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Full-Text Articles in Physical Sciences and Mathematics
Laminar Flow Of Two Miscible Fluids In A Simple Network, Casey Karst, Brian Storey, John Geddes
Laminar Flow Of Two Miscible Fluids In A Simple Network, Casey Karst, Brian Storey, John Geddes
John B. Geddes
When a fluid comprised of multiple phases or constituents flows through a network, nonlinear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a number of networks including the flow of blood through the microcirculation, the flow of picoliter droplets through microfluidic devices, the flow of magma through lava tubes, and two-phase flow in refrigeration systems. While the existence of nonlinear phenomena in a network with many inter-connections containing fluids with complex rheology may seem unsurprising, this paper demonstrates that even simple networks containing Newtonian fluids in laminar flow …
Noise-Induced Oscillations In An Actively Mode-Locked Laser, Kelly Black, John Geddes
Noise-Induced Oscillations In An Actively Mode-Locked Laser, Kelly Black, John Geddes
John B. Geddes
Oscillations induced by noise are examined for an actively mode-locked laser. Additive noise, proportional noise, and combined noise are considered. Spatial noise is approximated by Hermite expansions and temporal noise is approximated via an approximation of the variance of the random variable using a fourth-order Adams–Bashforth scheme. The approach is verified on a sample problem and used to explore the governing equations for a mode-locked laser. The inclusion of multiplicative noise leads to much wider pulses and much longer intervals between pulses.
Multiple Equilibrium States In A Micro-Vascular Network, David Gardner, Yiyang Li, Benjamin Small, John Geddes, Russell Carr
Multiple Equilibrium States In A Micro-Vascular Network, David Gardner, Yiyang Li, Benjamin Small, John Geddes, Russell Carr
John B. Geddes
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 Fåhræus–Lindqvist effect, which describes the apparent viscosity of blood in a vessel, and the plasma skimming effect, which governs the separation of red blood cells at diverging nodes. We show that multiple equilibrium states are possible, and we use our analytical and computational tools to design an experiment for validation.
Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth
Hexagons And Squares In A Passive Nonlinear Optical System, John Geddes, R.A. Indik, J.V. Moloney, Willie Firth
John B. Geddes
Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.