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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.
Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright
Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright
John B. Geddes
We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.
Extraction Of Signals From Chaotic Laser Data, John B. Geddes, Kevin Short, Kelly Black
Extraction Of Signals From Chaotic Laser Data, John B. Geddes, Kevin Short, Kelly Black
John B. Geddes
Several experimental groups have demonstrated communication with chaotic lasers. We analyzedata collected from a message-modulated erbium-doped fiber-ring laser (provided by VanWiggerenand Roy). We show that the transmitted signal is dominated by convolution of the message with theresponse function of the laser. A simple model based on the topology of the laser allows us to recovera hidden message. While prior estimates indicate that the laser dynamics are high dimensional, weshow that only four parameters are required, each of which can be recovered from the transmittedsignal alone.
The Onset Of Oscillations In Microvascular Blood Flow, John B. Geddes, Russell T. Carr, Nathaniel J. Karst, Fan Wu
The Onset Of Oscillations In Microvascular Blood Flow, John B. Geddes, Russell T. Carr, Nathaniel J. Karst, Fan Wu
John B. Geddes
We explore the stability of equilibrium solution(s) of a simple model of microvascular blood flow in a two-node network. The model takes the form of convection equations for red blood cell concentration, and contains two important rheological effects—the Fåhræus–Lindqvist effect, which governs viscosity of blood flow in a single vessel, and the plasma skimming effect, which describes the separation of red blood cells at diverging nodes. We show that stability is governed by a linear system of integral equations, and we study the roots of the associated characteristic equation in detail. We demonstrate using a combination of analytical and numerical …
Bistability In A Simple Fluid Network Due To Viscosity Contrast, John B. Geddes, Brian D. Storey, David Gardner, Russell T. Carr
Bistability In A Simple Fluid Network Due To Viscosity Contrast, John B. Geddes, Brian D. Storey, David Gardner, Russell T. Carr
John B. Geddes
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 flow, microfluidics, and other network flows governed by similar principles.
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.