ProgrammingInJulia

MS18 #discussion channel

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Project maintained by DhruvaSambrani Hosted on GitHub Pages — Theme by mattgraham

Check out the videos in order

1. Part 1 - Physical Introduction
2. Part 2 - Coding it
3. Part 3 - Visualisation
4. Part 4 - Discussion

Discussion topics

These were the side discussions discussed in Part 4.

1. Pluto - Cell dependency
2. Cyclic dependency
3. Pluto vs Jupyter
4. Optimizations
   1. Algorithmic - Barnes-Hut Optimization
   2. Implementation -
      1. Static Typing
      2. force calculation only once for each pair. Create an upper triangular matrix
      3. In-place updating force with .+= instead of =
      4. Preallocating trajectory and forces in simulate
   3. Hardware - GPU
5. Solving differential equations
   1. Euler
   2. Leap-frog
   3. Range-Kutta
6. Machine Learning solution to the N-Body problem - Associated Arxiv paper

Completed Pluto Notebook

nb1.jl

Results

Some animation. I forgot what the parameters were :P

Solar system

As mentioned in the video, I’ve taken planetary data from NASA and I’ve run an animation for 12 earth years (1 Jupyter year), with a time step of 1 day. dt of one week is too inaccurate

It ran in a pretty short time, so I suppose you could add the rest of the planets too, but I don’t suppose it will change much.

I’ve plotted at the 10th time step (10 days) and created a gif at 30fps. So every second is about 10 months

What next?

• Try to implement this in Python and see the speed difference. Use numpy and then compare.
• Try to optimize my code as I’ve mentioned in the Implementation Optimizations in the Discussion Topics. Use the julia docs to the fullest. Using BenchmarkTools to profile your code!
• Implement a 3d version of the code. You’ll see how easy it is to change it. Only force needs to be initialized as a 3 vector, and plot the z component too, as scatter(xs, ys, zs, ...). Try the same in Python. Note that gr doesn’t give you a nice rotatable 3d plot. You can either use the camera argument in the scatter(...) or, what I prefer, is to use the Plotly or PlotlyJS backends. More info can be found in the Plots.jl docs. FIRST PLOTS TAKE TIME. Use planetary data from NASA and also use the Orbital Inclination parameter in the dataset to set your initial conditions. If possible, use data for planets on some day, instead of the averages.
• Implement the Barnes-Hut Optimization. Don’t cheat.
• Collisions? Either simulate it using a central force which falls very quickly (see Patta’s notes for more detail), or make them “stick” together(How?). This will need you to add a radius to the planet.
• Perturb the system? Launch a small asteroid. See Jupiter’s screening effect in play.
• Add the Moon! You may need to zoom in by setting the xlims and ylims to see the moon separately from the earth.
• Set up 2 solar systems (Just use 4/5 planets) some distance from each other, such that there is a binary star system. You may need to give some initial velocity to the suns. Is a “stable” orbit possible? Simulate for long time scales.
• Should we use a variable dt? When objects are very close, they tend to accelerate quickly. Using smaller dt for this is better, while we can use larger dt for smaller forces. How will you calculate this dt? Try some guess functions. Make sure to use the same dt for each planet, otherwise they’ll end being in different times!