Symmetries of the Dirac operators associated with covariantly constant Killing-Yano tensors

The continuous and discrete symmetries of the Dirac-type operators produced by particular Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The Killing-Yano tensors considered are covariantly constant and realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. The Dirac operators are related among themselves through continuous or discrete transformations. It is shown that the groups of the continuous symmetry can be only U(1) and SU(2), specific to (hyper-)Kahler spaces, but arising even in cases when the requirements for these special geometries are not fulfilled. The discrete symmetries are also studied obtaining the discrete groups Z_4 and Q. The briefly presented examples are the Euclidean Taub-NUT space and the Minkowski spacetime.Comment: 27 pages, latex, no figures, final version to be published in Class. Quantum Gravit

Nonlinear dynamics and bifurcation behavior of a 2-DOF spring resonator with end stopper for energy harvesting

In this paper, the model of a two-degree-of-freedom (2-DOF) spring resonator with end stopper for an energy harvesting application is presented. Then we characterize its nonlinear dynamical behavior by numerical simulations when some suitable parameters are varied. The system is formed by two resonators subject to external vibrational excitation and with an end stopper. We present the continuous time dynamical model of the system in the form of a switched fourth order differential equation. Harmonic vibrations are considered as the main ambient energy source for the system and its frequency response representing the RMS value of the displacement is first computed. The dynamical behavior is unveiled by computing state-space trajectories, timedomain series and FFT spectra and frequency response as the excitation amplitude is varied.Peer ReviewedPostprint (published version

The pursuit of bright smile : tooth whitening among Hong Kong young adults

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Tunable membranes incorporating artificial water channels for high-performance brackish/low-salinity water reverse osmosis desalination

Membrane-based technologies have a tremendous role in water purification and desalination. Inspired by biological proteins, artificial water channels (AWCs) have been proposed to overcome the permeability/selectivity trade-off of desalination processes. Promising strategies exploiting the AWC with angstrom-scale selectivity have revealed their impressive performances when embedded in bilayer membranes. Herein, we demonstrate that self-assembled imidazole-quartet (I-quartet) AWCs are macroscopically incorporated within industrially relevant reverse osmosis membranes. In particular, we explore the best combination between I-quartet AWC and m-phenylenediamine (MPD) monomer to achieve a seamless incorporation of AWC in a defect-free polyamide membrane. The performance of the membranes is evaluated by crossflow filtration under real reverse osmosis conditions (15 to 20 bar of applied pressure) by filtration of brackish feed streams. The optimized bioinspired membranes achieve an unprecedented improvement, resulting in more than twice (up to 6.9 L center dot m-2 center dot h-1 center dot bar-1) water permeance of analogous commercial membranes, while maintaining excellent NaCl rejection (>99.5%). They show also excellent performance in the purification of low-salinity water under low-pressure conditions (6 bar of applied pressure) with fluxes up to 35 L center dot m-2 center dot h-1 and 97.5 to 99.3% observed rejection