This paper presents a study of generalized enrichment functions for three-dimensional curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of cur...

Ever since the inception of Transformation Optics (TO), new and exciting ideas have been proposed in the field of electromagnetics and the theory has been modified to work in such fields as acoustics and thermodynamics. The most well-known application of this theory is to cloaking, but another equally intriguing application of TO is the idea of an illusion device. Here, we propose a general met...

In this paper we present a prototype for a new type of solar thermal collector designed for architectural integration. In this proposal, the conventional geometry of a flat solar thermal collector is changed to a curved geometry, to improve its visual impact when mounted on a building facade or roof. The mathematical equations for the beam and diffuse solar radiation received by a collector wit...

We investigate microphase separation patterns on curved surfaces in three-dimensional space by numerically solving a nonlocal Cahn-Hilliard equation for diblock copolymers. In our model, a curved surface is implicitly represented as the zero level set of a signed distance function. We employ a discrete narrow band grid that neighbors the curved surface. Using the closest point method, we apply ...

The problem of tting a 2D broadcloth composite ply (modelled as a piece of deformable woven cloth) onto a 3D curved surface (modelled with a NURBS surface) is considered. \Fitting" means that a ply is deformed and applied to a surface so that it is everywhere in contact with the surface. A tting method is presented that incorporates a exible method for specifying initial conditions, and allows ...

We know how to integrate a function over a flat region in a plane, but what if the function is defined over a curved surface? To evaluate one of these so-called surface integrals, we rewrite it as a double integral over a region in a coordinate plane beneath the surface (Figure 16.38). Surface integrals are used to compute quantities such as the flow of liquid across a membrane or the upward fo...

– In the literature, different properties of propagating excitation waves on curved surfaces are published. Theoretical papers predicted critical properties of waves on curved surfaces. If an excitation wave propagates in a non-planar system, its geodetic curvature causes a transition from excitable to non-excitable dynamics. In this paper we present first experimental results of the transition...

In order to better understand light dosimetry issues for photodynamic therapy (PDT), we have used various tumor and normal tissue geometries to develop a diffusion model of light transport in tissues. We hypothesize that tumor tissues with curved surfaces will have significantly different internal fluence distributions, as compared to tissues with flat surfaces. Using a mouse subcutaneous tumor...

The influence of surface topography on protein conformation and association is used routinely in biological cells to orchestrate and coordinate biomolecular events. In the laboratory, controlling the surface curvature at the nanoscale offers new possibilities for manipulating protein-protein interactions and protein function at surfaces. We have studied the effect of surface curvature on the as...