Timeline for Why does distribution density seem to change though Liouville says it shouldn't?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2018 at 16:58 | vote | accept | Damon | ||
| Apr 17, 2018 at 15:54 | answer | added | Cosmas Zachos | timeline score: 0 | |
| Apr 17, 2018 at 13:18 | comment | added | honeste_vivere | Might be worth looking at: physics.stackexchange.com/a/177972/59023 | |
| Apr 17, 2018 at 7:03 | answer | added | user8153 | timeline score: 2 | |
| Apr 17, 2018 at 3:15 | comment | added | ZachMcDargh | Liouville's theorem states that phase space volume is preserved by the Hamiltonian flow. If I understand correctly, you are considering an initial particle distribution that has zero volume (it's just the sum of a few $\delta$-functions). The volume is still zero after time-evolving the system. | |
| Apr 16, 2018 at 22:43 | comment | added | Damon | I don't really understand the question. I'm sorry. This could be thought of as a waterfall problem in two-dimensions. In the y-direction is a constant velocity river of particles that approaches a cliff. The origin in the plot is where the particles go off the cliff (all x=0 before the cliff, so not zero density but high density). This turns it to a 4D phase space, but the y-velocity is constant and the spacing between points in vy is constant. The changes in the phase space density are only those from this plot. I don't know that this helps! | |
| Apr 16, 2018 at 22:32 | comment | added | JohnS | Is this really a Hamiltonian flow? At t=0 the density is zero, as your plot shows. What are your boundary conditions at the bottom of your system? | |
| Apr 16, 2018 at 22:14 | history | edited | Damon | CC BY-SA 3.0 |
added 635 characters in body
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| Apr 16, 2018 at 21:06 | comment | added | Damon | Sorry, I wasn't very clear. It is a plot of particle phase space (velocity vs. position). If particles are released at constant interval from the origin from rest and one takes a snap shot some time later, this shows the distribution of those particles in phase space when the snap shot is taken. Spacing between particles should be indicative of phase space density. | |
| Apr 16, 2018 at 20:55 | comment | added | ZachMcDargh | I'm a little unclear on what's going on here. What exactly is being plotted? | |
| Apr 16, 2018 at 18:19 | review | First posts | |||
| Apr 16, 2018 at 18:32 | |||||
| Apr 16, 2018 at 18:19 | history | asked | Damon | CC BY-SA 3.0 |