A magnetic helix wire is one of the simplest magnetic systems which manifests properties of both curvature and torsion. Possible equilibrium magnetization states in the helix wire with different anisotropy directions are studied theoretically. There exist two equilibrium states in the helix wire with easy-tangential anisotropy: a quasitangential magnetization distribution in the case of relativ...

In recent years there has been a growing interest in the study of shape formation using modern responsive materials that can be preprogrammed to undergo spatially inhomogeneous local deformations. In particular, nematic liquid crystalline solids offer exciting possibilities in this context. Considerable recent progress has been made in achieving a variety of shape transitions in thin sheets of ...

This paper presents a new and efficient algorithm for the decomposition of 3D arbitrary triangle meshes and particularly optimized triangulated CAD meshes. The algorithm is based on the curvature tensor field analysis and presents two distinct complementary steps: a region based segmentation, which is an improvement of that presented by Lavoue et al. [Lavoue G, Dupont F, Baskurt A. Constant cur...

A new class of spacetime defect solutions of Einstein Field equations of Edelen’s direct Poincaré Gauge Field theory without biaxial symmetry is presented. The interior solution describes a core of defects where curvature vanishes and Cartan torsion is nonvanishing. Outside the core (in vacuum) the solution represents a spacetime with vanishing curvature and torsion describing a nontrivial topo...

A1 and A2 being arbitrary constants. A natural generalization of this question to higher dimensions could be: ‘given an isometric immersion ψ : Mn → Rn+2 of a compact n-dimensional Riemannian manifold (Mn, g), obtain conditions for ψ(Mn) ⊂ Sn+1(c), where Sn+1(c) is the sphere of constant curvature c’. We write ψT , ψ⊥ as tangential and normal components of the position vector ψ in Rn+p and show...

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the features. The essential problem is to find a good radius for each ball to obtain a reliable curvature estimation. We propose an algorithm that finds suitable radii...

A new 8-dimensional conformal gauging avoids the unphysical size change, third order gravitational field equations, and auxiliary fields that prevent taking the conformal group as a fundamental symmetry. We give the structure equations, gauge transformations and intrinsic metric structure for the new biconformal spaces. We prove that a torsion-free biconformal space with exact Weyl form, closed...

An essential ingredient in the simulation of multiphase fluid flow with surface tension is the accurate computation of the interface curvature. Curvature effects become more significant as we decrease the length scale of the problem at hand and thus accurate computation of curvature is especially important when considering microscale multiphase flows. We compared the curvature field calculated ...

Surfaces can be described locally and classified by their curvature values at every point. In this paper we investigate a grey-level based curvature estimator in combination with a sampling-error free integration technique of the curvature image. We compute shape descriptors as the bending energy and a global topological invariant, the Euler characterization. The integration of curvature values...