a$.$ When simulating a vascular network and each blood vessel must be tracked

separately and we record the vessel location with a $(j,k$ scheme and record

the radius, length, and linear velocity in double$-$point precision $(8$ bytes$),$ then

how many vessels can be tracked if we have $12GB$ of RAM available? Estimate

how many levels in the vascular system this corresponds to for an $n=2$ and for

an $n=3$ bifurcating network?

b$.$ Using our equations for whole network volume, $V_{\text{n}\text{e}\text{t}}=V_N\frac{N_N^{(2a+b)}-n^{1-2a-b}{N}_N}{1-n^{1-2a-b}},$

investigate the limit as the number of levels $N->$ Infinity when $2a+b=1.$