A resolution-independent image models the true intensity function underlying a standard image of discrete pixels. Previous work on resolution-independent images demonstrated their efficacy, primarily by employing regularizers that penalize discontinuity. This paper extends the approach by permitting the curvature of resolution-independent images to be regularized. The main theoretical contribut...

Travelling wave solutions to the vortex filament flow generated by elastica produce surfaces in R that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the Bäcklund transformation for constant tors...

The quality of microscopic image of cryostat sections that had been subjected to microwave assisted fixation was compared with that resulting from conventional air drying of the sections. The role of microwaves in producing rapid special stains on cryostat sections was also assessed. Methods used permitted stains such as periodic acid Schiff, alcian blue, Gordon and Sweets's reticulin, Masson F...

This is of nonlinear an exposition of the variational and differential properties spline curves, based on the Euler-Bernoulli theory for the bending of thin beams or elastica. For both open and closed splines through prescribed nodal points in the euclidean plane, various types --. of nodal constraints are considered, and the corresponding algebraic and differential equations relating curvature...

A drop impacting a target cutout in a thin polymer film is wrapped by the film in a dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from a given target by slightly varying the impact parameters. A simplified model for a nonlinear dynamic Elastica coupled with a drop successfully explains this shape selection and yields detailed quantitative ...

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. A...

We study an energy functional that arises in a simplified two-dimensional model for lipid bilayer membranes. We demonstrate that this functional, defined on a class of spatial mass densities, favours concentrations on ‘thin structures’. Stretching, fracture and bending of such structures all carry an energy penalty. In this sense we show that the models captures essential features of lipid bila...