Forgive the recent apparent obsession (I’d call it a fascination) with the #cycloid but I’ve just discovered something I’d not heard of before. It is also called a #TautochroneCurve or #Isochrone curve, which means that a particle starting from any location on the curve will get to the #MinimumPoint at precisely the same time as a particle starting at any other point.
Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic#curve with #period over the #circle's circumference and has #cusps whenever the point is in contact with the surface (the two sides of the curve are tangentially vertical at that point).
Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.
Interestingly, the length of the path that a point on the circumference takes during one whole revolution of the circle is precisely equal to the length of the perimeter of the smallest square that contains the circle.
In a new paper, #researchers propose that the #dynamics of #rotatingblackholes is constrained by the principle of #gaugesymmetry, which suggests that some changes of parameters of a physical system would have no measurable effect.
"We observe that oxygen #dynamics in #chiral environments (in particular its transport) depend on nuclear #spin, suggesting future applications for controlled #isotope separation to be used, for instance, in #NMR. To demonstrate the mechanism behind our findings, we formulate theoretical models based on a #nuclear-spin-enhanced switch between #electronic spin states."