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- John B. Geddes, Russell T. Carr, Fan Wu, Yingyi Lao, Meaghan Maher
- Chaos
- 2010

Plasma skimming and the Fahraeus-Lindqvist effect are well-known phenomena in blood rheology. By combining these peculiarities of blood flow in the microcirculation with simple topological models of microvascular networks, we have uncovered interesting nonlinear behavior regarding blood flow in networks. Nonlinearity manifests itself in the existence of… (More)

- Russell T. Carr, John B. Geddes, Fan Wu
- Annals of Biomedical Engineering
- 2005

We have identified the simplest topology that will permit spontaneous oscillations in a model of microvascular blood flow that includes the plasma skimming effect and the Fahraeus–Lindqvist effect and assumes that the flow can be described by a first-order wave equation in blood hematocrit. Our analysis is based on transforming the governing partial… (More)

- Kelly Black, John B. Geddes
- J. Sci. Comput.
- 2001

- John B. Geddes, Brian D. Storey, David R. Gardner, Russell T. Carr
- Physical review. E, Statistical, nonlinear, and…
- 2010

We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an experiment using two miscible fluids of different viscosity-sucrose solution and water. Possible applications include blood… (More)

- David R. Gardner, Yiyang Li, Benjamin A. Small, John B. Geddes, Russell T. Carr
- Mathematical biosciences
- 2010

We use a simple model of micro-vascular blood flow to explore conditions that give rise to multiple equilibrium states in a three-node micro-vascular network. The model accounts for two primary rheological effects: the Fåhraeus-Lindqvist effect, which describes the apparent viscosity of blood in a vessel, and the plasma skimming effect, which governs the… (More)

- Kelly Black, John B. Geddes
- J. Sci. Comput.
- 2007

- Brian D. Storey, Deborah V Hellen, Nathaniel J. Karst, John B. Geddes
- Physical review. E, Statistical, nonlinear, and…
- 2015

We investigate the laminar flow of two-fluid mixtures inside a simple network of interconnected tubes. The fluid system is composed of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus… (More)

- Nathaniel J. Karst, John B. Geddes, Russell T. Carr
- Bulletin of mathematical biology
- 2017

We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are… (More)

- Kelly Black, John B. Geddes
- Computers & Mathematics with Applications
- 2010

- John B. Geddes, Willie J. Firth, Kelly Black
- SIAM J. Applied Dynamical Systems
- 2003

We consider pulse formation dynamics in an actively mode-locked laser. We show that an amplitudemodulated laser is subject to large transient growth and we demonstrate that at threshold the transient growth is precisely the Petermann excess noise factor for a laser governed by a nonnormal operator. We also demonstrate an exact reduction from the governing… (More)