# Question about n-Body and Fourier Transform

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Dear All, I'd like to experiment with a new method of solving n-Body problems. Wikipedia lists a method on this page(http://en.wikipedia.org/wiki/N-body_simulation) known as the Particle mesh method(other places mention it too, but I'll just list this reference). However there are two things I dont quite understand about this. First they state that rho is a function of density(number of parameters based on the space you are working in I assume). Does the hat over the rho mean that the I am to take the fourier transform of that function? That seems somewhat confusing if so. Can anyone explain this a little better? My second object of confusion is they reference comoving wavenumbers. I have no idea what these are, and my googling has not been too sucessful on this point. Can someone point me to a reference for this? Regards, Jesse

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 Original post by laeuchliDear All,I'd like to experiment with a new method of solving n-Body problems. Wikipedia lists a method on this page(http://en.wikipedia.org/wiki/N-body_simulation) known as the Particle mesh method(other places mention it too, but I'll just list this reference). However there are two things I dont quite understand about this.First they state that rho is a function of density(number of parameters based on the space you are working in I assume). Does the hat over the rho mean that the I am to take the fourier transform of that function? That seems somewhat confusing if so. Can anyone explain this a little better?My second object of confusion is they reference comoving wavenumbers. I have no idea what these are, and my googling has not been too sucessful on this point. Can someone point me to a reference for this?Regards,Jesse

Hi Jesse,

As the article states, the hat symbol represents the Fourier transform of the function. However, the hat over rho in the first equation is an error.

The 'comoving wavenumber' basically represents the scale that you're interested in and results directly from the Fourier transform of the derivative part of the Poisson equation. So the second equation represents the gravitational potential energy at a given spatial scale (or spatial frequency if you want to think of it that way).

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Ah thank you very much..
Jesse

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