Thread: The Barnes-Hut Algorithm as a solution for N-Body Problem

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Originally Posted by Shaula
Density waves can form spiral structure without dark matter.
This is very important message!
So technically, we could get the spiral structure without any help from dark matter.

However, there is a problem with kinematics:

Originally Posted by Shaula
But the kinematics of the resulting galaxies area not in accordance with observations.
I'm not sure that I fully understand the meaning of this kinematics problem.
Do you mean the - "Winding problem"?

As stated:

https://en.wikipedia.org/wiki/Density_wave_theory

"Originally, astronomers had the idea that the arms of a spiral galaxy were material. However, if this were the case, then the arms would become more and more tightly wound, since the matter nearer to the center of the galaxy rotates faster than the matter at the edge of the galaxy. The arms would become indistinguishable from the rest of the galaxy after only a few orbits. This is called the winding problem"

So, what isn't "in accordance with observations"?
Is it the expected "winding problem"?

However, if I understand it correctly, in order to get into this problem, our scientists have set their calculation/simulation on the basic idea that stars do not change their current orbital radius.
Is it correct?

If yes, than the "winding problem" must be a direct outcome of this simulation. That is very clear to me.

However, why our scientists are so sure that stars do not change their orbital radius over time?

How could it be that in one hand they claim that matter can move inwards the galaxy (as they claim that the galaxy eats nearby dwarf galaxies), but when it comes to verify the orbital cycles of the matter in the galaxy, they take it for granted that all the matter/stars must stay at the same radius?

Could it be that the "winding problem" would be solved by giving the matter/stars a freedom to change their orbital radius?
Why they didn't try to set the simulation without this key obstacle?
Last edited by Dave Lee; 2018-Jun-09 at 06:56 AM.

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Originally Posted by Dave Lee
So technically, we could get the spiral structure without any help from dark matter.
Of course, I've mentioned that before. It is just a correlation in orbital parameters that produces it.

Originally Posted by Dave Lee
I'm not sure that I fully understand the meaning of this kinematics problem.
Do you mean the - "Winding problem"?
No, I meant the rotation curves of the galaxy. You can make spiral galaxies without dark matter but they don't have the rotation curves we observe in real galaxies.

Originally Posted by Dave Lee
However, if I understand it correctly, in order to get into this problem, our scientists have set their calculation/simulation on the basic idea that stars do not change their current orbital radius.
Is it correct?
They have based their models on the idea that stars and gas obey the laws of gravity. N-body simulations (which is basically what this thread is about) don't fix things into locked orbits - in fact no model of a spiral galaxy can or you cannot induce the required correlations.

Originally Posted by Dave Lee
If yes, than the "winding problem" must be a direct outcome of this simulation. That is very clear to me.
The winding problem is a direct consequence of the observed rotation curved of galaxies. It has nothing to do with the simulation.

Originally Posted by Dave Lee
However, why our scientists are so sure that stars do not change their orbital radius over time?
They are not. They assume that stars obey the laws of gravity.

Originally Posted by Dave Lee
How could it be that in one hand they claim that matter can move inwards the galaxy (as they claim that the galaxy eats nearby dwarf galaxies), but when it comes to verify the orbital cycles of the matter in the galaxy, they take it for granted that all the matter/stars must stay at the same radius?
They don't make these claims.

Originally Posted by Dave Lee
Could it be that the "winding problem" would be solved by giving the matter/stars a freedom to change their orbital radius?
Why they didn't try to set the simulation without this key requirement?
They didn't set this requirement. They plugged in their particles of matter/dark matter and gave them the basic physical laws we observe. They didn't put in arbitrary rules like "orbits can't change".

And, as I said, the winding problem is a consequence of the observed properties of galaxies. Not this simulation or the way the Barnes-Hut algorithm works.

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I'll add that these questions highlight that you may not have really grasped the whole point of n-body simulations.

N-body simulations are used in precisely the cases where the system does not reduce to a series of nested two body approximations. i.e. in situations where you cannot simply assign well defined orbits and leave them fixed or semi-fixed. The perturbations in the system are strong enough that this is not a feasible simplification to make. Which is the whole reason why we have to use n-body simulations. And the rapidly scaling computational load of these simulations is why approximations like the Barnes-Hut algorithm are required for the largest ones.

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Originally Posted by Shaula
I'll add that these questions highlight that you may not have really grasped the whole point of n-body simulations.

N-body simulations are used in precisely the cases where the system does not reduce to a series of nested two body approximations. i.e. in situations where you cannot simply assign well defined orbits and leave them fixed or semi-fixed. The perturbations in the system are strong enough that this is not a feasible simplification to make. Which is the whole reason why we have to use n-body simulations? And the rapidly scaling computational load of these simulations is why approximations like the Barnes-Hut algorithm are required for the largest ones.
I'm very confused with regards to that n-body simulation.
I was sure that the whole purpose of the Barnes-Hut Algorithm is to simulate the gravitational interactions between all the objects in the galaxy. Which means - the gravitational interactions between a single star with all the stars/matter in the galaxy (including in the nearby spiral arm) and the center of the galaxy (which also includes dark matter).

As was informed by Strange:

Originally Posted by Strange
Anyway, apart from the fact it is about solving an N-body problem to simulate the formation of galactic structures (i.e. it is about gravity), gravity is explicitly mentioned at least three times in the paper.
Originally Posted by Strange
As you have been told multiple times, it is a result of gravitational interactions.
Therefore, it was quite clear to me that the simulations should also include the gravitational interactions between a single star and all nearby stars/matter in the spiral arm which are moving almost at the same velocity around the galaxy.
Now I know that this is not fully correct.
If I understand your answers correctly, we don't evaluate the gravitational interactions between the nearby stars in the spiral arm.
I still don't understand why the gravitational interactions between the nearby stars in the spiral arm is not part of this Simulation.
Last edited by Dave Lee; 2018-Jun-09 at 09:18 AM.

5. Originally Posted by Dave Lee
I'm very confused with regards to that n-body simulation.
I was sure that the whole purpose of the Barnes-Hut Algorithm is to simulate the gravitational interactions between all the objects in the galaxy. Which means - the gravitational interactions between a single star with all the stars/matter in the galaxy (including in the nearby spiral arm) and the center of the galaxy (which also includes dark matter).

As was informed by Strange:

Therefore, it was quite clear to me that the simulations should also include the gravitational interactions between a single star and all nearby stars/matter in the spiral arm which are moving almost at the same velocity around the galaxy.
Now I know that this is not fully correct.
If I understand your answers correctly, we don't evaluate the gravitational interactions between the nearby stars in the spiral arm.
I still don't understand why the gravitational interactions between the nearby stars in the spiral arm is not part of this Simulation.
I don't understand the source of your confusion. Shaula has said that the simulation models the gravitational interaction of all the matter (stars, gas, etc) and dark matter in the galaxy. So why do you think it isn't modelling gravitational interactions?

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"It sounds like you are thinking of the spiral arm as some kind of bound system again. It isn't. It is just a place where a number of correlated orbits converge. Remember the video of the idealised system? You cannot construct the overdensities in that without having mass in between these areas."

So, based on this answer I have understood that there is no gravitational interaction between the stars in the modeling.
If there is a gravitational interaction between the nearby stars in the modeling and we have got the spiral structure, than why at the end we reject the idea that there is gravity bounding between the stars in the spiral arms?

My confusion is very simple
We start the modeling by a basic idea that there is gravitational interaction between all the objects in the galaxies (one to all - all to all).
The outcome is - spiral structure.
However, at end of this modeling we claim that this spiral structure isn't part of the gravitational interaction between the objects in the spiral structure.
It is just a simple outcome due to the gravitational interaction between the object and the center (one to center - center to all)
Why is it?

Actually, we could easily find if there is no gravity bounding between the nearby stars in the spiral arms.
All we have to do is to run the simulation without the impact of the gravitational interaction between the stars in the modeling. ONLY the gravitational interaction between the stars and the center of the galaxy.
If in this case, we will still get the density wave (as expected), than it is a solid proof for all of us that the spiral arm isn't a bound system.
Last edited by Dave Lee; 2018-Jun-09 at 12:37 PM.

7. Originally Posted by Dave Lee

"It sounds like you are thinking of the spiral arm as some kind of bound system again. It isn't. It is just a place where a number of correlated orbits converge. Remember the video of the idealised system? You cannot construct the overdensities in that without having mass in between these areas."

So, based on this answer I have understood that there is no gravitational interaction between the stars in the modeling.
It is utterly baffling to me how you can get from such straightforward explanations to such bizarre misunderstandings that directly contradict everything you have just been told. That is not a valid conclusion from the quoted statement.

You need to listen to what people are telling you. You do not understand gravity. Quit trying to force the things people are saying into your broken mental model and ignoring the bits that don't fit.

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Originally Posted by Dave Lee
So, based on this answer I have understood that there is no gravitational interaction between the stars in the modeling.
In the idealised system there is no interaction between the orbiting bodies, they just orbit the centre of the system. The reason for that is that it is an idealised system that is easy to understand and shows you how the density wave comes about. In the n-body simulations these interactions are modelled.

Originally Posted by Dave Lee
If there is a gravitational interaction between the nearby stars in the modeling and we have got the spiral structure, than why at the end we reject the idea that there is gravity bounding between the stars in the spiral arms?
What we reject is that the spiral arms are bound structures or generated solely from local interactions.

Originally Posted by Dave Lee
My confusion is very simple
We start the modeling by a basic idea that there is gravitational interaction between all the objects in the galaxies (one to all - all to all).
The outcome is - spiral structure.
Nope. We start by assuming that the gravitational interactions can be simplified to nested two body solutions (the simple orbits in the idealised model). We show a density wave can happen. Then we develop more complex n-body simulations and show that the density wave is still there in systems much more complicated to visualise.

Originally Posted by Dave Lee
However, at end of this modeling we claim that this spiral structure isn't part of the gravitational interaction between the objects in the spiral structure.
It is just a simple outcome due to the gravitational interaction between the object and the center (one to center - center to all)
Why is it?
Because the effects of the other bodies are shown to be less significant than the induced orbital correlations.

Originally Posted by Dave Lee
Actually, we could easily find if there is no gravity bounding between the nearby stars in the spiral arms.
All we have to do is to run the simulation without the impact of the gravitational interaction between the stars in the modeling. ONLY the gravitational interaction between the stars and the center of the galaxy.
If in this case, we will still get the density wave (as expected), than it is a solid proof for all of us that the spiral arm isn't a bound system.
As I said, the idealised model does exactly that. So will you accept this solid proof?

And nobody has made the claim that there are no gravitational interactions between stars in the spiral arms. What has been said is that these local interactions are not what produce spiral structure.

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Originally Posted by Shaula
As I said, the idealised model does exactly that. So will you accept this solid proof?
Sure.
If you tell me that in Zurich modeling they have got the spiral structure while the modeling was based on idealized model (one to center - center to all; without any gravitational interactions between the objects) than this is a solid proof for me.

I just wonder why they claim that they have used the Barnes-Hut Algorithm as a solution for N-Body Problem (which specifically deal with gravitational interactions between the objects), while they have only used the idealized model.
Last edited by Dave Lee; 2018-Jun-09 at 04:02 PM.

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Originally Posted by Dave Lee
Sure.
If you tell me that in Zurich modeling they have got the spiral structure while the modeling was based on idealized model (one to center - center to all) than this is a solid proof for me.
Why are you fixated on the ERIS model? The ERIS model is an n-body simulation. I provided you, previously, with the idealised simulations of non-interacting orbits with an induced correlation. This is precisely what you asked for. Moving the goalposts and now demanding that a model that is designed to do one thing should somehow be made to do the opposite is not helpful or required.

Originally Posted by Dave Lee
I just wonder why they claim that they have used the Barnes-Hut Algorithm as a solution for N-Body Problem, while they have only used the idealized model.
They have not used the idealised system. I have no idea why this is apparently so confusing - I've laid out a couple of times now what these models were used for and what they each did.

The idealised model used a set of nested two body solutions to demonstrate that a spiral structure could be formed from orbital correlations. This model is not meant to be a simulation of a spiral galaxy, it is a toy model used to understand how the structures we see can form. This idealised model has nothing at all to do with ERIS. The output from it was the video I linked ages ago showing a two arm spiral form.

The ERIS simulation is an n-body simulation that uses the Barnes-Hut algorithm to simplify the computational load of simulating a large system. This model is meant to show that the basic physics we saw in the idealised model is relevant to more complex systems and to replicate a Milky Way like galaxy with minimal assumptions. The output from this was a huge dataset that was visualised in the video by Zurich University.

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Originally Posted by Shaula
Why are you fixated on the ERIS model?

Because that is the first modeling simulation success for a massive disk galaxy like the Milky Way.

As stated:

https://www.universetoday.com/88602/...f-galaxy-eris/

“Previous efforts to form a massive disk galaxy like the Milky Way had failed, because the simulated galaxies ended up with huge central bulges compared to the size of the disk,” said Javiera Guedes,

"In as much time as it takes to give birth to human life, a supercomputer and a team of researchers at the University of California, Santa Cruz, and the Institute for Theoretical Physics in Zurich have given rise to the first simulation of the physics involved in galaxy formation that produced the Milky Way. They named their child Eris…"

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Originally Posted by Dave Lee
Because that is the first modeling simulation success for a massive disk galaxy like the Milky Way.
Earlier models still showed spiral structure. They were successful, just not as successful as ERIS. And ERIS is not perfect.

But the fact that it is a good simulation of the galaxy is irrelevant to the point I am making. The spiral structure turns up in simpler models. Including those which are not full simulations. If the same thing shows up in both sets of models for the same reasons you can be fairly sure that it is independent of the details of the inter-body interactions in the spiral arms.

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Originally Posted by Shaula
Earlier models still showed spiral structure. They were successful, just not as successful as ERIS. And ERIS is not perfect.
Why they weren't successful as Eris?
Could it be that the idealized modeling by itself is not good enough to simulate real spiral galaxy?
Could it be that the missing gravitational interactions between the objects is critical for real modeling?
I wonder what might be the outcome of Eris if they only have used idealized modeling.

Originally Posted by Shaula
But the fact that it is a good simulation of the galaxy is irrelevant to the point I am making. The spiral structure turns up in simpler models. Including those which are not full simulations. If the same thing shows up in both sets of models for the same reasons you can be fairly sure that it is independent of the details of the inter-body interactions in the spiral arms.
So, can you please highlight one idealized modeling, that had been set by respectable University and Institute for Theoretical Physics (As they did in Eris), which can proof the spiral arm structure in the galaxy (not that kind of a brief video clip)?

14. No, I think not.
You have been given explanations into the extreme by shaula and hornblower et al. (thanks to you all)
This questionaire has reached its final point, as it seems clear to me that you are not putting any effort in actually obtaining some infirmation by yourself through for example reading the actual papers in which you will find all information.

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