Complete monotonicity of flow and cross-sectional impulse response functions for rigid right circular tubes

Abstract

Indicator dilution theory is the conceptual base for many flow measurement methods within living organisms; a whole animal, an organ, or an individual vessel. In this manuscript, we provide a characterization of the system impulse response function for flow-and cross-sectionally sampled indicator curves within a rigid right circular tube. The curves are measured downstream from the position of an injector, which labels uniformly the streamlines of a steady, laminar power law fluid flow. The system impulse response function is shown to be the weighted sum of a Dirac delta function and a completely monotonic function. A numerical example employing data from a physical experiment involving a vertically orientated, perfused glass tube is presented, illustrating the characterization of the impulse response function between cross-sectionally sampled upstream and downstream measurement sites.

Attenuation of pulsations in the reciprocating compressor piping system with an elbow-shaped surge tank

“…The impulse response analysis is widely used in studying engineering structures, hydrology, biology, acoustics, and so on. [19][20][21][22][23][24] For instance, Volkmer et al 25 provided the impulse response function to study the physiological flows. Todorovska and Trifunac 26 analyzed wave travel times from impulse response functions to detect earthquake damage.…”