Timeline for Movement of repelled particles in a ball
Current License: CC BY-SA 4.0
19 events
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| Mar 27, 2020 at 15:37 | vote | accept | asv | ||
| Mar 26, 2020 at 0:14 | answer | added | Dominik | timeline score: 8 | |
| Mar 25, 2020 at 22:19 | answer | added | Karl Fabian | timeline score: 3 | |
| Mar 25, 2020 at 19:22 | comment | added | MTyson | Let $r(t)$ be the distance of the farthest particle from the origin. It is piecewise analytic. When $r$ is not analytic, a particle has just passed another particle and it is easy to see that $r'$ doesn't decrease. When $r$ is analytic, the net force on an extremal particle is directed outwards and bounded below by some fixed $\epsilon$ (thanks to a short calculation with the $1/r^2$-law and the assumption that $r<R$), so $r''>\epsilon$. These two conditions show $r\to\infty$. This argument breaks down when the force is weaker than a $1/r$-law or isn't analytic. | |
| Mar 25, 2020 at 19:21 | comment | added | Steven Stadnicki | (To clarify a bit: it won't necessarily always be the case that that specific particle is outward-moving, but that whatever particle is currently furthest from the origin will be outward-moving.) | |
| Mar 25, 2020 at 19:19 | comment | added | Steven Stadnicki | An idle thought, I don't know if it can pan out but it's a possible angle: consider particles by their distance from the origin. Then if at any time $t_0$ the particle furthest from the origin is outward-moving (i.e., its velocity has positive dot product with the vector from the origin to its position), that will be true for all times $t\gt t_0$. It may be possible to show that in that case velocity of the most distant body is $\Omega(1/r)$, in which case the distance from the origin would have to grow as at least $\Omega(\log r)$; then all that's left is showing that it's true at some point. | |
| Mar 25, 2020 at 17:29 | comment | added | Steven Stadnicki | @SteveHuntsman Those are, unfortunately, for an attractive force; the repulsive case is very different. | |
| Mar 25, 2020 at 15:34 | history | edited | asv |
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| Mar 25, 2020 at 15:25 | comment | added | Steve Huntsman | en.wikipedia.org/wiki/N-body_choreography | |
| Mar 25, 2020 at 14:50 | comment | added | asv | @MichaelEngelhardt: Ok, corrected. | |
| Mar 25, 2020 at 14:49 | history | edited | asv | CC BY-SA 4.0 |
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| Mar 25, 2020 at 14:37 | comment | added | Michael Engelhardt | Nitpick: For $N=1$, it's possible. | |
| Mar 25, 2020 at 13:54 | history | edited | asv | CC BY-SA 4.0 |
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| Mar 25, 2020 at 9:07 | history | edited | asv | CC BY-SA 4.0 |
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| Mar 25, 2020 at 9:00 | history | edited | asv | CC BY-SA 4.0 |
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| Mar 25, 2020 at 8:46 | history | edited | asv | CC BY-SA 4.0 |
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| Mar 25, 2020 at 8:25 | comment | added | asv | @gmvh : I expect that this is impossible. | |
| Mar 25, 2020 at 8:06 | comment | added | gmvh | Why should one expect this to be possible? At least for $N=2$ (Coulomb scattering) it looks impossible. | |
| Mar 25, 2020 at 5:27 | history | asked | asv | CC BY-SA 4.0 |