A perfect invisibility cloak is commonly believed to be undetectable from electromagnetic (EM) detection because it is equivalent to a curved but empty EM space created from coordinate transformation. Based on the intrinsic asymmetry of coordinate transformation applied to motions of photons and charges, we propose a method to detect this curved EM space by shooting a fast-moving charged partic...

In this lecture I summarize recent developments on strings propagating in curved spacetime. Exact conformal field theories that describe gravitational backgrounds such as black holes and more intricate gravitational singularities have been discovered and investigated at the classical and quantum level. These models are described by gauged Wess-Zumino-Witten models, or equivalently current algeb...

This paper examines the problem of automatically grouping image curves. In contrast, most previous work has been restricted to points and straight lines. Some of the computational aspects of the groupings of continuation, parallelism, and proximity are analysed, and the issues of neighbourhoods, combinatorix, and multiple scales are discussed.

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when D < 3, stays the same when D = 3, and is higher when D > 3. Thus c...

Research on biped locomotion has focused on sagittal plane walking in which the stepping path is a straight line. Because a walking path is often curved in a three dimensional environment, a 3D locomotion subsystem is required to provide general walking animation. In building a 3D locomotion subsystem, we tried to utilize pre-existing straight path (2D) systems. The movement of the center of th...

In this paper we announce the following result: “Every manifold of dimension ≥ 3 admits a complete negatively Ricci curved metric.” Furthermore we describe some sharper results and sketch proofs.

Traditionally schematized maps make extensive use of curves. However, automated methods for schematization are mostly restricted to straight lines. We present a generic framework for topology-preserving curved schematization that allows a choice of quality measures and curve types. Our fully-automated approach does not need critical points or salient features. We illustrate our framework with B...

We describe the production and characterization of a form of nanostructured carbon consisting of fully connected, three-dimensional ~3D! sp networks. This form of carbon is characterized by interconnected thin layers forming a spongy structure with mesoand macroporosity. It is produced by a pulsed microplasma cluster source in the presence of a very low concentration of metallorganic catalyst. ...

The notion of a negatively curved group is at first highly non-intuitive because it links two areas of mathematics that are not usually associated with one another. Curvature is generally a property that we associate with geometric objects like curves or surfaces in R, while a group is an algebraic structure that we associate with objects like integers or matrices. However, there is a way to de...

We demonstrate a tunable focus liquid crystal (LC) lens by sandwiching a homogeneous LC layer between a planar electrode and a curved electrode. The curved electrode which is made of conductive polymer has parabolic shape with a large apex distance. Such design dramatically reduces the phase loss which leads to a short focal length (~15 cm). By using a thin top glass substrate on the curved ele...