This report concerns the observation that certain anionic detergents have a specific affinity for elastica, and because these anionic detergents precipitate cationic basic dyes in aqueous solution, a rather specific stain for elastica can be obtained. There are many satisfactory methods for the histologic demonstration of elastica, the most popular being: a) acid orcein (Unna), b) Verhoef's, c)...

The dynamics for a thin, closed loop inextensible Euler’s elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its tension. A Hasimoto transformation is used to rewrite the equations in convenient coordinates for the space and time derivatives of th...

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Du...

This paper investigates the Euler’s elastica (EE) model for high-dimensional supervised learning problems in a function approximation framework. In 1744 Euler introduced the elastica energy for a 2D curve on modeling torsion-free thin elastic rods. Together with its degenerate form of total variation (TV), Euler’s elastica has been successfully applied to low-dimensional data processing such as...

We construct a method for fairing given discrete planar curve by using the integrable analog of Euler’s elastica, which is version approximation algorithm presented Brander et al. first give brief review elastica proposed Bobenko and Suris, then we present detailed account algorithm, apply this to an architectural problem characterizing keylines Japanese handmade pantiles.

Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli Melas of a quantized elastica, a quantized loop with an energy functional associated with the Schwarz derivative, on a Riemann sphere P. Then it is proved that its moduli space is decomposed to a set of equivalent classes d...

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...

Continuum strain energy density functions are developed for soft biological tissues that possess slender, fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to obtain a continuum strain energy density function. Notably, we avoid solving the exact, fourth-order, nonlinear, partial differential equation f...

One of the oldest topics in the calculus of variations is the study of the elastic rod which, according to Daniel Bernoulli's idealization, minimizes total squared curvature among curves of the same length and first order boundary data. The classical term elastica refers to a curve in the plane or IR which represents such a rod in equilibrium. While the elastica and its generalizations have lon...

An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the rod were rigid. The closed curve is analytically determin...