# Scaling in Vlasov equations

This question is in reference to the paper, http://arxiv.org/abs/1301.7182

• What exactly is the argument being made on page 6 and 7?

One deduces that the function $\Delta$ has to be such that, $\Delta^2(k,\tau) = \Delta^2(\frac{k}{\lambda ^{\frac{4}{n+3}}}, \lambda \tau )$. Now from this how does this follow that, the following holds,

$\Delta^2(k,\tau) = \Delta^2(\frac{k}{k_{NL}})$ where $k_{NL}^{n+3} \propto \tau ^{-4}$

?

• How does 2.26 follow from 2.2?

In 2.2 aren't all the $c_{*}^2$s dimensionless?

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The $c$'s are speeds aren't they, so not dimensionless? (see discussion after eq 2.3). So in (2.26), although they're proportional to the ratio of the lambda squared's they have the dimensions of $\frac{x^2}{t^2}$ – twistor59 Jun 12 '13 at 11:04
@twistor59 If I calculate in mass-dimensions the only consistent assignment that I can think of for 2.1-2.3 is to declare, $[\delta] = [v] = [\phi] = 0$, $[\partial _ \tau] = [\nabla] = [h] = M$ and one is working in $speed-of-light = 1$ units (i.e "length=time"). Then all the $c$s become dimensionless. Do you see any alternate assignment that is consistent with those 3 equations? – user6818 Jun 12 '13 at 22:25
@twistor59 Also if you can help understand the first point... – user6818 Jun 12 '13 at 23:00