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\section{Payam \& Shura's Papers}     DNA electrophoresis in vicinity of a membrane pore: \citet{2013PhRvE..87d2722R} and \citet{Rowghanian_Grosberg_2013}     {\bf Some questions}     \begin{enumerate}   \item What happens if an {\it interior} or bulk DNA piece approaches the pore?     \item In \citet{2013PhRvE..87d2723R} page 5, it is claimed that motion will be a superposition of longitudinal and transverse. Is this true -- won't one of them be unstable (in the case where work done in dragging is less than $T$, say)?     \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.   %   \begin{enumerate}   \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 $t_{\rm h}$?   %   \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, or the vorticity of the fluid; or the characteristic time in the velocity autocorrelation of neighbouring particles. 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?}     \item So, {\it what should the time-scale be from }physical {\it reasoning: what is the physics behind establishing the flow profile $\vec{v}(\vec{x})$ in the fluid around the DNA/jet?}\\   \citet{1959flme.book.....L} argue $\vec{v}(\vec{x})$ purely from momentum conservation / Gauss' Law, and symmetries of the momentum flux tensor. Time plays no role.     \item {\it Does Payam assume incompressible fluid?} Yes -- he follows \citet{1959flme.book.....L} pp. 86-88 in setting up the submerged jet; they assume zero divergence in the velocity field \& use stress tensor for incompressible flow. (The derivation in \citet{Broman_Rudenko_2010} also assumes incompressibility.) This means that the sound speed in his model will be infinite, and sonic information transfer will be irrelevant.     \item {\it Should I re-visit the derivation with sound included?}   Method 1: I would have to derive the formulae for the submerged jet in a compressible fluid, and perhaps solve the time-dependent Navier-Stokes equation.\\   Method 2: tack some ad-hoc changes onto the existing work -- e.g. treat the DNA/jet as an extended source of spherical waves. This will be {\it inconsistent} and crude, but probably easier than method 1.\\   In any case, a model with sound might be a more accurate model (see references below). It may also be more illuminating as to how the velocity profile is set up, and the nature of interactions between neighbouring DNA molecules.     \item {\it Which process (sound or vorticity) carries more momentum?} Read \citet{1959flme.book.....L} chapter 8 (p. 245), on sound. Specifically: how does a sound wave get generated; how much momentum does it carry / how does it affect the surrounding medium; how does it compare with vorticity?\\   Sound waves are a higher-order effect than vorticity propagation.     \item Another thing to consider: {\it does it even matter?} The time-scale they use in the paper is much larger than the sound-time, and places a more stringent test on the steady-state assumption. So my objection would only strengthen the conclusion.\\The vorticity moves slowest, and the fluid velocity profile might only assume the anticipated form once this final contribution has had time to influence the entire profile.     \item Could the problems in Payam's other paper conceivably be explained by this phenomenon?     \item Some reading about propagation of hydrodynamic information:\\   \citet{Hinch_1975} application of Langevin equation to fluid suspensions; includes fluid inertia and interaction with suspension.\\   \citet{Ladd_1993} short-time motion of colloidal particles: theory.\\   \citet{1995PhyA..214..185E},   \citet{Espanol_Rubio_Zuniga_1995} for discussion of how HD disturbances propagate, and evidence for faster-than-vorticity interaction. One considers incompressible and the other considers compressible; the vorticity time-scale is not the only important time-scale.\\   \citet{Clercx_1997} scaling of diffusion coefficient.\\   \citet{Kao_Yodh_Pine_1993} high-speed experiment finds interaction between colloids is faster than the vorticity timescale. Single-particle theory simply scales with parameters to account for interactions at various volume fractions.\\   \citet{nderson_Mitchell_Bartlett_2002}: high-speed observations of two interacting colloids. Sonic effects.\\   \citet{Padding_Louis_2006} coarse-graining approach; Langevin does a poor job.     %\item (Sound speed shouldn't depend on viscosity at except for near-supersonic flow. (\href{http://iopscience.iop.org/0370-1301/66/5/303/pdf/0370-1301_66_5_303.pdf}{Or does it?} \href{http://www.engineeringtoolbox.com/sound-speed-water-d_598.html}{Speed of sound table}, \href{http://resource.npl.co.uk/acoustics/techguides/soundpurewater/content.html#LUBBERS}{$c(T,P)$ fits}.))     \end{itemize}     \item Payam has (equation 12) $v_{\rm DNA}=F_{\rm ext} \ln(\ell/d)/\eta\ell - \lambda E\ln(1+r_{\rm D}/d)/\eta$, which we use to calculate $t_{\rm D}$. He finds $t_{\rm D}\sim \ell\eta/E\lambda$ -- whence this simplification?   \end{enumerate}     \item {\it Is the elongated jet derivation valid?} (Since integration along length of the DNA may break L\&L's ``weak momentum injection'' assumption.) Yes it is valid -- this is explicitly addressed on pp. 2-3: the criterion for the submerged jet formulae to be valid is the same as the criterion for linear fluid velocity dependence.     \item Where does the {\it nonequilibrium} stuff happen? There is no mention of linear response or anything like that.   \end{enumerate}