Timeline for Long time behavior of noise process with flat spectral density and upper cutoff frequency
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 12 at 4:30 | vote | accept | DanielSank | ||
| Sep 12 at 4:29 | comment | added | DanielSank | Ohhhh, ok so the plot is for $x$, not for $\eta$. Now things make sense. | |
| Sep 11 at 21:23 | comment | added | Syrocco | And the formula $\dot x = \eta(t)$ is really just to say that the system is driven by some noise in an overdamped case. It is equivalent to your definition of the velocity having some power spectrum! This velocity spectrum being equal to the noise spectrum in the free overdamped case. | |
| Sep 11 at 21:18 | comment | added | Syrocco | MSD = mean square displacement = $\langle x(t)^2\rangle$ | |
| Sep 11 at 21:10 | comment | added | DanielSank | I have a few questions. 1) What is "MSD"? 2) I'm not sure I follow the logic. You're taking a case where $\dot{x}(t) = \eta(t)$ and then solving for the properties of $\eta$ such that the spectral density of $S$ satisfies the case described in the question. Ok, but what is plotted? Is that the MSD of $\eta$ or the MSD of $x$? | |
| Sep 5 at 15:15 | history | edited | Syrocco | CC BY-SA 4.0 |
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| Sep 5 at 15:00 | comment | added | DanielSank | Thank you. I'm going to wait a day or so for other answers but will likely accept this one. | |
| Sep 5 at 11:46 | history | edited | Syrocco | CC BY-SA 4.0 |
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| Sep 5 at 8:47 | history | edited | Syrocco | CC BY-SA 4.0 |
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| Sep 5 at 7:55 | history | answered | Syrocco | CC BY-SA 4.0 |