What Should I learn to do N-body simulations?

[Arman777]

What Should I learn in terms of concepts to do N-body simulations ? Is there any books that I can follow in this process ?

Thanks

 

[jedishrfu]

Differential equations, Classical Mechanics at the Goldstein undergrad level, Computational Physics and programming in some language.

More specifically, the Open Source Physics library and Java is one way. They have a three body example in java that shows the various known solutions to the problem. They have a book that teaches an intro to computational physics.

Another is Matlab and its collection of libraries and toolboxes. Youll have to search for a book or course that discusses the tecniques to use. Mathworks has many resources and notes on its website to get you going.

Python and Anaconda is yet another route.

There is a lot to learn here. While you could bash your way through some examples you’ll always have a doubt that your sim is correct if you don’t understand the math and physics.

I learned via the java route through a grad course i took based on the OSP book and code. I already knew java quite well so that part was easy and the prof guided us through the hard stuff. The funny part was he didn't fully understand java and the new version of the book switched from using basic to using java.

 

[Arman777]

Hmm so where should I start ?

 

[jedishrfu]

Take an assessment with what you know.

I'd start with the math:
- Algebra
- Geometry
- Algebra 2 ie trig in particular, series, sequences for Calculus ...
- Calculus 1,2,3
- Differential Eqns
- Linear Algebra


At this point, you should have a good basis for doing any classical mechanics, E&M Theory and Quantum Mechanics at the undergrad level using all the math you've studied so far.

Then the physics:
- Classical Mechanics

And lastly the programming:
- either Java+OSP or Matlab or Python

Finally, you need to understand the specifics of encoding a set of differential equations to solve for numerically in the environment chosen.

https://www.wired.com/2016/06/way-solve-three-body-problem/
Personally, I'd choose learning Java and using OSP because it's designed for doing computational physics in an academic environment. However, there's a lot to be said for using Matlab too.

https://www.compadre.org/osp/items/detail.cfm?ID=9777
https://stackoverflow.com/questions/5293535/programming-a-3-body-problem-using-matlab
Python I'm not as sure of although its heavily used in Data Science and Machine Learning work, but using Numpy and related libraries you could construct some good simulations and Python is easier to learn than Java.

https://github.com/htx1219/Python/blob/master/222/Three Body Problem.py
Miscellaneous resources:

https://www.newscientist.com/articl...dy-problem-has-over-a-thousand-new-solutions/
https://javalab.org/en/three_body_problem_en/

 

[berkeman]

Hmm so where should I start ?

With a 2-body simulation...?

How far along are you in your math learning? Have you had calculus yet?

What programming languages are you most familiar with?

 

[Arman777]

I am a physics undergrad student and this is my last year. I took CM, Diff Eqn. , linear algebra and many more courses.

With a 2-body simulation...?

Yes that also came to my mind today. I ll start from there.

What programming languages are you most familiar with?

python

Finally, you need to understand the specifics of encoding a set of differential equations to solve for numerically in the environment chosen.

Once I did a trajectory for an electron under the lorentz force. I guess this would be more complicated but I ll try.

I can't learn java currently so I ll go with python.

 

[aaroman]

'N-body simulator' is quite generic. You can do it like this: https://compphys.go.ro/Newtonian-gravity/ for the cases when you have forces acting on large distances, or like this: https://compphys.go.ro/event-driven-molecular-dynamics/ when you have only forces that act a very short distance.

Then the optimization issues appear: using Barnes-Hut, neighbors lists and so on... some things I mentioned on the blog. Unfortunately the associated projects are in C++, not python.