Planar elastica inside a curved tube with clearance

Area-constrained planar elastica.

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties; not only can the Euler-Lagrange equation be integrated to provide a quadrature for ...

Ineffective perturbations in a planar elastica

The bifurcation diagram for the buckling of a planar elastica under a load λ is made up of a “trivial” branch of unbuckled configurations for all λ and a sequence of branches of buckled configurations that are connected to the trivial branch at pitchfork bifurcation points. We use several perturbation expansions to determine how this diagram perturbs with the addition of a small intrinsic shape...

Self-similar curling of a naturally curved elastica.

We consider the curling of an initially flat but naturally curved elastica on a hard, nonadhesive surface. Combining theory, simulations, and experiments, we find novel behavior, including a constant front velocity and a self-similar shape of the curl that scales in size as t(1/3) at long times after the release of one end of the elastica. The front velocity is selected by matching the self-sim...

Superior chest drainage with an active tube clearance system: evaluation of a downsized chest tube.

PURPOSE We developed a small-diameter (20-French [Fr]) chest drainage system that incorporates an active tube clearance (ATC) system, and we evaluated its efficacy in an acute hemothorax model. DESCRIPTION The ATC system includes an internal guidewire that can be advanced into the lumen of the chest tube to keep the tube from clogging. In six pigs, a 20-Fr ATC tube was placed on one side and ...

Elastica with Hinges