The spinning top above illustrates an unusual asymmetry where it flips over if spun in a clockwise motion and stays upright when spun counterclockwise. This behavior is a result of chirality, a property in which something displays handedness. When an object or system is chiral, its mirror images can’t be exactly mapped to each other–like your right and left hands.
Tadashi Tokieda, director of studies in mathematics at Trinity Hall, University of Cambridge, investigates and invents toys like the one above that exhibit interesting behaviors. He’s also a fellow at Harvard’s Radcliffe Institute for Advanced Study, where he presented what he calls the world’s first chiral tippy top. See the video with this and other toys that display chirality below.
One of the most longstanding question in solar physics is why the Sun’s corona is hotter than its surface. This is known as the ’coronal heating problem’, and there’s no definite answer to that question. The Sun is a very complex magnetohydrodynamic system; there are different kinds of flows and instabilities that can play an important role in the energy-transport processes in the corona. The waves – pictured above, are initiated by a Kelvin-Helmholtz instability. The Kelvin–Helmholtz instability occurs not only in clouds and in the ocean, but also in various astrophysical environments. This instability occurs when two flows of different velocities move past one another in opposite directions with a strong enough shear to overcome the tension force. In the solar atmosphere, which is made of hot ionized plasma, the interplay of two hot-plasma jets and the embedded magnetic field might trigger turbulent flows which could help add heating energy to the corona.
The Navier-Stokes equation is one of the governing equations of fluid dynamics and is an expression of conservation of momentum in a fluid. With the exception of a few very specific and simplified cases, there is no known general solution to equation. Instead, the equation, or a simplified model, is solved numerically using supercomputers as part of direct numerical simulation (DNS) or other forms of computational fluid dynamics (CFD). These methods allow scientists and engineers to solve the equations of fluid motion for practical problems from flow through a pipe to flow around a re-entering spacecraft.
Existence and Smoothness
Although the Navier-Stokes equation has been known for more than 150 years and can be solved numerically for many situations, some basic mathematical aspects of the equation have not yet been proven. For example, no one has proven that a general solution always exists in three-dimensions and that the energy of such a solution is bounded at all points. Colloquially, this is known as the Navier-Stokes existence and smoothness problem. The Clay Mathematics Institute has a very specific problem statement (PDF) asking for a proof (or counter-proof) of the existence and smoothness of the Navier-Stokes equation for an incompressible fluid in three-dimensions. Otelbaev contends that he has provided such a proof.
Otelbaev’s Proposed Solution
Mukhtarbay Otelbaev is an experienced mathematician with numerouspapers addressing related mathematical problems. His latest paper, entitled “Existence of a strong solution to the Navier-Stokes equation,” is freely available online (PDF, in Russian, with an English abstract at the end). There is an ongoing project to translate the paper into English, and mathematicians are already evaluating the validity of this proposed solution. From what I can gather of the paper, it specifically address the Millennium Prize problem and presents Otelbaev’s proposed solution for the existence and smoothness of an incompressible fluid in three dimensions with periodic boundary conditions.
What It Means
As with any announcement of a major technical breakthrough, skepticism is warranted while experts evaluate the proposal. If the mathematical community upholds the validity of Otelbaev’s proof, he may be offered the Millennium Prize and other honors. More importantly, his solution could lead to a better understanding of the nature of the equation and the flows it describes. It is not, in itself, a general solution to the Navier-Stokes equation, but it may be a stepping stone in the path toward one. In the meantime, scientists and engineers will continue to rely on a combination of theory, experiment, and computation to progress our understanding of fluid dynamics.
I think somewhere between you being an electron and me being a proton, I fall in love with you so madly. We are electric, magnetic, and dynamic. You are attracted to the way I pull you off me, and nothing would kill you but the electroshock running through your veins every time you want to touch me.
And you put my molecules on fire and they cry while burning: I am in love, I am in love and I love you. Moreover, I pretend I don’t hear them cause it hurts too much to know that we are not a symbiosis, that you only take and take and never ever give anything back.
Why don’t you combine your cells with mine? Destroy the walls and let them float in this blood of madness. Because we are not from here and every element of us is calling towards the west coast, and why don’t you die on my heart? Let the scientists study who we are…
Because we are a different kind of species.
Science Is Writing About Us, Baby by Royla Asghar
I always thought those physics word problems were so stupid like “You’re a physics student so you decided to figure out the speed of ____ from the variables you’re given like the nerdy asshole you are” and I was always like “literally no one is like that” but today I was in the hall elevator and it’s always so fucking slow and so I was like “well if I measure the time it takes to go from one floor to the next while it’s at top velocity and I take the average length of a floor in my building I can figure out that this elevator travels at 2.3 m/s or 5.1 mph and then I can even take the average time it takes a person to climb a flight of stairs to figure out if this elevator is faster than the stairs or not IVE BECOME THAT NERDY ASSHOLE IN THOSE STORY PROBLEMS I HAVE BECOME THE ENEMY