\begin{table}%t4
%\centering
\par
\caption{Same legend as for Table~\ref{tab:resolutionz} but for the physical resolution ${\cal R}_R$ in the radial direction ($\ell=h$ for all examples). $N_{\rm left}$, $N_{\rm local}$ and $N_{\rm right}$ denote the number of cylinders populating the left-side, long-range, the local and right-side, long-range contributions respectively (see the Appendix \ref{ap:Parameters appropriate for the radial sampling}).}
\label{tab:resolutionr}
\begin{tabular}{lcc} 
\hline\hline
            &                & Finite-diff. \\
Radius &    This method  & methods \\  \hline \hline
$a \rightarrow a_{\rm in}$ & $\frac{a_{\rm in}}{L(N_{\rm left}-1)}\ln \frac{nha_{\rm in}}{(R-nh)(R-a_{\rm in})}$ & $\frac{1}{N_{\rm left}-1}$\\
(inner edge) & & \\[0.3cm]
$a \rightarrow R$ & $\frac{h}{2qL} \sqrt{\frac{n^2}{1+n^2}} \left(\frac{1}{N_{\rm local}-1}\right)^{\frac{1}{2q}}$ & $\frac{1}{N_{\rm local}-1}$ \\
(field point)& & \\
 \underline{examples} \\ 
$(N_{\rm local},q)$\\
    $(8,\frac{1}{2})$ & $0.1 \frac{h}{L}$ & $0.14$\\
    $(32,\frac{1}{2})$  & $0.02 \frac{h}{L} $ & $0.03$\\      
    $(128,\frac{1}{2})$ & $5 \times 10^{-3} \frac{h}{L} $ & $8 \times 10^{-3}$ \\
    $(128,\frac{1}{4})$ & $9 \times 10^{-5} \frac{h}{L}$  & $8 \times 10^{-3}$ \\ \\
$a = R \pm \ell$ &$\frac{hn(1+n^2)}{qL(N_{\rm local}-1)}$ & $\frac{1}{N_{\rm local}-1}$\\ \\
$a \rightarrow a_{\rm out}$ & $\frac{a_{\rm out}}{L(N_{\rm right}-1)}\ln \frac{a_{\rm out}-R}{nh}$ & $\frac{1}{N_{\rm right}-1}$\\
(outer edge) & \\ \hline 
\end{tabular}
\end{table}