We study the spontaneous symmetry breaking of the bending rigidity of lipid membranes in two principal directions by a Landau mean-field theory. When the temperature is below the tilting temperature (T(c)), the coupling between molecular orientation and membrane local curvature square leads to an increase of the bending rigidity in the tilting direction and therefore a spontaneous symmetry brea...

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially varying director pattern may be a source of bia...

The paper focuses on optimization of lightweight sandwich panels with prismatic cores subject to bending loads in the two principal in-plane directions. Comparisons are made with optimal designs of panels with corrugated cores: a limiting case. When optimized for loading transverse to the prism axis, prismatic panels outperform those with corrugated cores, especially at lower loads. In contrast...

In this paper, a 3D mesh retrieval method is proposed based on extracting geometric features of models. The method first finds three principal directions for a model by employing the principal component analysis method, and rotates the model to align it in a reference frame. Then, three sets of planes are used to slice the model along to the directions respectively. Subsequently, three characte...

In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad-dominant mesh with edges well aligned to the principal directions of the underlying surface. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to ...

By single crystal C1-NQR Zeeman spectroscopy, the five independent C1 nuclear quadrupole coupling tensors in a-parachloral, (Cl3CCHO)3, have been studied at 24 ± 2 °C. The directions of the electric field gradient (EFG) tensor components have been determined. The principal axes are within ± 0.8° parallel to the C-Cl bond directions found by X-ray diffraction. Very small asymmetry parameters in ...

It is well known that anisotropy plays an important role in discharge of groundwater to lakes; groundwater flows almost horizontally to a lake then over a short distance changes direction to an almost vertical direction in the vicinity of or right below the lake. At this scale anisotropy becomes important. However, usually most simulation studies assume that the principal directions of the hydr...

In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell’s equations as well as for the search, characterization, and study of exact solutions of Einstein’s equations. The first part of this paper is devoted to an algebraic study in which we g...

Estimating principal curvatures and principal directions of a smooth surface represented by a triangular mesh is an important step in many CAD or graphics related tasks. This paper presents a new method for curvature tensor estimation on a triangular mesh by replacing flat triangles with triangular parametric patches. An improved local interpolation scheme of cubic triangular Bézier patches to ...