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From: NZTideMan <mulgor@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Crater function plot.
Date: Thu, 29 Jan 2009 14:26:48 -0800 (PST)
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On Jan 30, 9:10=A0am, "Kallol Das" <shubhro.kal...@gmail.com> wrote:
> Walter,
> You made the right guess. Actually I have run some codes and I have found=
 that the atomic bombardment on the surface behaves very similarly like the=
 meteors hitting the earth. There are some differences though. But if you t=
ake an average of the heights made by hundreds of impacts, you will get a s=
tructure that closely matches with the craters made by the meteors.
>
> So I just need a function that can produce surfaces like those of the cra=
ters with a few parameters like angle of impact, maximum height or depth cr=
eated. There is going to be some exponential decay of the height or depth o=
f the crater as you go radially out of the point of impact.
>
> Can you help?
> Thanks.
>
> Walter Roberson <rober...@hushmail.com> wrote in message <8mngl.724$Xi1..=
..@newsfe16.iad>...
> > Kallol Das wrote:
>
> > > Actually I am modeling a molecular dynamics simulation. I need some s=
ample crater functions as
> > > the input files. The momentum, velocity and other stuffs are included=
 in my MD code. I just
> > > need some crater functions as a input to the code.
>
> > > The crater functions that I am looking for is something like a predic=
ted shape of surface if
> > > it is hit by an atom. I just need the surface shape. And some variabl=
es namely theta,
> > > maximum height of the ripple, and a decaying factor by which I can ch=
ange the shape of the surface.
>
> > > The surface will look very similar to the craters made on the earth s=
urface by the meteors?
>
> > Hmmm, something doesn't sound right.
>
> > If you are doing this for molecular dynamics then you need to take into=
 account the
> > electrostatic repulsion or attraction between the atom and the molecula=
r surface.
> > And your molecular surface will, on the scale of an atom, be quite bump=
y, and on
> > that scale it is *not* going to move like earth does. For one thing, wi=
th meteors
> > (or the like) hitting the earth, the meteor embeds itself in the earth =
(unless
> > the shockwave of compressed air is enough to push most of it back out o=
f
> > the hole), but an atom hitting a molecular surface has a non-negligible=
 chance
> > of bouncing out again, possibly after having knocked an atom or a chain=
 out of
> > the molecule. And the reaction of the molecule to having an atom or cha=
in knocked
> > out is going to depend upon the chemistry of the molecule. "Atom hittin=
g a molecule
> > or surface leading to a molecular change" is a fair description of norm=
al chemical
> > reactions involving gases or (simple) liquids around the target molecul=
e.
>
> > When you are working at the level of single atom interaction with somet=
hing, you
> > need to ask whether there will be quantum effects or relativistic effec=
ts or
> > wave-particle duality effects.
>
> > Are you trying to model something like "sputtering"?

If all you are looking for is a shape, then a DOG (difference of
Gaussians) will work (Google it!).  Order 2 is the Mexican Hat, but
higher orders are also available.  You might have to turn it upside
down, depending on how you do the differencing.

But if you're looking for something more realistic, Google Mars
topography craters.  A lot of work has been done on modelling Mars
craters (myself included), but they are generally numerical models
with associated CDFs for the shape parameters, not analytical shapes.