Timeline for Stokes-Einstein rotational diffusion and vector orientation time
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2014 at 16:12 | comment | added | Ayn | Sorry, I should have actually bothered to read the section before commenting. But very nice that the expression for $<t>$ is exact! | |
| Feb 17, 2014 at 15:38 | comment | added | Carlo Beenakker | no, these terms are not there because you have to set $\omega$ to zero (meaning no "desorption", no probability for the particle to enter the sphere, it stays on the surface). Concerning the factor $R^2$: your $D_r$ is in radians squared per second, so this factor should not be there. | |
| Feb 17, 2014 at 15:31 | comment | added | Ayn | "...we're neglected the latter summation/integral term as a small positive constant that does not scale with the diffusion coefficient..." This doesn't matter, but is it safe to assume that this term is $<<1$? | |
| Feb 17, 2014 at 15:28 | comment | added | Ayn | Ok, I see. Regarding the unnumbered equation after Eq. 57 in arXiv:1101.5043: we're assuming the unit radius sphere, otherwise it's: $\langle t\rangle=\frac{2R^2}{D_{r}}...$, we're dropping the terms involving contributions from $D_2$ (related to bulk diffusion) (which seems OK to me), and we're neglected the latter summation/integral term as a small positive constant that does not scale with the diffusion coefficient. | |
| Feb 17, 2014 at 15:19 | comment | added | Carlo Beenakker | typo (missing $D_r$) corrected; the expression for $\langle t\rangle$ is the unnumbered equation after Eq. 57 in arXiv:1101.5043, for $\omega=0$ (no bulk diffusion, only surface diffusion). | |
| Feb 17, 2014 at 15:18 | vote | accept | Ayn | ||
| Feb 17, 2014 at 15:18 | comment | added | Ayn | This answers my question! However, if you could point out where $<t>$ was derived (unless you did it yourself) that would be very helpful for me in terms of understanding. | |
| Feb 17, 2014 at 15:16 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Feb 17, 2014 at 15:05 | comment | added | Ayn | Also, is the expression for $<t>$ starting from $\theta_0 \in (0, \pi)$ from the linked arXiv paper? I can't seem to find the derivation for it in the 3D case section. | |
| Feb 17, 2014 at 15:02 | comment | added | Ayn | I agree with your interpretation of the problem. However, I'm a little confused about your expression for $<t>$ provided random uniform initiation, shouldn't there for a $D_r$ term somewhere? | |
| Feb 17, 2014 at 14:57 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Feb 17, 2014 at 14:30 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
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| Feb 17, 2014 at 14:21 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |