# Talk:N-body simulations (gravitational)

We thank the reviewers for their constructive suggestions that have improved the paper. In preparing this revised version we have taken into account all the comments by the referees, as detailed in the response below.

> Reviewer A:

> The article is nicely concise and reasonably complete, but I find a few points are still missing:

> - When tree methods are discussed, I think fast multipole methods should be included as a generalization of the method, including also some brief comments about their relative advantages/disadvantages (e.g. momentum conservation)

Done, now the FMM method has a self-standing description as a method.

> - Grid-based Poisson solvers based on multigrid methods (used e.g. in some AMR codes) should also be mentioned

We have also added this category.

> - I would find it interesting to briefly discuss the issue of gravothermal collapse in the context of relaxation in collisional systems

Done.

> - When the collisional operator in the Boltzmann equation is introduced, it is unclear in which areas this is used in practice. One possible example that could be mentioned here are studies of self-interacting dark matter.

Done.

> - Perhaps one could mention somewhere that the gravitational algorithms used in N-body methods are also widely applied to simulated self-gravity of gas with the SPH method.

Done we have added a section on the analogies between N-body and fluid dynamics in term of the Jeans vs. Navier-Stokes equations.

>Reviewer B:

>For minimal completeness, the article should include the methods often used in grid codes, e.g. successive overrelaxation and conjugate gradient.

We have added a section on Mean Field Methods.

>They should also include a section on Fast Mulitipole Methods and "hybrids". By hybrids, I mean codes like pkdgrav that use hexidecapole moments and local expansions becoming a hybrid of the tree and FMM.

Done (See also reply to Reviewer A above).

>As for the self consistent fields method, the notion that it was first used by Ostriker and Hernquist is comical. Richard Gott had such a method in his PhD thesis which must have been about 1972. There were numerous uses between.

We are sorry about the error. Now we refer to Clutton-Brock 1972 as one of the first paper to propose the idea. We have not been able to find a reference to Richard Gott thesis, but we will be happy to add it to the article if the referee can give us more information.

> I consider Fokker-Planck to be an alternative to N-body simulation whether than a "type".

Now is a self-standing type.

> I would have a bit more about pitfalls, e.g. the classic "exploding galaxy" problem and perhaps a link to the N-body Constitution.

Done.

>== User 4 (Editor): ==
>
>Hello,
>
>in my opinion you should change the starting definition
>
>*N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally,*
>
>because its seems to me that in Physics N-body simulations does not imply gravitational interactions, but any kind of >interactions:
>your definition seems not general but specific to astrophysics (and even in astrophysics why not simulating charged particles?)
>
>Wikipedia entry starts with
>
>*An N-body simulation is a simulation of massive particles under the influence of physical forces, usually gravity and >sometimes other forces. They are used in cosmology to study processes of non-linear structure formation such as the process of >forming galaxy filaments and galaxy halos from dark matter in physical cosmology. Direct N-body simulations are used to study >the dynamical evolution of star clusters.*
>http://en.wikipedia.org/wiki/N-body_simulation

Thanks for your comment, we have clarified in the title that we limit this article to gravitational N-body simulations.

## User 6 (User:): GPUs no longer limited to single precision.

Modern GPUs fully support double precision. Nvidia's Fermi architecture even supports new IEEE 754-2008 floating point standard.

> Thanks! Main text revised. Next time feel free to modify directly the main article. Best, Michele