Julia Diffusion of Orbits for Keplerian Actions.
Install Julia by following the instruction at https://julialang.org/downloads/platform/.
To invoke Julia in the Terminal, you need to make sure that the julia command-line program is in your PATH.
On MacOS, we must create a link in /usr/local/bin (here for Julia 1.5):
$ sudo ln -s /Applications/Julia-1.5.app/Contents/Resources/julia/bin/julia /usr/local/bin/julia
Open the terminal in the folder packages and type
$ julia Install-pkg.jl
to install the following packages:
StaticArraysHypergeometricFunctionsBenchmarkToolsHDF5DelimitedFilesInterpolationsArgParseSpecialFunctionsDistributionsPlots
DO NOT INTERRUPT THE DOWNLOADING OF THE PACKAGES !!!!
To modify the background of the S-Cluster, open the folder code/background
and open the file inputBath.txt.
Do not change the line 1, which serves as legend. Starting from line 2, enter the values for each family, one family per line. Enter the four values, separated by a tabulation.
The numbers describe:
gamma: Cusp power of the family.mass_star[Msun]: Mass of the family's individuals, which can be stars or BHs (in solar masses).a0[mpc]: scale factor of the family (in mpc).Mtot(<a0): Enclosed mass of the family within the radius a0 (scale factor given previously).
To compute the diffusion coefficients DRR_j and DRR_jj at some
sma a and some angular momentum j, one needs to open
code/tests/Compute.jl.
Then, one needs to write for which sma a and angular momentum j one wants
to compute DRR_j(a,j) and DRR_jj(a,j). Once this is done, save the file and run the command
$ julia Compute.jl
To compute a mapping of the diffusion coefficients DRR and DNR at fixed
semi-major axis, and depending on reduced angular momentum, one needs to open
code/tests/Cut.jl.
Then, one needs to write for which sma a one wants to compute DRRjj(a,j).
Once this is done, save the file and run the command
$ julia Cut.jl
within the folder code/tests. If one wants to run this with parallelization,
one needs to run the following commands (supposing one is using bash)
$ export JULIA_NUM_THREADS=4
$ export JULIA_CPU_THREADS=4
$ julia -p 4 Cut.jl --parallel yes --lmax 10
where 4 is the number of parallelized threads. One can check the number of threads by opening the Julia terminal and by running the command
julia> Threads.nthreads()
The resulting file will be created in the folder code/data under the name
Dump_Diffusion_Coefficients_Cut.hf5.
Once one has recovered the Dump_Diffusion_Coefficients_Cut.hf5 file using the latter
method, one can plot the a-cut in orbital space of the relevant coefficients.
Go to the folder code/tests/Julia and run the file PlotCut.jl using the command
$ julia PlotCut.jl
A log-log plot of the diffusion coefficients which have just been computed is
displayed on a window. To terminate the programm, close the window and type
the Enter key on the terminal.
Once this is done, the figure is recovered as a PNG file of the name DjjCut.png
in the folder code/graphs/Julia.
Go to the folder code/tests/Mathematica and evaluate the Mathematica script
Diffusion_Coefficients_Cut.m using the command
$ math -script Diffusion_Coefficients_Cut.m
If math is not defined on Mac OS, then define an alias through the command
$ alias math="/Applications/Mathematica.app/Contents/MacOS/MathKernel"
Once done, we recover the plot as a PNG file of the name DjjCut.png
in the folder "code/graphs/Mathematica".
To compute an orbital space map of the SRR diffusion coefficients DRRjj and DNRjj,
one needs to access the code/tests folder and run the following command in
the terminal:
$ julia Mapping.jl
If one wants to run this with parallelization, one needs to run the following commands (supposing one is using bash)
$ export JULIA_NUM_THREADS=4
$ export JULIA_CPU_THREADS=4
$ julia -p 4 Mapping.jl --parallel yes --lmax 10
where 4 is the number of parallelized threads. One can check the number of threads by opening the Julia terminal and by running the command
julia> Threads.nthreads()
The resulting file will be created in the folder code/data under the name
Dump_Diffusion_Coefficients.hf5.
Go to the folder code/tests/Julia and run the file PlotContours.jl using the command
$ julia PlotContours.jl
A log-log plot of the diffusion coefficients which have just been computed is
displayed on a window. To terminate the programm, close the window and type
the Enter key on the terminal.
Once this is done, the figure is recovered as a PNG file of the name Djj.png
in the folder code/graphs/Julia.
Go to the folder code/tests/Mathematica and evaluate the Mathematica script
Diffusion_Coefficients.m using the command
$ math -script Diffusion_Coefficients.m
If math is not defined on Mac OS, then define an alias through the command
$ alias math="/Applications/Mathematica.app/Contents/MacOS/MathKernel"
Once done, we recover the plot as a PNG file of the name Djj.png
in the folder code/graphs/Mathematica.
We are grateful to A. Generozov for his suggestions for improving this code.