Behavior of atoms in a 2D universe with different physics (no kinetic energy)

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MrY
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Behavior of atoms in a 2D universe with different physics (no kinetic energy)

Postby MrY » Wed Apr 26, 2017 8:23 pm UTC

Hi,

Imagine a cube: its surface is a 2D universe, so a closed universe that loop on itself.
This universe contains "atoms": little circles with the same radius, but there are different type of atoms (A, B, C, ...).
Some atoms have a "movement" vector: this atoms move according to the direction of the vector, and with a constant speed according to the length of the vector. Atoms are created by pair with opposite "movement" vector and all atom vectors have the same length.
There is no kinetic energy or bouncing: If an atom in motion touches another atom, it pushes it and continues its path without slowing down, and the pushed atom keeps its direction and velocity.
Some atoms can bind and form molecules, for example: A + B -> AB
The "movement" vector of the molecules is the sum of the vectors of its atoms.
Also, some atoms can steal binds, for example: AB + C -> A + BC
Moreover, the space has a local agitation moving slightly and randomly atoms and molecules, and too much agitation can lead to break binds between atoms.

What can I expect from this universe?

Depending of the density of the universe, can I expect atoms and molecules streams or rather molecules with vectors which cancel each other out and so a static universe?
If A atoms can assemble into a large structure (with A + A -> AA rule), can it be in motion and push everything in its path? Or will this structure eventually be slowed down by aggregating atoms and molecules going the other way?
Are locally particles and molecules going in the same direction?

I know this is a very open question, do not hesitate to add your hypotheses and to be imaginative!

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LaserGuy
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Re: Behavior of atoms in a 2D universe with different physics (no kinetic energy)

Postby LaserGuy » Thu Apr 27, 2017 5:15 pm UTC

By "pushing" do you actually mean "non-interacting"? From your description, it sounds like they essentially just pass through each other.

I think that large structures will tend towards rest. If you add up a bunch of random vectors, the resulting vector is going to be smaller in magnitude.

For the single atom system...

If the atoms are created through a pair production process, at low density the most likely event will be that they will travel through the entire space until they meet up with their partner on the opposite side, at which point, if they can do A + A = AA, then they'll combine and end up at rest. This is actually fairly likely unless the mean free path per atom is quite short compared to the total size of the space.

If the density is quite high, then you'll probably get several large clusters forming. These may or may not coalesce into one big one... given enough time they might, but since their velocity vectors tend towards rest, then I think it's more likely you'll get several.

If you can't do A + A = AA in this system, then obviously nothing interesting ever happens since they all just maintain their initial orbits forever. So I think in this case, given enough time, you're pretty much going to get either a static universe (A+ A = AA is true) or one with essentially stable orbits forever (A + A = AA is not true).


The multi-atom case depends a lot on the relative populations of the atoms and what rules apply. It also depends on the behavior of molecules. Eg. suppose you have the following rules:
A + B = AB
B + C = BC
How does molecule AB interact with atom C? Does it behave like molecule A, like molecule B, or does it have its own rules that aren't necessarily the behavior of A or B? If it's this latter case, then you need to develop some universal rule system that can handle all possible molecules that you can generate. Depending on which rules you use, you could get lots of very interesting and complicated structures forming in this scenario. If you pick the right rules, you can probably turn it into a Turing Machine and then you could use this system to do computations if you wanted.

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Soupspoon
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Re: Behavior of atoms in a 2D universe with different physics (no kinetic energy)

Postby Soupspoon » Thu Apr 27, 2017 7:27 pm UTC

LaserGuy wrote:For the single atom system...

If the atoms are created through a pair production process, at low density the most likely event will be that they will travel through the entire space until they meet up with their partner on the opposite side,

It's not a spherically curved universe, though, with a clearly defined antipode. Among other things, I was trying earlier to work out if your trajectory that passes through a corner point then what happens. If exactly 45°, then along the edge, out at 45° on the opposite side and then meet the reverse route (that would also have edge-surfed), just like an edge-parallel route (and perpendicular to the other edges) would neatly wrap. But any other angle on any other transitionary face-to-face(-to-face) transfer and the straight line spirals to greater or lesser degree around any number of 'sides' before popping over to the top (and/)or bottom face at an angle likely to now treat top/bottom/opposite-sides as a vertical loop to spiral round, until it again hits the new 'polar' sides, the other two that we weren't vertically spiralling through) and, depending on whether it transitions from top/bottom or the sides, a new (perpendicularly) vertical or horizontal spiral...

Eventually, the track and counter-track would close the loop at the 'antipode' on this Great Circle analogue, but I'm not entirely sure that there's a reason why it needs to be on the opposite face (I think it could wrap around via various transformations to reintersect with itself, at right angles to the departure angles, on the same side as we started), and it only must meet because of finite space for it to pass through, so it cannot continue to just miss itself forever as the spiral tracks 'comb' past each other, eventually (but after arbitrary number of loops and such) they will coincide once more... But I got tied up in this, for some reason, so never got to seriously consider the rest of the problem. And I'm probably wrong on what I did work out, but it seems right to me...

MrY
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Re: Behavior of atoms in a 2D universe with different physics (no kinetic energy)

Postby MrY » Sat Apr 29, 2017 12:32 am UTC

Thank you for your replies !

LaserGuy :
By "pushing" do you actually mean "non-interacting"? 

Yes, you are right, with the local agitation, atoms that meet (and do not react) just cross each other.
But for molecules It's different, they are bigger, they can block an atom moving in the opposing way, even if after a while I think agitation causes the atom to free itself and continue on its way.

About multi-atom case, I can say more :
There are 27 atoms, named by the 26 letters of the alphabet + &.
They are created in the same proportions in the universe, about 1/27th each.
Atoms combine into molecules to form chains.
There are only 3 atoms that combine with itself:
A + A → AA
N + N → NN
& + & → &&
And of course :
A + AA → AAA
AA + AA → AAAA
etc...

But the same molecule can have different forms, and therefore some properties.
For now I would say that some molecules manage to inhibit certain reactions :
For example, the atom A can combine with atom A, B, C, D, G, J, S
But the MNNE molecule (in a specific form) may weakly associate with an atom A and prevent it from reacting with D and G.

Well guessed, my goal is to get to more complex behaviors (;

Soupspoon :
Yes I agree, atoms must make several time around the universe before returning to around their point of departure.
Currently I rework the creation of atoms, the current rules does not please me and what I had in mind does not work. I thought that all atoms were created at the same place. As a result, they all collide at the different antipodes. Perhaps a pattern can emerge with atoms going only in one direction in the upper part of the cube and in the other direction in the lower part. But now I do not know how to explain that the universe did not come to fill completely.


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