Wave transfer matrix of an arterial segment (source code)

= Wave transfer matrix of an arterial segment
{title2=$\begin{pmatrix}p_u\\q_u\end{pmatrix}=\begin{pmatrix}\cos\beta&i\sin\beta/Y\\iY\sin\beta&\cos\beta\end{pmatrix}\begin{pmatrix}p_d\\q_d\end{pmatrix}$}

= Wave transfer matrices of an arterial segment
{synonym}

For time dependence $e^{i\omega t}$ and a segment of length $\ell$, let $\beta=\omega\ell/c$. Adding the forward and backward <arterial pressure waves> gives the displayed upstream-to-downstream matrix. The flow orientation is downstream at both ends. At a junction, <pressure> is continuous and incoming <volumetric flow rates> balance outgoing ones.