The Case for Dwarf K Stars

61 Cygni, a binary K-type star system - via commons
The stellar main-sequence is a strip that cuts diagonally the Hertzsprung-Russell diagram, a star's plot of stellar color versus brightness. The main feature of main-sequence stars is that they burn hydrogen. In this group the K dwarfs, or orange dwarfs, are intermediate stars in size between red M stars (red dwarfs) and yellow G stars. Their mass is between 0.5 and 0.8 times the Sun's mass and surface temperature is bewteen 3900 and 5200 K.
In the last few years these type of stars have become particularly interesting to astronomers, as they appear to have the characteristics to host life-as-we-know:

Uchuu: Universes' creator

If you are a superheroes' comics readers, you probably know All-Star Superman by Grant Morrison and Frank Quitely (if you want, I could publish a review of this comic). At some point in the story, Superman designs a small cubic universe to see what would happen on a planet like Earth without his presence. The development of intelligent life was also included in the Superman's simulation, but in essence even those of astronomers are structured in the same way: a cube of space of finite dimensions whose evolution is driven by a network of dark matter and dark energy.
At the end of the july 2021 it was realased Uchuu, presented as a suite of large high-resolution cosmological N-body simulations, in practice, a simulation that shows the evolution of dark matter structures in a cube of 9.63 billion light years on each side and made up of 2.1 trillion particles.
Uchuu's main goal is to shed light on the dark matter halos surrounding galaxies, but the researchers think that another field of use for their simulation is the study of gravitational lenses.
In any case, it is a tool that could be very useful for improving the algorithms generally used in astronomy to process the data collected by instruments such as satellites and telescopes.
Ishiyama, T., Prada, F., Klypin, A. A., Sinha, M., Metcalf, R. B., Jullo, E., ... & Vega-Martínez, C. A. (2021). The Uchuu simulations: Data Release 1 and dark matter halo concentrations. Monthly Notices of the Royal Astronomical Society, 506(3), 4210-4231. doi:10.1093/mnras/stab1755 (arXiv)
Skies & Universes
Uchuu project on Git-Hub

The dog-bone asteroid

Using the European Southern Observatory's Very Large Telescope (ESO's VLT), a team of astronomers have obtained the sharpest and most detailed images yet of the asteroid Kleopatra. The observations have allowed the team to constrain the 3D shape and mass of this peculiar asteroid, which resembles a dog bone, to a higher accuracy than ever before. Their research provides clues as to how this asteroid and the two moons that orbit it formed.
Kleopatra also possesses another characteristic: a two-moon system discovered in 2008 by Franck Marchis' team at the Keck Observatory.
It is interesting to observe that the dynamics of Kleopatra's three-body system and its moons turn out to be chaotic. I hope to soon publish an article on the problem of the three bodies to clarify this aspect.

Marchis, F., Jorda, L., Vernazza, P., Brož, M., Hanuš, J., Ferrais, M., ... & Yang, B. (2021). (216) Kleopatra, a low density critically rotating M-type asteroid. Astronomy&Astrophysics, 653. doi:10.1051/0004-6361/202140874
Broz, M., Marchis, F., Jorda, L., Hanuš, J., Vernazza, P., Ferrais, M., ... & Yang, B. (2021). An advanced multipole model for (216) Kleopatra triple system. Astronomy&Astrophysics, 653. doi:10.1051/0004-6361/202140901
Descamps, P., Marchis, F., Berthier, J., Emery, J. P., Duchêne, G., De Pater, I., ... & Macomber, B. (2011). Triplicity and physical characteristics of Asteroid (216) Kleopatra. Icarus, 211(2), 1022-1033. doi:10.1016/j.icarus.2010.11.016

Professor Politzer and the Rho Mesons: Simple Harmonic Oscillator

I want to talk today about things that shake and I hope my words aren't too opaque. One degree of freedom moving to and fro just how it moves we'd like to know we can represent all kinds of things by a single mass between ideal springs. Each spring's connected to a wall so the outer ends don't move at all
Let the mass be $m$ spring constant $k$ but don't let friction get in the way use Newton's laws and what have we got $F$ equals $m$ psi double dot that is also minus escape psi times 2 so now we have a diff eq and we can write down the general solution for the simple harmonic time evolution
Let omega be root 2 $k$ over $m$ here's the answer won't repeat again size a cosine omega t plus a phase call it $b$ so it's all very simple and you can see for any initial psi and velocity we can find the constants $a$ and $b$ and the equations exact for all time $t$
Now look again at the diff eq. It's homogeneous and linear too so if you add two solutions together there sums a solution that's even better. We call it the principle of superposition. You can use it to fit the boundary condition in fact there is no contradiction if we use it in a system that does have friction
In a real system nothing's perfect of course we have to include the frictional force suppose it goes as the velocity right minus $m$ gamma d psi dt now if the damping is not too strong our old solution is close but wrong see it starts out with some amplitude $a$ but after a while it just dies away
The amplitude decays exponentially as you can see experimentally as $e$ to the minus half gamma $t$. Now it's almost right but you see the frequency is lower as we can compute omega is now given by the square root of the quantity $k$ over $m$ times two minus quarter gamma squared now we're through
So now we have the complete solution for an oscillator's time evolution and when there's damping as everyone knows the amplitude decays and the frequency slows if we have two solutions no matter how chose you know we can always superpose and since you all find physics such fun to problems 12 18 and 21.

Class dismissed
In the video I use the notation used on en.wiki (audio source)

Slender Galaxies

The tradition of horror stories is full of hooded characters, but the great success of creepy pasta, short stories, but also animations and illustrations spread online, has led to the success of a particularly disturbing character, Eric Knudsen's Slender Man. And the above shot taken by the Hubble Space Telescope on June 19, 2019 is somewhat reminiscent of that disturbing kidnapper of children. From an astronomical point of view, the image captured a particularly advanced collision of two galaxies.
But as a fan of superhero comics I find that also Mr. Bloom, a Batman's villain recently introduced (2015), could be a very good alter ego of Arp-Madore 2026-424.

Maths in Europe: Seven cosmic messengers

Let us suppose we travel from Earth to the furthest observable point in the universe. We have seven satellites on our spacecraft, used to keep communications between us and the Earth. Let’s suppose that the speed of the satellites coincides with that of light, or in any case equal to a speed whose difference with c is negligible, while the speed of the spacecraft is $v = 2 / 3c$. The satellite, once it reaches Earth orbit, transmits the information we have loaded into its memory, then heads back to us to collect the new information. Meanwhile, within 24 hours of each other, we launch all the satellites.
The time each probe takes will be given by the formula $t = \frac{y_1+y_0}{c}$ where $y_0$ is the distance traveled on the outward journey (or if you prefer the relative position of the spacecraft respect to the Earth at the time the first probe was launched), $y_1$ the distance of the return (or the position of the spacecraft when the first probe returns) and c is the speed of the probe.
(continue on Mathematics in Europe)

Great number

The Large Numbers hypothesis asserts that all the large dimensionless numbers occurring in Nature are connected with the present epoch, expressed in atomic units, and thus vary with time. It requires that the gravitational constant G shall vary, and also that there shall be continuous creation of matter. The consistent following out of the hypothesis leads to the possibility of only two cosmological models. One of them, which occurs if one assumes that the continuous creation is a multiplication of existing matter, is Einstein’s cylindrical closed Universe. The other, which occurs if one assumes the continuous creation takes place uniformly through the whole of space, involves an approximately flat Minkowski space with a point of origin where the Big Bang occurred.
Dirac, P. A. M. (1974). Cosmological models and the large numbers hypothesis. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 338(1615), 439-446. doi:10.1098/rspa.1974.0095