The connection of curves and surfaces in R3 to some nonlinear partial differential equations is very well known in differential geometry [1], [2]. Motion of curves on two dimensional surfaces in differential geometry lead to some integrable nonlinear differential equations such as nonlinear Schrödinger (NLS) equation [3], Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations [...

Soft materials with layered structure such as membranes, block copolymers and smectics exhibit intriguing morphologies with nontrivial curvatures. Here, we report restructuring the Gaussian and mean curvatures of smectic A films with free surface in the process of sintering, that is, reshaping at elevated temperatures. The pattern of alternating patches of negative, zero and positive mean curva...

To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the differential of the Gauss map of the underlying surface. The Gauss map assigns to each point in the surface the unit normal vector of the tangent plane to the surface...

This is the second of two papers wherein we estimate multiscale least squares approximations of certain measures by Menger-type curvatures (defined in Part I). More specifically, we study an arbitrary d-regular measure μ on a real separable Hilbert space, where d ∈ N. The main result of this paper bounds the least squares error of approximating μ at any ball B by an average of the discrete Meng...

This work describes a laser based technique to adjust curvatures of silicon microcantilevers used for chemical and biological detection. In batch fabricated silicon cantilever arrays used for parallel sensing, it is often desirable that all cantilevers have nearly identical curvatures or flatness. We demonstrate that using the laser technique, it is possible to adjust curvatures by an amount as...

We prove that every Kähler metric, whose potential is a function of the timelike distance in the flat Kähler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kähler manifolds with the above mentioned metrics. New examples of Sasakian space forms are obtained as real hypersurfaces of a Kähler space form ...

In simulating two-phase flows, interface normal vectors and curvatures are needed for modeling surface tension. In the traditional approach, these quantities are calculated from the spatial derivatives of a scalar function (e.g. the volume-offluid or the level set function) at any instant in time. The orders of accuracy of normals and curvatures calculated from these functions are studied. A ne...

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced...

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, and industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Four different algor...

Body posture defined by Kutzner-Kozińskiej depends on 3 groups of factors: morphological, functional and environmental. First group indicates that musculo-skeletal-ligament system cooperates (supports) with nervous system. Functional factors are connected with movement habits whereas environmental ones relate to surroundings [1, 2]. To keep upright position posture muscles are required to coope...