Dynamic response for a network with vessel radii that follow Murray’s law.

Abstract

<p>A: Real and imaginary parts of the response of the network (in <i>m</i>⁴) as a function of the level <i>n</i> at which obstructions occur. B: Real and imaginary parts of the ratio of two sequential resistances </p><p></p><p></p><p></p><p><mi>a</mi><mi>i</mi></p><mo>=</mo><p></p><p><mi>R</mi><mi>i</mi></p><p><mi>R</mi></p><p><mi>i</mi><mo>−</mo><mn>1</mn></p><p></p><p></p><p></p><p></p><p></p> as a function of the level <i>i</i> of the underlying network. Note that we use the subindex <i>i</i>, whenever we refer to a property of the underlying network, we use the subindex <i>n</i> whenever we refer to the response of the whole network when obstructions occur at level <i>n</i>.<p></p