Timeline for Electrons on a pancake ellipsoid
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jan 2, 2017 at 0:06 | comment | added | Wlodek Kuperberg | The perfectly flat pancake (a circular disk) could also be considered, as the limiting case. What would the configurations of a reasonably small numbers $k$ of electrons look like? One can predict some configurations for $k\le 7$ maybe a few beyond $7$. At which value of $k$ lack of symmetry occurs first? | |
| Feb 28, 2016 at 15:35 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 353 characters in body
|
| Feb 28, 2016 at 15:21 | comment | added | user21349 | The continuous case has been solved for a more general class of shapes that includes oblate ellipsoids. See I W McAllister 1990 J. Phys. D: Appl. Phys. 23 359 doi:10.1088/0022-3727/23/3/016 and math.stackexchange.com/questions/112662/… . | |
| Feb 28, 2016 at 14:54 | comment | added | Yoav Kallus | A little Googling came up with this homework problem(?): (physics.princeton.edu/~mcdonald/examples/ellipsoid.pdf), but I haven't checked the calculation. The electrostatic calculation gives the asymptotic density when the number of electrons is very large. | |
| Feb 28, 2016 at 14:44 | comment | added | Manfred Weis | For an experimental answer, you might try to obtain such an oblate ellipsoid made metal and then apply some ferrofluid to it youtube.com/watch?v=5APHa7vscoI | |
| Feb 28, 2016 at 14:42 | comment | added | Carlo Beenakker | software that will calculate this for you is provided in Charged particles constrained to a curved surface | |
| Feb 28, 2016 at 14:42 | comment | added | Yoav Kallus | The answer for minimizing the potential energy (I am assuming a Coulomb potential) and maximizing the minimum distance are going to be very different. The latter gives an asymptotically uniform distribution, while the former will give an uneven distribution with much lower density on the top and bottom. The transition between asymptotic uniformity and nonuniformity is discussed in Hardin and Saff, 2005 dx.doi.org/10.1016/j.aim.2004.05.006 | |
| Feb 28, 2016 at 14:32 | comment | added | Manfred Weis | Is the ellipsoid an isolator? Would be yet another variant under which the solutions may be different. | |
| Feb 28, 2016 at 13:54 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
"flying-saucer" is not as good an analogy as "pancake."
|
| Feb 28, 2016 at 3:01 | comment | added | Gerhard Paseman | I was going to suggest capacitor design, but this is a different situation. Nevertheless, you might have some success asking this in an electrical engineering forum, even if they are less concerned with precision. Gerhard "Or Do I Mean Accuracy" Paseman, 2016.02.27. | |
| Feb 28, 2016 at 2:35 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |