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## Full-Text Articles in Physics

Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes

#### Spontaneous Oscillations In Simple Fluid Networks, Nathaniel Karst, Brian Storey, John Geddes

*John B. Geddes*

Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in ﬂuid networks containing either multiple phases or constituents. In many systems, such behavior might be attributed to the complicated geometry of the network, the complex rheology of the constituent ﬂuids, or, in the case of microvascular blood ﬂow, biological control. In this paper we investigate two examples of a simple three-node ﬂuid network containing two miscible Newtonian ﬂuids of diﬀering viscosities, the ﬁrst modeling microvascular blood ﬂow and the second modeling stratiﬁed laminar ﬂow. We use a combination of analytic and numerical techniques to identify and track saddle-node and ...

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 ...

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.

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.