Grow your own planet
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00:00
Grundraumt-TestNobelpreis für PhysikDemoszene <Programmierung>Minkowski-MetrikSolar-terrestrische PhysikComputersimulationPhysikalisches SystemComputervisualistikComputeranimationJSONVorlesung/Konferenz
01:09
Nobelpreis für PhysikRechter WinkelObjekt <Kategorie>NeuroinformatikRuhmasseMinkowski-MetrikSolar-terrestrische PhysikGrundraumBitDunkle EnergieMereologieVorlesung/KonferenzComputeranimation
02:11
GravitationEnergiedichteWärmeausdehnungOrbit <Mathematik>Dunkle EnergieGrundraumMereologieNeuroinformatikOrbit <Mathematik>MultiplikationsoperatorSpezielle unitäre GruppeComputervisualistikComputersimulationProzess <Informatik>Vorlesung/Konferenz
03:27
FluidSpezialrechnerPunktwolkeDichte <Physik>Physikalisches SystemMini-DiscSymplektische GeometrieRuhmasseImpulsMini-DiscPunktwolkeBitFluidWhiteboardSkalarproduktPartikelsystemBildschirmmaskeDialektDatenflussProzess <Informatik>RuhmasseFlächentheoriePhysikalisches SystemEnergiedichteNumerische MathematikBeweistheorieAggregatzustandVierTwitter <Softwareplattform>Deskriptive StatistikQuaderBildgebendes VerfahrenGeschwindigkeitWasserdampftafelMultiplikationsoperatorNatürliche ZahlAlgorithmische ProgrammierspracheKreisbewegungDemoszene <Programmierung>NeuroinformatikMAPSkriptspracheImpulsHyperbelverfahrenKrümmungsmaßWeg <Topologie>GrundraumGravitationComputervisualistik
09:15
Symplektische GeometrieNeuroinformatikQuaderGraphfärbungDatenstrukturRuhmasseInnerer PunktPunktSkalarproduktValiditätMini-DiscFlächeninhaltMereologieSchnitt <Mathematik>Dichte <Physik>DigitalisierungPartikelsystemStreaming <Kommunikationstechnik>DatenflussVorlesung/KonferenzComputeranimation
10:48
DatenflussPunktMathematikDichte <Physik>DatensatzDichte <Physik>Derivation <Algebra>DatenflussFlächentheorieGeschwindigkeitMathematikFluss <Mathematik>SymboltabelleDreieckQuaderMultiplikationsoperatorEinflussgrößeTermRuhmasseNobelpreis für PhysikDeskriptive StatistikOrtsoperatorMAP
12:03
RuhmasseImpulsErhaltungssatzEnergiedichteTeilbarkeitNichtlineares GleichungssystemStokes-IntegralsatzRuhmasseErhaltungssatzEnergiedichteMultiplikationsoperatorPartikelsystemMathematikQuaderNobelpreis für PhysikNumerische MathematikImpulsDatenkompressionSchlussregelGeschwindigkeitPunktAbgeschlossene MengeProdukt <Mathematik>Arithmetisches MittelFluidObjekt <Kategorie>CASE <Informatik>Nichtlineares GleichungssystemDruckverlaufComputersimulationMinimalgradOrtsoperatorZellularer AutomatFlächeninhaltHauptidealVektorpotenzialGravitationAdditionPhysikalischer EffektTeilbarkeitComputeranimation
15:31
Dichte <Physik>Eulersches PolygonzugverfahrenVolumenFlächentheorieOrtsoperatorMultiplikationsoperatorTeilbarkeitAdditionDreieckMathematikComputervisualistikDerivation <Algebra>Nobelpreis für PhysikAusdruck <Logik>NeuroinformatikDichte <Physik>QuaderFluss <Mathematik>PlotterVorlesung/KonferenzDiagramm
16:48
Eulersches PolygonzugverfahrenFlächentheorieVolumenMultiplikationsoperatorTwitter <Softwareplattform>KurvenanpassungOrtsoperatorFluss <Mathematik>GeradePunktDichte <Physik>SimulationÄhnlichkeitsgeometrieQuaderDifferenteKerr-LösungVorlesung/Konferenz
18:17
Dichte <Physik>Rungescher ApproximationssatzMittelwertGeradeTwitter <Softwareplattform>RichtungMultiplikationsoperatorMittelwertBitDichte <Physik>KurvenanpassungPunktQuaderTonnelierter RaumGraphfärbungObjekt <Kategorie>DifferenteProzess <Informatik>Numerische MathematikZeitrichtungAuflösung <Mathematik>Diagramm
21:04
SpezialrechnerMini-DiscObjekt <Kategorie>Bildgebendes VerfahrenDigitale PhotographieMini-DiscDatenstrukturAuflösung <Mathematik>Web logAsymmetrieSimulationSymmetrische MatrixSpiraleComputeranimation
22:19
Mini-DiscComputerMini-DiscBitGeradeBildgebendes VerfahrenMultiplikationsoperatorDatenstrukturZellularer AutomatMereologieSimulationNeuroinformatikPhysikalisches System
23:51
ComputerMini-DiscRippen <Informatik>Physikalisches SystemDifferenteSchnittmengeElektronische UnterschriftObjekt <Kategorie>CASE <Informatik>OrtsoperatorMini-DiscMultiplikationsoperatorTemperaturstrahlungEingebettetes SystemAutomatische HandlungsplanungComputeranimation
25:20
Data MiningMini-DiscLuenberger-BeobachterDifferenteMultiplikationsoperatorMathematikFormation <Mathematik>MinimalgradDynamisches SystemPhysikalisches System
26:13
Rippen <Informatik>ComputerDichte <Physik>RuhmasseDichte <Physik>QuaderSimulationAbgeschlossene MengeRelativitätstheoriep-BlockWechselsprungSymmetrieNichtlineares GleichungssystemFlächeninhaltMini-DiscBitPunktComputersimulationDatenstrukturSpiraleDifferenteNobelpreis für Physik
27:58
Orbit <Mathematik>Interaktives FernsehenRuhmasseSimulationSkalarproduktComputersimulationBinärcodeDatenstrukturMini-DiscRechter WinkelDifferenteNichtlineares GleichungssystemNobelpreis für PhysikWhiteboardAutomatische HandlungsplanungGrundsätze ordnungsmäßiger DatenverarbeitungArithmetisches MittelObjekt <Kategorie>EinfügungsdämpfungComputeranimation
31:00
FlächentheorieExpertensystemQuantenmechanikPunktMini-DiscPhysikalisches SystemKondensation <Mathematik>BitFlächentheorieMonster-GruppeDichte <Physik>DifferenteRuhmasseStereometrieWasserdampftafelRechter WinkelMultiplikationsoperatorGeradeAggregatzustandDruckverlaufAerothermodynamikVorlesung/Konferenz
33:09
Web-SeiteGeschwindigkeitDruckverlaufDruckverlaufMini-DiscAnfangswertproblemImpulsAerothermodynamikPunktGeschwindigkeitSpezielle unitäre GruppeDatenstrukturURLPhysikalisches SystemFlächentheorieAbstandInelastischer StoßGeradeRechter WinkelMathematikZweiKonditionszahlData MiningSchnittmengeWasserdampftafelDifferenteComputeranimation
34:55
Anpassung <Mathematik>SimulationPhysikalisches SystemSpiraleGeradeDialektWasserdampftafelQuaderSimulationRandwertComputersimulationZellularer AutomatFluidAbstimmung <Frequenz>ProgrammierungNobelpreis für PhysikRichtungShape <Informatik>GrundraumMini-DiscSolar-terrestrische PhysikSkalarproduktRepository <Informatik>DatenflussScherbeanspruchungPolygonnetzComputeranimation
37:51
SimulationAnpassung <Mathematik>Open SourceVersionsverwaltungNobelpreis für PhysikGraphikprozessorEnergiedichteGlobale OptimierungSolar-terrestrische PhysikMaschinencodeDemoszene <Programmierung>Inklusion <Mathematik>Mini-DiscVektorpotenzialOpen SourceNeuroinformatikMini-DiscEin-AusgabeDifferenteElektronische PublikationSpiraleWort <Informatik>MereologieVersionsverwaltungProgrammierungSolar-terrestrische PhysikNumerische MathematikRuhmasseParametersystemFunktion <Mathematik>RechenschieberNotebook-ComputerSkalarproduktVerdeckungsrechnungProgrammcodeMaschinencodeMultiplikationsoperatorVirtuelle MaschineRepository <Informatik>Bildgebendes VerfahrenNobelpreis für PhysikDynamisches SystemComputeranimation
41:42
Demoszene <Programmierung>SimulationFunktion <Mathematik>ParametersystemKeilförmige AnordnungGravitationKoordinatenPhysikalisches SystemMaß <Mathematik>MaschinencodeOpen SourceMini-DiscBitGravitationsfeldGravitationKoordinatenMultiplikationsoperatorNobelpreis für PhysikQuaderSimulationAnfangswertproblemRandwertEin-AusgabeElektronische PublikationProgramm/QuellcodeComputeranimation
42:54
Demoszene <Programmierung>RechnernetzStokes-IntegralsatzNotebook-ComputerDatenverarbeitungssystemLeistung <Physik>KnotenmengeGraphikprozessorBefehlsprozessorSimulationFlächentheorieGravitationComputervisualistikTeilbarkeitMultiplikationsoperatorFunktion <Mathematik>Nobelpreis für PhysikSoftwaretestParametersystemTypentheorieSimulationZentrische StreckungLeistung <Physik>ProgrammierungEinsNeuroinformatikNotebook-ComputerComputersimulationRandwertTUNIS <Programm>Rechter WinkelWasserdampftafelDatenfeldTemperaturstrahlungMinkowski-MetrikGraphikprozessorSpieltheorieGüte der AnpassungSkalarproduktSISPVererbungshierarchieMeterLesen <Datenverarbeitung>Offene MengeComputeranimation
46:10
SimulationMigration <Informatik>RuhmasseFlächentheorieGravitationOffene MengeOrbit <Mathematik>RuhmasseSweep-AlgorithmusWasserdampftafelInelastischer StoßOffene MengeSISPPhysikalisches SystemDruckspannungSolar-terrestrische PhysikProgrammierungComputersimulationDatenfeldOrbit <Mathematik>Nobelpreis für PhysikVorlesung/Konferenz
47:24
MenütechnikMessage-PassingOffene MengeNobelpreis für PhysikDeskriptive StatistikHybridrechnerNichtlineares GleichungssystemMini-DiscComputeranimationVorlesung/Konferenz
48:18
VersionsverwaltungOpen SourceGruppenoperationObjekt <Kategorie>MaschinencodeMomentenproblemGravitationElektronische PublikationPhysikerAutorisierungDifferenteTypentheoriePhysikalisches SystemOrdnung <Mathematik>BitHilfesystemStatistikBesprechung/Interview
49:35
TypentheorieSpannweite <Stochastik>Physikalisches SystemMereologieSpezielle RelativitätstheorieBimodulModallogikBinärcodeEnergiedichteGrundraumNumerische MathematikRechenschieberSimulationComputersimulationMini-DiscVorlesung/KonferenzBesprechung/Interview
50:35
EnergiedichteWärmeausdehnungMini-DiscComputersimulationSimulationProgrammierungBenutzerfreundlichkeitGüte der AnpassungAdditionPhysikerPhysikalisches SystemInternetworkingQuick-SortGruppenoperationBesprechung/InterviewVorlesung/Konferenz
51:57
Endliche ModelltheorieLuenberger-BeobachterSimulationEinflussgrößeMAPNobelpreis für PhysikPhysikalisches SystemStatistische HypotheseParametersystemSolar-terrestrische PhysikPhysikalische TheorieMultiplikationsoperatorProzess <Informatik>Dichte <Physik>TaskVererbungshierarchieBildgebendes VerfahrenVorlesung/Konferenz
53:57
WärmeausdehnungEnergiedichteART-NetzDichte <Physik>NeuroinformatikNumerische MathematikGeschwindigkeitAlgorithmusBitPunktFluss <Mathematik>Zellularer AutomatKontrollstrukturRuhmasseEinflussgrößeVererbungshierarchieGruppenoperationAnfangswertproblemVorlesung/KonferenzBesprechung/Interview
55:14
AnfangswertproblemMini-DiscDichte <Physik>BitLuenberger-BeobachterOrdnung <Mathematik>ParametersystemPaarvergleichAggregatzustandKonditionszahlSchnittmengePhysikalisches SystemGruppenoperationMeterMarketinginformationssystemVererbungshierarchieSichtenkonzeptVorlesung/KonferenzBesprechung/Interview
56:41
Zellularer AutomatRuhmasseNumerische MathematikKalkülGravitationsgesetzKomplex <Algebra>Gesetz <Physik>RichtungQuadratzahlObjekt <Kategorie>PartikelsystemBefehlsprozessorGrenzschichtablösungVorlesung/Konferenz
57:43
EbenePartikelsystemObjekt <Kategorie>AnströmwinkelWinkelTechnische OptikSimulationStrategisches SpielProgrammierungGruppenoperationMultiplikationsoperatorSystemzusammenbruchComputeranimationVorlesung/Konferenz
58:43
Funktion <Mathematik>MultiplikationsoperatorSimulationDifferenteRechenbuchVorlesung/Konferenz
59:51
KonditionszahlProgrammierungComputersimulationSpiraleMultiplikationsoperatorTopologieTurbulente StrömungCoxeter-GruppeVorlesung/Konferenz
01:00:53
Coxeter-GruppeVorlesung/KonferenzComputeranimation
Transkript: Englisch(automatisch erzeugt)
00:21
impressed about how much we already learned about space, about the universe and about our our place in the universe, our solar system. But the next speakers will explain us how we can use computational methods to simulate the
00:40
universe and actually grow planets. The speakers will be Anna Penzlin, she is PhD student in Computational Astrophysics in Tübing and Karoline Kimmich, she is physics master student at Heidelberg University. And the talk is
01:00
entitled Grow Your Own Planet, How Simulations Help Us Understand the Universe. So hi everyone. It's a cool animation, right? And the really cool
01:24
thing is that there's actually physics going on there, so this object could really be out there in space but was created on a computer. So this is how a star is forming, how our solar system could have looked like in the beginning.
01:41
Thank you for being here and that you're interested in how we make such an animation. Anna and I are researchers in astrophysics and we're concentrating on how planets form and evolve. She's doing her PhD in Tübing and doing my master's in Heidelberg. And in this talk we want to show you a little bit
02:03
of physics and how we can translate that in such a way that a computer can calculate it. So let's ask a question first. What is the universe or what's in the universe? The most part of the universe is something we don't
02:21
understand yet. It's dark matter and dark energy and we don't know what it is yet and that's everything we cannot see in this picture here. What we can see are stars and galaxies and that's what we want to concentrate on in this talk. But if we can see it, why would we want to watch a computer? Well,
02:44
everything in astronomy takes a long time. So each of these tiny specks you see here are galaxies just like ours. This is how the Milky Way looks like and we're living in this tiny spot here. And as you all know, our Earth takes one year to orbit around the Sun. Now think about how long it
03:03
takes for the Sun to orbit around the center of the galaxy. It's 400 million years and even the star formation is 10 million years. We cannot wait 10 million years to watch how a star is forming, right? That's why we need computational methods or simulations on a computer to understand these processes.
03:28
So when we watch to the night sky, what do we see? Of course we see stars and those beautiful nebulas. They are gas and dust and all of these
03:40
images are taken with Hubble Space Telescope. Oh, so there's one image that doesn't belong in there. But it looks very similar, right? This gives us the idea that we can describe the gases in the universe as a fluid. It's really complicated to describe the gas in every single particle. So we cannot
04:07
track every single molecule in the gas that moves around. It's way easier to describe it as a fluid. So remember that for later. We will need that. But first let's have a look how a star forms. A star forms from a giant cloud of
04:24
dust and gas. Everything moves in that cloud. So eventually more dense regions occur and they get even denser. And these clumps can eventually collapse to one star. So this is how a star forms. They collapse due to their own
04:47
gravity. And in this process a disk forms and in this disk planets can form. So why a disk? As I said, everything moves around in the cloud. So it's likely that the cloud has a little bit of an initial rotation. As it collapses
05:04
this rotation gets larger and faster. And now you can think of making a pizza. So when you make a pizza and spin your dough on your finger you get a flat disk like a star, like a disk around a star. That's the same process actually. In this disk we have dust and gas. From this dust in the disk the
05:29
planet can form. But how do we get from tiny little dust particles to a big planet? Well it somehow has to grow. And grow even further and compact till
05:42
we have rocks. And even grow further until we reach planets. How does it grow? Well that dust grows. We know that. At least that's what I observed when I took those images in my flat. Well, so dust can grow and grow even
06:02
further and compact. But when you take two rocks, we are now in this state, when you take two rocks and throw them together you do not expect them to stick. Right? You expect them to crash and crack into a thousand pieces. So we're standing on the proof that planets exist. How does this
06:26
happen? And it's not quite solved yet in research. So this is a process that is really hard to observe because planets are very very tiny compared to stars. And even stars are only small dots in the night sky. Also as I said
06:43
planets form in a disk and it's hard to look inside the disk. So this is why we need computation to understand a process that how planets form and other astronomical processes. So let's have a look at how we simulate it on
07:00
a computer. OK. So somehow we have seen nature. It's beautiful and just like a tank of water and a bubbly fluid we already have. So now we have this bubbly fluid and here in the middle demonstrated. But now we have to teach
07:22
our computer to deal with a bubbly fluid and that's way too much single molecules to simulate them as we already said. So there are two ways to discretize it in a way that we just look at smaller pieces. One is the description just like taking small bubbles or balls of material that have
07:47
a fixed mass. They have a certain velocity that varies between each particle and they have of course a momentum because they have a velocity and a mass. And we create a number of those particles and then just see
08:01
how they move around and how they collide with each other. That would be one way that was described last year in a very good talk. I can highly recommend to hear this talk if you're interested in this method. However there's a second way to also describe this not just going with the flow of the particles but we are a bit lazy we just box it. So we
08:24
create a grid and as you see down here in this grid you have a certain filling level a bit of a slope. So what's the trend there. And then we just look for each box what flows in what flows out through the surfaces
08:44
of this box. And then we have a volume and or a mass filled within this box. And this is how we discretize what is going on in the disk. And actually since we are usually in the system of a disk we do not do it in this nice box way like this but we use boxes like those because they
09:06
are already almost like a disk. And we just keep exactly the same boxes all the time and then you just measure what goes through the surface in these boxes. So this is how these two methods look like
09:21
if you compute with both of them. So they one was done by me I'm usually using this boxing method and the other was done by my colleague. And you see this like when you look at them at the colors at the structure here you have the slope inwards you have the same slope inwards here you have even this hilly
09:43
structure here the same here. But what you notice is you have this and large dots that are really these are really the mass particles we saw before these bubbles. And here you have this inner cut out. This is because when you create this grid you
10:00
have the very region at the inner part of the disk where the boxes become tinier and tinier. And well we can't compute that. So we have to cut out at some point the inner part. So here when you go to low densities these bubbles blow up and distribute their mass over a larger area. So it's not
10:24
very accurate for these areas. And here we have the problem we can't calculate the inner area. So both methods have their pros and cons and are valid. But now foremost we will focus on this one just so we have this nice actually
10:46
stream features. So again going back to the boxes we have to measure the flow between the boxes this flow in physics we
11:01
call it flux and we have a density row one a density row two and the flux is the description of what mass moves through the surface here from one box to the next. So if we write this in math terms it looks like this. This says the
11:25
time derivative of the density meaning the change in this the change over time. So how much faster or slower you go that velocity would be a change in time. And then this
11:43
weird triangle symbol it's called nabla is a positional derivative. So it's like a slope. So how much how do we change our position actually. So if we change look at the
12:07
we have over position. That is what that says. So and then we have in physics a few principles that we have always to obey because it's just almost common sense. One of them
12:20
is well if we have mass in a box well like this the mass should not go anywhere unless someone takes it out. So if we have a closed box and mass in that box nothing should disappear magically. We should stay it should all stay in this
12:40
box. So even if these particles jump around in our box with a certain velocity it's the same number of particles in the end. That's again the same equation just told in math. So and the second very rudimentary principle is if we have energy in it in a completely closed box. So
13:04
for example this nice chemicals here and we have a certain temperature. So in this case our temperature is low maybe like outside of around zero degree Celsius. And then we have this nice chemicals down here and at some point
13:22
they react very heavily. We suddenly end up with much less chemical energy and a lot more thermal energy. But overall the complete energy summed up here like the thermal and the chemical energy also the energy of the movement
13:42
and the energy of potential added up to this variable U. That should not change over time if you sum up everything because our energy is conserved within our closed box. And then the third thing is I think you all know
14:01
this. If you have like a small mass with a certain velocity very high velocity in this case and it bumps into someone very large. What happens. Well you get a very small velocity in this large body and the smaller mass
14:22
stops. And the principle here is that in momentum is conserved meaning that the velocity times the mass of one object is the same as then later for the other one. But since it's larger this product has to be the same.
14:41
That doesn't change. And we have also to like in our simulations to obey these rules and we have to to code that in so that we have physics in them. So you say OK this is really simple these rules right. But actually well it's not quite as simple. So this is the Navier-Stokes
15:01
equations a very complicated equation it's not completely solved. And we have here all that is marked red are derivatives. Here we have our conservation law that was the nice and simple part. But now we have to take other physical things and into accounting for pressure
15:23
accounting for viscosity and for compression so squeezing and like how sticky is our fluid and also gravity. So we have a lot of additional factors additional physics we also have to get in somehow. And all of these also depends
15:42
somehow on the change of position or the change of time and these derivatives aren't really nice for our computers because they well they don't understand this triangle. So we need to find a way to write an algorithm so that it can somehow relate with this math
16:03
formula in a way that the computer likes. And one of the way to do this is well the simplest solution actually is just we say OK we have now this nasty derivatives and we
16:25
want to get rid of them. So if we look just at one box now and we say that in this box the new value for the density in this box would be the previous density plus the
16:43
flux in and out times the time step over which we measured this flux. And so and we have to somehow get to this flux and we just say OK this flux now is if we
17:00
start here and the slope of this curve the trend so to say where this curve is going right now so it would look like this. So in our next step time step we would have a density down here. And well then we do this again we again look at this point where's the trend going with
17:21
the line going and then we end up here same here. So again we just try to find this flux and this is the trend at this position in time. So this goes up here
17:40
and then if we are here now look at this point it should go up here. So this is what our next trend would be. And we do this over all the times and this is how our simulation then would calculate the density for one box over a different time steps. So that kind of works.
18:04
So the blue curve is the analytical one the red curve. Well it's kind of similar as it works but can we do better. It's not perfect yet right. So what we can do is we refine this a bit taking a few more steps making it a
18:23
bit more computationally heavy but trying to get a better resolution. So first we start with the same thing as before. We go to this point find the trend in this point that point like the line would go in this direction
18:41
from this point and then we go just half a step now. Sorry. And now we look at this half a step to this point now and do it again the same saying OK where's the trend going now. And then we take where this point
19:00
would go and add it to this trend. So that would be that the average of this trend of this exact point and this trend this dark orange curve. And then we go back to the beginning with this trend now and say this is a better trend than the one we had before. We now use
19:22
that and go again and search the point for half a time step. And then again we do the same thing. Now we again try to find actually the trend and average it with the arrow before. So it's not exactly the trend
19:43
is a bit below the trend because we averaged it with the arrow before. And now we take this averaging trend from the beginning to the top like this. OK this is already quite good but we can still do a little bit better if we average it with our ending point. So we
20:01
go here and look where is the trend going that would go quite up like this. And we average this and this together and then we end up with a line like this. This is so much better than what we had before. It's a bit more complicated to be fair but actually it's almost on the line. So this is what
20:24
we wanted. So if you compare both of them we have here our analytical curve. So over time in one box this is how the density should increase. And now with both of the numerical method the difference looks like this. So if we have
20:43
smaller and smaller time steps even the Euler gets closer and closer to the curve. But actually the Runge-Kutta, this four step process works much better and much faster. However it's a bit more computationally difficult. When we simulate
21:07
objects in astronomy we always want to compare them to objects that are really out there. So this is a giant telescope consisting of a lot of small telescopes but they can be connected and
21:21
used as a giant telescope. And it takes photos of dust in the sky and this is used to take images of disks around stars and these disks look like this. So these images were taken last year and they are really cool. Before we had those images
21:42
we only had images with less resolution so they were just blurred blobs. And we could say yeah that might be a disk but now we really see the disks and we see rings here, thin rings and we see thicker rings over here and even some spirally structures here. And also some features
22:04
that are not really radially symmetric like this arc here. And it's not completely solved how these structures formed. And to find that out a colleague of mine took this little object with
22:24
the asymmetry here. And so this is the image we just saw and this is his simulation. So this is how disk looked like in the beginning probably. And he put in three planets and let the
22:41
simulation run. And so what we see here is that the star is cut out as Anna said. We have to so the grid cells in the inner part are very very small and it would take a lot of time to compute them all. So that's why we're leaving out that spot in the middle. And what we see
23:04
here is three planets interacting with the material in the disk. And we can see that these planets can make this thing here appear so that in the end we have something looking very similar
23:23
to what we want to have or what we really observe. So we can say three planets could explain how these structures formed in this disk. It's a little bit elliptical you see that that's because it's tilted from our side of line. It
23:42
would be round if you watch that it face on but it's a little bit tilted. That's why it looks elliptical. So we already saw we can put planets in the gas and then we create structures. And one very exciting thing that we
24:02
found in the last year or two years ago it started but then we found more is this system PDS 70. In this system for the very first time we found a planet that was still embedded with completely within the disk. So the gas and
24:22
dust usually because the gas and dust is the main thing that creates a signal some radiation because of heat. We only observe that and then we can't observe the planet embedded. But in this case the planet was large enough and in
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the right position that we actually were able to observe some signature of accretion on this planet that was brighter than the rest of the disk. And then later just this year just a few months ago we actually found out well this
25:00
is not the only object here. This is a very clearly a planet. But actually like this spot here is also something. So it's we can see it in different grains like every picture here is a different set of grains observed. And we can see this in four different five different kinds of
25:27
observations. So there is a planet here and then there's also something we don't know what it is yet but it's point like and actually creates the feature that we reproduce in different kinds of observational bands or
25:42
different kinds of signals here. This is very interesting. For the first time we actually see a planet forming right now within the disk. So a colleague of mine also is very interested in the system and started to
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simulate how does how do two planets in a disk. So here we have of course this disk again tilted because it's not face on it's like 45 degrees tilted like not like this but like
26:20
this. And so he had it face on. This is what his simulation looks like. So there are two planets that these blobs here again as in the simulation. Here we have a close up. You can actually see this little boxes are actually our simulation boxes in which we have our
26:41
densities. And then he just looked at how the planets would change the structure in the gas and also how the gas would interact with the planets shifting them around. And it's interesting. So the planets tend to clear out an area open a gap within the disk that block a
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lot of gas around here so you have a brighter ring here again and then clearing out more and more. And at some point in the simulation he saw they get a bit jumpy. So it's very nice.
27:23
You also see that the planets induce in the whole disk some kind of features like like spiral features. And so a single planet will change the symmetry and the appearance of a whole disk. So the reason why the planet is staying
27:41
at this point is that because we are rotating with the planet. So it's actually going around the disk but the like camera is rotating with the planet. So it's staying at the fixed place we put it in. So but there's more because as I
28:01
already said in the Navier-Stokes equation we have a lot of different kinds of physics that we all have to include in our simulations. One of the things of course is we maybe don't have just a star and a disk. We have planets in there and maybe two stars in there and all of these larger bodies have also an interaction
28:21
between each other. So if we have a star every planet will have an interaction with a star of course. But then also the planets between each other they have also an interaction right. So in the end you have to take into account all of
28:42
these these interactions. And then also we have accretion just looking like this. So accretion means that the gas is bound by some objects. It can be the disk the planet or the star that
29:02
takes up the mass the dust or the gas and bounce it to this object. And then it's lost to the disk or the other structures because it's completely bound to that. So the principle of this would be a simulation I did last year
29:24
and published. We have here a binary star. So these two dots are stars. I kind of kept them in the same spot. But every picture will be one orbit of this binary. But since we
29:41
have interactions you actually see them rotating because of the interactions which is other. And then also we have here a planet and here a planet. And the interesting thing was that these two planets interact in such a way that they end up on exactly the same orbit. So one
30:00
star further out the orange one and then very fast they go in and they end up on exactly the same orbit if it now would play nicely. OK. So another thing is with the accretion
30:27
here we actually see clouds from above dropping down onto the new forming star here. So all of this what you see here would be gas,
30:40
hydrogen. And it's a very early phase so that this is not completely flat. It has a lot of material and then you actually have this info from above towards the star and then the star keeps the mass. And we have to take this also into account in our simulations. Another
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thing we have to take into account up till now we just cared about masses and densities but of course what we actually see is that stars are kind of warm hopefully otherwise temperatures here would also not be nice. And different chemicals
31:22
have different condensation points. And this is also true in a system. So we start with the star temperature at the surface of the star we have a temperature around 4000 Kelvin. And then we go a bit into the disk and there is a point
31:42
where we for the first time reach a point where we have any material at all because it starts to condensate and we actually have something solid like iron for example at 1500 Kelvin. And then if we go further in we reach a point where we have solid water and this is at 200 Kelvin.
32:05
This is what we then would need actually to have a planet that also has water on it because if we don't get the water in the solid state it will not fall onto a terrestrial planet and be bound there. Right. So this is important for
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our earth actually. And then if we go even further out we have also other gases condensating to solids like CO2 or methane or things like that. And since we only get water on a planet when we have a temperature that is low enough so
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that the water actually forms a solid it's important for us to think about where that is in our forming disk. Where do we start to have a planet like Earth that could have some water. Right. But it's not just the simple
33:01
picture where we have all these nice ring structures where we have a clear line actually. It gets more complicated because we have pressure and shocks and thermodynamics is a lot like pogo dancing right. You crash into each other and it's all about collisions. So the gas
33:22
temperature is determined by the speed of your gas molecules like here bouncing and crashing into each other exchanging momentum. So there's two ways to heat up such dance. First thing is you get a large amount of velocity from the
33:41
outside like a huge kick a shock into your system. A second way would be if we have a higher pressure like more molecules then also you of course have more collisions and then a higher temperature. So if you change because you have a planet now in the system the pressure at
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some point you actually get a higher temperature. So that is not then we lose this nice line because suddenly we have different different pressures at different locations. And a
34:22
it starts all night. So this is the initial condition. We just assumed OK if we have no disturbance whatsoever we have our nice planet here at one a you so same distance as Earth to the sun and here too. But here we assume that less and less heat gets transferred from
34:44
the surface of the disk. And here we have a planet far out like Jupiter or something. And now we actually let this planet change the structure of the disk. And what happens is we found these spirals and within the spirals we
35:01
change pressure. And with this actually if you see this orange everywhere where it's orange it's hotter than the ice line. So we don't have water where it's orange and where it's blue we can have water. And the interesting thing is even if we put a planet out here like Jupiter we
35:22
still form this regions in the inner system where we have less water. And one problem in astrophysical simulations is that we don't always know how to how to shape our boxes or
35:41
how to or how how small these boxes have to be. So we use a trick to reshape the boxes as we need them. It's called adaptive mesh and this is a simulation of the red fluid flowing in this direction and the blue fluid in the other one. So at the boundary the two
36:03
fluids shear and they mix up somehow and we don't know how in advance. So we start a simulation and as the simulation starts we reshape those boxes here. So in the middle we don't need much reshape because it's not that
36:22
complicated here it's just the flow. But at the boundary we see those mixing up of the two fluids. And so we reshape the cells as we need them. This is done in some in a program in
36:41
an astrophysical program called a repo. We will later show you some more programs to use for simulations. But another simulation I want to show you first is also done with a repo and it's a simulation of the universe. So from here
37:01
to here it's very big. It's 30 million light years. So each of these dots you see here is the size of a galaxy or even more. And here you can actually see that at some regions it's very empty. So we're rotating around this universe the simulated universe here and these
37:23
regions here are empty and we don't need a lot of boxes there. The big boxes are enough here. But in this dense regions where we have a lot of material we need smaller boxes. And this is this method I showed you where we reshape the
37:41
boxes as we need them is used for this simulation. So actually you see it's all the beginning of the universe. Basically the initial mask collapsing to the first galaxies and first supernovae starting. Very beautiful
38:06
simulation. So there are different programs as I already mentioned in astrophysics. Three of
38:20
those three are all open source. So you can download them and use them on your own machine if you like. And that there are more a lot more. Some of them open source some of them are not. Sometimes it's hard to get them. We will in the following we will present the two Fargo 3D and Pluto in a detailed version or
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more detailed version than a repo because yeah we usually yeah we usually use those two for our simulations. What I want to show you with this slide is that it depending on what you want to simulate you need to choose a
39:02
different program. And one thing is that in astrophysics we sometimes call the whole program code. So if I use the word code sorry about that. It's I mean the whole program. So let's have a look at Fargo 3D. It's a
39:21
hydrodynamics code. And what you see here is an input parameter file. There you define how the disk looks like. What how much mass does it have. How big is it. And what planet. So here at Jupiter. Do you see that. Jupiter is put in. And we also define how our how big
39:45
our boxes are. This program is written in C which is quite nice because a lot of astrophysical programs are still written in Fortran. So this is good for me because I don't know any Fortran. We can run this. And what's typical
40:06
for Fargo so that's a compilation. Actually on my computer so I don't need a fancy computer I just did it on my small laptop. And now we run it. And now typical for Fargo as you will see
40:21
are a lot of dots. So here it will print out a lot of dots. And it will create at certain times some outputs. And these outputs are huge files containing numbers. So if you look at them they are not really interesting. They just are numbers in something like a text file. So a big
40:44
part of astrophysics is also to visualize the data not only to create it but also to make images so that we can make movies out of them. For that I prefer to use Python but there are a lot of tools and Python Matplotlib but there are a lot of different
41:02
tools to to visualize the data. So this is actually that output that first one we just saw. The Jupiter planet in the disk that I defined in this parameter file. And it's already started to do some spirals. And if I would
41:21
have let it run further then the spirals were more prominent. And yeah. Now we have a planet here on our computer. So we also have
41:44
Pluto. Pluto somehow has a bit more set up files. So what I need is three files here. Looks a bit complicated to break it down. This file defines my grid and initial values and the simulation time here. We input
42:02
actually what physics do we want to need. What is our coordinate system. So do we want to have a disk or just like spherical boxes or like squared boxes. And how is the time defined. And here we then actually write a bit
42:22
of code to say OK now how do I want a gravitational potential. So what's the source of gravity or what will happen at the inner region where we have this dark spot. We have somehow to define what happens if gas reaches
42:40
this boundary. Is it just falling in. Is it bouncing back or something. Or is it looping through the one end to the next. And this is also something we then just have to code in. And if we then make it and let it run it looks like this. So again our
43:02
nice thing we hopefully put in or wanted to put in. The time steps. What our boundaries were. Parameters of physics. Hopefully the right ones. And then nicely we start with our time steps. And if we see this it's hooray it
43:21
worked actually because it's actually not quite simple usually to set up a running program a running problem because you have to really think about what should be the physics. What's the scale of your problem. What's the time scale of your problem. And specify this in a
43:40
good way. But in principle this is how it works. There are a few test problems if you actually want to play around with this to make it easy for the beginning. And this is how we do simulations. So as I already said we can just start them on our laptop. So here this is my laptop. I just type dot slash Fargo
44:04
3D and it should run right. And then I just wait for 10 years to finish the simulations of 500 time steps or something like 500 outputs. Well that's not the best idea. So we need more power. And both of us for example are
44:24
using a cluster for Baden-Württemberg and that takes down our computation time by a lot. Usually like a factor of maybe 20 which is a lot.
44:41
So I would need on my computer maybe a year and then I just need maybe five hours a few days or a week on this cluster which is usually the simulation time about a week for me. So what you see here is that we use GPUs.
45:01
Yes but we do not or mostly not use them for gaming. We use them for actual science. Yeah it would be nice to play on that right. But yeah that just just said. So back to our Earth actually. So can we
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now we wanted to grow our own planet. We can do that. Yes of course. Can we grow Earth. Well Earth is a very special planet. We have a very nice temperature here right. And we have not a crushing atmosphere like Jupiter like a huge planet that we could not live under. We have a
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magnetic field that shields us from the radiation from space and we have water but just enough water so that we still have land on this planet where we can live on. So even if we fine tune our simulations the probability that
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we actually hit Earth and have all the parameters right is actually tiny. It's not that easy to simulate an Earth. So and there are a lot of open questions too. How did we actually manage to get just this sip of water on our surface. How did we manage to collide
46:23
enough mass or aggregate enough mass to form this terrestrial planet without Jupiter sweeping at all the mass in our system. How could we be stable in this orbit when there are seven other planets swirling around and interacting
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with us. All of this is open in our field of research actually and not completely understood. This is the reason why we still need to do astrophysics and even in all our simulations there is no planet B and the Earth is quite unique and perfect for human life. So please
47:03
take care of the Earth and take care of yourself and of all the others people on the Congress. And thank you for listening and thank you to everyone who helped us make this possible and to the people who actually coded our programs with which we simulate. Thank you.
47:37
Thank you for the beautiful talk and for the message at the end. The paper is open for
47:43
discussion. So if you guys have any questions please come to the microphones. I'm asking my signal angel. No questions right now but microphone 2 please. Thank you very much. Very beautiful talk. I can agree. I have
48:02
two questions. The first is you showed you are using Navier-Stokes equation but you have on the one hand you have the dust disk and on the other hand you have solid planets in it. And so are you using the same description for both or is it a hybrid. It very much depends
48:20
like this is one of the things I showed you that for Pluto we write this C file that specifies some things and about every physicist has somewhat his or her own version of things. And so some usually the planets if they are large they will be put in as a gravity source and
48:45
possibly one that can accrete and pebbles are usually then put in in a different way. However also pebbles are at the moment a bit complicated. There are special groups specializing in understanding pebbles because as we said in
49:02
the beginning when they collide usually they should be destroyed. If you hit two rocks very hard together or two rocks together they don't stick. If you hit them hard together they splatter around and we don't get up with bigger objects. Just to explain pebbles are small rocks or like big sandstones or something like that.
49:24
Yeah. So bigger bigger rocks but not very big yet. So yes. So it depends on which code you use. Yes. Very short maybe one. Do you also need to include relativistic effects or is that completely out.
49:41
It's a good question. Mostly if you have this solar type system you're in a range where this is not necessary. For example with the binaries if they get very close together then at the inner part of this that is something we could
50:02
consider and actually I know for Pluto it has modules to include relativistic physics too. Yes. Thank you. OK. We have quite some questions so keep them short. Number one please. Thank you. Yeah. Thank you very much for your
50:20
interesting talk. I think you had it on your very first slide that about 70 percent of the universe consists of dark matter and energy. Is that somehow considered in your simulations or do you handle this. Well in the simulations we make we are doing
50:41
planets and disks around stars. It's not considered there. In this simulation we showed you about the universe. At the beginning the bluish things were all dark matter so that was included in there. OK. Thank you. OK. Microphone three. Hi. Thanks. Sorry. I think you talked about
51:01
three different programs. I think Pluto Fargo 3D and a third one. I was wondering say you're a complete beginner. Which program would you suggest is like you more use like if you want to learn more which one is user friendly or good. I would suggest Fargo first. It's kind of user friendly has somewhat good support and they are always also always very thankful for
51:23
actual comments and additions if people actually are engaged in trying to improve on that because we are physicists we're not perfect programmers and we're all so happy to learn more. So yeah Fargo I would I would suggest it has some easy ways of testing some
51:42
systems and getting something done. And it also has a very good documentation and also and yeah a manual how to make the first steps on the Internet so you can look that up. Awesome. Thank you. Let's get one question from outside from my signal angel.
52:01
Thank you for your talk. And there's one question from ISC. How do you know your model is good and when you can only observe snapshots. That's a good question. We have to as we said we're in theoretical astrophysics so there are theoretical models and these models cannot include everything
52:24
so every single process it's not possible because then we would calculate for years and yeah to know if a model is good you have to So usually you have a hypothesis or an
52:44
observation that you somehow want to understand with most of the necessary physics at this stage to reproduce this image. So also from the observation we have to take
53:00
into account what our parameters kind of should be how dense the end of the simulation should be and things like this. So by comparing to observations that's the best measure we can get if we kind of agree. Of course if we do
53:20
something completely wrong then it will just blow up or we will get a horribly high density. So this is how we know it's physics will just go crazy if we do two large mistakes. Otherwise we would try to compare two observations that it actually is sensible what we did.
53:40
Yeah that's one of the most complicated tasks to include just enough physics that the system is represented in a good enough way but not yeah so but not too much that our simulation would blow up in time. Number two please. I've got a question about the adapted grids.
54:02
How does the computer decide how to adapt the grid because the data where the high density comes after making the grid. This is actually quite an interesting and also not quite easy to answer question. Let me try
54:23
to give a break down nutshell answer here. The thing is you measure and evaluate the velocities or in the flux you also evaluate the velocity and if the velocity goes high you know
54:41
there's a lot happening so we need a smaller grid than there. So we try to create more grid cells where we have a higher velocity. In a nutshell this is of course in an algorithm bit harder to actually achieve. But this is the idea. We measure the velocities at each point and then if we measure a high velocity we
55:02
change to a smaller grid. So you can predict where the mass will go and where the densities are getting high. Exactly. Step by step. So to say. Thanks. We stay with microphone two. Okay I've got a bit of a classical question. So I guess a lot relies on your initial
55:21
conditions and I have two questions related to that. So first I guess they are inspired by observations. What are the uncertainties that you have and be them. What is the impact if you change your initial conditions like the density in the disk. Yeah I'm right now. My main
55:40
research is actually figuring out sensible initial conditions or parameters for a disk. If you just let it have an initial set of conditions and a sensible set of parameters and let it run very long. You expect a system hopefully to converge to the state that it should
56:02
be in. But your parameters are of course very important. And here we go back to what we can actually understand from observations and what we need for example is the density for example and that is something we try to estimate from the light we see in these disks that you saw
56:24
in this nice grid with all these disks we estimate OK what's the average light there. What should then be the average densities of dust and gas in comparable disks. OK. Thanks.
56:41
OK. One more at number two. Yes. Thank you for the talk. When you increase the detail on the grid and you learn more. You have to when you want to compute the gravitational force in one cell you have to sum all the masses from all
57:03
the other cells. So the complexity of the calculus grows quite practically at the square of the. How do you solve that. Or just put more CPUs. Well that would be one way to do that. But there are ways to simplify if you
57:21
have a lot of particles in one direction and they are far away from the object you're looking at. So. Yeah. So if you have several balls here and one ball here then you can include all these balls or you can you can think of them as one ball. So it
57:42
depends on you look at. So how you define how many particles you can take together is when you look at the angle of this. Yeah. The the big or the many particles will
58:00
have from seen from the object you're looking at. And you can define a critical angle and if it's if an object gets smaller than this or if a lot of objects get smaller than this angle you can just say OK that's one object. So that's a way to simplify this method. And there are some. Yeah I think that's the main
58:22
idea. OK. We have another one. Do you have a strategy to check if the simulation will give a valuable solution or does it happen a lot that you wait one week for the calculation and find out OK it's total crash that trash or it crashed in the time.
58:43
So that also depends on the program you're using. So in Fargo it gives this output after a certain amount of calculation steps and you can already look at those outputs before the simulation is finished. So that
59:00
would be a way to control if it's really working. Yeah. But I think it's the same for Pluto. So you get every you set. There's a difference between time steps and actually output steps. So and you could define your output steps not as the whole simulation but
59:22
you can look at each output step as soon as it's produced. So I usually get like 500 outputs but I already can look at the first and second after maybe half an hour or something like that. Yeah but it also happens that you start a simulation and wait and
59:42
wait and wait and then see you put something wrong in there and well then you have to do it again. So this happens as well. Thanks. OK. One final question. Yeah. OK. Is there a program in which you can calculate it.
01:00:00
so that you don't have the starting conditions, but the ending conditions and you can calculate how it had started? Not for hydrodynamics. If you go to n-body there is a way to go backwards in time but for hydrodynamics the thing is that you have turbulent, almost like chaotic conditions
01:00:28
so you cannot really turn them back in time with n-body, because actually it's not analytically solved
01:00:40
but it's much closer than turbulences, streams, spirals and all the things you saw in the simulations. Okay, I guess that brings us to the end of the talk and of the session. Thank you for the discussion and of course thank you guys for the presentation.