5 Most #Amazing #Mathematical #Discoveries Made by #Amateurs : Medium
#Singularities Could Be #Doorways to Completely New Realities, #Scientists Suggest : Misc
When you might start #Speaking to #Robots : Tech Review
Check our latest #KnowledgeLinks
Recent searches
Search options
#singularities
0 posts0 participants0 posts today
The #Zhukovsky #Aerofoil (sometimes transliterated as #Joukowsky from #Russian), is a 2D model of #streamlined #Airflow past a #wing. It uses #ComplexVariable and is an #AnalyticFunction (i.e. #Differentiable everywhere, save at isolated #Singularities). Take a circle in the #ComplexPlane which is not quite centred at the #origin but passes through the #coordinate (1,0) or (z=1+0i).
GIF
I've just discovered (should be Sir) Roy Kerr (https://en.wikipedia.org/wiki/Roy_Kerr) , #NewZealand mathematician famous for his solution for rotating black holes published a paper last month which showed #singularities do not have to exist in a #BlackHole, at least not how the 2020 Nobel prize winner Sir Roger Penrose described. For #Physics this is a huge deal. For #NewZealand media it wasn't worth a mention. But, here is a description of what he's done if you are game. https://flip.it/iwDh4a
en.wikipedia.orgRoy Kerr - Wikipedia
"Although Roger Penrose won the Nobel Prize in physics just a few years ago for demonstrating how black holes come to exist in our Universe, singularities and all, the subject isn't closed. We've never peered beneath the event horizon, and have no way of detecting what's inside. Using a powerful mathematical argument, [Roy] Kerr argues that singularities shouldn't physically exist. He may be right."
https://bigthink.com/starts-with-a-bang/singularities-dont-exist-roy-kerr/
Big Think"Singularities don't exist," claims black hole pioneer Roy KerrThe brilliant mind who discovered the spacetime solution for rotating black holes claims singularities don't physically exist. Is he right?
Mathematical analysis of singularities in the diffusion model under the submanifold assumption
It occurred to me that #resolution of #singularities is very similar to giving birth. The outcome is an exceptional line and a total transform of your life … #mathjoke (with apologies to #algebraicgeometers )
The new result shows that #blackholes gain #mass in a way consistent with them containing #vacuumenergy, providing a source of #darkenergy and removing the need for #singularities to form at their center.
https://phys.org/news/2023-02-scientists-evidence-black-holes-source.html
Phys.orgScientists find first evidence that black holes are the source of dark energy
> One of the central problems in fluid dynamics is to figure out if the [Euler] equations ever fail, outputting nonsensical values that render them unable to predict a fluid’s future states.
> Mathematicians have long suspected that there exist initial conditions that cause the equations to break down. But they haven’t been able to prove it.
> In a preprint posted online last month, a pair of mathematicians has shown that a particular version of the Euler equations does indeed sometimes fail.
...
> Perhaps in some situations, the equations will proceed as expected, producing precise values for the state of the fluid at any given moment, only for one of those values to suddenly skyrocket to infinity. At that point, the Euler equations are said to give rise to a “singularity” — or, more dramatically, to “blow up.”
> Once they hit that singularity, the equations will no longer be able to compute the fluid’s flow.
...
Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations
https://www.quantamagazine.org/computer-helps-prove-long-sought-fluid-equation-singularity-20221116/
Very important and interesting work, if you're a mathematician, a physicist or an engineer that has ever 'crashed' with Euler/Navier-Stokes equations.
Quanta MagazineComputer Helps Prove Long-Sought Fluid Equation Singularity | Quanta MagazineFor more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.
Anyone here do #resolutions of #singularities explicitly?
A Plurality of #Singularities at the #GalacticCenter
#Astronomy #Picture of the Day
