Cato edited Payam.tex  almost 11 years ago

Commit id: 004acc4bedfa9b6e354249da1f26762ca2796ab3

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\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.  \item {\it What should the time-scale be from physical reasoning: what is the physics behind establishing the flow profile $\vec{v}(\vec{x})$ in the fluid around the DNA? DNA/jet?  (Read \citet{Broman_Rudenko_2010}, \citet{1959flme.book.....L} pp. 86-88). 86-88).\\ Which process (sound or vorticity) carries more momentum?} Read \citet{1959flme.book.....L}, chapter 8, on sound.  \item Which process (sound or vorticity) carries more momentum?} Read \citet{1959flme.book.....L}, chapter 8, on sound. {\it Does Payam assume incompressible flow?} Yes -- he follows \citet{1959flme.book.....L} pp. 86-88 in setting up the submerged jet; and 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!\\   {\it Would there be any point in re-visiting the derivation with incompressibility assumption dropped?}  \item Another thing to consider: {\it does it even matter?} The time-scale they use is 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. 

\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 {\it Does Payam assume incompressible flow?} Yes -- he follows \citet{1959flme.book.....L} pp. 86-88 in setting up the submerged jet; and 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!\\   {\it Would there be any point in re-visiting the derivation with incompressibility assumption dropped?}     %\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}