In this paper we investigate an analogue for curves of the famous Kakeya conjecture about straight lines. The simplest version of the latter asks whether a set in R that includes a unit line segment in every direction must necessarily have dimension n. The analogue we have in mind replaces the line segments by curved arcs from a specified family. (This is a quite different problem from that con...

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures,...

The electromagnetic scattering by an array of finite cylindrically curved thin screens is investigated in this paper, and the normally incident plane wave can be either TMzor TEz-polarised. The mathematical treatment here is based on the direct integral equation technique combined with the Galerkin's procedure, and the induced currents on the curved thin screens or apertures are expanded in ter...

We investigate some apparent discrepancies between two different models for curved graphene: the one based on tight-binding and elasticity theory, and the covariant approach based on quantum field theory in curved space. We demonstrate that strained or corrugated samples will have a space-dependent Fermi velocity in either approach that can affect the interpretation of local probe experiments i...

A dramatic effect of crystal morphology, photoreactivity and photosalient property is observed in a zinc(II) complex due to solvent effects and fluorine substitution at the backbone of the ligand. Of the two crystal forms with a 3-fluoro derivative, one yielded a curved morphology of single crystals and the second form shows photoreactivity in the solid state, whereas crystals of the 2-fluoro d...

In this study, the performance of triangular added damping and stiffness (TADAS) dampers combined with curved dampers (Curved-TADAS damper) is evaluated in moment resisting steel frame (MRSF). These dampers are passive and install in the beam-column connection region. Variable parameters of this study involve the width of curved damper (50, 75 and 100 mm), the thickness of TADAS damper (5 and 1...

Free-form deformation is an important geometric shape modification method in computer animation and geometric modeling. We explore it by means of functional composition via shifting operators. Our method takes a polygonal model as input but yields a curved model described by triangular Bézier patches as output. The proposed method also solves the sample problem of free-form deformation. keyword...

A high precision illumination model is indispensable for lighting simulation and realistic image synthesis. For the purpose of improving realism, research on global illumination has been done, and several papers on radiosity methods have been presented. In the most recently proposed methods, the shapes of light sources and objects are restricted to polygons or simple curved surfaces. We present...

In a recent paper [13], the Fast Marching farthest point sampling strategy (FastFPS) for planar domains and curved manifolds was introduced. The version of FastFPS for curved manifolds discussed in the paper [13] deals with surface domains in triangulated form only. Due to a restriction of the underlying Fast Marching method, the algorithm further requires the splitting of any obtuse into acute...