Thread Subject:

Crater function plot.

Hello,
I need to plot a crater function. Suppose you are hitting a surface with an iron ball. Now the direction will be varied by a 5 degree interval from normal to the surface to 85 degree off normal. Depending upon the angle of impact the shape of the surface will change.
Can anyone help me produce a function in the form of Z = f (x,y, theta, h) that takes angle of impact theta as input and the value 'h' as the maximum ripple amplitude?
I want to plot a 3D surface with this function.
Thanks

"Kallol Das" <shubhro.kallol@gmail.com> wrote in message <glspr6$bep$1@fred.mathworks.com>...
> Hello,
> I need to plot a crater function. Suppose you are hitting a surface with an iron ball. Now the direction will be varied by a 5 degree interval from normal to the surface to 85 degree off normal. Depending upon the angle of impact the shape of the surface will change.
> Can anyone help me produce a function in the form of Z = f (x,y, theta, h) that takes angle of impact theta as input and the value 'h' as the maximum ripple amplitude?
> I want to plot a 3D surface with this function.
> Thanks

  There is no way to answer your question until it is known what assumptions are being made about the impact conditions. How realistic is it expected to be? What is the velocity of impact? How much resistance is to be expected from the surface material? Is momentum imparted to the surface causing it to spread apart from contact with the ball. Etc., etc., etc. ...

  In any case, this is hardly the appropriate newsgroup for this sort of question.

Roger Stafford

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <glsrea$fr0$1@fred.mathworks.com>...
> "Kallol Das" <shubhro.kallol@gmail.com> wrote in message <glspr6$bep$1@fred.mathworks.com>...
> > Hello,
> > I need to plot a crater function. Suppose you are hitting a surface with an iron ball. Now the direction will be varied by a 5 degree interval from normal to the surface to 85 degree off normal. Depending upon the angle of impact the shape of the surface will change.
> > Can anyone help me produce a function in the form of Z = f (x,y, theta, h) that takes angle of impact theta as input and the value 'h' as the maximum ripple amplitude?
> > I want to plot a 3D surface with this function.
> > Thanks
>
> There is no way to answer your question until it is known what assumptions are being made about the impact conditions. How realistic is it expected to be? What is the velocity of impact? How much resistance is to be expected from the surface material? Is momentum imparted to the surface causing it to spread apart from contact with the ball. Etc., etc., etc. ...
>
> In any case, this is hardly the appropriate newsgroup for this sort of question.
>
> Roger Stafford

agreed... they use supercomputers to model this kind of stuff and years and years of work... there is no simple 'function' to predict it. consider the extreme differences, hit glass with a slow moving ball and you get nothing, but hit a powdery surface with a supersonic ball and you get a huge effect, hit water with anything and you get nothing after some time period, but initially you get some kind of movement.

Thanks Roger and David for your reply.

I agree what you all have said. Actually I am modeling a molecular dynamics simulation. I need some sample 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 predicted shape of surface if it is hit by an atom. I just need the surface shape. And some variables namely theta, maximum height of the ripple, and a decaying factor by which I can change the shape of the surface.

The surface will look very similar to the craters made on the earth surface by the meteors like this one http://darwin.bio.uci.edu/~sustain/bio65/lec02/barringer.jpg.

There should be some more variables like the frequency of some probable sine functions and some exponential terms for the decaying amplictude (height). And I don't want any time dependent variables.

Please let me know if you want some more information. Thanks for your reply.

"David" <dave@bigcompany.com> wrote in message <glssfh$lin$1@fred.mathworks.com>...
> "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <glsrea$fr0$1@fred.mathworks.com>...
> > "Kallol Das" <shubhro.kallol@gmail.com> wrote in message <glspr6$bep$1@fred.mathworks.com>...
> > > Hello,
> > > I need to plot a crater function. Suppose you are hitting a surface with an iron ball. Now the direction will be varied by a 5 degree interval from normal to the surface to 85 degree off normal. Depending upon the angle of impact the shape of the surface will change.
> > > Can anyone help me produce a function in the form of Z = f (x,y, theta, h) that takes angle of impact theta as input and the value 'h' as the maximum ripple amplitude?
> > > I want to plot a 3D surface with this function.
> > > Thanks
> >
> > There is no way to answer your question until it is known what assumptions are being made about the impact conditions. How realistic is it expected to be? What is the velocity of impact? How much resistance is to be expected from the surface material? Is momentum imparted to the surface causing it to spread apart from contact with the ball. Etc., etc., etc. ...
> >
> > In any case, this is hardly the appropriate newsgroup for this sort of question.
> >
> > Roger Stafford
>
> agreed... they use supercomputers to model this kind of stuff and years and years of work... there is no simple 'function' to predict it. consider the extreme differences, hit glass with a slow moving ball and you get nothing, but hit a powdery surface with a supersonic ball and you get a huge effect, hit water with anything and you get nothing after some time period, but initially you get some kind of movement.

"Kallol Das" <shubhro.kallol@gmail.com> wrote in message <glstl2$5tm$1@fred.mathworks.com>...
> Thanks Roger and David for your reply.
>
> I agree what you all have said. Actually I am modeling a molecular dynamics simulation. I need some sample 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.

well, if you already are modeling the molecular dynamics of your surface just hit it with a point impulse and let your simulation do the work.

Kallol Das wrote:

> Actually I am modeling a molecular dynamics simulation. I need some sample 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 predicted shape of surface if
> it is hit by an atom. I just need the surface shape. And some variables namely theta,
> maximum height of the ripple, and a decaying factor by which I can change the shape of the surface.

> The surface will look very similar to the craters made on the earth surface 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 molecular surface.
And your molecular surface will, on the scale of an atom, be quite bumpy, and on
that scale it is *not* going to move like earth does. For one thing, with 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 of
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 chain knocked
out is going to depend upon the chemistry of the molecule. "Atom hitting a molecule
or surface leading to a molecular change" is a fair description of normal chemical
reactions involving gases or (simple) liquids around the target molecule.

When you are working at the level of single atom interaction with something, you
need to ask whether there will be quantum effects or relativistic effects or
wave-particle duality effects.

Are you trying to model something like "sputtering"?

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 take an average of the heights made by hundreds of impacts, you will get a structure that closely matches with the craters made by the meteors.

So I just need a function that can produce surfaces like those of the craters with a few parameters like angle of impact, maximum height or depth created. There is going to be some exponential decay of the height or depth of the crater as you go radially out of the point of impact.

Can you help?
Thanks.


Walter Roberson <roberson@hushmail.com> wrote in message <8mngl.724$Xi1.317@newsfe16.iad>...
> Kallol Das wrote:
>
> > Actually I am modeling a molecular dynamics simulation. I need some sample 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 predicted shape of surface if
> > it is hit by an atom. I just need the surface shape. And some variables namely theta,
> > maximum height of the ripple, and a decaying factor by which I can change the shape of the surface.
>
> > The surface will look very similar to the craters made on the earth surface 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 molecular surface.
> And your molecular surface will, on the scale of an atom, be quite bumpy, and on
> that scale it is *not* going to move like earth does. For one thing, with 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 of
> 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 chain knocked
> out is going to depend upon the chemistry of the molecule. "Atom hitting a molecule
> or surface leading to a molecular change" is a fair description of normal chemical
> reactions involving gases or (simple) liquids around the target molecule.
>
> When you are working at the level of single atom interaction with something, you
> need to ask whether there will be quantum effects or relativistic effects or
> wave-particle duality effects.
>
> Are you trying to model something like "sputtering"?

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.

Thanks NZTideMan,
I think DoG is the answer. I have to work it out though to match the shape I am looking for.
Thanks a lot to everyone.


NZTideMan <mulgor@gmail.com> wrote in message <f8a8b002-4035-4817-bc43-11e27f86607a@b38g2000prf.googlegroups.com>...
> 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.

The sinc function [sin(x)/x] and Bessel functions look similar - big
pit with lots of side ripples - but I'm not sure how to skew them to
simulate a particle coming in at an angle. And if the particle goes
really deep, you'll have a tube extending into your surface, possibly
at an oblique angle. I have no idea how to model that.