is, was
that a reasonable 
> assumption?
> 
> Roger Stafford
> 
> 


yes Roger that assumption was what I was thinking of, that
the density of spacing is inversely proportional to f(x).
The function f(x) is also scaled so that it only takes
positive values. So functions that takes negative values are
  simply lifted by a constant, in example for sin(x):
f(x)=-sin(x)+constant.


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. However as the number
of particles can be altered I have a feeling that it would
be cumbersome to do such a program (since the number of
equations will change). So that stopped me from that idea.
And now I am thinking of some easier way, as just
multiplying the distance by 1/f(x)) and scale it until it
fits within the boundaries. As you see the problem is not
well defined yet, as I want to have an easy solution. Ideas
would be of great interest.

 Matias