[00:02.280 --> 00:04.280]  Okay, welcome everybody to my talk.
[00:04.920 --> 00:06.500]  My name is Mark Vogelsberger.
[00:06.860 --> 00:09.700]  I'm a PhD student of astrophysics in Germany.
[00:10.760 --> 00:15.340]  And my talk will be a bit different from the other talks in the morning in this room.
[00:15.700 --> 00:19.500]  So actually I'm not talking about hacking computers, Pantrusting and stuff like this.
[00:20.220 --> 00:22.400]  But I'm talking about, so to speak, hacking the universe.
[00:23.020 --> 00:31.580]  So what we are trying to do is understand how the universe was created, how the structures, the galaxies and all these things come up.
[00:32.820 --> 00:35.120]  So this is what I'm mainly doing during my PhD.
[00:35.800 --> 00:46.980]  And I will try to give you some insights into this business, how we do this, why we do this, and how we run currently the largest simulations worldwide to answer these questions.
[00:48.240 --> 00:50.900]  So this is more or less an overview of my talk.
[00:51.180 --> 00:53.580]  So the goal is to create some kind of matrix of the universe.
[00:53.580 --> 01:04.380]  So I will first show you some kind of motivation, then show you results of very recently finished very, very large simulations, currently the world's largest simulations.
[01:04.760 --> 01:15.520]  Then I will show you the scientific output we get from these simulations and in the end give a quite detailed explanation of the methods, the numerical methods we use to do these simulations.
[01:17.000 --> 01:21.220]  So first of all, let me introduce the playground we are working on.
[01:21.220 --> 01:24.740]  So the playground is you are all used to the Earth.
[01:25.180 --> 01:28.600]  This has a size of about 12,000 kilometers in diameter.
[01:29.040 --> 01:31.380]  So these are the typical scales we are used to.
[01:32.180 --> 01:35.300]  But the Earth itself is embedded in the solar system.
[01:36.040 --> 01:38.440]  So this is already a size of 6 billion kilometers.
[01:38.940 --> 01:41.760]  And you see all the planets there with the sun in the center.
[01:42.140 --> 01:44.480]  And the Earth actually is only a very small planet.
[01:45.760 --> 01:56.560]  So if you take the time that light needs to travel from the sun to the outer edge of the solar system, this takes the light already 5.5 hours to travel this distance.
[01:57.200 --> 02:00.880]  The light traveling from the sun to the Earth takes about eight minutes.
[02:01.240 --> 02:02.740]  So this is already a lot larger.
[02:02.940 --> 02:09.580]  And currently some spacecrafts and so on can reach the outer edge of the solar system.
[02:09.580 --> 02:14.440]  So this is the limit where we can get currently, like the Voyager, just to approach the outer edge.
[02:16.180 --> 02:21.280]  So then if you look at the sky, you actually see this bright stripe of stars that's the Milky Way.
[02:21.580 --> 02:25.960]  So the Milky Way is the galaxy where the solar system and the Earth is embedded in.
[02:26.240 --> 02:30.560]  And if you look at this schematically, so the Milky Way is one of these spiral galaxies.
[02:31.300 --> 02:36.800]  And the sun is just one of a million stars in this Milky Way.
[02:38.320 --> 02:41.040]  So then you can go to even larger scales.
[02:41.320 --> 02:44.200]  So this is then the so-called local group.
[02:44.480 --> 02:49.800]  So the Milky Way as a galaxy itself is again embedded in a whole group of different galaxies.
[02:50.440 --> 02:53.740]  So there's also the very well-known Andromeda galaxy in it.
[02:53.860 --> 02:56.540]  That is also quite large, comparable to the Milky Way.
[02:56.660 --> 02:59.400]  And lots of other dwarf galaxies, these are very small things.
[03:00.640 --> 03:05.480]  But then there's even... so this is for example a picture of Andromeda that is also a spiral galaxy.
[03:06.400 --> 03:08.200]  But then there are even larger scales.
[03:08.700 --> 03:14.480]  So all galaxies, all groups of galaxies are again arranged in so-called superclusters.
[03:15.200 --> 03:19.400]  So this is now a very large scale already and you can see different bright things.
[03:19.520 --> 03:23.140]  These are places where galaxy clusters actually cluster.
[03:23.380 --> 03:25.140]  And these are called superclusters.
[03:26.120 --> 03:28.680]  And then you can go to the whole visible universe.
[03:28.680 --> 03:31.320]  So to everything we see today.
[03:31.940 --> 03:36.980]  And this accounts for about three times ten to the twenty-two stars.
[03:37.660 --> 03:40.840]  So this is three with twenty-two zeros.
[03:41.160 --> 03:42.100]  So this is quite a large number.
[03:42.260 --> 03:44.420]  And this is the whole visible universe we see today.
[03:45.480 --> 03:49.580]  Now the question is where does all this structure come from?
[03:49.720 --> 03:51.040]  Where do the galaxies come from?
[03:51.040 --> 03:55.340]  Where does this grouping of galaxies in small groups and in superclusters?
[03:55.440 --> 03:56.760]  And where does all this structure come from?
[03:57.020 --> 04:01.020]  And this is the whole science of so-called structure formation.
[04:01.280 --> 04:09.240]  Where people from cosmology and physics try to understand how from the beginning of the universe to today all this structure actually...
[04:09.240 --> 04:12.820]  So today we have some kind of standard picture of structure formation.
[04:13.220 --> 04:16.780]  Where everything started with a big bang as most of you might know.
[04:17.660 --> 04:20.240]  And then the universe expands from this big bang.
[04:21.160 --> 04:26.380]  And in the beginning there was a phase called inflation.
[04:26.820 --> 04:28.420]  Where the universe expands very rapidly.
[04:28.880 --> 04:29.740]  A lot faster than today.
[04:30.500 --> 04:37.460]  And during this phase small fluctuations in the density and the mass density were imprinted in the universe.
[04:37.660 --> 04:39.600]  So you have regions where you have more mass.
[04:39.740 --> 04:43.140]  And you have regions where you have less mass at different places in the universe.
[04:43.140 --> 04:48.180]  And these are, so to speak, the initial conditions of the structures.
[04:48.440 --> 04:50.920]  So you have these small density perturbations.
[04:51.160 --> 04:54.960]  And then the universe evolved for about 30 billion years.
[04:55.140 --> 04:57.120]  And built up all the structures from this.
[04:57.660 --> 05:07.560]  And it's actually quite nice that today we have satellites in orbit that can observe the universe at an age where it was only 400,000 years old.
[05:07.560 --> 05:14.980]  And this is actually the universe at its earliest time that we can observe today.
[05:15.340 --> 05:18.020]  And you see these different colors there.
[05:18.320 --> 05:22.700]  This is actually the density fluctuation I was speaking about.
[05:22.840 --> 05:26.580]  So from this different colors all the structure we see today.
[05:26.660 --> 05:29.640]  The earth, humans, everything just evolved.
[05:30.100 --> 05:36.760]  So then the question is the structure at the beginning of the universe where the universe was only 400,000 years old.
[05:36.760 --> 05:38.600]  Then put this into a computer.
[05:39.300 --> 05:41.980]  And then develop some models how the universe should evolve.
[05:42.600 --> 05:45.000]  Can we then create a universe that looks like ours today?
[05:45.560 --> 05:48.440]  So if we can do this, then we know that our models are correct.
[05:48.720 --> 05:51.800]  Then we understand how the universe more or less evolves.
[05:52.180 --> 05:56.200]  If we get a very different result at the end of the simulation, then we know that something was wrong.
[05:56.400 --> 05:57.760]  So our model was incorrect.
[05:58.580 --> 05:59.820]  So we have to fine tune it.
[06:00.020 --> 06:02.960]  So this is the whole idea of the structure formation simulations.
[06:04.760 --> 06:10.080]  So the key question is, can we create such a virtual universe with these initial conditions?
[06:11.720 --> 06:16.060]  And to run these simulations, you have to account for a very important fact.
[06:16.440 --> 06:28.100]  So everything you are used to, like the earth, the wood, and all these things, and ourselves, we only account for about 4% of the total energy content in the universe.
[06:29.220 --> 06:33.240]  So about 73% of the universe are made up of dark energy.
[06:33.520 --> 06:37.520]  So this is a form of energy, no one currently knows what it is.
[06:37.660 --> 06:39.440]  But we know for sure that it is there.
[06:39.600 --> 06:41.840]  And it makes about 73%.
[06:41.840 --> 06:44.940]  And another large component is so-called dark matter.
[06:44.940 --> 06:49.180]  This is a form of matter that also nobody knows what it is.
[06:49.380 --> 06:50.580]  But we know that it is there.
[06:51.440 --> 06:58.040]  And you see that in total both of them account for 96% and only 4% are left for the usual things we are used to.
[06:58.240 --> 07:00.520]  Like the planets and the stars and these things.
[07:01.180 --> 07:09.620]  So if you want to run simulations to understand the universe, you are mainly concerned about simulating the dark energy and simulating the dark matter.
[07:09.620 --> 07:14.680]  Because all the other things, these 4%, doesn't influence much the behavior of the universe.
[07:15.460 --> 07:19.220]  So the main influence for structure formation comes, for example, from the dark matter.
[07:19.660 --> 07:23.060]  So you have to simulate with a computer how the dark matter evolves.
[07:23.960 --> 07:27.060]  So this sounds a bit complicated because we do not know what dark matter is.
[07:27.180 --> 07:28.500]  And we do not know what dark energy is.
[07:28.600 --> 07:30.160]  So how can you simulate this with a computer?
[07:30.660 --> 07:34.160]  So you have to make some assumptions how these things behave.
[07:34.940 --> 07:42.980]  And then you just put this in a computer, run the simulation, and look at the end whether it fits the observation of the universe, whether it looks like ours.
[07:43.320 --> 07:50.780]  If this is the case, then you seem to be in the good fight and have guessed the correct conditions for these dark matter and dark energy.
[07:51.000 --> 07:54.480]  So you have to imagine we do not know what it is made of, but we know how it more or less behaves.
[07:55.640 --> 07:56.680]  So this is the thing.
[07:56.820 --> 07:59.940]  It is like you know how a person behaves, but you do not know its name.
[08:00.140 --> 08:01.320]  So it is something like this.
[08:02.980 --> 08:09.780]  So this is... so the simulations I will show you in the next slides are mainly dealing with the dark energy and the dark matter.
[08:09.940 --> 08:14.660]  So we don't... in these simulations we do not simulate this 4%.
[08:14.660 --> 08:16.580]  We only simulate the dark matter and the dark energy.
[08:18.040 --> 08:24.900]  So in one of the biggest simulations that was ever done for this dark matter and dark energy is the so-called millennium run.
[08:25.140 --> 08:29.660]  This is a simulation that was finished now already four or five years ago.
[08:29.660 --> 08:33.780]  So it's a quite old one, but for a long time it was the biggest simulation ever done.
[08:35.420 --> 08:43.460]  So what you do is you simulate this dark matter and the colors, this pattern you see there, this is actually only dark matter.
[08:43.760 --> 08:48.900]  So this filamentary structure and this web structure is pure dark matter.
[08:50.160 --> 08:55.180]  So you have to imagine any slides I show you now is only dark matter.
[08:55.180 --> 09:00.940]  So you cannot observe this because as the name says, we cannot observe dark matter because it does not interact with light.
[09:01.120 --> 09:03.080]  But the simulations tell you how it behaves.
[09:03.560 --> 09:11.200]  So what you can then do, you run the simulation and then you can zoom in to see the structure.
[09:11.380 --> 09:16.880]  So this is now a zoom in in this millennium simulation where we focus on one very massive dark matter structure.
[09:17.840 --> 09:21.820]  So on these bars there always show the length scales in parsec.
[09:21.820 --> 09:23.680]  So one parsec is about three light years.
[09:24.060 --> 09:26.240]  So there's a factor of three between light years and parsec.
[09:26.780 --> 09:31.060]  And this is now mega parsec, so million parsecs.
[09:31.140 --> 09:33.860]  And we focus on this very bright structure here.
[09:33.920 --> 09:37.160]  This is a very massive bunch of dark matter, so to speak.
[09:37.840 --> 09:39.760]  And you can see this filamentary structure.
[09:39.960 --> 09:42.500]  So you have sheets and filaments and this is called the cosmic web.
[09:42.680 --> 09:46.140]  And this is a key prediction of this dark matter scenario.
[09:46.640 --> 09:50.800]  that the universe is just arranged in such a web.
[09:50.960 --> 09:57.240]  So you have places where you have these knots, where you have very high concentration, but you have also places where you have nearly nothing, no matter at all.
[09:57.640 --> 09:58.500]  And these are called voids.
[09:58.940 --> 10:00.320]  So this is a typical prediction.
[10:00.940 --> 10:06.600]  So now we zoom in in the structure and you see a whole bunch of small little dots there.
[10:06.600 --> 10:12.660]  And these are so-called... these are all collapsed dark matter objects.
[10:13.120 --> 10:19.040]  Now we zoom out again and we can see again this pattern and the web and all this structure.
[10:21.960 --> 10:26.260]  So as I said, the simulation was finished now four or five years ago by our institute.
[10:26.820 --> 10:30.000]  And you might be interested in how long something like this takes.
[10:30.140 --> 10:33.220]  And actually from today's point of view it doesn't look that impressive.
[10:33.220 --> 10:36.280]  So the machine that was used was the IBM Regatta machine.
[10:36.760 --> 10:40.760]  And to simulate this we needed about one terabyte of RAM.
[10:41.200 --> 10:47.600]  It was running on 512 processors in parallel and took on this machine then 350,000 CPU hours.
[10:48.960 --> 10:52.220]  So from today's point of view, as I told you, it doesn't look that impressive anymore.
[10:54.680 --> 10:57.260]  But what's more impressive is a recently finished simulation.
[10:57.460 --> 11:01.220]  So this is actually a simulation called the Aquarius simulation that was finished four weeks ago.
[11:02.100 --> 11:07.740]  And the goal of this simulation is not like for this millennium simulation to simulate a large fraction of the universe.
[11:07.960 --> 11:12.140]  But to focus on one of these very massive clumps where we zoomed in.
[11:12.660 --> 11:17.180]  So what we did is we only focused the simulation on this very massive thing.
[11:17.760 --> 11:23.640]  And then sampled this with a very high resolution to see very fine effects on the structure.
[11:24.300 --> 11:26.900]  So this simulation was already a lot more complicated.
[11:26.900 --> 11:29.800]  So actually it took about 4 million CPU hours.
[11:31.080 --> 11:34.140]  And only the output of the simulation was about 50 terabyte.
[11:35.380 --> 11:39.820]  And we were running this at this time when it was running on a top 10 machine.
[11:41.480 --> 11:45.220]  So I can show you here how the structure evolves, if this works.
[11:46.500 --> 11:50.660]  So this is how the structure evolves from the beginning of the universe.
[11:50.660 --> 11:57.920]  So we picked this structure in a way that it looks at the end today more or less like a Milky Way dark matter halo.
[11:58.420 --> 12:05.100]  So you have to imagine that the Milky Way galaxy, the stars and everything, is embedded in a halo of dark matter.
[12:05.300 --> 12:12.660]  And this shows you how for the Milky Way such a halo evolves from time zero, the beginning of the universe, to today.
[12:13.460 --> 12:16.320]  So in the upper right you see the time in giga years.
[12:16.920 --> 12:20.320]  So the universe today has an age of about 17 giga years.
[12:20.460 --> 12:24.240]  So this runs from zero to 13, sorry, to 13 giga years.
[12:25.160 --> 12:27.060]  And we rotate around the structure.
[12:27.800 --> 12:29.900]  So you might wonder why it doesn't expand.
[12:30.040 --> 12:33.720]  Because I told you in the beginning that the universe expands and you do not see any expansion here.
[12:34.020 --> 12:41.540]  The reason is that for visualization and also for the calculation, what you usually do, you divide out the expansion of the universe.
[12:41.540 --> 12:44.860]  So you can do this and then it's fixed in this coordinate frame.
[12:45.000 --> 12:46.460]  So it has always the same size.
[12:46.660 --> 12:48.180]  And this is why it doesn't expand.
[12:49.040 --> 12:52.940]  So what you can again see is the dark matter and again this filamentary structure.
[12:53.300 --> 13:00.340]  And if you look very precise then you can see how smaller objects fall into this bigger object, this brighter object in the middle.
[13:00.640 --> 13:05.760]  And this is actually the typical way how these dark matter things build up.
[13:05.760 --> 13:13.260]  So they accrete material from the surrounding and smaller things fall in and rise the mass of this object.
[13:13.800 --> 13:17.200]  So now we are already at about 4 giga years.
[13:18.240 --> 13:25.660]  And you have to imagine that every of these small blobs you see, these dots, are collapsed dark matter objects.
[13:25.780 --> 13:27.320]  And they are called also subhalos.
[13:27.740 --> 13:30.800]  So the main object is called halo, dark matter halo.
[13:30.980 --> 13:32.680]  And the smaller objects are called subhalos.
[13:33.080 --> 13:36.760]  And every of these halos has a whole population of these subhalos.
[13:38.820 --> 13:40.940]  So I can make this a bit faster.
[13:41.220 --> 13:42.420]  So we go further.
[13:44.440 --> 13:47.660]  So now you can see that it's also growing in size during time.
[13:48.040 --> 13:52.160]  And at the end of the simulation it will have the correct mass of the Milky Way dark matter halo.
[13:52.160 --> 13:54.440]  So it will have all the correct properties.
[13:54.820 --> 14:01.600]  So this is the way how the dark matter, although we do not know what it is made of, could look like in our Milky Way-like system.
[14:02.820 --> 14:06.320]  So the scale is here again in kiloparsec.
[14:06.500 --> 14:09.020]  So as I said there is a factor 3 between light years.
[14:10.360 --> 14:13.620]  And now we are nearly at the end, as you can see.
[14:14.400 --> 14:19.320]  So at this time the object has all the correct properties of the Milky Way dark matter halo.
[14:21.600 --> 14:24.440]  So this simulation was a bit more complicated to run.
[14:24.740 --> 14:29.640]  So it was actually run on a machine in Germany called the HLRB2.
[14:29.760 --> 14:31.060]  This is an Altex based machine.
[14:31.540 --> 14:34.120]  And you can see the circles there on the Google Maps.
[14:34.420 --> 14:38.560]  So the machine is actually located in a cube of 36 cube meters.
[14:38.920 --> 14:40.480]  So it looks something like this.
[14:42.180 --> 14:45.180]  So you can only enter through the small corridor there.
[14:45.400 --> 14:46.800]  And there the supercomputer sits.
[14:47.260 --> 14:49.900]  And if you go in, then it looks something like this.
[14:50.180 --> 14:51.900]  Like all the supercomputers actually look.
[14:53.540 --> 14:56.100]  So currently it has about 10,000 cores.
[14:56.420 --> 15:02.240]  And when it was built it was, I think, in the top 5 supercomputers worldwide.
[15:02.680 --> 15:09.280]  But since the new list came out in June, it is now only on place 23 or 24, something like this.
[15:10.560 --> 15:12.340]  But it is still a quite fast machine.
[15:12.460 --> 15:14.560]  And we used this machine to do these simulations.
[15:15.960 --> 15:21.940]  And just one word on the size of this all-know Moore's law, how computing power is increasing.
[15:22.480 --> 15:25.660]  And actually this is also true if you look at the quality of the simulation.
[15:25.960 --> 15:31.760]  So the quality of these simulations is given by the number of particles you use to simulate the dark matter.
[15:31.760 --> 15:33.360]  So these are particle-based simulations.
[15:34.420 --> 15:36.560]  So on the y-axis you see the number of particles.
[15:37.140 --> 15:39.860]  And on the x-axis you see just the time.
[15:40.000 --> 15:44.120]  And you can see that in about 17 months the number of particles more or less doubles.
[15:44.940 --> 15:51.760]  So this is a typical trend you also have in other computer science areas.
[15:52.820 --> 15:57.880]  So of course this is not only computing power increase but also better algorithms and all these things.
[15:59.780 --> 16:03.840]  So just to show you some other machines that are used for these kind of simulations.
[16:04.140 --> 16:10.240]  So one machine is the NASA supercomputer called Project Columbia supercomputer.
[16:10.660 --> 16:12.680]  This is one of NASA's fastest machine.
[16:13.040 --> 16:20.760]  And a year ago another research group from Princeton and Santa Cruz actually used this machine to do similar simulations like the Aquarius.
[16:20.760 --> 16:25.120]  And on the lower left you see a machine in Spain, in Barcelona.
[16:25.960 --> 16:29.420]  This is a machine that actually sits in a church.
[16:29.860 --> 16:31.460]  So it's installed in a church.
[16:31.680 --> 16:35.900]  And for a long time it was the fastest machine in Europe.
[16:36.240 --> 16:38.960]  But recently Germany installed a faster machine.
[16:39.720 --> 16:43.520]  So these are all machines that are used for these cosmological supercomputing simulations.
[16:45.860 --> 16:53.620]  So now the question is we run these simulations and we waste millions of CPU hours.
[16:53.720 --> 16:54.680]  So what can you get out of it?
[16:54.760 --> 16:59.780]  I mean I showed you some nice pictures but of course this is no science so you would want to get something out of it.
[17:01.760 --> 17:07.740]  So the key problem with cosmology is it's not like doing material science or engineering or whatever.
[17:07.740 --> 17:09.980]  You cannot do any experience with an object.
[17:10.220 --> 17:12.800]  You cannot do an experiment with the planet, with the sun, with the galaxy.
[17:13.120 --> 17:15.860]  You can only simply observe the things.
[17:16.100 --> 17:19.300]  So to test your models you have to run models.
[17:19.540 --> 17:24.980]  You have to do calculations of your models and then compare to the actual observation.
[17:25.580 --> 17:32.280]  And the only way to do these calculations because they are quite time consuming and complicated is just to run these supercomputing simulations.
[17:32.280 --> 17:35.920]  So the only way to test models is to do these simulations.
[17:40.480 --> 17:47.860]  And what you then can do is you can compare this result of the simulation to the observation and this is shown here.
[17:48.480 --> 17:57.520]  So you do not have to care about the details but this map actually shows the distribution of galaxies around us in a certain range.
[17:57.520 --> 18:04.560]  So every small blue dot on this thing is just a galaxy and you can see they form some kind of structure.
[18:05.240 --> 18:10.480]  So the Earth is in the center and then we look around and then we can see this galaxy structure.
[18:11.100 --> 18:13.580]  And this was done with some kind of telescopes.
[18:14.820 --> 18:18.060]  And then you end up with a structure and then you do the same with the simulation.
[18:18.480 --> 18:23.460]  So now in blue and red you see the result for the simulation and the result for the observation.
[18:24.100 --> 18:33.180]  So the question is now, if you compare these two and nobody tells you what is the real universe and what is the virtual universe, then it's actually hard to distinguish both.
[18:33.420 --> 18:35.940]  So the structure looks more or less the same.
[18:36.140 --> 18:39.020]  If you do statistics on these things, they look more or less the same.
[18:39.440 --> 18:42.660]  If you look at the mass scales and all these things, they also look more or less the same.
[18:42.920 --> 18:58.840]  So this means that with the current models, with the current assumptions we have of the creation of the universe, We actually can, from the Big Bang, or 400,000 years after the Big Bang, create a universe that looks more or less like our universe.
[18:59.120 --> 19:02.120]  So the understanding of this process is quite well today.
[19:02.440 --> 19:09.340]  And actually the supercomputer simulations were a key tool to prove the correctness of these models.
[19:11.680 --> 19:22.480]  Another finding is, that was also only possible with these computer simulations, if you look at the very massive dark matter halos I showed you in the beginning where we zoomed in.
[19:22.940 --> 19:33.100]  If you then look at the mass density, so how the density increases towards the center, then it was a finding of computer simulations that this has a universal shape.
[19:33.720 --> 19:35.440]  This was not known before.
[19:35.640 --> 19:37.900]  You cannot calculate this on a sheet of paper.
[19:38.160 --> 19:40.820]  This was a pure finding of numerical simulations.
[19:41.060 --> 19:47.700]  And the interesting thing is that every structure that forms in the universe has this kind of density profile, every dark matter halo.
[19:48.860 --> 19:51.080]  So this was a finding already ten years ago.
[19:52.540 --> 19:55.020]  And this is for this current simulation we did.
[19:55.180 --> 19:57.580]  So for the zikvarius, the same kind of density profile.
[19:57.720 --> 20:00.820]  So again, we find the same density profile I showed you before.
[20:01.480 --> 20:04.400]  Again, proving that there is a universal density profile.
[20:07.970 --> 20:14.830]  So, I told you that we know that there is dark matter, and we know that there is dark energy, but we do not know what it is composed of.
[20:14.830 --> 20:21.910]  So, for sure, one of the next Nobel Prizes will go to the person that actually discovers dark matter.
[20:22.690 --> 20:31.930]  So the question is how can you discover something that doesn't interact with the light, that doesn't shine, that's just there and only interacts by gravitation.
[20:33.130 --> 20:38.630]  So you have to imagine the Earth and the Milky Way is embedded in a sea of dark matter.
[20:38.890 --> 20:44.130]  So through each of you, in the second, billions and billions of dark matter particles go through you.
[20:44.130 --> 20:46.750]  But we just do not know what it is made of.
[20:46.850 --> 20:50.790]  And you, of course, do not feel because they just interact only very weakly.
[20:51.910 --> 20:54.170]  So the question is how can you detect these things?
[20:54.350 --> 20:55.250]  How can you catch them?
[20:55.690 --> 20:59.070]  And there are actually two schemes possible to detect them.
[20:59.170 --> 21:00.530]  One is based on a direct detection.
[21:00.550 --> 21:12.750]  So this means you build a quite large detector on Earth and then hope that when one particle passes through this detector, that it accidentally just interacts with this detector and you catch this event.
[21:12.750 --> 21:18.090]  So currently there are 25 experiments running worldwide searching for dark matter in this way.
[21:18.510 --> 21:23.670]  Another possibility is what I called shining dark matter.
[21:24.530 --> 21:33.990]  So although dark matter does not shine itself because it doesn't interact with light, there's a possibility that it produces light in a process called annihilation.
[21:33.990 --> 21:45.970]  So all of you knowing Star Trek and these things, they have this, yeah, to get the energy, they use matter, antimatter and then hit them on each other so they get lots of energy out of this.
[21:46.550 --> 21:52.670]  And for dark matter particles, what we currently think, the dark matter particles are the antiparticles to themselves.
[21:52.930 --> 21:58.470]  So if they collide to each other, then they also produce this energy and they radiate away some kind of radiation.
[21:59.410 --> 22:04.870]  And this radiation, in principle, can be observed by satellites that are around the Earth.
[22:05.290 --> 22:16.510]  So the hope is that if this model is correct, if dark matter can annihilate, because it's its own antimatter particle, then probably we can see this.
[22:19.050 --> 22:23.950]  So four weeks ago, NASA actually launched a satellite called GLAST.
[22:24.230 --> 22:25.890]  So this is a gamma ray.
[22:26.130 --> 22:32.350]  So gamma rays are very energetic light, so to speak, like X-rays, only a bit more energetic.
[22:33.430 --> 22:42.050]  So NASA last launched this satellite and the hope is to find with this satellite actually this signature of dark matter.
[22:42.370 --> 22:44.110]  So it was launched now four weeks ago.
[22:44.110 --> 22:47.110]  So currently the calibration and all these things are going on.
[22:47.350 --> 22:55.070]  But as soon as it starts to collect all the radiation it sees, then it could see a map like shown above.
[22:55.330 --> 23:01.070]  So this is a map of how dark matter would shine observed with such a satellite.
[23:01.690 --> 23:09.950]  So the very bright thing in the center is actually the center of this dark matter halo, where most of the mass is just there, so it's brightest.
[23:09.950 --> 23:13.830]  And the other things are quite, you know, are just not that bright.
[23:14.530 --> 23:27.590]  So if the satellite really detects something like this, and you can rule out any other source, then this would immediately prove that there is dark matter and would be quite a big step in science.
[23:27.810 --> 23:33.850]  Because people know about dark matter since 80 years, but it's still not known, so what it actually is made of.
[23:35.730 --> 23:43.710]  So the simulations I showed you so far were only concerned with dark matter, dark energy, and didn't account for anything we are used to.
[23:43.890 --> 23:47.050]  So no stars, no galaxies, and all these things.
[23:47.490 --> 23:51.790]  So these components are called baryonic objects.
[23:52.010 --> 23:55.330]  So baryonic means they are made of normal atoms we are used to.
[23:55.850 --> 23:59.150]  And you can also use these simulations to simulate these objects.
[23:59.410 --> 24:01.890]  So you are not restricted to simulating dark matter only.
[24:03.150 --> 24:06.230]  So you want, for example, to simulate such a spiral galaxy.
[24:06.790 --> 24:07.850]  So how to do this?
[24:08.210 --> 24:11.590]  Or you want to simulate the collision of two spiral galaxies.
[24:11.890 --> 24:21.510]  So this is quite often in the universe that two spiral galaxies, like the Andromeda and the Milky Way, collide each other, and then build a structure that is called a merging object.
[24:21.510 --> 24:24.010]  So these are actually two galaxies that collide.
[24:24.790 --> 24:26.470]  And the question is, can you simulate this?
[24:26.590 --> 24:28.070]  And does it look similar to these pictures?
[24:29.030 --> 24:35.710]  And to do this, the first thing you should care about is, you have to create such a spiral galaxy.
[24:35.870 --> 24:36.530]  And this is shown here.
[24:37.090 --> 24:39.690]  So this is the gas component, so no dark matter anymore.
[24:39.870 --> 24:42.690]  So this is what we really are used to, so normal atoms.
[24:43.710 --> 24:46.430]  This is the gas of a spiral galaxy.
[24:47.230 --> 24:48.790]  You can see the spiral arms.
[24:50.150 --> 24:53.610]  And in the center of this object, there is actually a black hole.
[24:54.550 --> 25:01.410]  So it is today well known that in every galaxy, or nearly every galaxy, you have a very massive black hole in the center.
[25:01.650 --> 25:03.530]  And this is also done in this simulation.
[25:04.830 --> 25:08.990]  So you can see it, it's quite thin if you look edge on it.
[25:09.690 --> 25:14.390]  And then you can also zoom into the...
[25:14.390 --> 25:14.990]  Oh, sorry.
[25:15.830 --> 25:18.610]  You can zoom in to see this black hole region better.
[25:18.830 --> 25:19.270]  So here.
[25:19.770 --> 25:23.130]  So in the center, there is this black hole that works there.
[25:24.370 --> 25:26.230]  And below you again see the scale.
[25:26.370 --> 25:29.350]  It's now quite small scale compared to the things I showed you before.
[25:30.530 --> 25:32.850]  So this would be typical Milky Way, for example.
[25:33.950 --> 25:38.310]  So then the question is, what happens if we collide two of these objects?
[25:38.490 --> 25:41.270]  Does it look the same as the picture I showed you in the beginning?
[25:41.770 --> 25:45.250]  And this series of pictures is actually one of these collisions we did.
[25:45.750 --> 25:48.630]  And you can also look at the movie.
[25:49.630 --> 25:52.990]  So here are the two spiral galaxies that approach each other.
[25:52.990 --> 25:57.330]  So to the upper left you see the time now in mega years.
[25:58.370 --> 25:59.830]  So it's not giga years anymore.
[25:59.990 --> 26:02.170]  It's a comparable short time scale.
[26:02.770 --> 26:05.770]  Then they interact and you can see how the gas gets heated up.
[26:06.350 --> 26:10.730]  And they fly by and build these so-called tidal features.
[26:10.770 --> 26:12.230]  So these arms that you show.
[26:13.210 --> 26:15.330]  And again there are two black holes in the center.
[26:16.850 --> 26:20.790]  So now they are again away from each other and collapse for the second time.
[26:23.110 --> 26:24.250]  So this you see now.
[26:26.950 --> 26:33.930]  And if you look at these pictures and compare it to observations of Hubble Space Telescope or something like this, it looks quite similar.
[26:35.330 --> 26:40.470]  And these effects that you see the gas blowing away is now just a feedback effect of the black holes in these things.
[26:40.630 --> 26:43.390]  So you will see that the object gets totally disrupted in the end.
[26:44.990 --> 26:46.430]  So now they are quite nearby.
[26:47.590 --> 26:50.330]  And now the things just blow away.
[26:52.530 --> 26:56.070]  So this means we can also simulate these objects quite well.
[26:56.250 --> 26:59.650]  And they also quite well agree with the observation.
[26:59.910 --> 27:04.050]  Although these simulations are a lot more complicated to do than the dark matter only simulations.
[27:04.050 --> 27:09.090]  Because the gas physics and this baryonic physics are a lot more complicated actually.
[27:18.340 --> 27:24.240]  So, since I showed you now some of the simulations and some of the results, the question is how do you do this?
[27:24.520 --> 27:26.220]  I mean you have to have a fast computer.
[27:26.580 --> 27:30.020]  But of course you also have to have somebody who writes the code for this.
[27:30.680 --> 27:32.800]  And the codes are quite tricky.
[27:34.080 --> 27:37.860]  And this is why I will focus on one aspect of the programming.
[27:38.080 --> 27:42.800]  Namely on the programming of a code that does the dark matter and dark energy only simulations.
[27:43.120 --> 27:47.220]  So I will not show you how to simulate stars or gas or something like this.
[27:47.220 --> 27:52.880]  But how the Millennium simulation and this Aquarius simulation, how they were done, this I will show you in the next slides.
[27:53.840 --> 28:01.660]  So this is just an overview slide that tells you how or what cosmological simulations currently can do.
[28:02.620 --> 28:04.380]  So there are mainly two parts.
[28:04.620 --> 28:06.260]  On the left hand side there is the gravity.
[28:07.520 --> 28:09.680]  So how things are attracted by gravity.
[28:09.920 --> 28:11.860]  And on the right hand side you see the hydrodynamics.
[28:11.980 --> 28:15.200]  So these are the baryonic components, the stars and the gas.
[28:15.780 --> 28:19.440]  And you can see there are lots of things in this hydrodynamic thing that play a role.
[28:21.200 --> 28:23.860]  And as I told you before this is the more complicated part.
[28:23.980 --> 28:26.360]  So I will focus on the left part of the gravity.
[28:26.920 --> 28:29.240]  Because dark matter only interacts by gravity.
[28:29.240 --> 28:34.200]  So it is in principle quite simple to simulate compared to the gas physics.
[28:37.560 --> 28:39.100]  So how do you do this?
[28:39.380 --> 28:42.840]  You know you have lots of dark matter around you.
[28:43.060 --> 28:45.020]  And now you want to simulate this in the computer.
[28:45.160 --> 28:51.200]  So what you do is you model the dark matter by particles in the simulation.
[28:51.400 --> 28:55.220]  So you have lots of particles and they give you the dark matter density field.
[28:56.880 --> 29:01.560]  And so what you have to do, you have to follow the motion of these particles.
[29:03.000 --> 29:06.300]  And this is then a quite complicated system of equations.
[29:06.820 --> 29:15.640]  Because you have, I mean those of you familiar with time integration and equation of motions, know that this is then a system of three and coupled differential equations.
[29:15.640 --> 29:18.540]  And this makes it a bit complicated.
[29:20.200 --> 29:24.020]  So the code we used for this is our in-house codes.
[29:24.160 --> 29:27.000]  It's the so called gadget code and it's publicly available.
[29:27.780 --> 29:30.000]  So in principle you can download it from this site.
[29:30.180 --> 29:31.380]  And you can play a bit around.
[29:32.100 --> 29:34.820]  So this code was used for this millennium simulation.
[29:34.820 --> 29:37.140]  It was also used for this various simulation.
[29:37.680 --> 29:41.840]  It's a standard C code and has currently about 75,000 lines.
[29:43.680 --> 29:47.300]  And as I told you, these codes run on supercomputers.
[29:47.340 --> 29:48.840]  So you have to parallelize them.
[29:49.020 --> 29:52.160]  And it's just a standard MPI parallelization.
[29:53.860 --> 29:56.200]  And it also needs the FFTW.
[29:56.200 --> 29:59.340]  So this is the library for doing fast Fourier transformations.
[30:00.600 --> 30:01.780]  But this is all you need.
[30:01.780 --> 30:04.100]  And then you can compile it in principle also on your laptop.
[30:04.540 --> 30:06.240]  And play a bit around with it.
[30:08.700 --> 30:12.160]  So I told you that we model the dark matter by these particles.
[30:12.640 --> 30:13.500]  So what you have to do?
[30:13.560 --> 30:16.560]  You have to integrate the equations of motions of the particles.
[30:17.160 --> 30:26.040]  So those of you not familiar with physics can just see these equations as the equations that describe you how a certain particle moves from there to there.
[30:26.680 --> 30:29.880]  So it's just... these equations just tell you how the particles move.
[30:30.820 --> 30:35.180]  So when you have to solve these equations with a computer.
[30:36.080 --> 30:40.420]  And for the experts among you, so you have to be a bit careful.
[30:40.580 --> 30:42.960]  You cannot use the standard Newtonian potential.
[30:43.160 --> 30:45.840]  You have to introduce some kind of what is called softening.
[30:46.520 --> 30:53.340]  And the reason why you have to introduce the softening is because if you do not introduce it, then you do not model the dark matter correctly.
[30:53.340 --> 30:57.240]  So this softening is needed to simulate the dark matter in a way it behaves.
[30:59.020 --> 31:01.800]  So you have to solve these equations.
[31:03.040 --> 31:08.160]  And the problem is that the number of particles you need to do the proper simulation must be very high.
[31:08.620 --> 31:11.360]  So this is the so-called large N problem.
[31:11.940 --> 31:13.960]  And this makes the simulation so expensive.
[31:13.960 --> 31:17.120]  So you cannot do a simulation with 10 or 20 particles.
[31:17.440 --> 31:20.520]  You have to use at least 10 to the 6 or 10 to the 7.
[31:20.700 --> 31:24.120]  So 10 million or even billion particles to get a proper representation.
[31:25.300 --> 31:27.540]  And this makes it quite time consuming.
[31:30.160 --> 31:37.620]  So what you need to do to solve how a particle moves is you have to calculate how the forces on these particles is.
[31:37.620 --> 31:39.900]  So this is shown here.
[31:40.220 --> 31:44.440]  You have one particle, the red one, that is embedded by lots of other particles, the green ones.
[31:44.960 --> 31:48.060]  And now this red one interacts with all the green ones.
[31:49.160 --> 31:52.460]  This gives for N particles then N interactions, for example.
[31:52.920 --> 31:54.880]  But now you go to a different particle.
[31:55.740 --> 31:58.740]  And then again it has N interactions with the other particles.
[31:59.060 --> 32:01.420]  So this gives you in the end an N square problem.
[32:02.160 --> 32:13.500]  Those of you familiar with computer science know that N square problems are quite bad because if you increase the number of particles by a factor of 10, you increase the computing time by a factor of 100.
[32:13.760 --> 32:15.940]  So this is actually not what you want.
[32:16.080 --> 32:18.960]  It's the same like for sorting algorithms.
[32:19.160 --> 32:30.260]  You do not want to sort algorithm that if you want to sort 100 numbers and then want to sort 1,000, you do not want that the algorithm takes 100 times longer for the 1,000 compared to the 100.
[32:30.620 --> 32:33.220]  So the N square scaling is a very bad scaling.
[32:33.220 --> 32:35.700]  So the question is can we get better?
[32:37.000 --> 32:38.460]  And the answer is yes.
[32:38.680 --> 32:43.300]  So there are in principle two different methods to calculate the forces in a more efficient way.
[32:44.260 --> 32:50.200]  So the first way is you use a particle mesh method.
[32:50.500 --> 32:56.460]  So these methods are, for example, very well known for any gas simulations, for example.
[32:56.580 --> 32:58.720]  But you can also apply them to these dark matter simulations.
[32:59.680 --> 33:09.120]  So what you exploit with using this method is actually that the equations for the forces are very simple in Fourier space.
[33:09.660 --> 33:13.000]  So who of you is familiar with Fourier transformation and things like this?
[33:13.400 --> 33:14.060]  Okay.
[33:14.480 --> 33:15.160]  So some.
[33:15.980 --> 33:18.920]  So Fourier space is just... how should I explain?
[33:18.920 --> 33:24.680]  You have a function, for example, f function of the position, f of x.
[33:24.860 --> 33:29.080]  And then you can transform this function in a different function that is then called Fourier space.
[33:29.240 --> 33:32.040]  And it has some different very nice properties in this Fourier space.
[33:32.240 --> 33:36.500]  And what you can do, you can transform the force equations to this Fourier space.
[33:36.800 --> 33:41.260]  And then it can be solved very easily just by this Fourier transformation.
[33:42.100 --> 33:44.380]  And this is actually what is explored in this method.
[33:44.900 --> 33:49.160]  So the only thing you have to do, you have to do a very large, parallel Fourier transformation.
[33:50.280 --> 33:54.980]  So this is the complication, but the method itself is very fast, and this is the pro.
[33:55.440 --> 34:04.340]  But it also has some cons, namely that I showed you in the beginning this movie of the Millennium Simulation when we zoomed in, and you saw that there are lots of different scales.
[34:04.560 --> 34:09.560]  So there are regions where you have nearly no dark matter, and you have regions where you have lots and lots of dark matter.
[34:09.560 --> 34:17.080]  So ideally you want a simulation that has a high resolution in the region where you have lots of things going on, so where it's lots of dark matter.
[34:17.300 --> 34:21.720]  And you want a low resolution, of course, in the regions where just no dark matter is sitting in the voids.
[34:22.240 --> 34:30.380]  And this is a problem with the grid, because if you imagine a regular grid, for example, in two dimensions, then you have the same resolution at each point.
[34:30.580 --> 34:34.760]  So the grid size is always the same at each point, and this means it has the same resolution.
[34:34.760 --> 34:41.740]  So if you want now, at some point, a very high resolution, then you have to increase the size of the grid in total.
[34:42.360 --> 34:50.200]  But those of you who worked with a Fourier transform know that increasing the size of cells in a Fourier transform is quite expensive.
[34:50.380 --> 34:52.720]  So there's a certain natural limit due to computational power.
[34:52.860 --> 34:55.240]  So you cannot increase this infinitely large.
[34:55.740 --> 35:01.680]  So this method, so to speak, lacks the resolution between low resolution and high resolution regions.
[35:01.680 --> 35:06.280]  So you have problems in resolution with this method, although it's quite fast.
[35:07.700 --> 35:12.380]  So the way to come around this, to get the resolution done, is using a different trick.
[35:12.480 --> 35:13.680]  And it's actually quite simple.
[35:14.000 --> 35:21.000]  So if you remember the picture I showed you in the beginning with the red circle and the green ones.
[35:21.500 --> 35:24.480]  So then I showed you that the red interacts with all the green.
[35:25.180 --> 35:30.460]  But what happens if the red one is quite far away from a group of green ones?
[35:30.460 --> 35:36.220]  Then you can just say, okay, these green ones are so far away, I just group them together as one particle.
[35:36.520 --> 35:39.580]  And calculate the force of this group to the red one.
[35:40.120 --> 35:44.300]  So you just make some kind of group building, and then the number of particles, so to speak, reduces.
[35:44.560 --> 35:45.980]  Because you only have to account for the groups.
[35:46.320 --> 35:49.660]  So as soon as particles are far away, you just group them.
[35:50.120 --> 35:55.160]  And then it's a lot... then you do not have to account for n square, but only for n log n.
[35:55.640 --> 35:57.620]  And this is a quite good scaling, n log n.
[35:58.200 --> 36:01.360]  So this is of course not linear, because linear scaling would be n.
[36:01.500 --> 36:04.780]  But you have reduced the n square, at least to this logarithm.
[36:05.160 --> 36:07.080]  So all of you are familiar with the n log n scaling?
[36:07.740 --> 36:08.920]  From sorting algorithms?
[36:10.640 --> 36:11.440]  Who is familiar?
[36:12.140 --> 36:13.240]  Ah, very good.
[36:14.280 --> 36:17.420]  So it's just a better scaling with n than this n square.
[36:18.140 --> 36:20.960]  And these methods are called tree algorithms.
[36:21.300 --> 36:29.260]  And they are called tree algorithms because if you look at the structure, if you group all these particles, then it looks in the end like a tree, something like this.
[36:31.220 --> 36:35.140]  So the best way is just to combine these two methods.
[36:35.320 --> 36:37.220]  So combine the particle mesh with a tree.
[36:37.440 --> 36:40.480]  So you use the tree in the regions where you want to have high resolution.
[36:40.480 --> 36:44.840]  And you use the mesh in the regions where you do not need this high resolution.
[36:45.120 --> 36:49.720]  And this is then called tree PM, so tree particle mesh method.
[36:49.980 --> 36:55.100]  And this is today one of the standard techniques to do these dark matter simulations.
[36:55.400 --> 37:03.380]  So also the millennium and the sigvarius run used exactly more or less this light to calculate the whole dark matter evolution.
[37:04.100 --> 37:07.240]  So it's... you shouldn't try to understand the details.
[37:07.420 --> 37:10.920]  It's just about... you split the force in a short range and a long range.
[37:11.100 --> 37:12.580]  And the short range, you use the tree.
[37:12.920 --> 37:15.060]  And the long range, you use the particle mesh method.
[37:15.380 --> 37:17.480]  And this is quite efficient and quite fast.
[37:18.520 --> 37:21.000]  And it's also quite accurate.
[37:21.340 --> 37:23.960]  So it's currently one of the best ways to do the simulations.
[37:26.560 --> 37:33.360]  Once you have the forces, then you have to think about how to evolve the system forward intentionally.
[37:33.380 --> 37:36.400]  Imagine you now have the force that is acting on a particle.
[37:37.040 --> 37:41.980]  So this force will try to pull the particles, for example, in a certain direction or push it away.
[37:42.200 --> 37:43.300]  Or, you know, pull it.
[37:43.380 --> 37:44.140]  Of course, it's quotation.
[37:44.500 --> 37:45.840]  So pull it in a certain direction.
[37:46.380 --> 37:48.740]  Then this particle will follow this force.
[37:49.640 --> 37:53.620]  So as soon as time goes on, this particle will follow the force and follow and follow.
[37:53.800 --> 37:55.380]  So this is called the time integration.
[37:55.640 --> 38:02.240]  So you have to write the code in a way that as soon as the force acts, it has to move the particle during time.
[38:03.100 --> 38:07.300]  And the time integration is, in this kind of simulation, a quite critical thing.
[38:09.320 --> 38:20.440]  So, those of you who did any kind of numerical integration, so there are different schemes to integrate functions or differential equations, know that there are lots of methods out there.
[38:21.100 --> 38:25.840]  But one method is very well suited for this kind of application.
[38:25.840 --> 38:27.820]  It's the so-called leapfrog scheme.
[38:29.740 --> 38:33.020]  So, the leapfrog scheme is a second-order integrator.
[38:34.180 --> 38:37.500]  And it has the very nice property that it's symplectic.
[38:37.800 --> 38:42.380]  So, what you see here is how the positions are advanced and how the velocities are advanced.
[38:42.500 --> 38:44.660]  So, x is the position and v is the velocity.
[38:45.280 --> 38:48.380]  And you see how they are... and delta t is the time step of the simulation.
[38:48.600 --> 38:53.340]  And you see how the things just get advanced by the scheme.
[38:53.800 --> 38:56.760]  And as I told you, the symplectic property is the most important thing.
[38:56.760 --> 39:02.480]  And symplectic seems to be a quite complicated word, but it's quite easy to understand what it means.
[39:02.760 --> 39:05.520]  So these are two different integrations done here.
[39:06.260 --> 39:16.060]  So the upper two figures are done with a standard integrator that is very often used in numerical science.
[39:16.840 --> 39:25.240]  And you can see the left hand figure shows you the energy of the system, while a particle is orbiting around another particle, and this shows you the energy.
[39:25.820 --> 39:29.900]  So from physics, we know that the energy should be constant over time.
[39:30.120 --> 39:32.760]  This is just a physical law, the law of energy conservation.
[39:33.520 --> 39:38.860]  But you see that the energy drifts in this thing, so this is very bad, because you have energy drift.
[39:39.060 --> 39:41.480]  This is not physical, this is just pure numerical effect.
[39:42.260 --> 39:47.200]  But if you then look to the lower two figures, that is actually where we use the leapfrog.
[39:47.640 --> 39:53.000]  You see that there's no energy shift at all, so there's no secular energy shift.
[39:53.140 --> 39:54.100]  And this is the important thing.
[39:54.100 --> 39:57.280]  So we do not want that the energy of our system gets wrong.
[39:57.400 --> 39:58.860]  We want the whole time the correct energy.
[39:59.040 --> 40:01.440]  And this is why we actually use this algorithm.
[40:04.080 --> 40:07.480]  Okay, and I'll come already to the end of my talk.
[40:08.680 --> 40:11.280]  So I told you that this gadget code is actually freely available.
[40:11.540 --> 40:17.940]  So you could come up with the idea that you want to simulate the universe on your own laptop.
[40:18.200 --> 40:19.720]  So in principle this is possible.
[40:19.720 --> 40:25.860]  Of course you cannot do it with that resolution and with that quality like on the supercomputers.
[40:26.040 --> 40:34.360]  But you can do it more or less exactly the same calculation we did for this millennium or for the sigvarius run using this public available code.
[40:35.540 --> 40:38.760]  So the code comes with some examples.
[40:40.320 --> 40:43.780]  So I showed you for example this pair of colliding galaxies.
[40:44.120 --> 40:45.520]  And this is included in this code.
[40:45.520 --> 40:56.660]  So there's an example initial conditions file and there's an example parameter file and a make file that generates this simulation code and then you can run it on your laptop.
[40:56.920 --> 41:03.860]  And the initial conditions and all the settings they are done in a way that these simulations run within two or three hours on a normal laptop.
[41:05.080 --> 41:08.720]  And then you get the same output more or less what I showed you in the beginning.
[41:08.720 --> 41:12.880]  Of course not that quality, not that nice, but the principle thing works.
[41:13.420 --> 41:18.960]  And there are also some other examples around like the structure formation.
[41:19.180 --> 41:21.460]  Well this was this millennium thing I showed you in the beginning.
[41:21.580 --> 41:24.920]  You can also do such a structure formation simulation, of course a bit smaller.
[41:25.660 --> 41:29.420]  But you can again see the things, how they work.
[41:29.420 --> 41:34.360]  And the good thing is all the examples just can be finished in two or three hours on the laptop.
[41:34.380 --> 41:37.540]  So you do not have to wait for weeks or use a big cluster or whatever.
[41:38.120 --> 41:38.800]  Just things.
[41:39.440 --> 41:45.820]  In case you have access to a big computing cluster, then you can of course also use this code.
[41:45.900 --> 41:50.800]  And it's already parallelized, so it's more or less the standard code we use for the simulations.
[41:50.800 --> 41:55.560]  And then you can also run it on 1024 CPUs or whatever you want.
[41:55.720 --> 41:56.640]  If you have access to it.
[41:57.760 --> 41:58.100]  Okay.
[41:58.740 --> 41:59.700]  So I'm at the end.
[41:59.840 --> 42:01.200]  And we have time for questions I guess.
[42:05.530 --> 42:06.670]  All the listeners!
[42:14.440 --> 42:22.360]  So based on the class code is based on measuring dark matter particle interactions.
[42:22.900 --> 42:23.100]  Right.
[42:23.160 --> 42:25.020]  But you want it exclusively as a collision.
[42:25.400 --> 42:25.740]  Right.
[42:25.900 --> 42:26.380]  This is right.
[42:27.580 --> 42:28.340]  Yeah, right.
[42:28.340 --> 42:34.560]  So in the simulations we consider them as collisionless because the interaction rates are extremely small.
[42:34.860 --> 42:37.060]  So it's extremely seldom that they collide.
[42:37.300 --> 42:39.660]  So in the simulations we do not account for this effect.
[42:40.080 --> 42:49.060]  So actually what we do in the simulations, one particle in the simulation, these green circles for example, is just a whole bunch of dark matter particles.
[42:49.440 --> 42:52.920]  Because in the Milky Way alone we have about 10 to the 80.
[42:53.100 --> 42:56.940]  So this is one with 80 zeros dark matter particles.
[42:56.940 --> 43:02.220]  So the simulation dark matter particles are not... do not correspond to single dark matter particles.
[43:02.540 --> 43:05.420]  So we group them, so to speak, in large groups together.
[43:05.620 --> 43:07.260]  And then we do not account for this.
[43:07.360 --> 43:09.760]  We just assume that these groups then move collisionless.
[43:09.960 --> 43:10.760]  But you're right.
[43:10.760 --> 43:11.240]  Of course.
[43:11.240 --> 43:15.440]  Because if you want to really simulate every dark matter particle then you have also to account for this.
[43:16.240 --> 43:16.600]  But...
[43:16.600 --> 43:16.900]  Okay.
[43:17.500 --> 43:17.740]  Yep.
[43:18.520 --> 43:27.080]  I'm somewhat familiar with the projects that have the large underground collectors looking for neutrinos and looking for dark matter.
[43:27.200 --> 43:32.400]  I guess the question is how do we know if we actually saw one of these things in one of these collectors?
[43:32.940 --> 43:42.060]  I know there's some concern that, for example, we see a flash of light in one of these collectors that it's a proton decay rather than an actual neutrino collision or something like that.
[43:42.620 --> 43:44.640]  How do we actually recognize...
[43:44.640 --> 43:44.900]  Yeah.
[43:46.260 --> 43:48.040]  ...what it is that we're trying to observe?
[43:48.340 --> 43:48.780]  Yeah.
[43:48.880 --> 43:49.820]  That's a good point.
[43:50.060 --> 43:54.580]  I mean, as I told you, there are lots of experiments out that search for dark matter.
[43:54.580 --> 43:59.500]  And what they search for is the interaction of dark matter particle with the material in the detector.
[43:59.800 --> 44:04.120]  And a big problem for these experiments is actually a very big concern is the background.
[44:04.380 --> 44:11.020]  I mean, you have a large background to different other events and you have to exclude all of this to be really sure.
[44:11.920 --> 44:12.360]  So...
[44:12.360 --> 44:19.420]  And another problem what you mentioned is, of course, if something hits the detector, whether you can really know whether this is dark matter or something else.
[44:20.960 --> 44:30.680]  So, people from theory just... from particle physics theory, they just develop some models and say, okay, dark matter should behave like this and this should be its energy.
[44:31.320 --> 44:38.260]  So, you search in the detector for these things and then the range you search is then quite small and restricted by these theories.
[44:38.440 --> 44:44.960]  And then, if it fits in this theoretic model and has the correct properties, then you say it's a dark matter particle.
[44:46.080 --> 44:46.520]  Yeah.
[44:46.520 --> 44:50.240]  Can you talk about the initial state for your simulation?
[44:50.540 --> 44:53.820]  For example, I think your name happens at time zero.
[44:54.060 --> 44:54.240]  Yeah.
[44:54.320 --> 44:59.240]  When your simulation is starting, what is the initial set of distribution?
[45:00.060 --> 45:00.580]  Okay.
[45:01.320 --> 45:06.520]  So, the simulations do not exactly start at the beginning of the universe.
[45:06.680 --> 45:10.000]  They start 400,000 years after this.
[45:10.100 --> 45:11.360]  So, not directly at the Big Bang.
[45:11.360 --> 45:18.840]  And 400,000 years after the Big Bang, this time we still can observe by this satellite.
[45:19.540 --> 45:25.240]  So, we observe this radiation that comes from 400,000 years after the Big Bang.
[45:25.680 --> 45:28.780]  And from this, we construct the initial conditions of our codes.
[45:29.700 --> 45:31.460]  And then we just run this.
[45:31.580 --> 45:34.740]  So, it's not from time zero, but it's from time 400,000 years.
[45:35.440 --> 45:38.160]  Because this, you know, we can still observe this.
[45:38.380 --> 45:42.680]  We know that this is the correct set of initial conditions and we can just calculate forward in time.
[45:42.920 --> 45:50.180]  It's of course true that these simulations then do not tell anything about the time before this 400,000 years.
[45:50.340 --> 45:53.200]  So, we can only calculate this time span.
[45:53.200 --> 45:59.660]  All the things that go on beyond this natural limit, there are lots of speculations out there.
[45:59.920 --> 46:04.440]  So, there are many strange theories like strength theory and all these things you might have heard of.
[46:04.620 --> 46:07.920]  But there is currently no way to observe beyond this limit.
[46:08.200 --> 46:15.660]  And the reason why we cannot observe beyond this limit is, if you look for example at the sun, you actually only observe the surface of the sun.
[46:15.780 --> 46:18.440]  You cannot see from the Earth directly to the center of the sun.
[46:18.440 --> 46:21.880]  And the reason for this is that light just cannot go through the sun.
[46:22.140 --> 46:23.980]  It just... you can only see the surface.
[46:24.480 --> 46:26.580]  You cannot directly observe the center.
[46:26.720 --> 46:28.400]  And it's the same at the beginning of the universe.
[46:28.640 --> 46:29.980]  Everything was extremely hot.
[46:30.180 --> 46:33.920]  So, there's natural border and you cannot look beyond this border.
[46:34.220 --> 46:43.980]  And there are currently plans to find ways to look beyond this border, just way back to the Big Bang.
[46:43.980 --> 46:50.280]  And these methods use spacecrafts that should be used in 10 or 20 years.
[46:50.780 --> 46:52.660]  And they search then for gravitational waves.
[46:53.020 --> 46:58.440]  So, whenever something moves, when you run around or so, you just emit some kinds of waves in spacetime.
[46:58.860 --> 47:01.620]  So, these are gravitational waves that Einstein predicted.
[47:01.880 --> 47:07.800]  And these waves actually can travel back or come back from the Big Bang.
[47:07.800 --> 47:11.720]  So, there we are not limited by this 400,000 years limit.
[47:11.940 --> 47:14.500]  So, then we can really look at the very, very early time.
[47:14.680 --> 47:17.100]  And test all these theories beyond that natural limit.
[47:17.760 --> 47:18.160]  Okay.
[47:18.160 --> 47:21.640]  I was wondering, what happens?
[47:22.400 --> 47:29.240]  Like, how are the gas forces coupled to the dark matter forces that you were on?
[47:29.360 --> 47:31.480]  Like, did you put it in the fine structure of gas?
[47:31.620 --> 47:36.400]  And you put it in the fine structure of star interaction, I guess?
[47:36.760 --> 47:38.360]  How does that influence that?
[47:39.280 --> 47:40.800]  Yeah, that's also a good question.
[47:41.260 --> 47:46.580]  So, the simulations, for example, the Sequoia simulation only accounts for dark matter.
[47:46.580 --> 47:49.420]  It simulates the dark matter component of the Milky Way.
[47:50.680 --> 47:53.600]  So, and I showed you in the beginning that dark matter only accounts for 4%.
[47:54.820 --> 47:58.800]  For, sorry, that baryonic gas and all these things only account for 4%.
[47:58.800 --> 48:04.380]  But at the scales of the Milky Way, you saw the spiral and all this.
[48:04.520 --> 48:05.980]  This becomes important.
[48:06.240 --> 48:10.660]  So, there's gravitational interaction between the dark matter and the gas.
[48:10.940 --> 48:15.100]  So, well, if there's lots of dark matter, then there will also be lots of stars and lots of gas.
[48:15.100 --> 48:16.640]  Because it just attracts everything.
[48:17.700 --> 48:24.080]  So, it's true that current simulations, especially, for example, this Aquarius simulation, are limited by the fact that they cannot...
[48:24.080 --> 48:28.440]  I mean, you cannot simulate gas and dark matter at that resolution currently.
[48:28.660 --> 48:31.400]  This is just impossible because the computers aren't fast enough.
[48:31.600 --> 48:34.880]  But if you want a proper answer, then you should do this.
[48:34.880 --> 48:38.440]  So, this is, so to speak, the follow-up project of this.
[48:38.660 --> 48:44.120]  That some groups already did this, but it's just very expensive from a computational point of view.
[48:44.240 --> 48:47.100]  But you should do this if you want a very precise answer.
[48:47.360 --> 48:47.700]  That's right.
[48:49.060 --> 48:51.860]  I have a question about the supercomputer architecture.
[48:51.860 --> 48:52.840]  Yeah?
[48:53.860 --> 49:02.720]  Is it like the old supercomputers where you gave one instruction that would simultaneously operate on many pieces of data?
[49:04.680 --> 49:14.640]  Sending single instruction or data or using more kind of a purpose force since that's an element that adds to every processor's opportunity.
[49:16.380 --> 49:24.400]  Well, yeah, so the supercomputing simulations use... so what we do is we do a work sharing.
[49:24.660 --> 49:29.580]  So, for each processor, we give it a certain bunch of particles.
[49:29.760 --> 49:33.040]  And for this bunch of particles, it should calculate the gravity among these particles.
[49:33.520 --> 49:39.320]  So, if you have 1,024 processors, and we say, okay, processor 1, please calculate the forces in that group of particles.
[49:39.740 --> 49:42.840]  Processor 10, calculate the forces in that group of particles.
[49:42.840 --> 49:46.580]  And we try to balance the work over all processors.
[49:47.380 --> 49:49.260]  And we also share the memory.
[49:49.480 --> 49:51.040]  So, this is also a shared memory architecture.
[49:51.320 --> 49:59.800]  So, I told you that the Millennium, for example, needed one terabyte of memory, and the Aquarius took about three terabyte of random access memory.
[50:00.060 --> 50:02.140]  So, you have to split this over many processors.
[50:02.460 --> 50:10.340]  So, you split the work, and you split the memory over lots of processors to do these simulations with a MPI standard architecture.
[50:10.340 --> 50:13.880]  So, I'm not sure whether this answers your question in every detail.
[50:15.080 --> 50:16.180]  Final question.
[50:16.620 --> 50:20.880]  Do you assume that the constant of gravity is the same throughout the universe?
[50:21.720 --> 50:22.100]  Yeah.
[50:23.020 --> 50:24.580]  In this simulation, it's assumed.
[50:24.820 --> 50:25.900]  But it's still under discussion.
[50:26.060 --> 50:26.340]  Yeah, right.
[50:26.780 --> 50:35.440]  So, for those of you who don't know, today we know that gravity between two massive bodies acts with a certain force.
[50:35.440 --> 50:41.760]  So, if you have here one kilogram and here one kilogram and one meter distance, then there's a certain strength of force.
[50:41.980 --> 50:48.920]  But it's not clear whether, if you go back five giga years or five billion years, whether this force is the same.
[50:49.100 --> 50:53.420]  So, maybe the gravitational constant that gives you the force changes over time.
[50:53.420 --> 51:00.540]  But I think there were recent results observing spectra very long time ago of some objects.
[51:01.000 --> 51:13.960]  And if you observe spectra, so in light of galaxies, for example, then you can infer that some natural constants are really the same at that time than they are today.
[51:13.960 --> 51:19.240]  And currently, I think there are very strong constraints that they are the same over the history of the universe.
[51:20.200 --> 51:25.440]  So, but for these simulations, we assume that the gravitational constant is constant.
[51:25.720 --> 51:31.160]  But it's also true that there are different simulations who account for change in the gravitational constant.
[51:31.460 --> 51:34.520]  So, people also try this and look how it behaves.
[51:34.740 --> 51:36.420]  But I'm not an expert on this.
[51:37.500 --> 51:38.140]  Okay.
[51:39.680 --> 51:41.020]  So, any other questions?
[51:44.940 --> 51:45.580]  Okay.
[51:48.180 --> 51:51.460]  There are a lot of major structures beyond superclusters.
[51:51.740 --> 51:55.720]  I think still the largest structure that we know of is the Great Wall.
[51:55.920 --> 51:56.220]  Right.
[51:56.420 --> 51:56.500]  Yeah.
[51:57.200 --> 52:01.640]  Have these simulations discovered any higher structure beyond walls?
[52:01.820 --> 52:04.820]  Does this reveal the possibility of any larger structure in the universe?
[52:05.280 --> 52:06.800]  No, as far as I know not.
[52:06.980 --> 52:12.500]  Because the agreement between the simulations and the observation is best at the larger scales.
[52:12.780 --> 52:15.220]  So, and there's nothing discovered beyond this.
[52:15.440 --> 52:20.820]  So, if you look at the very large scales and go to small scales, then the agreement gets, so to speak, worse.
[52:20.960 --> 52:23.360]  So, on the very large scales, the agreement is nearly perfect.
[52:23.540 --> 52:26.320]  But if you go to very small things, then you get discrepancies.
[52:26.500 --> 52:27.960]  But this is related to the other questions.
[52:28.160 --> 52:32.300]  On very small scales, you again have the gas and the stars that play a role.
[52:32.300 --> 52:34.280]  So, this is another point, huh?
[52:36.360 --> 52:38.560]  I'm interested in the gadget code itself.
[52:38.800 --> 52:49.600]  And for owners on home clusters, will the speed picker be exponential or logarithmic if you add more CPUs to your home cluster?
[52:49.860 --> 52:51.340]  Thank you.
[52:51.640 --> 52:52.860]  Oh, that's a good question.
[52:55.880 --> 53:01.880]  Actually, I'm not sure how exactly it's because, you know, I'm not the main author of this code.
[53:02.420 --> 53:03.620]  I haven't mentioned the name.
[53:03.780 --> 53:07.360]  So, he's a staff member of our institute.
[53:07.560 --> 53:09.620]  And he also runs all the simulations.
[53:09.780 --> 53:18.640]  But I know that we had some trouble for this Aquarius simulation where we used also more than 1,000 CPUs because there was a sorting in it.
[53:18.800 --> 53:21.580]  And the sort at some point became problematic.
[53:21.580 --> 53:23.700]  So, it didn't scale that well anymore.
[53:24.700 --> 53:29.960]  But I think... I mean, I cannot tell you about the details and how it's scaling exactly.
[53:30.160 --> 53:34.940]  But, I mean, there's always the concern that it should scale as good as possible, of course.
[53:35.040 --> 53:36.780]  So, I think it's quite optimized.
[53:36.920 --> 53:38.560]  But I cannot tell you any details.
[53:38.780 --> 53:38.860]  Sorry.
[53:39.140 --> 53:40.200]  But you can drop him in the mail.
[53:40.280 --> 53:42.940]  He can tell you any detail about this code.
[53:42.940 --> 53:43.300]  Okay.
[53:43.960 --> 53:44.300]  Thank you.
[53:45.260 --> 53:45.400]  Yep.
[53:45.800 --> 53:50.540]  You said NASA simulated something very similar to your data simulation.
[53:51.200 --> 53:53.720]  And I was wondering how well they correlated it?
[53:54.900 --> 53:56.380]  This is also a good question.
[53:56.680 --> 53:57.960]  So, right.
[53:58.160 --> 54:00.960]  NASA and Princeton and Santa Cruz did a simulation.
[54:00.960 --> 54:05.720]  This is, so to speak, the American part, whereas we have the European part.
[54:06.040 --> 54:10.040]  And their simulation is currently three or four times smaller than our simulation.
[54:10.220 --> 54:15.360]  And the agreement is not that... I mean, it's not a totally disagreement.
[54:15.360 --> 54:18.460]  But there are certain important points where we disagree.
[54:20.980 --> 54:22.780]  And it's not yet figured out.
[54:23.000 --> 54:24.500]  I mean, the general things look the same.
[54:24.500 --> 54:27.940]  But if you look at details, then there are small deviations.
[54:28.120 --> 54:37.340]  And it's, you know, it's not yet figured out whether this is just due to some different kind of numerical methods they use.
[54:37.400 --> 54:42.680]  You have to imagine that for the force and all these things, these in principle are only approximations to the correct physics.
[54:43.320 --> 54:46.720]  Because you group the particles together as one very heavy particles.
[54:46.920 --> 54:49.300]  And also the time integration introduce problems.
[54:49.300 --> 54:56.640]  So, it's not clear whether these discrepancies are real physical or whether they are just due to different methods.
[54:56.860 --> 55:02.280]  And our feeling currently is that this is more due to numerical differences in the different codes.
[55:03.500 --> 55:04.680]  So, this is all I can say.
[55:04.780 --> 55:07.600]  But there's a strong competition in this field.
[55:07.780 --> 55:08.940]  So, we do not know.
[55:09.460 --> 55:09.740]  Okay.
[55:10.540 --> 55:11.300]  Any other questions?
[55:13.320 --> 55:13.760]  Okay.
[55:14.240 --> 55:14.320]  Yeah.
[55:14.480 --> 55:15.100]  Then thank you again.
[55:15.610 --> 55:16.120]  Thank you.