Embedding Versus Immersion in General Relativity

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory since the causal structure of the immersed space-time is not preserved by the immersion.Comment: 5 page

RF CMOS transceiver at 2.4 GHz in wearables for measuring the cardio-respiratory function

This paper presents a radio-frequency (RF) transceiver for operation in the 2.4 GHz ISM band. The RF CMOS transceiver can be supplied with only 1.8 V, and it was designed to establish wireless links for distances up to 10 m, for a maximum baud-rate of 250 Kbps with a Bit Error Probability less than 10 6. The transmitter can deliver a output power of 0 dBm with a consumption of only 11.2 mW, while the receiver has sensitivity of 60 dBm and consumes only 6.3 mW. The goal of RF CMOS transceiver is for co-integration with sensors in the same die using microsystems techniques. The target application of such microsystems is in wearables (e.g., in wireless electronic shirts) for measuring biomedical data of patients. The wireless electronic shirt (WES) measures the heart rate and the respiratory frequency, and at the same time it allows patients to maintain their mobilit

Remarks on Legendrian Self-Linking

The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our definition is based upon a reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.Comment: 42 pages, many figures; v2: minor revisions, published versio

On the embedding of spacetime in five-dimensional Weyl spaces

We revisit Weyl geometry in the context of recent higher-dimensional theories of spacetime. After introducing the Weyl theory in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Weyl geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a Weyl bulk. We discuss the problem of classical confinement and the stability of motion of particles and photons in the neighbourhood of branes for the case when the Weyl bulk has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the Weyl field. We construct a classical analogue of quantum confinement inspired in theoretical-field models by considering a Weyl scalar field which depends only on the extra coordinate.Comment: 16 pages, new title and references adde

Fabrication methodology of microlenses for stereoscopic imagers using standard CMOS process

This paper presents the fabrication technology of microlenses maintaining a high reproducibility of their characteristics with low cost. The objective of microlenses is to be integrated into imagers in CMOS technology to allow stereoscopic vision. The fabricated microlenses form cylindrical arrays to be placed above the optical filters and photodetectors, in order to potentiate stereoscopic vision and at the same time maximizing the color fidelity. An array of optical filters centered at the primary colors will enable a multicolor usage. The AZ4562 material was the photoresist selected for fabricating the microlenses. The cylindrical shape is obtained by reflowing the photoresist using the hot-plate technique.This work and Rui Pedro Rocha were fully supported by the Portuguese Foundation for Science and Technology under the project FCT/PTDC/EEA-ELC/109936/2009 and the financial grant SFRH/BD/33733/2009, respectively

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures

The relative abundance of wheat Rubisco activase isoforms is post‑transcriptionally regulated

Diurnal rhythms and light availability affect transcription–translation feedback loops that regulate the synthesis of photosynthetic proteins. The CO2-fixing enzyme Rubisco is the most abundant protein in the leaves of major crop species and its activity depends on interaction with the molecular chaperone Rubisco activase (Rca). In Triticum aestivum L. (wheat), three Rca isoforms are present that differ in their regulatory properties. Here, we tested the hypothesis that the relative abundance of the redox-sensitive and redox-insensitive Rca isoforms could be differentially regulated throughout light–dark diel cycle in wheat. While TaRca1-β expression was consistently negligible throughout the day, transcript levels of both TaRca2-β and TaRca2-α were higher and increased at the start of the day, with peak levels occurring at the middle of the photoperiod. Abundance of TaRca-β protein was maximal 1.5 h after the peak in TaRca2-β expression, but the abundance of TaRca-α remained constant during the entire photoperiod. The redox-sensitive TaRca-α isoform was less abundant, representing 85% of the redox-insensitive TaRca-β at the transcript level and 12.5% at the protein level. Expression of Rubisco large and small subunit genes did not show a consistent pattern throughout the diel cycle, but the abundance of Rubisco decreased by up to 20% during the dark period in fully expanded wheat leaves. These results, combined with a lack of correlation between transcript and protein abundance for both Rca isoforms and Rubisco throughout the entire diel cycle, suggest that the abundance of these photosynthetic enzymes is post-transcriptionally regulated

Microlenses for stereoscopic image formation

This paper presents microlenses for integration on a stereoscopic image sensor in CMOS technology for use in biomedical devices. It is intended to provide an image sensor with a stereoscopic vision. An array of microlenses potentiates stereoscopic vision and maximizes the color fidelity. An array of optical filters tuned at the primary colors will enable a multicolor usage. The material selected for fabricating the microlens was the AZ4562 positive photoresist. The reflow method applied to the photoresist allowing the fabrication of microlenses with high reproducibility.This work was fully supported by the Portuguese Foundation for Science and Technology under the project FCT/PTDC/EEA-ELC/109936/2009

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.