The filament-bundle elastica

Non-euclidean geometry of twisted filament bundle packing.

Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly on...

The elastica: a mathematical history

This report traces the history of the elastica from its first precise formulation by James Bernoulli in 1691 through the present. The complete solution is most commonly attributed to Euler in 1744 because of his compelling mathematical treatment and illustrations, but in fact James Bernoulli had arrived at the correct equation a half-century earlier. The elastica can be understood from a number...

An elastica arm scale.

The concept of a 'deformable arm scale' (completely different from a traditional rigid arm balance) is theoretically introduced and experimentally validated. The idea is not intuitive, but is the result of nonlinear equilibrium kinematics of rods inducing configurational forces, so that deflection of the arms becomes necessary for equilibrium, which would be impossible for a rigid system. In pa...

Deformation by Discrete Elastica

Modeling a physically plausible deformation of a flexible object from its naturally planar (curved) state is a fundamental and challenging topic in digital surface processing with applications to computer animation and game design. We propose a new variational model for detail preserving surface-based deformation of a body based on total curvature energy. We demonstrate the efficacy of the mode...

Elastica with Hinges