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Cato edited Payam.tex
almost 11 years ago
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\item In \citet{Rowghanian_Grosberg_2013} page 5, second column, they use dimensional analysis to justify a steady-state approximation used in the paper: the time taken to establish the fluid velocity profile around a section of DNA must be much shorter than the time taken the DNA to ``move past'' the velocity profile.
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\begin{enumerate} \begin{enumerate}[a]
\item I want to try to do a better job than Payam's scaling argument: what are the coefficients in the ``$\# \ll 1$'' relationship? This might be interesting because of a problem acknowledged in Payam's other paper: his predictions do not fit the experimental data.
\item Dimensional analysis argument not fully understood: I guessed $t_{\rm h}\sim \ell/c_{\rm s}$ on physical grounds, but Payam says $t_{\rm h}\sim \ell^2\rho/\eta$ from dimensional analysis. What is the interpretation of Payam's $t_{\rm h}$?
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\begin{itemize}[a] \begin{itemize}
\item The two $t_{\rm h}$s are measuring different things. Payam's $t_{\rm h}$ is considering the {\it diffusion }of a particle's momentum: the characteristic time in the velocity autocorrelation. My $t_{\rm h}$ is about information flow via sonic waves: this is much smaller than the vorticity time-scale.\\
I want to think about {\it which time scale is more appropriate in this context and why?}