Real-time edge tracking using a tactile sensor

Object recognition through the use of input from multiple sensors is an important aspect of an autonomous manipulation system. In tactile object recognition, it is necessary to determine the location and orientation of object edges and surfaces. A controller is proposed that utilizes a tactile sensor in the feedback loop of a manipulator to track along edges. In the control system, the data from the tactile sensor is first processed to find edges. The parameters of these edges are then used to generate a control signal to a hybrid controller. Theory is presented for tactile edge detection and an edge tracking controller. In addition, experimental verification of the edge tracking controller is presented

Manufacture of Gowdy spacetimes with spikes

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.Comment: 25 page

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated

Supersymmetry and Lorentz Violation

Supersymmetric field theories can be constructed that violate Lorentz and CPT symmetry. We illustrate this with some simple examples related to the original Wess-Zumino model.Comment: 4 page

A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (i.e., discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein-Euler equations.Comment: 24 page

Initial Helioseismic Observations by Hinode/SOT

Results from initial helioseismic observations by Solar Optical Telescope onboard Hinode are reported. It has been demonstrated that intensity oscillation data from Broadband Filter Imager can be used for various helioseismic analyses. The k-omega power spectra, as well as corresponding time-distance cross-correlation function that promises high-resolution time-distance analysis below 6-Mm travelling distance, were obtained for G-band and CaII-H data. Subsurface supergranular patterns have been observed from our first time-distance analysis. The results show that the solar oscillation spectrum is extended to much higher frequencies and wavenumbers, and the time-distance diagram is extended to much shorter travel distances and times than they were observed before, thus revealing great potential for high-resolution helioseismic observations from Hinode.Comment: 6 pages, accepted for publication in PAS

Global dynamics of the mixmaster model

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly known cases where the spacetime can be smoothly extended through a Cauchy horizon. For types VIII and IX it is shown that there are at most two possibilities for the evolution. When the first possibility is realized, and if the spacetime is not one of the explicitly known solutions which can be smoothly extended through a Cauchy horizon, then there are infinitely many oscillations near the singularity and the Kretschmann scalar is unbounded there. The second possibility remains mysterious and it is left open whether it ever occurs. It is also shown that any finite sequence of distinct points generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be realized approximately by a solution of the vacuum Einstein equations of Bianchi type IX.Comment: 16 page

An analysis of the optimal band gaps of light absorbers in integrated tandem photoelectrochemical water-splitting systems

The solar-to-hydrogen (STH) efficiency limits, along with the maximum efficiency values and the corresponding optimal band gap combinations, have been evaluated for various combinations of light absorbers arranged in a tandem configuration in realistic, operational water-splitting prototypes. To perform the evaluation, a current–voltage model was employed, with the light absorbers, electrocatalysts, solution electrolyte, and membranes coupled in series, and with the directions of optical absorption, carrier transport, electron transfer and ionic transport in parallel. The current density vs. voltage characteristics of the light absorbers were determined by detailed-balance calculations that accounted for the Shockley–Queisser limit on the photovoltage of each absorber. The maximum STH efficiency for an integrated photoelectrochemical system was found to be ~31.1% at 1 Sun (=1 kW m⁻², air mass 1.5), fundamentally limited by a matching photocurrent density of 25.3 mA cm⁻² produced by the light absorbers. Choices of electrocatalysts, as well as the fill factors of the light absorbers and the Ohmic resistance of the solution electrolyte also play key roles in determining the maximum STH efficiency and the corresponding optimal tandem band gap combination. Pairing 1.6–1.8 eV band gap semiconductors with Si in a tandem structure produces promising light absorbers for water splitting, with theoretical STH efficiency limits of >25%