I had been asked about n-body simulations.

I have found a very interesting article about The N-Body Problem.

http://beltoforion.de/article.php?a=...imulator&hl=en

"A region of space contains the number of N bodies. Each body has its own potential and a resulting force field. This could be charges causing an electrical field (Coulomb's law) or planets in space (Law of Gravity). The potential of the bodies can be summed up yielding a combined potential which depends on the location of each of the bodies and its physical properties (i.e. mass or charge). According the Newtons first law the bodies themself will experience an acceleration caused by the field."

As we add high number of objects it become too complicated:

"Lets assume Fij is the force acting between particles i and j. The total number of force calculations needed to compute the state of the system is N*(N-1) and according to Newtons third law every force has an opposite forces equal to itself: Fij = -Fji. The total number of force calculations can then be reduced to:

The problem is of order O(N2). If the number of particles double the number of calculations quadrupels. If the number of particles is increased by factor ten the number of calculations increases by a factor of 100 and so on... From this simple relation it is clear that computing the N-Body problem for large numbers of particles will quickly become very costly in terms of computational power. A more effective algorithm that scales better with increasing number of particles is needed."

There is a solution for that and it's called: "The Barnes-Hut Algorithm".

"The Barnes-Hut Algorithm describes an effective methood for solving n-body problems. It was originally published in 1986 by Josh Barnes and Piet Hut [1]. Instead of directly summing up all forces it is using a tree based approximation scheme which reduces the computational complexity of the problem from O(N2) to O(N log N)."

So far so good.

Now, let's focus in Animation 1:

"Animation 1: The animation shows a distribution of 5000 particles. The quadrants that are shown are the ones that are used for calculating the force excerted on the particle at the origin of the coordinate system. The higher θ is, the fewer the number of nodes that are necessary for the force calculation (and the larger the error)."

So, now that I have better understanding on this issue, I wonder how our scientists in Zurich have used the simulation for the spiral galaxy:

1. Did they set in the calculation only real stars measurements in the density wave (spiral arms) and outside the arms?

2. Did they set special quadrants for the stars in the spiral arms and outside the spiral arms? (This is very critical in my opinion)

3. What is the ratio in the milky way between the star densities in the arms to the one outside the arms that they have used (Is it 10% or close to 20%)?