The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...

The O(3) nonlinear sigma model with boundary, in dimension two, is considered. An algorithm to determine all its soliton solutions that preserve a rotational symmetry in the boundary is exhibited. This nonlinear problem is reduced to that of clamped elastica in a hyperbolic plane. These solutions carry topological charges that can be holographically determined from the boundary conditions. As a...

A stiff one-armed swimmer in glycerine goes nowhere, but if its arm is elastic, exerting a restorative torque proportional to local curvature, the swimmer can go on its way. Considering this happy consequence and the principles of elasticity, we study a hyperdiffusion equation for the shape of the elastica in viscous flow, find solutions for impulsive or oscillatory forcing, and elucidate relev...

We propose a novel method for constructing illusory foreground and background shapes from convex corners. We first introduce a new class of visual cues called corner bases, which expands 0-dimensional corner points to 2-dimensional micro structures. These corner bases are then fused together by the functionalized elastica energy imposed upon an admissible phase field. The optimal phase field se...

We propose a method for minimizing a non-convex function, which can be split up into a sum of simple functions. The key idea of the method is the approximation of the convex envelopes of the simple functions, which leads to a convex approximation of the original function. A solution is obtained by minimizing this convex approximation. Cost functions, which fulfill such a splitting property are ...

of Bruch'-s membrane at the optic n-erve. Three cases of partial cross ruptures of the optic nerve are reported histologically. All three are discovered at the very insertion of the lamina elastica chorioideae. The tear was caused in all cases (traumatic, expulsive haemorrhage and haemorrhagic glaucoma) by an instantaneous, probably arterial, subiretinal bleeding. Traumatic retropulsion of the ...