Okay, I think we're live. So, hello everybody and welcome to this 85 first series of the Latin American webinars on physics. Today, I'm going to be the host of this very interesting webinar that is going to be given by Johannes Herms from the Technician University of Munich. And he's going to talk about anti-nuclear cosmic rays and the potentiality sources and the potential for discoveries. So, for all the people that is following the webinar, please, you can ask questions using our YouTube chat system in the YouTube channel. And please, you have to be aware that there is a small delay between the live transmission that we are having using Zoom here between all the people in the webinar and what is showing us in what is showing in YouTube. So, please write a little bit in the head your questions to Johannes to be able to ask them at the end of the webinar. So Johannes, whenever you want, you can start. Excellent. Thank you very much for the kind introduction and to all of you for the opportunity to talk to you. I'm very happy to take part in this project of bridging oceans and mountains with physics. So let's get right to it. I will talk to you about galactic cosmic rays and what we can learn from them for fundamental particle physics and how anti-nuclear fit into that picture. So galactic cosmic rays are energetic charged particles that are accelerated either by astrophysics in the vicinity of very violent events in our galaxy, or potentially by interesting particle physics. And once they're produced, they, their movement in the galaxy is governed by magnetic fields because space is mostly empty. And it's more astrophysics onto these cosmic rays. Now I'm a particle physicist and I'm interested in fundamental particle physics. So the fundamental question for me in doing astrophysical physics is how can we separate the astro from the particle. And in the case of cosmic rays, this goes towards rare cosmic rays. There's one big difference between astrophysics and particle physics. One big difference is the baryon asymmetry of the universe. Astrophysics accelerates lots of cosmic rays from the baryon dominated into the stellar gas. So the cosmic rays that we get from that are lots of protons, some helium, some metals, but it's going to be dominated by baryons. On the other hand, particle physics, if you have enough energy, you can do pair production. Anti-meta, meta pairs in one-to-one correspondence. So that if you look at anti-meta cosmic rays instead of baryon cosmic rays, you get a huge background suppression. So you can hope that you can look only maybe at the particle physics that you're interested in, not at the astrophysical background. So this plot here shows, for example, the flexes of protons and helium, and then of rare cosmic rays of electrons, positrons, also anti-meta, but lighter than anti-proton, so they're easier to produce. And then anti-proton, and you can see that just by looking at anti-proton, instead of protons, you put many orders of magnitude of background suppression. And one additional advantage compared to gamma rays is that charged cosmic rays accumulate in the galaxy. So the magnetic field of the galaxy confines them, and they take about 10 million years to escape. So if we're looking at rare events like dark metal annihilation, then there's also some signal enhancement from that. So in this talk, I will first talk a bit about cosmic rays to get you the basics and the context of what we're doing here. And then we are talking about sources of anti-meta in cosmic rays, of anti-nuclear in cosmic rays, specifically, which is the main motivation in this whole topic about dark matter and a bit about primordial back-hole evaporation. Before, in the end, we can then look into the different anti-nuclear, anti-proton, anti-dutron, and anti-hedium, and see what they will tell us. Anti-proton have been measured to astounding precision recently. There's much to learn from that. Anti-dutrons, there's a dedicated experimental program just for anti-dutrons underway. And then in the end, there's some very exciting hints about anti-hedium from the AMS experiment. So let's get right into it. We start with cosmic rays. The life of cosmic rays starts at birth. So for most of the galactic cosmic rays, that is an acceleration. And the greed upon source of galactic cosmic rays is that an exploding star in a supernova creates a shockwave. The shockwave leaves the star and now it propagates through the interstellar gas, which you can see, for example, here in an optical in the yellow shockwave. And at the shockwave in the interstellar plasma, what happens is what's called first-order Fermi acceleration. So it's acceleration by a plasma shockwave. It's acceleration not like on Earth with electric fields, but there is stochastic acceleration around the shock. And this is the source of the ubiquitous power laws in cosmic rays that we see. And this process is so efficient that 10th of percent of the kinetic energy of the supernova can be dumped into accelerated cosmic rays and B-field turbulence. Evidence for this or proof of this has only recently been determined by looking at this supernova remnant and others and seeing that there is a pi M decay spectrum coming from there, which is evidence for the fast protons that hit interstellar gas there. Once they're produced, they escape into the galaxy. Now this is a picture of a typical disk galaxy like ours. But if you look into that using radio waves, what you see is this. It's a big, a synchroton halo around the galaxy created by electrons that move in the magnetic field that are confined close to the galaxy and by being bent by the magnetic fields emit radio radiation. What we can infer from that is that there is a magnetic field that extends many kiloparsec above the disk of the galaxy and can diffusively confine cosmic rays like electrons there. And we can describe the movement of cosmic rays in this turbulent magnetic field by diffusion with the diffusion coefficient that mostly depends on the rigidity R of the particle. Rigidity is how easy a particle is to bend by a magnetic field. So it's momentum over charge. And this is the, so the interactions with the magnetic fields are the reason that we often use this quantity of rigidity to talk about cosmic ray spectra. There's other processes than just diffusion going on in the galaxy. So for example, the magnetic field is attached to the movement of the magnetized plasma. So if in the galaxy, there is a convective wind that blows the plasma out from the disk, then the cosmic rays will be connected along with the magnetized plasma. Also, there might be acceleration happening there by random waves in the magnetized plasma. So if you look at the upper picture, it's clear that there is also stuff, not just magnetic fields. So this interstellar gas can be in the way nuclear collisions can happen, cosmic rays can lose energy by ionization or Coulomb energy losses. And all of that can be described by this diffusion convection equation for the flux of cosmic rays. The time evolution of the flux density is source term from injection, for example, by the supernova remnants or from dark matter for that matter. Mine is a loss term by hitting interstellar gas and being lost. Then there's the diffusion term, the convection term, and we have a energy redistribution and reacceleration term and some discontinuous losses. Now that's the differential equation and we just need to model our galaxy or the geometry of our galaxy in which this takes place. And what is often used is a two-zone diffusion model, what we have in green here, the diffusive halo. Then it's the zone through which this magnetic field extends and in which the galactic cosmic rays are confined. And in the middle there's a thin galactic disk with all the stars and the supernova remnants and the gas and the sun. Now having defined all of these things we can move on and calculate what should happen. So we look at a source and think what kind of cosmic rays should this source accelerate. If it's a shock wave then it will accelerate all the elements that are abandoned in the abundant in the interstellar gas like protons and helium and carbon. There are some elements which are not abundant in the interstellar gas, so that's what this chart shows that the open circles show the abundance in the solar system or the interstellar gas. You can see that helium and hydrogen are very abundant and carbon, nitrogen, oxygen also, but lithium, beryllium, boron are not. Now the black circles show what we find in cosmic rays. And you can see that there's a large abundance of boron generated somewhere on the way. And we call these cosmic rays here secondary cosmic rays because they are not accelerated by the primary source like proton and helium. But they must be created as a secondary product somewhere else. They're created by carbon and oxygen and so on hitting interstellar gas and fragmenting into smaller nuclei. So then during all of the propagation of the carbon nucleus, this boron to carbon ratio will record how often this carbon nuclei hit interstellar gas particles. And this is a very sensitive probe of galactic cosmic ray propagation. And we can measure that with our instruments by just dividing the carbon flux by the boron flux by the carbon flux. And that's what this plot shows here. And you can see that we have really precise measurements of this. And we can now use this to tune our models of propagation and see whether models of propagation are any good. And different implementations of models of propagation, for example, are the very well known Galprop code. So the Dragon code, both are fully numerical. And then in this study what we, or in my work, what we use for semi analytical to zone diffusion model, which is, has recently also become available as a pre implemented code for you to use. Should you be interested. Of course, the galaxy is not the only thing that stands between a supernova remnant and us there's also. So for cosmic rays to reach detectors on Earth, there's a few more obstacles to overcome. So the next one will be the solar system, the solar wind. So what happens here is that the solar wind carries the magnetic field of the sun outwards. And any cosmic ray that needs that reaches at Earth in the center eventually needs to propagate against this conductive wind. And that shields us from some of the cosmic rays. For example, this can be seen here. This is cosmic rays recorded by Voyager as it leaves the solar system. This blue curve is low energy cosmic rays created by the sun. And they drop as Voyager leaves the termination job. Whereas higher energy cosmic rays that come from the galaxy, they suddenly rise as Voyager leaves the solar system, which is again evidence that the solar wind shields some of the galactic cosmic rays. In the end, if you have this geometry of propagation versus convection and you approximate that as one dimension of just the radial part, you take the stationary approximation, so then you can approximate this by a force field. So that you can effectively describe this as an energy loss so that the kinetic energy of cosmic rays that we observe at Earth is just the interstellar one minus some force field potential. And there is some attenuation that comes with propagating against this force field. So the flux that we observe is also lower than the flux that would be observed in the interstellar medium. Of course, there are some caveats to this very simplified pictures. The real problem is three dimensional, there's time evolution in the sun. This in the end needs to charge sign dependence so the solar modulation is not the same for protons as it is for anti protons. But for the moment, I'm looking at larger energy cosmic rays, this should suffice. Finally, the last barrier is the Earth's magnetic field. So the magnetic field of the earth thankfully shields us from many most of the low energy cosmic rays. For experiments, if we want to look at low energy cosmic rays, of course that's not so good. Also the Earth's magnetic field extends far up into the atmosphere so even if we have some low Earth orbit satellites, we're still influenced by this. What you can see here on the right is a map with the vertical rigidity cutoff below which cosmic rays cannot propagate to the height of 50 kilometers. So if you want to look at cosmic rays of only one G, the energy, you'd better build your experiment at the pole. So that's just this context for why many of the experiments that we're looking at are either on satellites which have an inclined orbit so that they also pass the areas with lower cutoffs or high altitude balloon flights over the poles. So much for the life of cosmic rays, standard astrophysical cosmic rays from birth to detection at Earth. Now we're going to look into sources of anti-nuclear cosmic rays, which is what we're actually interested in. The first one we already talked a bit about are these secondary cosmic rays, which come from some primary cosmic ray species, i.e. hitting an interstellar gas atom day, and producing in a high-energy particle physics process an anti-nuclear and some other things. In more maths that can be written as the flux of primary cosmic rays hitting a density of interstellar gas atoms, and then we have to integrate over the differential cross-section of producing anti-nuclear in here. And we know the average density of gas in the galaxy. We can measure fluxes of primary cosmic rays at least at our position of the Earth and extrapolate from there. And these production cross-sections, for example from proton hitting a proton going into an anti-proton, we can measure that on Earth in our colliders. And then to calculate this we can either use an analytical parameterization of the data, so some fit function to the data, or we can use a Monte Carlo generator, tune that to all of the data that we have, and then also use it here. This will be the main background towards all the interesting particle physics searches that we want to do, right? I'm interested in not just in supernova rems and electric cosmic ray propagation and what's going on in the galaxy out there, you know the main motivation is dark matter. As all of you are probably aware, there's a set of observations from the length scales of the CMB to large-scale structures, to galaxy clusters, to individual galaxies that can all be explained with one new thing, which would be a new particle. New particle that is collisionless and that is very slow and doesn't do a lot. And the simplest particle model for dark matter, the arguably simplest, is WIMP dark matter, a weakly interacting massive particle dark matter that is produced by a free sound in the Earth universe, which means for this discussion that the measured abundance of dark matter today predicts the annihilation cross-section of what's the cross-section for annihilation when two particles, two dark matter particles, hit each other. Now, we know that in the center of the galaxy and all through the galaxy, in fact, there should be, there is lots of dark matter. We can infer that from the rotation curves and the movement of stars in our own galaxy. So we expect, in this model, production of high-energy particles, possibly including anti-nuclear in our galaxy today. If we want to calculate the flux that comes from that, we need to get a bit more concrete. So for example, this was in the dark matter annihilation picture. Of course, dark matter, there could also be decaying particles producing fast particles that also produce antiprotons and whatever fancy things. But in this wind picture, what's most interesting is annihilation into some high-energy final state, like 2B quarks or W bosons. And these particles, of course, we're talking about astrophysics, right? They are not stable. They decay very fast into other things. And if there is a hadronic channel here, then in the end, what we get are lots of protons, pions, gamma rays, antiprotons, possibly anti-neutrons. And the source term for that then looks like this. So we have the density or number density of dark matter squared times this annihilation cross-section, for which we have the theory expectation, times then the spectrum of anti-nuclear that are produced for annihilation into a channel F, like BB bar. The halo profile is reasonably fixed by stellar movement or by simulations. We take very often in studies of charge cosmic rays of anti-protons, BB bar or WW as representative annihilation channels. And then for the analysis in the end, we take the annihilation cross-section or the decay radius free parameters. And the spectrum, of course, we cannot observe at Earth. We have unfortunately never seen dark matter annihilate on Earth, so we don't know what the spectrum is going to look like. Instead, what we do is we use all that we know from collider experiments and tune them on to Carlo, like Pithya to that. And that then tells us the spectrum of anti-nuclear that comes from this. And these look like this. So what is shown here in blue are the spectra, source spectra for BB bar, final states, and in red is for WW, final states. And for our purposes, what is important here is that all of these spectra are peaked at low energies. So in terms of rarity of observing these, it would be most promising to place a detector to build something that is sensitive to low energies. And on the other hand, the astrophysical backgrounds are these steep power laws that drop as energy to the two, to the minus. And so they drop very steeply. So that actually in anti protons, they tend to stand out against the astrophysical background, which goes like this at higher energies. Now, this is the biggest motivation for looking for anti protons in terms of particle physics. And there's one more interesting source that I'm going to talk about now, which are primordial black holes. So that goes like this in the early 70s, Stephen Hawking discovered that there's a possibility of forming tiny or about black holes of all kinds of sizes in the early universe by just statistical large density fluctuations or in phase transitions in the early universe. Their masses could be very small, which, so for example, for a permanent black hole of mass of 10 to 13 gram, that's 1.5 femtometer size. Now, of course, as you were saying, that's pretty tiny right so let's look into quantum effects. This prompted him to look into quantum effects of black holes, leading to the celebrated theoretical result. And black holes should emit particles as if they were hot bodies with a temperature that can reach DB if the masses only small enough 10 to 13 gram is pretty small for a astrophysical masses. So the sun is 10 to the 33 gram. So this is a very, very tiny black hole. And this evaporation and the emitting particles leads to mass loss so this black hole should in the end evaporate and bent. And this result also predicts that if in the early universe black holes were formed with mass smaller than five times 10 to the 14 gram, they should have evaporated by now. So if you have a black hole of mass 10 to the 13 grams, then it's already one GB hot. And it will only last for 10,000 years until it's completely gone. So as I said, the, it's the emission is expected to look as if from a body. So the elementary particle emission rates from one promote black hole or from one black hole looks like this. So just thermal here depending on the spin of the particle that you're emitting, the energy of the particle and the temperature of black hole. So there's some gray body factor. So it's not, not a perfect black body, but there's this additional factor that comes from the fact that the black hole is in size comparable to the part of the wavelength of the particle you're emitting. So then, then in this picture, the black hole should admit if it's very massive, only massless particles. So if it's very massive, the temperature is small. So the energy of the particle you're emitting also needs to be small. So only massless particles like gravitons, photons, maybe neutrinos should be a minute.  And as the temperature goes above lambda QCD, you expect emission to be described by an element, emission of elementary quarks and nuance, that then later hadronize into stable particles like maybe anti protons.  For that, of course, well, we have to, so for the spectrum of anti nuclei from permanent black holes. We have to integrate here over the emission rate of elementary particles quarks and blue ones that later hadronize into the anti nuclear nuclear that we want to look at. So we have to multiply that by a fragmentation function of some of the initial particle radiated like an up quark, fragmenting how many anti protons do we get from that. Of course, we're not interested just in a single back hole, but we want to look at the spectrum that's emitted from all of the black holes in the galaxy. So we need some information about the black hole mass distribution that we have in the galaxy. So here on the left, if we take this, these two examples of what might be the initial mass distribution after formation of black holes. And they look like this. If we then take into account that these black holes lose mass and the smaller the mass, the faster they lose their mass. This means that the spectrum evolves and it evolves fastest for the lightest black holes. So for black holes that are smaller than this mass of black holes that has evaporated by now, there is a universal spectrum that we obtain just from this vibration law, which is the dndm should rise as m squared. Quite independently of what complicated shapes the spectrum might look like as long as it is kind of smooth around here.  That means that we can calculate the primary black hole source term without many assumptions on what the mass distribution of black holes actually looks like. So we're taking what we had here, the single black hole spectrum and folding that with this dndm, which is just m squared. And then again, what we get from that is a one parameter spectrum. The only parameter here is the normalization. It is very predictive in the sense that the shape is completely fixed by a primary black hole evaporation plus this universal mass spectrum and the low mass primary black hole range. So why maybe it's not as exciting as dark matter it is a very interesting benchmark to look into and to compare data to. And actually look into the data. So now we're going to talk about experiments and observations and how to explain them. And the very big role here in place the instrument that has observed most and most cosmic ray anti proton so far, which is the AMS or two experiments experiment that you can see here, which is on board of the International Space Station. This is orbiting the earth and 100 kilometers high. And the idea is that cosmic rays come in from here and then hit all of the detector parts inside here. And then we can analyze that this detector is built like that. So it's a quite similar to the particle detectors that we used to in our collider experiments on earth. So it has a tracker system, it has a magnet for deflection. And it's built through this from from the incoming cosmic ray direction. So let's say there's a cosmic ray coming in here it hits the tracker here. Here there's a position radiation detector that is built to separate electrons from nuclear. Then it hits the inner part of the detector where there's a strong magnetic field and it's deflected. So then it leaves a track in the in the tracker, from which we can reconstruct the particles rigidity. It leaves the time of light system, which is used for velocity determination, if the particles not too fast. And then here it hits the ring imaging to rank of detector, which is used for velocity determination if the particles a bit faster. And in the bottom here there's an electron calorimeter which we're not interested in because this is a talk about anti nuclear. And the interesting thing here and why it really changes all of these collected cosmic ray discussions is that they for the first time have percent level precision for galactic cosmic rays over large range in energies. So this for example is all results from 2015, but you can see that you cannot even see the error bars in the anti proton to proton ratio here. It's really a very precise measurement. So it's interesting to ask, is there anything exciting in there? And if you ask the ams people if there's anything exciting, they will come up with something so they always have something exciting. So if you compare the spectrum it's the same as before just your net linear scale instead of the box scale and compare that to the secondary expectation from some old paper. Then you would conclude that, well, there's a huge gap here, what is happening? And of course they also offer the explanation of what might be happening, right? There could be dark matter annihilating, which would be amazing. Now it turns out that if you really take into account also the other measurements that ams did on the proton flux and the helium flux. This secondary production line here is no longer tenable, but still with these data you can make very careful analysis, which these people here have done a few years ago. So what you can see here again is the, now this is the anti proton flux multiplied with some rigidity scaling here so that you can, it's easier to see the shape. And it's very hard because the error bars to see anything in here because the error bars are so small. But what they find when they fit secondary production, plus a possible dark matter component to this, is the spot here on the right where depending on the dark matter mass, you get limits on the dark matter annihilation cross-section, which here this range here is for different propagation models, so it kind of shows the uncertainty in propagation, which are much better than the gamma ray limits from that time. And excitingly there is about a three sigma excess around here, which is very hard to see in this spot. But it's very clear that there is a three sigma excess, at least in this paper here, which lies right at the thermal annihilation cross-section, which we expected all along, right, if we believed in the WIMP. So that's very exciting. Now what's the status today? It's unfortunately not as simple, so because if you look at them, then you see that the signal is just 10-20% of the overall flux. So we are looking really into a precision measurement with cosmic rays, so that it's not that easy. And the picture today looks more like this. I took this slide from a recent workshop last week actually by Michael Cosmeier, so one of the authors of the previous slide, where he summarizes the recent developments on this anti-proton excess, if you like. So there's been a few studies. The main thing is that AMS has not yet published any covariance matrices, any correlations between their errors.  That's one thing. Then you need to be really careful in accounting for the propagation errors. So in the previous study, they just used a few example realizations of the galaxy, for example, of propagation models. One of these guys here, they really scanned over propagation models and seeing, in many cases, a joint fit of the boron to carbon ratio to constrain the propagation model and then the anti-proton to proton ratio. Another big thing is, and that's maybe best seen here in this lower right hand plot, so in black that's the, these are residuals to some best fit. But what you see is that the errors of the measurement are smaller than this green band by a factor of two, something like that. And green is the cross-section uncertainty. The fact that we know too little about anti-proton production to be able to predict the anti-proton flux to the same accuracy as the experiment can measure. And somehow, the Michael Cosme and Phil Anseldonato and other people have, people from this community here have initiated a push to measure more anti-proton production cross-sections to be able to take more out of this measurement. And until then, wow. So at the moment it looks a bit like there's 1.1 sigma, very nice limits, but no excess to other people claiming there's maybe up to 4.7 sigma and a robust excess, which is also consistent with the Galactic Center DEV excess. So there is some excitement still around. And in the end it will get settled by the experiment publishing their own error correlations would be one thing. And then better knowledge about anti-proton production would really help us out. Okay, there is one other exciting option, which is to look at a channel that has less background, which is where anti-dutrons end of the day. So anti-dutrons are one anti-barrier in more. Now, if you look at the secondary production, what happens is mostly one proton hits another proton produces, let's say an anti-dutron and barrier number in here must be conserved. That means that in addition to the anti-dutron, which has barrier number minus two, if we start up with barrier number two, we need to produce four more nucleons. So that the threshold energy in this process is six times the nuclear mass. And the threshold energy for an incoming cosmic ray proton needs to be 16 GB, which is quite a lot already. So three times more than for anti-proton production. That suppresses the background, of course, but there is this other effect than anti-dutrons or a larger anti-nuclear like anti-helium will always be produced boosted because you need so much energy in this fixed target in natural state. There cannot be, there is some energy below which there cannot be anti-dutrons produced. And that gives a huge signal to background boost for low energy anti-nuclear because secondary production of anti-dutrons drops precipitously at low energies. So if you now look for dark matter, which we saw was peaked at low energies, here at these low energies, there's going to be almost no background. If you look in anti-dutrons. Okay, so let's calculate how many anti-dutrons do we have. The problem is that anti-dutrons are quite rare and the experimental data is not sufficient to get a data driven differential anti-dutron multiplicity. For example, proton-proton collisions. So we have to do some phenomenology, some modeling. The simplest model you can do is the factorized coalescence model where you just say, well, okay, I look at my process. Look at the anti-proton multiplicity and then let's see what's the probability, so to say for an anti-proton produce with this momentum and with this momentum. Okay, and then there's this coalescence factor some probability that these two anti-proton and anti-nuclear neutron will merge into an anti-dutron. And this is works and so on so empirically this works well for high multiplicity processes so for heavy ion collisions at the Large Hadron Collider, this can describe the data quite well. But it's quite clear that this will not work for example close to the anti-dutron production threshold, where the anti-proton multiplicity doesn't know anything about the fact that we are really interested in only processes that have two anti-nuclear ions produced. So the next best thing that you can do is to do event by event coalescence which is kind of state of the art of how this is done or used to be done. Which is that we generate lots of Monte Carlo events and look into those that have two anti-nuclear ions. So we run our Monte Carlo and let it do all of the heteron section and stuff and then we look at all of the events that have two anti-nuclear ions. Now if their momenta are aligned enough that so the physical picture that the binding energy of the anti-dutron can overcome the momentum difference. So that their momenta are close enough, they're close enough in momentum space that the binding energy can overcome the difference then they will merge into an anti-dutron. This is obviously physically not a nice model because we know there's quantum mechanics and this sharp cutoff in momentum space has nothing quantum mechanical to it. So it fares on formal grounds already. So what in practice we do is we take this as a logical model as a one parameter model for the differential anti-dutron multiplicity. And we determine this coalescence momentum not from this theoretical hand-baby argument with binding energies but from data. And even then it turns out then we have to allow for different coalescence momenta P0 for different processes. Which kind of makes that so. Proton-Proton collision says lots of, at 7 TV has a lot of patterns, large multiplicity, many things going on, far less clean than electron-electron collisions at 10 TV. So doing this and then using the coalescence momentum that we determined from proton-Proton collisions for the secondary background which is mostly proton-Proton collisions. And from cleaner, higher energy particle physics processes like clean processes like electron-positron annihilation for the dark matter process or here ZDK for example dark matter going into WWW it makes sense it's kind of similar to ZDK. That's how we calculate our spectrum. Yeah, so recently there's been some some nice developments on building a more quantum mechanical and maybe a physically more correct picture to this but I don't have time to go into it. And in the end, this is what we get. The future prospects given the anti-proton levels. So this top row of clouds shows anti-proton spectrum for different secondary types. Then here black is always secondaries. So the astrophysical background. And these other lines are chosen large enough so that they're just compatible with the data plus secondaries. So you can see that all of the interesting contributing the things that we interested in dark matter and permanent vehicles can only make up about 10% of the flux. So in anti-proton we really need to do a precision study if we want to learn anything about anti-neutrons, sorry, anything about dark matter or permanent vehicles. Whereas if you look at anti-neutrons you can see that the secondary flux drops a lot towards lower energies. Whereas the dark matter and permanent vehicle flux is not affected by that. So if we build a detector that is sensitive to these kinds of fluxes, that would be and then found anti-neutrons. That would be a very strong indication that there's something interesting going on here. Okay, so let's do that. There's actually an experiment planned and set to fly in the next year over Antarctica, which is the gaps experiment. It's an Antarctic balloon mission and is specifically purpose built for low energy anti nuclei. So it's built to have very good separation between anti-neutrons and anti-propons. And that works like this. So let's have an anti-neutron coming in. Speed is measured in the time of flight detector here and then there is a very thick target detector system in which the anti-neutron has actually stopped and then forms an exotic atom, so the negative anti-neutron with the silicon nucleus. As this exotic atom de-excites, it emits characteristic x-rays that are different between anti-propons and anti-neutrons. And then in the end, of course, we have the annihilation signal of the anti-neutron actually eating up part of the silicon nucleus, from which we will get lots of finance. Many more than from an anti-proton annihilator. So this is very exciting and it might find something and we will know into years. Until then, we have some other exciting things to talk about if we want, although they are a bit more speculative, which brings me to anti-heal. There have been claims, but no published articles about anti-heal events being observed at the AMS or two experiments. So this is an event display of an anti-healium candidate event where they measure that it's a particle with charge minus 2 and mass 3.8 plus minus something. So actually the mass is even more consistent with anti-healium 4 than anti-healium 3, which is very exciting and hard to believe. And the reason for that is like this. If we want to calculate, make predictions for anti-healium, we are in even more trouble than for anti-heal neutrons because there is even less data for anti-healium than for anti-neutrons. But the general trend is that this shows something like a normalized multiplicity for anti-nuclear neurons of some mass number A. So this would be anti protons and then in the same type of collision observed at Alice, this would be anti-neutrons. This would be the anti-healium 3 multiplicity and this is the anti-healium 4 multiplicity. And there is a factor of a few hundred for each anti-nuclear that you had. Now we have measured anti protons. So we know how many anti protons are out there. And for all of the components for a secondary for dark matter for permanent black holes, all the particle things. If you want to produce some anti-healium, you're going to produce lots more anti protons in the process and those we can compare to what we've seen. Yeah, so we can do the same exercise that we did for anti neutrons. So taking the observed anti proton spectrum, looking how much anti neutrons can there be, and we can also look at how much anti-healium can there be. And we did that for anti-healium 3 and this is the result. So here is different secondary production of anti-healium. These are the maximum possible fluxes from dark matter without overshooting anti protons. If dark matter annihilates into W bosons or B quarks, or here for permanent black holes. And what you see is that the projected AMSO2 18 year limit for the detection of anti-healium is above all of these. Maybe if so, this uncertainty is related to the uncertainty and coalescence of anti-healium, which is huge because we have so little data. It's really hard to make it work out for anti-healium 3. Most of the time the observed anti-healium flux is an order of magnitude. At least above the secondary expectation. And even with dark matter, it's hard to make it work. Some other people who were made some much, much more conservative assumptions about anti protons, they find that the anti-healium flux, if these events by AMS are actually anti-healium, then they would be marginally maybe compatible with a dark matter origin. But this event that we looked at two slides ago looked like anti-healium 4 and 2 sigma. So how is that going to work? If particle production with particle physics processes with coalescence drop by a factor of few hundred for every anti-nuclear that you have. So that's what these people here looked into. So here this is the secondary prediction of anti-healium 3 and anti-healium 4 compared to the AMS 5 year sensitivity. So you can see that maybe if you're really, really good, if there's something that we really misunderstood about anti-healium coalescence or a galactic cosmic rays, then maybe you can make this intersect here. Maybe. But there's no way that there's a secondary anti-healium flux that can be detected at these points. And that holds true for all of the particle physics processes where you produce the anti-nucleus by coalescence. Of course, if you ask, well, if you put it to a dark matter phenomenologist, it's impossible that dark matter can do this. Then a good phenomenologist will come up with a model that does it, even if it looks very strange. Now if we took these anti-healium 4 events for granted, this would mean either some extremely involved complex, really on dark matter model, or it would mean that there is anti-healium somewhere in our galaxy, that there are anti-matter regions in our galaxy, either as clouds or as compact anti-matter objects. That would be a very extreme conclusion and the kind of evidence that AMS has until now is in no way sufficient to support them. But it's not unheard of in theory. So there's been, for example, this paper of Baryogenesis, which predicts a small fraction of the mass density of the universe to be in the form of compact anti-baryonic regions. So though extreme, it's not impossible. Yeah, this brings me to my conclusions and summary. We talked about anti-nuclei in cosmic rays. Why they are very promising detection channel for exotic particle physics in the galaxy, first and foremost dark matter annihilation. We looked into the state of the arc of what's going on in antiprotons. Antiprotons place competitive limits on web annihilation, but the secondary background limits the discovery potential. So it's really hard to convince the seasoned particle physicists that what you find there is actually particle physics and not just an astro. But for inter-neutrons, there's the promise that the secondary background would be orders of magnitude lower, so that even with nothing visible in antiprotons, low energy inter-neutrons may have a signal from dark matter annihilation orders of magnitude above the secondary background. And in the end, there was a fun excursion about anti-heating events that MSO do and what they would if true imply amount the universe we live in. Thank you very much for your attention and I look forward to questions. Thank you very much Johannes. It was very interesting webinar, your talk. In fact, it was very interesting listening because it's been my area. So let's start with the for the people that isn't in YouTube. Please start to write a question because you know there is a small delay between what we are living here inside the Zoom session and what you see in YouTube. So for the moment, we're going to start with the question from the same people that are here in the Zoom session. I don't know if some of the other coordinators want to start with the first question. No, anyway, I have a question. Nicholas. So thanks first for the super nice talk. If you go to, I think it was just like number 14 or 15, I'm not sure. You showed a spectrum for the anti-deuterance. No, I think it was previous one or after. Where? Dark matter. That one. Yes, exactly from dark matter. So for instance in the 10GV in the right hand side, so you have like this peak at exactly that. So what's that? Yeah, so in the B quark, there's always, in the B quark channel, what you can form is there is a, you can form a B meson. So all of the low energy tail here is just from, for example, the strength fragmentation of your quark gel. But for the specific case of the B quarks, there's always some additional stuff from the leading quark, so to say. And that's what gives you this peak and this peak here and also this peak here. That's D. Yeah. What are D? So, okay. I see. Yeah, so we're looking into light quarks back to them that should be absent. Okay. Thank you. So another question. Johannes, I have a question about the, about the coalescent factor. There are other models than the one that you presented because since it's quite, it's rather seem to trying to, because there are no data as you said. Yeah. So the biggest problem is that if you don't have lots of data, then the whatever model you make must not be very complex, because you cannot determine so many parameters from the data. Nevertheless, it should capture the relevant physics so that you trust it where you don't have data, which is the whole point of the model point. And for this factorized coalescence model, the simplest thing you can do. It's been investigated where it fails and that's the reason why people today mostly use event by event coalescence. So as you say this classical description is not very trustworthy. Recently, there's been some developments. So this one here can be made totally fine. There's been some, some developments on starting with heavy iron, iron collisions, like the room and others and determining the coalescence factor there and then using some arguments to extend the model from here from the case where it works to also the other ones. And then the most exciting one is this are these recent developments where they actually do a quantum mechanical description of coalescence. So what they do is they, they use Monte Carlo and to determine the distribution of protons and neutrons and protons and neutrons. And they calculate the two particle wave functions from there. And then they project them onto an anti neutron bounce day, which is what you would do right so that sounds like a sensible quantum mechanical description of what should be going on. And then they came up with a nice week, a nice week now function based approach in which you can use Monte Carlo to take care of the of the correlations between anti protons and anti neutrons that you have and characterize them and then analytically do the quantum mechanical part of projecting that onto the pond state. And that looks very promising, though so far it hasn't been as far as been tested on the energy data. So, to me it's not clear yet whether it also works close to threshold, but I hope it would because in. So it looks like a much more sensible model than what came before. Yeah, kind of ahead of the state of the art at the moment. So, but in that sense, another, I mean one question related with this. Because since we know so few about these coalescence factor coalescent momentum could be it could be also a possibility that there are kind of resonance in this coalescent factor that make more visible to in some coalescent processes, you coalescence more than in other point that what we can see here in the same table that you're presenting that for low energy, you have much smaller coalescent momentum, and for high energy using just PTA tune coalescent momentum because also it's very big the spread between Monte Carlo. That's, that's, that's possible so what that effectively would correspond to is that now at the moment one so for example in this event by event simple event by men coalescence model. There's this sharp cut off. So there's 100% probability to merge at very low momentum separation and then drops to zero abruptly. What you would suggest is that there might be something where maybe at low relative momentum there's a large probability to merge and maybe then there's a resonance later. Maybe. Yeah, it happens with the with the P mess on production like when there is the resonance you produce more and so on. Oh, anti protons because this be messing is everywhere especially at low energy. So the coalescence modeling is definitely is the weak point of anything involving anti neutrons. So anti neutrons you cannot really use them to put constraints on dark matter, because we don't really know how much we expect of anti neutrons. The other way around it works that we say if we find anti neutrons, then they cannot come from secondaries, or if we find anti neutrons at some, and at this level for example, then we can be quite sure because there's orders of magnitude in between here. Yeah, that it's not so that way around it works. It's more of a detection channel not so much constraints channel. So it's more curiousity. How large is that our 70. I mean the impact of the coalescent momentum in the flags. Like, where. Yeah, so if you think about three of the Okay, it goes as a factor. So so to say about like like the volume in momentum space of the ball within which all the momentum coalesce. And here there's about depending on the process maybe you can take there's a factor of two or even more of uncertainties. So that gives you a factor of 10. Yeah. So, yeah, yeah. That is very important for the, yeah, to establish some constraints. Yeah. I mean, I have more questions but I'm going to let the other people to ask. I don't know if the other guys here in the, and also in YouTube, you'll still have time to make some questions. I don't know. Okay, so, because I'm very interested in this coalescence function because it's the key part of the, of the production of anti-antideuter. But for instance, have you, I mean, have you tried or other people have since you read more about this. I mean, you're working on that to try to use the same coalescent factor or coalescent model for the function of the ethereal. I mean, since it should be more abundant in, I mean, it's more messy the signal, but or is it expected that it's symmetrical. You can form the ethereal in the same way that you're from, you're from, I mean, I started from a proton and proton neutron, proton, antiproton neutron. Yeah. Yeah. Um, for high energy collisions, like at Alice, the result, the experimental result is that it's pretty much equal. So the entire neutron to neutron ratio if you have 70 the proton proton collisions is pretty much one. So for that you then also infer the same coalescence parameter. And the problem is done. So for using this with low energy processes where it's not clear that the, so for proton-proton collisions at smaller energies where it's not clear then should be symmetric. It's unclear how much we can learn from that because we anyway have this really big process dependence here. So what it's done at the moment is to calculate the secondary production, you use the measurement of the P zero that you infer from proton-proton collisions. And for a production from dark matter you use the one that you infer from Z decay or from, from leptonic processes. Yeah, because they're more cleaner. Yeah, not production is not clear on that. But of course, I mean, I'm pretty sure that the people here for the plus and minus where there's no variant number involved in the initial state. I'm sure that for the determination of the P zero, they took into account neutrons and neutrons. Okay. One more question. But not all coalescence because it's a bit too much question. I mean, I don't know if you didn't present, or maybe you didn't, you're exploring also the case of decay that matter because in that sense you don't have the restriction because of the annihilator cross-section of the wave particle. Yeah. It's able to observe these kind of processes in, in AMS for instance. So, the only thing that really changes between annihilating dark matter and decaying dark matter is the spatial distribution of sources. So annihilating dark matter is proportional to the dark matter density square. So it's more peak towards the center of the galaxy. Decaying dark matter has a gentler slope because it's only in proportion to the number density. But the spectrum is going to look the same. So in analysis, we treat the annihilation cross-section and the decay rate as three parameters anyway. The normalization of this is basically limited or fixed by anti protons. And the results for what you could get in anti-duperons are basically the same. And also, that also implies that all of these fancy, these limits here on dark matter annihilation can be pretty easily recast into limits on dark matter decay. So in terms of this diffusive process in galactic cosmic ray propagation, the different density, the different source profiles for annihilation and decay don't matter much. They can not influence the spectrum a lot. It can practically directly translate this into a limit on dark matter decay. Okay. So I'm going to take YouTube for question for Johannes. It seems there are no questions here in YouTube. So for the people that is following us following this transmission, please, you still have time. I don't know people here from the Zoom session. You have questions, you can unmute yourself and ask the question to Johannes. Yes, I did. I did sorry. So I'm going to go for it. I was, I was hesitating because I think a previous speaker mentioned the excess that you were mentioning before and discussed the dark matter explanation for this. I think I asked the same question at that time, but I'm going to do it again because I remember the answer. So the question was, if dark matter direct detection, the bounds have an effect in the possible explanation of dark matter as a source of the excess, in case the excess is there. Of course, if it's a decaying dark matter, of course, there's no wish, but in the case of it's a coenilating, I was wondering if there's anything coming from the direct search bounds. Yeah, so the, as soon as you specify model, yes. So if you have a model of dark matter, say it's a, I don't know, some real scale is saying the dark matter by the Higgs portal, then you can calculate correlations. But if you don't have a model, then it's possible that the particle physics, where it depends on the, on your more detailed model. So if there is, you can have dark matter direct detection suppressed by some velocity dependent operators by different couplings to the quarks. Whereas the annihilation is always kind of fixed by by production line, as long as you have wind dark matter, there is a quite clear prediction except for the final state of the annihilation of what the annihilation rate should be. Now for the dark matter direct detection, there is no such clear prediction depending on the model. If it's a simple contact interaction, which again would be a model. Then there would be a prediction, and then typically direct detection bonds are very strong. Right, so if we have like an ultralino dark matter or something like this. I mean, would that be able to avoid balance and explain it simultaneously? I don't know. I really don't know much about neutral dark matter. I just came in. I think you can suppress. So now we're talking about dark matter direct detection, right? How can you suppress dark matter direct detection to comply with bounds? Because the annihilation cross section is going to be close to the thermal one. Okay, unless you do co annihilation. I would really out of my field here, but yes, maybe you have dark matter annihilation on the Higgs resonance, then the section to be and today would be the same as in the universe. But the dark matter direct detection could be suppressed because you have tiny cuttings. Sure. I'm sure there can be examples. Okay. Great. Thank you very much. So yeah, I was me. Sorry. So I guess for, I don't know for the people here and also in YouTube, there are no more questions. So I guess it's a good time to finish the webinar. So first of all, I want to thank you, Johannes, because of your talk that was very interesting. Indeed, I like it a lot. Thank you very much. Take it for the, especially for all the reference. There are many reference that I was looking in the past, but I couldn't find when they were in the first part in the first part of the introduction. And for all the work that you are done also for your that you're doing your PhD, so on. So thank you Johannes, thank you all the people that participated of the webinar and all the viewers in YouTube. And in two weeks, we're going to have Carlos, Oscar, sorry, from the University of Valencia, that he will give also a webinar. So for all the rest, have a good weekend and so on. See you on the next time. Thank you very much.


Fellow Longmont residents, I'm Harrison Earl and I'm excited, eager, and humble to be running for your City Council Ward 1 seat in November to fight for an affordable, livable, and sustainable Longmont. I want to briefly introduce myself, share my vision, and lay out the pressing issues I'm deeply passionate about. I have cherished the last six years living in Longmont, and I love this city. I've worked in the aviation industry for the past 15 years, and locally here in Longmont, as a chairperson of the Airport Advisory Board, I have actively worked to bring economic benefit to our city. My wife, Elizabeth, is a family medicine physician at Salute Family Health Centers here in town. Together with our Golden Doodle Maximus, Elizabeth and I are regulars at Stephen Day Park, and enjoy walking along Longmont's trails and greenways. Our experience living in Longmont, coupled with my professional work background, provide a foundation for my commitment and vision to a brighter, more prosperous Longmont. When I say I'm running for an affordable, livable, and sustainable Longmont, here's what I mean. Affordability. Our city's soul is its residents, and that's why we need a housing approach that serves everyone, and allows our residents to afford to live in Longmont for the long term. That's going to require us to revisit some zoning ordinances, prioritize affordable, and attainable housing, and keep our taxes low. Let's ensure that our city's growth doesn't force our residents to move away. On livability, our parks, open spaces, and greenways aren't just land, they're the heartbeat of this city. It's critical that we maintain them as a resource for all, but it's equally essential that our residents feel safe with enhanced community policing, improved pedestrian safety, and reimagined transportation networks that let us move around the city and region more easily. And last, on sustainability, we must act today for a green tomorrow. This is not just about reaching carbon zero, but about making sustainable living a part of Longmont's DNA. We must incentivize green investments and ensure that our infrastructure and finances are stable and prepared for the future. In this campaign, I'm not representing a political party but you, the residents of Longmont. I will serve with honesty, integrity, and respect. Even if we have differing views, know that my door will always be open and my ear will always be keen to listen. I promise to bring common sense to a city council where it's often missing. Visit my website at HarrisonforLongmont.com to learn more about me and to share your support. Because I believe Longmont's more than just a city, it's our home. Together, let's usher in an era where every resident thrives, everyone is valued, and our community's fabric is stronger than ever. I'm Harrison Earl, and I'm proud to be fighting for an affordable, sustainable, and livable Longmont for all of us. Thank you.


Hey there, I'm Charlie Comstock the model railroad hobbyist magazine. I'm here with Nick Muff Nick has got this Kansas City Southern layout downstairs in his house, and it's a very unusual layout In fact, we have to take quite a walk to get through it. He's got a Passenger car down there and we're gonna hike through that and he's got a bit of a station down here You can hear some of the sound effects in the background Nick, where did you you live in Northwestern Washington? How did you get started the Kansas City Southern? Well short story is my grandparents lived in Northwest Arkansas So we travel from Southern, California where we live to Kansas City and down to Arkansas each summer Visit my grandparents. Of course it allowed me to see trains that I didn't see in Southern, California Particularly the Kansas City Southern Okay So you want to show us what you got here? Sure. I'd be glad to. Okay. Let's go. All right Well, my real love is a passenger trains and passenger train travel So here in the basement I've recreated in full scale and in an HO scale an experience in passenger train travel the lobby here simulates the Midway at Kansas City Union Station and To the left is the entrance to the Pullman car so the right here is what looks like part of the side of an F unit and the Numenate new the enigmatic door Operates and this represents the mock-up of a Pullman car People ask where I got it. I built it. I tell them that everything that's in this car I carried down those stairs. So come on in So there's a roomette and museum restroom Come on in here and see the museum With Miss Southern Bell standing on the left and like all passenger trains, it's cramped around the corner here and down the hall is Vafe Lounge and again, this is all a mock-up Probably about one-third the length of a real passenger car And like all model railroaders do it's been selectively compressed So that it creates a feeling of being in a passenger car Even only it's only one-third as long as one And the table setting here. That's Kansas City Southern's Roxbury pattern China and Kansas City Southern flatware and hollowware on the table and Come on through this way through the door is the layout room Hobos jokingly referred to box cars as side door Pullmans This is a real side door Pullman and out here. We're in the layout room To the left here is the passenger car And then the locomotive As opposed to the passenger car the locomotive is not a mock-up. It's the real thing and then Across the room from right to left is Kansas City downtown In the late 40s early 50s Nick, uh, would you tell me about this station here? So well, this is the centerpiece of the layout charlie It's kansas city union station again as it might have appeared in the late 40s or early 50s And it's a monument By model railroad standards. It's six feet wide four feet deep and all put together it weighs 80 pounds So that weight is in the castings the two-part resin castings that are in there and What people don't generally realize unless I tell them it's not full scale I realized right at the start that within the confines of a 30 by 40 foot basement I couldn't make it full scale. There just isn't enough room. What would full scale have been? Well, you know, it would be 20 larger than it is now So I put it the other way around I built it at 80 scale Even at that it dwarfs trains and buses and people and so it's it's effective and it looks right And manage fit as it is the throat One end of the layout to the other 40 feet in this room is just long enough to go throat to throat for the union station You've got more than one or two lights in here Yes, there's almost a thousand leds in it. I haven't really counted them all but in the in the main chandeliers in the waiting room There's 82 leds in each of the three chandeliers So there's over 200 leds just in the three chandeliers. It's pretty bright in there. It's bright. It's nice You know, I see the original architect did a good job with lighting that interior Now there's wall sconces around the edge So there's lighting in the center lighting around the edge which provides a very even lighting. I like to Tell people that the great majority of little railroad station modelers bill would fit in the grand lobby In fact, our pomeranian will fit in the grand lobby. Have you tried that? I've tried that. Yes And how did uh, how did the palmie take it? Oh, he's fine. He never knows what's going on anyway. Yeah Okay, so Yeah, how did you get the lights in the cars? Well, you know Those are micro leds. I think they call them surface mount leds They're 0.3 by 0.2 millimeters and you can buy them with leads attached or you can put your own leads on I've done that it's a little tedious the main thing is I would not have attempted to put all the lights in the cars and the trucks were it not for the availability of leds Incadescent bulbs are going to burn out eventually even if only 10 of them burned out that would be a disaster And so they're tiny little leds on a tiny little I call them gnats whiskers wires And drill a hole bring them out the bottom put resistors under there Getting back to the station Did you get plans for this from somewhere? Well, that would be nice. In fact, I actually know where the plans are now I didn't know then But so I called I wrote the Kansas city terminal railway and asked if they had plans that was kind of bold this is a long time ago and They said yeah, they did so I went back there and I met with a gentleman in this room right here Where's that right here? Unfortunately when I came in he was asleep at his desk So I had to kind of wait there and him and haw for a while and finally he woke up And what he provided me was a very nice um Front elevation in eighth inch scale And an elevation of the waiting room only the side view in 16th inch scale And one other piece of paper that I didn't realize the value of at first it was just It listed the elevation of the roof the ceiling the mezzanine everything From top to bottom, of course that turned out to be very valuable in scaling the model And that is one I realized I was going to have to learn how to do CAD drawings And so I used a CAD program To use what I did have and then slides and photographs to create what I didn't have to produce all the interior and exterior plans for the station Now what's the station made from? Uh in real life or the model well the model the model is made from you know I tell people all the flat surfaces you see that's eighth inch sheet styrene Eighth inch eighth inch. Yes. That's pretty thick. Well, it is but I need stability and strength if you For instance the floor of the union station is eighth inch all these heavy castings, you know They have they're actually screwed to that with little screws from the bottom Really has to be pretty stable, you know tiny recess screws I went down to Cadillac plastics and I buy it by the four by eight sheet So that's the only way to buy For this it is for the union station At the driveway and the railway express building consume three four by eight Sheets of eighth inch styrene plastic Send all the other pieces here The complex pieces The masters were built primarily out of styrene plastic Then I made our tv rubber molds and used two-part casting resin to pour the copies One one mold for one column and then that turned out to be a total of 12 columns and so forth Okay What about the built parts of building here on the side? Is anything you had to do there for well actually? Yes, and I learned something Which was very helpful This was the issue right here These corners are highly visible So if I made castings and tried to mitre those with a saw and sandpaper And try to get it right I can imagine that being a real nightmare and it's got to look good It's right here where it's very visible. So what I did is I Created the u-shaped master And I used high density blue Styrofoam to make a block that filled that Just a block that fit in the back of the u and made it a solid piece And then I made the rtv rubber mold And pull the whole thing out Then I pour resin in the mold and put the styrofoam block back in Now I checked with joel bragden who's my expert on this To make sure that the resin would not attack the styrofoam, which it doesn't So then it was set I pull everything out of the mold I pull the styrofoam block out of the back and I have a u-shaped casting And so the joints I don't have to mitre the joints. They're all they're already made And that led me to be bold enough that on these corner pieces here I cast All four sides at once in one piece the roof and all four sides are cast in one piece There's a styrofoam block in the center that you pull out And so that meant that I didn't have to mitre any of these corners after the model was After the molds were poured This is a separate piece. It's hollow. You can actually see light through the little windows It had a styrofoam block in it And then the only other trick is these columns are separately cast and applied Now to get that out of the mold you have to split one side of the mold So they take a scalpel and split one side of the mold so it can open up You can take the casting out Then you tape it back together for the next casting that turned out to be an immense help and save me all the fussy Trying to mitre those corners now What you see isn't what all what you get here like an iceberg You're seeing the top part of the building. That's true.  And so I thought well, you know Show us how crazy Yeah, I wanted people to appreciate number one that there was more of the station underground and above ground And and how efficiently it was built so that all of the baggage handling went On underground where you weren't aware of it And so this panel on the front has a little description of the station How much it cost when it was built then when you open this panel You're seeing now the the plaza or street level The basement level which is where local baggage in express was handled And the sub basement were through baggage in express were handled So that here is a little baggage lighted baggage truck with the Parcels in it also down at this level is where the mail was delivered It came from across the street down the length of the express building under here all on a conveyor belt And a conveyor belt had automated Flappers that would divert the mail where it was supposed to go So there's little carts under atlanta denver los angeles And then those carts went out underground through a tunnel to the end of the platform And there was an elevator at each platform So that there was no trucking of baggage at platform level at all all went down Everything happened underground and you never saw it of course by separating through baggage in express From local baggage in express it made sure that they didn't get mixed up That if you were headed for kansas city your bag didn't accidentally go on to new york What year are you modeling here? I I had to pick a year 1951 1951. Yes. So this is pretty much what would have been going on in 1951. It is. Yes. That's correct. That's correct. Yes Okay, so I like to have animations on the layout Okay visitors really are interested in those things And but I want real realistic animations So a kite on the end of a piece of music while it goes around on around isn't going to work for me Okay, and so first animation on this end of the layout is this little Rock Island switcher number one. Aren't you afraid it's going to come off the end of the trestle? Well, we've arranged so it doesn't actually there is a diode In here that blocks this section of track so it can only run so far and it will stop automatically The same on the other end when it gets in behind the buildings where it's hidden And the other thing is this simulates the rock island crossing Simulates another railroad. Actually, there isn't any rock island railroad except for three feet of it right here Okay, but every once in a while in fact every three minutes that little switcher comes In and out with that a load of coal for kansas city power and light And of course, it's fun to see how many people think it actually is going to run off the end of the trestle I said it as close as I could and be on the safe side People make diving grabs. Yeah. Hey, you're trains running. Yeah, and they're trying to get over there to catch it Of course, it stops about three quarters of an inch from the end of the trestle So next animation here is a hobo campsite Actually, the model was built by a friend of mine when he was just a teenager I've replaced the fireplace electronics with something a little more modern. So it gives a very nice effect One of the things that's easy to do is just little wisp of cotton here that simulates smoke There isn't very much of it surprising what an effect it creates One nice thing is to have Buttons that visitors can operate on the edge of the layout and so there's a button here that says here the lonesome hobo call So you push that and And although you can buy circuits, it'll do that Some of them are relatively expensive What drives this particular circuit is the insides of a greeting card The greeting cards that you open and they play a song Well, somebody gave me one that played the wall bash cannonball So I took the little electronics out of it put it under the layout hooked a push button up But it was too soft And so went down to the thrift store got a speaker set for a computer with a little amplifier in it Hooked that up and and that's what makes that work Next effect is this blast furnace inside sheffield steel And the interesting thing about that is that it's created using a transistor radio You just connect the speaker leads connect them to a red light bulb And the advantage of that is it provides a random effect Creating a random effect with electronics is a little bit of a challenge, but you tune the am radio to a Static and it's the static that drives the flickering light This is kansas city iron and scrap metal animation here is this little pillar crane That's an alexander scale models kit and although those have been around for a long time Detailed and weathered it looks really nice on the layout Again, it's a realistic animation. It's something that would happen in real life The visitors are always surprised when the crane starts to move these scrap piles I wanted them realistic So I think the only way to get this to look like individual pieces is to use individual pieces And so underneath this is crumpled tinfoil I use Rustolium's ruddy iron ready red primer. I think that's the correct name For this iron color. I sprayed the tin foil that color I kept all these scrap pieces from projects put them in a box sprayed them iron color Shook them up till they were all coated And then glued them on starting with the largest Least detail pieces first and working up to these medium sized pieces And then saving the finest detailed tiny pieces to put on top Then I went around with a little grimy black here and there A little silver paint here and there and then came back with a black and Rust powdered chalk colors to create that effect So on the left side of union station here is powerhouse number one And in that I stole and stole a sooth smoke generator The power plant was originally coal burning hence the tall smokestack And so to animate that I put a smoke generator in This roof lifts off And you can see there's a plug in socket that connect that to the Power plant. So if anything goes wrong with it, you can just simply lift it off and replace a little smoke generator inside So where I grew up in california deer knots berry farm There was one of the famous copper tone signs And it was an animated sign So no one I know of makes this sign in ho scale Or any scale So I thought wouldn't it be fun to recreate the sign? And considering it's only one of eighth of an inch thick Wouldn't it be neat if I could find a way to animate it like the one that I grew up with And so there's a little motor down inside the building which animates the sign The sign is on sheet brass The dog in the swimsuit are on thin sheet brass And at the pivot points where her hand are And the dog's backside is our tiny pieces of brass tubing And there is a hairpin shaped piece of brass that bends across the front of the sign and the back of the sign on the front of the sign it supports The swimsuit and the dog and on the back side of the sign There's a little wire with a loop in it that moves those wires up and down and creates the animation When I grew up I always enjoyed the animated industrial signs And so I've incorporated a number of them on the layout One of this one of them is this commercially available sign for arctic refrigeration As the sign Changes the words come on The thermometer goes down the ice forms and then it says we take the heat out Nick we're standing in front of an f7 cab that's correct actually the you know the whole front end of an f7 That's it. So what on earth were you thinking of to have this thing, but how did you do it? How did you get this into your basement? Well, what I was thinking of a long time ago in model railroad or there was an article on building sort of a half scale throttle And brake stand which I as a kid. I thought that was really cool and so Then a friend asked me if I wanted to buy a kansas city southern nw2 control stand he said I know usually collect paper. That's a little big I said sure So I bought that and restored it and then I wanted a road unit throttle, you know switcher throttle. They It's just like your car the accelerator goes from zero to a hundred percent just by moving it Whereas on a road locomotive. They have those eight discrete notches which allows The prime movers to come up together so I Got ahold of the scrap yard in dakoma and asked them if I could buy a throttle and a brake stand and a dash and a chair and I said sure so I went down there and went around the scrap yard and while the throttle was 75 dollars and the Brake stand was 25 dollars and the chair was 25 dollars and the dash was 15 dollars and Then he said well, what are you trying to do mock up the cab of a diesel locomotive?  Yeah. No, I mean, what would you do with it? How would you get it home? Where would you put it? And then I got the thinking well, you know So if you cut off the nose and cut the cab in half, so I just have the engineer's side Which is what I was trying to do to begin with Um, that's let's see eight feet by five feet put a giant mirror there That'd be weird. You'd see yourself. But anyway, that's doable So I went back and I told him I'll take the engineer's side He said oh man the fireman's side. We just cut it up for scrap make toyotas out of it I'll just give it to you. I mean, there's nothing in it of value. You can just have it I thought oh, okay Now we're talking 10 by eight feet And then bless my dear supportive wife's heart on the way home. She said well, what will happen to the nose I said don't cut it up make toyotas out of it. She said well, can you stand to see that happening? That's the nicest part of the whole locomotive So that's how we ended up with the cab but from Tacoma to Up here north of seattle. That's a bit of a trip and I don't think you just I don't think you just took this and walked down the stairs in the basement with it. No, uh, you know and so there are there lies a tale because Yes, I still had to cut into three pieces had the nose cut off I had the cab cut in two halves that allow us to haul it on a U haul trailer that we could rent for $19 a day for two days Versus a commercial trucker since it's an over-width load at at 10 feet I didn't know how much that cost. I didn't want to find out how much that cost And so it came home in three pieces just like I'd originally intended And uh, I bolted it together Would you fill the seams with squat? Well, I didn't fill them right away It's set in the backyard and in the backyard we sandblasted it Filthy job and we repainted it and restored it and of course then when it came time to dig the basement It was sitting right on top of where we would dig the basement So you didn't already have a basement? No had to move it alongside the garage so we could dig the hole for the basement So we dug the basement. They laid up the concrete block poured the cement And then uh, well, it's we have a church member who owns a trust company And he was very gracious to come out all three times with his trust crane and move the cab around And so the final time we set it in the basement Uh, there's a tube steel frame under it which allows it to rock back and forth and ultimately I had it welded back together that was a command decision I was going to just bolt it body putty it But if you're going to rock it back and forth seams are going to open up fiberglass is going to be popping out That's not good. So I call my friendly welder and they welded it back together down here in the basement and then I Body putted it and sanded it and repainted it down here in the basement Now this cab is Operational isn't obviously you don't have to prime movers behind it anymore. Yeah, but the headlight here works Yes, the defroster fans the heater fans. In fact one engineer Used to run a few and it said wow, this is a lot different than the ones I used to work in and I'm thinking Well, you know, I try to be really accurate and I said how so he said the things in it work Well, there you have it


वैज्ध सलिएत Fashion,😭 अपतिमा�派 धफाव पर्मकिन। वैजध आझोसबाटूendra विजध क чет कराथगि। बजअ़िमर बाद़नoused Power表 on on on on the outcome of differences ना�otte गुँउउउउउउउउउउउउउ If we called demand Backday As a result within its resources. So, today we will talk about its preferences. You know that in economics we use the concept of utility to show preferences. And, for this we have a very useful tool, the tool of Indifference Curve. We show the preferences of any individual through Indifference Curves. माएक्रोए्रामिख्सके, बाजी कोर्सेिज में आप विसकी डेटेल सपाट्रुके हैं के अःटिप्रन्स कर्व कै है, अःटिप्रन्स कर्व actuali, यए उन उन कुमबिनश्यच को शुक हरता है, जिस परुटिलेटी कोंस्च्ट्रन कैं ती हैं. यक यागा ड़ेटिये यागा ती? अच्ट़ागराम देखें, हम ने दो अ आपस तावाग बब़ी इस्टी करीगें. आपस औक यह दिखात नहीं उरड़़ी एक यह आपस उटी थी थी अजोग़े थी बारी ख़।. total utility remains constant. So, if you move along this ic1 all points on this ic1 for example, we have three points x, y and z. So, according to the definition of the indifference curve the total utility on all these three points x, y and z is same. And ic2 is another indifference curve. And similarly, on this ic2 all the different points will give the same utility. We will note two or three things regarding the indifference curve. The first thing is that indifference curves are negatively sloped. y negatively sloped If you compare points z and x, then on z current consumption is 63000 and future consumption is 39000. So, if you reduce current consumption when you move along z to x, then what will happen? Your current consumption is decreasing. So, to keep the total utility constant current consumption is decreasing and your current consumption is decreasing. So, to keep the total utility constant it is necessary to increase the future consumption. So, that is why these negatively sloped indifference curves are coming. And higher indifference curve, higher level of satisfaction. ic2 is to the right of ic1. So, ic2 from ic1 the higher level of satisfaction is seen. ic2 has all the points, for example w. This is the only point. These all the points of ic1, x, y and z, you can compare them. So, w is giving more utility than any point on ic1. Why is that? इसके रीजन्त आप अगरगे जी और ऐक हो देक हैं जी पर मैंने बता है कि करन्ड क्नडम्स्यन खेर्च ती टी शुक्ची टी खुएक। तर्छी आईन उत्वाईन तोवो याखश्तको ठारेत है आपक लोगा पुटी एक दिया से अंत्री म्रगले था तो इस दी तोनो को ज़ाएन कर रहें, तो इस टेट लाएन पर दब्लुपाईट रहें। तो क्या दब्लु क्या दब्लु is simply the, you can say the average, weighted average of X and Z. तोनो की एक अपरच है. दब्लुपर क्या वर है? कि वो वो अपनी कंडंदमशन को समुथ कर रहें. अपर करन्द जाडा है, फुछर काम है, और X पर इसके रिवर सूरते हालगेद, जबको दब्लुपर करन्द तोर फुछर दोनो 51,000 है. तो समुथिंग प्रन्चीपल हम इस पर भी बात कर चुकें, इन्दिविच्छल तुहें वो ये चाते है, कि उसंका लाइप पेट्रन वो समुथ हो, उनके इंकमस में तो फुलक्टूऊशन जाती रहती है, लेकन उन फुलक्टूऊशन को सेविंग के दरिये से वो कोशिष करते है, तो समुथ कंदम्षन को हमेश्या वो एकस्ट्रीम कंदम्षन से प्रेफर करेंगे, आज्स वाई व जे है, वो एक हाईर इंदिविच्छल करव पर है, अगर आप इसको अख्सर जी से कमपेर करेंगे, इन बातों को हम समराएस करेंगे, इन बातों को हम समराएस करेंगे, पहला पुण्ट इंदिविष्ट्रीम करव के बारे में क्या है, के इट्स लोग्स दाऊवर्ट from left to right, less consumption in one period requires more consumption in the other period so that the total utility is constant. Second, हम ने क्या देखा, के higher इंदिविष्ट्रीम कर, higher level of satisfaction. So, third is that indifference curves are bored towards the origin. They are convex to the origin. In the microeconomics course, you are diminishing the concept of marginal utility. They will be familiar. Because it is not a microeconomics course, it is a microeconomics course, that is why we are not going into detail. So, we are simply saying that these indifference curves are convex to the origin. So, now we have seen two things. One is that the budget constraints have been discussed about the available resources available to the consumer. And with the help of indifference curves, we have understood its utility preferences. We have shown it. So, the budget constraint, the red line, you have a budget constraint. I told you that this triangle is actually showing what is available to it. Which current and future consumption pairs can be afforded in the resources available to it. It cannot be out of this triangle. For example, point T, we have drawn three indifference curves. The highest point T is the utility which is available to it. So, the highest point T is if you compare it with any other D, E or B. But since it is outside of its budget space, this is unattainable for it. For it, B is attainable, E is attainable and D is attainable. But, who will choose that? B and E are on a lower indifference curve. B, D and E are on a total expenditure same. Because they are coming above the budget line on the same line.  But the total utility is more than B and E on D. So, D is on a higher indifference curve. B and E are on a lower indifference curve. So, where will its utility maximization be? In microeconomics, you know, where the indifference curve becomes the tangent of the budget line. So, this is the tangency point. This is D. So, D is the optimal level of consumption. What is D? According to D, current consumption is 45000. And future consumption is 49500. So, this is its current and future consumption. So, this is the pair which is given to the available resources. It provides maximum satisfaction level. It is the highest possible indifference curve. So, we are using numerical values. So, on this point, on D point, if you want to calculate its saving, if you recall, we said that its current income is 42000 in the last module. What is the consumption? 45000. So, how much will its saving be? Minus 3000. Okay. And future AF. We are using AF that in the future period, when it starts, it will have what assets, what wealth, it will have available. What will be available? Y plus A minus C, right? Y current income A, which was available to it, wealth, C is the consumption. We are putting these values. We are putting the value of Y is 42000. A's value was 18000. Condumption was 45000. So, these are the answers to this. These are the resources available to us in the current period. And we can carry this in the future period. But we will multiply these with 1.1. Because we will get an interest on these. So, if you do this calculation, you will get its answer. 16500. So, what will be the future consumption? First, these 16500, which you have brought from the previous period, these resources are with it. Plus, in the second period, it will do ARNB, it will provide some labour services. These are the value of YF. So, these are 49500. In the second period, there will be total available resources. And since we have assumed that its lifespan is on two-time periods, in the second period, all its resources will be spent. So, CF is 49500. So, in this way, you can see these numerical things. Thank you very much.


Support Accounting Instruction by clicking the link below, giving you a free membership to all of the content on our website, broken out by category, further broken out by course. Each course then organized in a logical, reasonable fashion, making it much more easy to find what you need than can be done on a YouTube page. We also include added resources such as Excel practice problems, PDF files, and more, like QuickBooks backup files, when applicable. So once again, click the link below for a free month membership to our website and all the content on it. 30,000 here, we need to amortize over the life of the bond. So we're basically just going to divide it out by the number of payments and then reduce it at the same time of each payment. And we're going to reduce it to the other side will be interest expense. Why? Because that 30,000 came about because of the difference in the market rate and the rate that was on bond. So let's think about that type of amortization schedule we'll have, which is just going to be straight line amortization. So when we put the bond on the books at one one, we had a 30,000 unamortized discount here and the carrying amount of the bond then was issued at 240,000 minus or plus in this case, the 30,000 and entered. So it was the carrying amount then was the 270, which is of course the 240 and 30. Then after six months, we're going to pay off some interest on 630 and therefore, how much are we going to pay off? Let's take off the calculator here. There's a couple of ways we can calculate it. We're going to say that we have a 30,000 amount that we have to amortize over the life of the bond. We could divide it by the number of years divided by 15 years. Enter that would give us 2000. That's per year. But we're going to do this every six months, so twice a year. So we could then divide it by two and it's going to be 1,000. Next way we can think about it, we can say 30,000. It's 15 years, but we do it twice a year, therefore it's 30 periods that we're talking about. So we could just divide it by 30 and that would give us the same 1,000. So let's do that calculation here. I'm going to say this equals the 30,000 divided by, in this case just 30 periods, 15 years times two basically. And enter that's 1,000. Then what's going to happen to the unamortized premium equals the 30,000 minus the 1,000 that we're going to reduce it by brings it to 29. Then the carrying amount then will be, we can think of it this way, it's going to be the 240,000, which is the face amount of the bond here, plus the 29 and it went down by 1,000 to 269. So after we post this transaction, this journal entry then we would assume that this amount is going to stay the same because we're not paying off any of the principle. This amount is going to go down to 29 and this minus this will be the carrying amount of 269. So therefore what we have to do then is we got to take this premium, we got to reduce it by this $1,000. So this has a credit balance, therefore we're going to do the opposite thing to it, which in this case would be a debit. So I'm going to copy that, I'm going to right click and copy, I'm going to put this over here in C26, right click and paste 1,2,3. And we will debit that amount for $1,000. Okay, so now the interest expense is going to be the difference between those two obviously. So I'm going to do that with the negative sum function. I'm going to say negative sum and we could move this out of the way. You could put it here and move it up here and you could highlight from the bottom up. So it's going to be then 86, 86 plus the $1,000 equals the $9,6. Debits equal the credits. If we highlight all of these cells then the debits minus the credits equals zero. A couple of things to note here, note that I put this on the bottom because it was helpful for me to build the journal entry. But if you're in a picky system that wants the two debits on top, you might have to adjust that and put the two debits on top. It really doesn't matter as long as they're in the right column and they're in the right format in terms of a negative number in this case. But some systems, you're going to need that on top. And also note that this amount is actually kind of reducing the interest expense which can be a little bit confusing and that's because of course we're at a premium. We issued it at a premium in this case rather than a discount. All right, so let's post this out. We're going to say the bond interest expense is here, it's going to be here on the trial balance. We're going to post it to the blue section in I-29. So within I-29 we're going to select equals and point to that 86. It's going to bring this up in the debit direction, put us out of balance, going to bring net income down. So note that the interest expense, just like kind of rent expense, we're renting the money, brought net income down like so. And then we're going to post the cash. So here's the cash here. Here it is on the trial balance, there's something in it. Therefore we're just going to double click on it, go to the end of it and plus. And then post to that cash, 96, that's going to bring the cash down. Then we're going to go to the premium on bond payable. Once again something's in there, so I'm going to double click on it, go to the end of it and plus point to the 1,000 here. That's going to bring this 30,000 down to 29. So now we have the 240 didn't go down because we're not paying any principle off. And we amortized the premium down like so, the carrying amount if we highlight both of them, 269,000, 269,000. Again a lot of people get disturbed by the fact that the principle doesn't go down at all as it does in other types of liabilities like a mortgage or like a car payment. That's just going to be the terms of the note. We're just paying the rent on it. We'll pay the entire 240 at the end of the term being in 15 years in this case. All right, so we're going to do the same type of thing again. We're going to have the 1231 record bond interest in straight line amortization. So on 1231 we will basically do a very similar journal entry here, pretty much the same journal entry here. So, but let's think through it one more time. What we're going to do is cash affected our first question. And yes, cash is affected. It's now all the way out in 1231. We are going to pay the interest once again and cash has a debit balance. We need to make it go down. Therefore, we're going to do the opposite thing to it, which in this case would be a credit. So I'm going to copy the cash, copy the cash. We're going to put that under the date. I'm in cell C29, right click, paste 123. And then how much are we going to credit for? Well, let's pull out the calculator one time and do the calculation with a calculator one more time. And the question being, how much are we going to pay when we calculate it? We take the stuff that's been written in stone, not the market value stuff. We have the face amount, which is already on the bond. It's written on the bond 240,000. And then we're going to multiply it times the rate that is written on the bond, not the market rate, the rate that's on the bond. It's written in stone times 0.08 in this case. That gives us 19-2. Remember that any time we talk about interest, we mean for a year. And then we have to say, well, did we rent it for a year? No, it's only been rented for six out of 12 months. So if we think that's one half, six 12s. So we could think of that in terms of a ratio. I could think of it, let's break it down to a monthly amount divided by 12. Which means that we're paying 1,006 per month times six months. And that will give us the 9,6. I'm going to do that same calculation over here in E29. I'm going to start with a negative to make it a negative number. We're going to have the 240,000 face amount times 0.08 interest. This time I'm just going to divide it by 2 for half a year. Because it's 612ths of a year, one half of a year divided by 2. All right, so there is that. Then, of course, the other side is going to go to bond interest expense. Why? Because it's just like rent in the house. We rented the money, we've got to pay the rent on it. Rent's called interest when we rent money. And we can see that we have a debit balance here. We need to make it go up in the debit direction because expenses always go up. How do we do that? We do the same thing to it, which in this case would be another debit. So I'm going to copy that, I'm going to paste that up top in C28. Right click and paste it 1, 2, 3. Now you would think that we would debit it by the 9.6, but we've got the premium over here that we need to amortize over the life of the bond. And we're going to amortize it using a straight line method. So if we go to our amortization table, as we do this on 12.31, we're going to do the same thing here. So how much are we going to amortize? Well, of course, we're going to amortize the same 1000 because it's a straight line method. But how did we get that? We get the 30,000 divided by 15 years times 2, meaning we have 30 periods divided by 30 is going to give us the 1000 per period. And then what should the unamortized premium be? Well, we have 29. So it's going to equal this 29 that it was before minus the amount that's been amortized for this period, 1000. So we're going to bring it down to 28. And then we can calculate the carrying amount as being the 240 face amount. That's this amount here. And then we're going to add to it the 29,000 gives us a carrying of 268. And of course, we could also calculate that by the 269 minus the 1000 here. All right. So what does that mean? That means that at the end of the day, this is going to stay at 240 after we record this journal entry. This is going to go down to 28, which means that this minus this once we're done will be the 268,000. So that also means that we're going to have to bring down the premium by 1000. So here's the premium. It's at 29. We can see it has a credit balance. We need to bring it down. How do we bring something down? We do the opposite thing to it, which in this case is a debit. So I'm going to copy that right click and copy it. We're going to put that down here in C 30 right click and paste 123 in D 30. We're going to put that $1,000. And now, of course, we have a credit of 96, a debit of 1000 difference is 86. That's what we need up here in the debit. That's what's going to be the bond interest expense. So I'm going to do that with our negative sum formula like so I'm going to move this out of the way because it's always in my way right there, but I could have just highlighted from the bottom up and left it there and it would have been okay too. And that will give us our 86, 86 plus 1000 gives us the 96, which equals our credit. And if we highlight all of them also in balance in that format as well. Okay, so just remember to note that we do, I did put this on the bottom and we don't have our two debits on top. So that could cause problems depending on who's, you know, grading your software. If you're using actual software in practice, it won't be a problem and I highly recommend building your journal entries in such a way that makes the most sense to you. If you had to go back and look at it and be audited on it so you can tell the auditor, Hey, this is what we did. But if you're doing it for software for grading purposes, sometimes they can be really picking in terms of how the format looks. So we're going to post this. Here's bond interest expense. Here's the bond interest expense here. We're going to post this to I 29 something is in it, therefore, I'm going to double click on it. We'll go to the end of it and plus we're going to post this 86 right there. That's going to bring the interest expense up, put us out of balance and bring that income down. So remember net income is the sales in this case revenue minus the expenses and the expense of interest is similar to rent expense. We're renting the money called interest increase in the expense decreasing that income. Then we have the cash here cash is here on the trial balance and we're going to post it to I 20 going to double click on it because something is in it. We're going to go to the end of it and select plus and then we'll point to that 96 and that will bring cash down because we're paying off the interest. Then we're going to post the premium of 1000 here it is the premium here. Here's the premium here. We're going to go to the blue area in I 24 double click go to the end of it and plus and we're going to post that 1000 and enter. So that puts us back in balance. Hopefully you can see the trend that is happening now of course in that there's no change to the bond payable because we're not going to pay that off until the end of the period and that's just the term of the bond after 15 years. The premium will go down by the 1000 and we're going to make it go down in a straight line method by 1000 per period 30 periods because there's 15 years and we pay semi annually twice a year and then of course the expense will be reflected as the difference. The carrying a value in this case is 268,000. It will be at the end of 15 years just 41,240,000 because we will have to amortize of this down to zero thereby leaving us with a 240 that we will have to then pay as of the end of the term of the bond being 15 years in this case.