I. <i>On the mechanical conditions of the deposit of a submarine cable</i>

Airy, George Biddell

doi:10.1080/14786445808642526

Cited by 12 publications

(12 citation statements)

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“…If the chain is moving, then we see in equation (1.12) that this simply requires a constant addition λv 2 to T(s), and that the equations are still solved by any inverted catenary [9]. Thus, we expect the chain to take on the form…”

Section: MMmentioning

confidence: 99%

Understanding the chain fountain

Biggins

Warner

2014

Proc. R. Soc. A.

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If a chain is initially at rest in a beaker at a height h 1 above the ground, and the end of the chain is pulled over the rim of the beaker and down towards the ground and then released, the chain will spontaneously 'flow' out of the beaker under gravity. Furthermore, the beads do not simply drag over the edge of the beaker but form a fountain reaching a height h 2 above it. We show that the formation of a fountain requires that the beads come into motion not only by being pulled upwards by the part of the chain immediately above the pile, but also by being pushed upwards by an anomalous reaction force from the pile of stationary chain. We propose possible origins for this force, argue that its magnitude will be proportional to the square of the chain velocity and predict and verify experimentally that h 2 ∝ h 1 .

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Section: MMmentioning

confidence: 99%

Understanding the chain fountain

Biggins

Warner

2014

Proc. R. Soc. A.

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“…The problem of laying and recovery of cable is a hybrid of towing and reeling problems, with a history that begins with the work of Thomson [6] and Airy [5] in the mid-19th century, and continues into the modern day [69][70][71][72]. Thomson neglected drag forces, while Airy unrealistically assumed the forces to be linear and isotropic, corresponding to our limit R ν = 1.…”

Section: Discussionmentioning

confidence: 99%

“…This was perhaps first recognized by a Tripos examiner in 1854, one of whose victims, Routh, incorporated the fact in a mechanics text a few years later [4]. By that time, the discovery had also been made by Airy (Astronomer Royal) and Thomson (Lord Kelvin), whose impetus to study this problem was the massive failure of the first attempt to lay transatlantic telegraph cable [5,6]. Their treatments of the effects of the fluid medium fell short, with Airy modeling drag as isotropic with respect to the cable geometry, and Kelvin neglecting it entirely.…”

Section: Introductionmentioning

confidence: 96%

Catenaries in viscous fluid

Chakrabarti

Hanna

2016

Journal of Fluids and Structures

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Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body (θ). Phase portraits in the anglecurvature (θ, ∂ s θ) plane are generated, that can be shown to be π periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points. AcknowledgmentLet me start by thanking my parents and kaka. Like always, they have been very supportive over the last two years. They have been with me through some of my difficult phases and have always kept their faith in me. It would not have been possible to finish this work without their love and encouragement.

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“…where c is the shape's curvature and f t , f n and f b are the components of f along t, n and b, respectively (see also [58]). Letting f lie in the (x, y) plane, f b vanishes identically as long as the filament's shape lies in that plane as well.…”

Section: (C) Inverted Catenarymentioning

confidence: 99%

Dissipative shocks behind bacteria gliding

Virga

2014

Phil. Trans. R. Soc. A.

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Gliding is a means of locomotion on rigid substrates used by a number of bacteria, including myxobacteria and cyanobacteria. One of the hypotheses advanced to explain this motility mechanism hinges on the role played by the slime filaments continuously extruded from gliding bacteria. This paper solves, in full, a nonlinear mechanical theory that treats as dissipative shocks both the point where the extruded slime filament comes into contact with the substrate, called the filament's foot, and the pore on the bacterium outer surface from where the filament is ejected. I prove that kinematic compatibility for shock propagation requires that the bacterium uniform gliding velocity (relative to the substrate) and the slime ejecting velocity (relative to the bacterium) must be equal, a coincidence that seems to have already been observed.

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I. On the mechanical conditions of the deposit of a submarine cable

Cited by 12 publications

References 0 publications

Understanding the chain fountain

Understanding the chain fountain

Catenaries in viscous fluid

Dissipative shocks behind bacteria gliding

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