We propose a geometric approach to the BRST-symmetries of the Lagrangian of a topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded q-differential algebra, where q is a primitive N -th root of unity, we also propose a notion of ZN -connection which is a generalization of a superconnection. In our approach the Lagrangia...

This paper presents an approach for generating curvature-adaptive finishing tool paths with bounded error directly from massive point data in three-axis computer numerical control (CNC) milling. This approach uses the moving least-squares (MLS) surface as the underlying surface representation. A closed-form formula for normal curvature computation is derived from the implicit form of MLS surfac...

In this paper we present a novel method to estimate curvature of iso grey-level surfaces in grey-value images. Our method succeeds where isophote curvature fails. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation field of the surface. This orientation field and a description of local structure is obtained by the Gradient...

Cosmological perturbation theory fails in the new ekpyrotic scenario before the scale factor of the Universe reaches zero. As a result, the scenario does not provide a mechanism for generating the observed curvature perturbation at the bounce. Introduction It is now clear that the dominant cause of large-scale structure in the Universe is a perturbation in the spatial curvature [1]. The perturb...

Vacuum energy density and stresses are investigated for a scalar field with general curvature coupling parameter in (D+1)-dimensional de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions. The corresponding expectation values are presented in the form of the sum of the vacuum expectation values in uncompactified dS spacetime and the part induced by the non-t...

We present a computational methodology for incorporating thermal effects and calculating relative free energies for elastic fluid membranes subject to spatially dependent intrinsic curvature fields using the method of thermodynamic integration. Based on a simple model for the intrinsic curvature imposed only in a localized region of the membrane, we employ thermodynamic integration to calculate...

Tangent curves are a powerful tool for analyzing and visualizing vector fields. In this paper two of their most important properties are examined: their curvature and torsion. Furthermore, the concept of normal surfaces is introduced to the theory of 3D vector fields, and their Gaussian and mean curvature are analyzed. It is shown that those four curvature measures tend to infinity near critica...

The hormetic morphogen theory of curvature (Fosslien 2009) proposes that hormetic morphogen concentration gradients modulate the synthesis of adenosine triphosphate (ATP) by cells along the gradients (field cells) and thus regulate their proliferation and induce curvature such as vascular wall curvature; however, it is unclear whether such morphogen gradients can also determine the histological...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or light-like, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fie...