Add the Long 1974 piecewise collision kernel #1785

ekdejong · 2026-01-08T22:53:56Z

Includes additional functionality in pair methods to support comparison and "where"
Adds a new option for collision kernel dynamics
Includes a new unit test in collision kernels

slayoo · 2026-01-08T22:57:06Z

thank you @ekdejong !!!
CC-ing @yoctoyotta1024, @jbarr444 and @emmacware

codecov · 2026-01-09T01:38:00Z

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.82%. Comparing base (c30b62d) to head (babf080).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1785      +/-   ##
==========================================
+ Coverage   86.76%   86.82%   +0.06%     
==========================================
  Files         414      415       +1     
  Lines       10485    10536      +51     
==========================================
+ Hits         9097     9148      +51     
  Misses       1388     1388

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ekdejong · 2026-01-09T20:50:06Z

@slayoo Can you help me understand the test that is currently failing? I made the linter happy, but it seems like black is still acting. Do I just need to run Black locally?

slayoo · 2026-01-09T22:23:28Z

@slayoo Can you help me understand the test that is currently failing? I made the linter happy, but it seems like black is still acting. Do I just need to run Black locally?

black is executed automatically via a pre-commit hook after doing pre-commit install. Following it, a git commit ... command will trigger black, which will alter the files, and will stop the commit. Here, you can do git diff to make sure all of the automatic changes to the code are OK, following which repeating the same git commit ... command should work.

(this is mentioned in the README: https://github.com/open-atmos/PySDM/blob/main/README.md?plain=1#L131-L135, but any feedback on how to better explain the workflow warmly welcome!)

…d_longkernel

ekdejong · 2026-01-10T03:47:46Z

Thank you, @slayoo ! It's been some time since I contributed, clearly...

(this is mentioned in the README: https://github.com/open-atmos/PySDM/blob/main/README.md?plain=1#L131-L135, but any feedback on how to better explain the workflow warmly welcome!)

And speaking of which, thank you for bringing to my attention that the README has some valuable information on contributing! My bad for overlooking this.

slayoo · 2026-01-11T14:43:18Z

PySDM/dynamics/collisions/collision_kernels/long1974.py

+        self.particulator = builder.particulator
+        builder.request_attribute("volume")
+        builder.request_attribute("radius")
+        for key in (


we're allocating 8 temporary arrays here, and since some of these are anyhow named just tmp, perhaps we could do fewer allocations, e.g., by noting that v_ratio could be reused instead of copying it to tmp2 (i.e., no need for tmp2).

Thanks for pointing this out! Yes, this attempt to use a shared "pythonic" descriptor rather than separate numba and GPU backends allocates many arrays.

slayoo · 2026-01-11T14:43:41Z

PySDM/dynamics/collisions/collision_kernels/long1974.py

+            "tmp",
+            "tmp1",
+            "tmp2",
+            "condition",


condition would best be of type bool rather than float, right?

Yes, good point!

slayoo · 2026-01-11T14:44:31Z

tests/unit_tests/dynamics/collisions/test_kernels.py

+    def test_long1974_regimes(radius):
+        # arrange
+        env = Box(dv=None, dt=None)
+        builder = Builder(backend=CPU(), n_sd=radius.size, environment=env)


adding GPU support here seems to require the two new backend methods, right?

Indeed, I added those now.

slayoo · 2026-01-11T14:45:34Z

tests/unit_tests/dynamics/collisions/test_kernels.py

+
+        radius_lg = np.max(radius.data)
+
+        # assert


I'd suggest adding a basic notebook reproducing any of the figures from Long paper, and a smoke-test executing that notebook and making assertions on the result of a simulation featuring the new kernel

a good first candidate here seems Fig. 9:

I decided that replicating figures 10-11 and 13-14 is perhaps even more informative, as it includes comparisons with other relevant kernels like Golovin

slayoo · 2026-01-11T14:46:03Z

PySDM/dynamics/collisions/collision_kernels/long1974.py

@@ -0,0 +1,72 @@
+"""
+piecewise kernel from
+[Long 1974](https://doi.org/10.1175/1520-0469%281974%29031%3C1040%3ASTTDCE%3E2.0.CO%3B2)


let's specify precisely which eq. from the paper is implemented here (the paper discusses many kernels)

Eq 11, noted

slayoo · 2026-01-11T14:50:12Z

PySDM/dynamics/collisions/collision_kernels/long1974.py

+"""
+
+
+class Long1974:


BTW, in #1714, @yoctoyotta1024 pointed to the Simmel et al 2002 paper with an alternative mathematical formulation of the Long kernel. There is also a link there to Clara's implementation in CLEO. This could be perhaps a reason to name this class in a more mathematical manner, and offer different flags for calculations as in Long 1974 or as in Simmel et al. 2002? Comparing the two would be a great scenario for a unit test.

I think for the purpose of this PR (which is selfishly done to enable benchmakring against the Long kernel specifically), I will stick with the original formulation and include an example to compare against Golovin kernel, as is done in the Long paper.

slayoo · 2026-01-11T21:47:33Z

(let me also clarify that from all the above comments, adding an example notebook reproducing a figure from the paper is by far my key suggestion here, and I'm happy to help with equipping it later with a smoke test executing the notebook code)

…d_longkernel

ekdejong · 2026-01-16T19:48:24Z

(let me also clarify that from all the above comments, adding an example notebook reproducing a figure from the paper is by far my key suggestion here, and I'm happy to help with equipping it later with a smoke test executing the notebook code)

Thanks @slayoo! I've added a notebook to replicate some of the DSDs in the Long paper. I think an appropriate smoke test could be to confirm the size of the mode in the DSD, and/or to confirm a comparison between the mean size predicted using the Long kernel versus Golovin kernel.

slayoo · 2026-01-16T23:44:03Z

(let me also clarify that from all the above comments, adding an example notebook reproducing a figure from the paper is by far my key suggestion here, and I'm happy to help with equipping it later with a smoke test executing the notebook code)

Thanks @slayoo! I've added a notebook to replicate some of the DSDs in the Long paper. I think an appropriate smoke test could be to confirm the size of the mode in the DSD, and/or to confirm a comparison between the mean size predicted using the Long kernel versus Golovin kernel.

Thank you @ekdejong !

BTW, fun fact (thanks to @emmacware): Golovin's solution was actually given a bit earlier in the same journal by Safranov, which is why it is called Safranov kernel/solution in astrophysical literature: Safranov, V. S. (1962). "A particular solution of the coagulation equation" [in Russian: "Частный случай решения уравнения коагуляции"]. Bull. Acad. Sci. SSSR Geophys. Ser., 147 (1), 64—67. https://mathnet.ru/dan27172

ekdejong added 2 commits January 8, 2026 11:05

Add functionality for Long 1974

77bea54

Add unit tests

0f41bf5

ekdejong added 3 commits January 8, 2026 16:19

linting

6f838ca

fix output size in test

b482c85

fix unit test again

02cedda

ekdejong added 2 commits January 9, 2026 19:45

run pre-commit (Black)

ed76d2d

Merge branch 'main' of https://github.com/open-atmos/PySDM into ej/ad…

c5163dc

…d_longkernel

ekdejong requested review from emmacware and slayoo January 10, 2026 05:16

slayoo added 2 commits January 10, 2026 13:25

fix paper link, add entry to docs bib file

d98a620

missing https:// added

babf080

slayoo reviewed Jan 11, 2026

View reviewed changes

ekdejong added 12 commits January 15, 2026 19:59

add equation #; remove extraneous array allocation

b082716

Change condition array to bool

5489b83

add GPU storage methods; switch to bool condition

c2cfc8d

add GPU testing to kernel unit test

c516183

black

2d32565

more black

c6c4ce1

add example for Long kernel

3e6865c

black & badges

820a89b

parameterize backend for long unit test

4ac08bf

fix the backend pytest oops

593a009

add long to bib

ec94f73

Merge branch 'main' of https://github.com/open-atmos/PySDM into ej/ad…

c86207e

…d_longkernel

ekdejong added 2 commits January 16, 2026 11:49

add missing comma

f8b462e

update link in example init

5ad9b13

remove unused import

36785c1

Add the Long 1974 piecewise collision kernel #1785

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Add the Long 1974 piecewise collision kernel #1785

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slayoo commented Jan 11, 2026

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ekdejong commented Jan 16, 2026

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