Addition of additive coagulation example including comparison against PySDM and Droplets.jl

[emmacware]

No description provided.

[slayoo]

• include Julia Droplets.jl in the notebook
• make the setup common also with the Julia code by using a dictionary of settings and writing it to a JSON file (as in the Trixi example in PyMPDATA)
• switch settings and the plot construction to match Shima's box-model plot
• add asserts wrt analytical solution
• try if all works on Colab, mybinder and ARM JupyterHub
• (sectional scheme via PartMC (Bott)) - for another PR
• analytic (PartMC & PySDM)

[slayoo]

https://github.com/open-atmos/PySDM/blob/main/PySDM/dynamics/collisions/collision_kernels/golovin.py#L22-L44

[slayoo]

• one thing we are certainly missing here is a reference to Shima's paper - perhaps we could add a markdown cell at the beginning explaining the setup, linking to the paper, and introducing the aim of comparing three models (with links to the model pages)

[slayoo]

• it is worth indicating if adaptivity is turned on or off for PySDM and Droplets.jl

[slayoo]

@emmacware, trying to debug the Windows issue by logging into the CI machine, I ruled out any problems with Jupyter or all the execution machinery. The problem seems to be within Julia, is not deterministic, and the only symptom is that Julia quits silently at random stages of the computation returning exit code 127:

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# julia.exe script.jl 
    Updating registry at `C:\Users\runneradmin\.julia\registries\General.toml`
   Resolving package versions...
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Project.toml`
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Manifest.toml`
Running simulation...
Time: 0.0 seconds
Time: 120.0 seconds
Time: 240.0 seconds
Time: 360.0 seconds
Time: 480.0 seconds

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# echo $?                                                                                                                                                                                                          
127

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# julia.exe script.jl 
    Updating registry at `C:\Users\runneradmin\.julia\registries\General.toml`
   Resolving package versions...
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Project.toml`
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Manifest.toml`
Running simulation...
Time: 0.0 seconds
Time: 120.0 seconds
Time: 240.0 seconds
Time: 360.0 seconds
Time: 480.0 seconds
Time: 600.0 seconds
Time: 720.0 seconds

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# echo $?                                                                                                                                                                                                          
127

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# julia.exe script.jl 
    Updating registry at `C:\Users\runneradmin\.julia\registries\General.toml`
   Resolving package versions...
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Project.toml`
  No Changes to `C:\Users\runneradmin\.julia\environments\v1.11\Manifest.toml`
Running simulation...
Time: 0.0 seconds

runneradmin@fv-az1212-152 MINGW64 /d/a/PyPartMC/PyPartMC
# echo $?
127

[jcurtis2]

In the spirit of the pyOpenSci feedback, I'm wondering if some more commenting/narrative could be applied. While it is clear to me what is going on, this notebook (I hope!) will be useful for either others to add their model for this coagulation case or follow this general framework for combining models to look at other things.