[HN Gopher] Gravitational Collapse of Spongebob
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Gravitational Collapse of Spongebob
Author : raattgift
Score : 159 points
Date : 2024-03-17 00:12 UTC (22 hours ago)
(HTM) web link (twitter.com)
(TXT) w3m dump (twitter.com)
| raattgift wrote:
| That x/twitter account has some beautiful physics (especially
| gravitation-related) animations on it. Worth scrolling through
| it.
| omoikane wrote:
| Also, an interesting visualization of Bach's Cancrizans:
|
| https://twitter.com/PeRossello/status/1763909652025078009
| nozzlegear wrote:
| You have to have an X account to do that now right? Whenever I
| try to scroll through an account's tweets lately, I just get a
| list of their tweets from random dates in no apparent order.
| morder wrote:
| yeah, if you're not logged in you get shown tweets in random
| order.
| squigz wrote:
| Yes. The Platform Formerly Known as Twitter is now basically
| unusable if you're not logged in, which is really quite
| unfortunate.
| pfdietz wrote:
| It would be interesting to view the evolution over long periods
| of time.
|
| This simulation is 2D, but it's similar to what happens in
| globular star clusters. In these, there's a phenomenon called the
| "gravothermal catastrophe".
|
| The particles (stars, sponge bits) relax to thermal equilibrium,
| where the kinetic energy of a particle has a distribution where
| probability declines exponentially in energy/temperature. Some of
| the particles will have energy high enough to escape to infinity
| (to "evaporate"). When they leave, the remaining particles are
| more tightly bound, so the cluster shrinks. The particles then
| move faster (by the virial theorem, total kinetic energy is
| always 1/2 the negative of the gravitational potential energy).
| Evaporation accelerates until the cluster basically explodes.
|
| Why this doesn't happen to actual star clusters was eventually
| determined to be due to three body collisions that cause binary
| stars to form, and these stars then inject energy into passing
| stars (causing the binary star orbits to shrink). This energy
| injection reheats the cluster, inflating it again and preventing
| runaway evaporation.
|
| I'm not clear that the simulation here can handle formation of
| such binaries.
| scotty79 wrote:
| This looks cool:
| https://twitter.com/PeRossello/status/1754253187731599760
| pfdietz wrote:
| >The only force at play is newtonian gravity, which we modify
| by adding a softening length, e.
|
| > This way we avoid numerical instabilities due to divergent
| forces when two particles get to close together.
|
| So it appears he doesn't handle close encounters that form
| binaries. Probably reasonable if he's using heavier discrete
| particles as a proxy for dark matter.
| hermitcrab wrote:
| I wrote my own toy gravity simulation. 2 stars that come
| very close together at a clock tick will experience a
| massive force that throws them both right out of the
| system. This is an artefact of artificially dividing time
| into clock ticks to make the calculation tractable. As I
| understand it, 'softening length' is a fudge to stop that
| happening.
| pfdietz wrote:
| You'd have to use a more sophisticated algorithm with
| variable time steps for closely interacting particles, I
| think. And then some way to deal with particles that
| become bound.
| hermitcrab wrote:
| That sounds like a bit of a nightmare. Especially when
| you have a large number of bodies.
| andbberger wrote:
| yup. molecular dynamics simulations are hard-core. and
| the parallelization is highly non-trivial so you need
| fast fabrics and complex message passing to scale. one of
| the raisons d'etre for supercomputers
| pfdietz wrote:
| Did your simulation use the O(n) gravitational potential
| algorithm? You don't need to spend O(n^2) time per time
| step.
| hermitcrab wrote:
| IIRC I was calculating forces for every pair, which is ok
| for small N (e.g. a solar system, rather than a galaxy).
| andrewflnr wrote:
| > Evaporation accelerates until the cluster basically explodes
|
| This sounds very much like what happens at the end of a black
| hole's lifetime as it evaporates by Hawking radiation. Any
| chance that's a real connection?
| pfdietz wrote:
| I don't think so? The physics is completely different.
| andrewflnr wrote:
| Well yeah, probably, but sometimes very weird analogies
| between systems turn out to produce real physics, and it
| doesn't even seem impossible to me that there's something
| similar happening behind the event horizon of a black hole.
| I'm just hoping someone smarter than me has already done
| the math.
| SiempreViernes wrote:
| Hawking radiation is due to process outside the black
| hole.
| raattgift wrote:
| > Hawking radiation is due to process outside the black
| hole.
|
| Hm, yes, the Hawking quanta originate outside the event
| horizon, and not very nearby outside either (Giddings
| 2015 <https://arxiv.org/abs/1511.08221>, Unruh "Dumb
| Holes" 2007 <http://pos.sissa.it/cgi-
| bin/reader/conf.cgi?confid=43>).
|
| However it's best to think of "the black hole" as the
| entire spacetime (in Hawking's 1974 treatment and
| similar; or alternatively out to somewhere in the
| asymptotic flatness), in which there are two regions
| without a horizon, one to the past of the event horizon
| formation, and one to the future of final evaporation.
|
| What goes into the horizon doesn't stay in, therefore
| what happens inside is part of the picture (and has been
| speculated about for fifty years! Fifty!)
| raattgift wrote:
| There is a relationship in that both the "Spongebob
| cluster" and a black hole has negative heat capacity. The
| math is already there in the virial theorem. See <https:/
| /en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...>
| . Detailed treatments of the non-relativistic case you
| can find in an undergrad astronomy textbook; the
| relativsitic singleton case ehhhhh I don't think you're
| ready for it but Wald's _General Relativity_ SS12.5 &
| SSSS14.3-14.4 would be a good choice (and he shows you
| the math, which has been known for several decades), and
| for relativistic orbits I think you need to go beyond
| textbooks (although you probably could start with
| numerical relativity textbooks, like Baumgarte & Shapiro
| or Alcubierre, although I don't have either handy to
| double-check where they go with thermodynamics. Oh and
| the paper I linked in a sibling comment has a good and
| relevant bibliography. <https://academic.oup.com/mnras/ar
| ticle/516/3/3266/6668807>).
| hermitcrab wrote:
| As far as I am aware the virtual particles near the event
| horizon of black hole behave nothing like stars in a
| galaxy. For a start, stars much more massive (many many
| orders of magnitude) and aren't influenced by quantum
| mechanical effects in the same way as individual
| particles.
| dotnet00 wrote:
| I think the relation is just that it's a sort of positive
| feedback loop. Another example that comes to mind is a
| runaway nuclear fission reaction.
| Enginerrrd wrote:
| No, but also maybe yes, but it's way over my pay grade as a
| physicist. In short, I think the fact that gravitational
| systems have negative specific heat capactiy is very
| relevant.
|
| As gravitational systems lose energy, the "temperature" of
| the ensemble of particles goes up. (I.e. objects with smaller
| orbits have higher velocities.)
|
| It is probably not exactly an accident that this relationship
| holds for blackholes as well: the hawking radiation formulas
| suggest a larger and larger temperature for blackholes with
| smaller and smaller event horizons. The hawking radiation
| stuff is built upon entropy / temperature relationships so I
| think there is actually some kind of connection there.
|
| There might even be something baked into the energy
| conditions / bianchi identities of GR that is manifesting in
| that way, but I'm speculating.
| raattgift wrote:
| I like your comment, it provoked some catch-up reading, so
| forgive me pecking a bit at what you wrote.
|
| The visualization is pretty limited, and was probably just a
| fun way for the astrophys student to use his choice of tools.
| (Which we should encourage! His work is great!)
|
| I am also not the only person to think the visualization would
| be useful when teaching early astro or astrophys undergrads.
| For example,
| <https://twitter.com/BenShappee/status/1769066245339402612>.
| (BTW, Shappee was in ASAS-SN from the start. ASAS-SN is
| awesome, I promote them whenever I can squeeze them in:
| <https://www.astronomy.ohio-state.edu/asassn/index.shtml>).
|
| Digging deeply into the consequences of this example of
| obviously physically improbable initial conditions could be
| somewhere between entertaining and enlightening, but would
| quickly go over the head of early astro students first
| encountering the virial theorem and negative heat capacity.
| "Getting the physics right" would be a significant research
| project. You'd also generally have to do without animations,
| unless you are very patient and have a big compute time budget
| (see the acknowledgments section of the MNRAS paper below, and
| my final paragraph).
|
| Motivated by the previous paragraph's themes I found a recent
| (2022) MNRAS open access paper which among other things has a
| good overview of the (recent) state of the art in modelling
| star clusters, some good teaching material in section 2, and in
| section 3 we see their software packages. I'd suggest you begin
| with the summary in section 6.1.
|
| https://academic.oup.com/mnras/article/516/3/3266/6668807
|
| In principle simulating the Spongebob cluster could produce
| information in the top two graphs of figure 7, and a 2d version
| of one or two of the graphs in figure 6. The additional
| information in those figures is certainly interesting, but
| nowhere near as pretty as the Spongebob animation. And I'm not
| sure what extracting similar figures for the Spongebob
| simulation would be useful for.
|
| Conversely, the Spongebob simulation could not generate figure
| 9, and that figure is especially interesting to me (q.v. SS4.2
| & final sentence in SS3.2).
|
| And finally, "The movies of the full simulations, from which
| Fig. 6 was produced, will be made available upon reasonable
| request as well and will be uploaded publicly in the future".
| Not sure the upload ever happened, although I didn't really
| search much (e.g. it's not linked at the arxiv
| <https://arxiv.org/abs/2205.04470> or in DDG media searches on
| title or a few of the authors).
| throw5323446 wrote:
| Anybody can post the text for those without an account?
| bagels wrote:
| Primary content is an animation.
| Izmaki wrote:
| Imagine a pencil drawing of Spongebob, but using tiny dots
| rather than strokes, collapsing onto itself, forming what looks
| like two separate masses (of sponge particles?) which then
| collapse together in the end.
| emmanueloga_ wrote:
| https://www.youtube.com/watch?v=C6eY6HMBa2Q
| noobcoder wrote:
| Correct me if i am not wrong they probably defining initial
| conditions for the particles (such as positions (to create the
| spongebob (althought I wish there was a way to convert an image
| to these n bodies), velocities, and masses) Then you set up the
| gravitational interactions between them and futher iteratively
| update their positions and velocities over time using some
| numerical integration method (Euler's method/Runge-Kutta method?)
| to simulate their motion
| buescher wrote:
| Looks like it. A.K. Dewdney did a computer recreations column
| in Scientific American back in the eighties with a nice
| exposition of how to do a basic star cluster simulation. Only
| practical with a lot fewer "stars" on the gear I had available
| then. It used Euler's method iirc.
| jhbadger wrote:
| Speaking of which, Dewdney recently passed away on March 9th
| but I haven't seen any notice of it on HN or other CS-related
| sites. I know he alienated a lot of people with his
| unfortunate turn to conspiracy theory after 9/11, but he
| really contributed a lot to popular interest in CS and
| recreational mathematics in the 1980s and 1990s through his
| Scientific American articles and his books.
| buescher wrote:
| I'm sorry to hear that. His columns and books were a big
| influence.
| epiccoleman wrote:
| Oh man, what a trip to see Dewdney mentioned.
|
| I have a copy of The Magic Machine on my shelf which I
| (unintentionally) stole from my university library at the end
| of my senior year. His work was pretty influential on me,
| inspiring me to keep exploring programming at a time when my
| day to day work in the subject was often painfully boring.
| comicjk wrote:
| Probably a symplectic Verlet method instead of Euler or Runge-
| Kutta, since you want energy and momentum to be conserved in
| this simulation.
| gus_massa wrote:
| I was going to link to the article about sympletic
| integration, but it's toooo technical. This other article
| explains the problem
| https://en.wikipedia.org/wiki/Energy_drift
| vorticalbox wrote:
| Does anyone know what software was used?
| jpendry wrote:
| From his reply tweet:
|
| N-body simulation made with Python, parallelized with numba,
| and animated with matplotlib.
|
| N=100.000. Computation time around 5h for 2.000 steps. Around
| 1s of compute time per step. Collisions are handled with a
| softening length.
| thih9 wrote:
| I'd prefer if the larger areas like eyes consisted of a single
| large circle with greater gravitational pull, as opposed to
| multiple small dots.
| dudeinjapan wrote:
| Check out the album "The Mollusk" by Ween--supposedly the musical
| inspiration for Spongebob.
| amelius wrote:
| No collisions?
| hermitcrab wrote:
| IIRC two galaxies can pass through each other with no
| collisions, because the space between the stars is so large
| compared to the size of the stars. Quite how well that applies
| to Spongebob is an open question.
| mort96 wrote:
| This is cool!
|
| ...but 1 second per time step is a lot. I wonder how fast it
| would've been if it wasn't in Python. I think we as a society are
| doing a whole lot of people (especially physicists) a disservice
| by mainly teaching them Python rather than languages which are
| literally hundreds of times faster in some cases. Python works
| well when you just want to glue together existing fast C or
| Fortran libraries with Python APIs, but it quickly proves
| limiting.
|
| I've personally been caught by the Python trap, where the easiest
| way to do something was to write a Python script to do it, and it
| worked, but then I wanted to try to process more data or
| whatever, and suddenly Python is a huge limiting factor. I then
| spend more time parallelizing the Python code to make it run
| faster, and it becomes a beast that's hard to debug and which
| maxes out 32 CPU cores and is still 10x slower than what a single
| threaded Rust program would've been and I regret my choice of
| language.
| hermitcrab wrote:
| I believe it is using Numba which converts to machine code.
|
| https://numba.pydata.org/
| mort96 wrote:
| Right, and compiling Python to machine code does get rid of
| the overhead associated with opcode dispatch... but it's not
| magic, Python is still a wildly dynamic language. It's mainly
| the dynamicness that makes it slow, not the fact that each
| opcode has to go through a switch statement in the cpython
| interpreter
|
| To get significantly better performance with a JIT, you need
| one which analyzes the code at runtime to detect patterns,
| such as "this function is always called with an integer
| argument" or "the dictionary passed to this function always
| has this shape", like what V8 does. AFAIK Numba doesn't do
| that.
|
| (Though if I'm wrong and there are benchmarks which shows
| Numba coming close to something like Rust in normal dynamic
| Python code, please do correct me! I haven't done much
| research on Numba specifically)
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