Cavity optomechanics with stoichiometric SiN films

We study high-stress SiN films for reaching the quantum regime with mesoscopic oscillators connected to a room-temperature thermal bath, for which there are stringent requirements on the oscillators' quality factors and frequencies. Our SiN films support mechanical modes with unprecedented products of mechanical quality factor $Q_m$ and frequency $\nu_m$ reaching $Q_{m} \nu_m \simeq2 \times 10^{13}$ Hz. The SiN membranes exhibit a low optical absorption characterized by Im$(n) \lesssim 10^{-5}$ at 935 nm, representing a 15 times reduction for SiN membranes. We have developed an apparatus to simultaneously cool the motion of multiple mechanical modes based on a short, high-finesse Fabry-Perot cavity and present initial cooling results along with future possibilities.Comment: 4 pages, 5 figure

Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

Self-consistent treatment of the self-energy in nuclear matter

The influence of hole-hole propagation in addition to the conventional particle-particle propagation, on the energy per nucleon and the momentum distribution is investigated. The results are compared to the Brueckner-Hartree-Fock (BHF) calculations with a continuous choice and conventional choice for the single-particle spectrum. The Bethe-Goldstone equation has been solved using realistic $NN$ interactions. Also, the structure of nucleon self-energy in nuclear matter is evaluated. All the self-energies are calculated self-consistently. Starting from the BHF approximation without the usual angle-average approximation, the effects of hole-hole contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using the self-consistent self-energy, the hole and particle self-consistent spectral functions including the particle-particle and hole-hole ladder contributions in nuclear matter are calculated using realistic $NN$ interactions. We found that, the difference in binding energy between both results, i.e. BHF and self-consistent Green function, is not large. This explains why is the BHF ignored the 2h1p contribution.Comment: Preprint 20 pages including 15 figures and one tabl

Energy Distribution associated with Static Axisymmetric Solutions

This paper has been addressed to a very old but burning problem of energy in General Relativity. We evaluate energy and momentum densities for the static and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen and the gamma metrics, belonging to the Weyl class. We apply four well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and M$\ddot{o}$ller to compute energy-momentum density components. We obtain that these prescriptions do not provide similar energy density, however momentum becomes constant in each case. The results can be matched under particular boundary conditions.Comment: 18 pages, accepted for publication in Astrophysics and SpaceScienc

On the energy of charged black holes in generalized dilaton-axion gravity

In this paper we calculate the energy distribution of some charged black holes in generalized dilaton-axion gravity. The solutions correspond to charged black holes arising in a Kalb-Ramond-dilaton background and some existing non-rotating black hole solutions are recovered in special cases. We focus our study to asymptotically flat and asymptotically non-flat types of solutions and resort for this purpose to the M{\o}ller prescription. Various aspects of energy are also analyzed.Comment: LaTe

Predicting shape and stability of air–water interface on superhydrophobic surfaces with randomly distributed, dissimilar posts

A mathematical framework developed to calculate the shape of the air–water interface and predict the stability of a microfabricated superhydrophobicsurface with randomly distributed posts of dissimilar diameters and heights is presented. Using the Young–Laplace equation, a second-order partial differential equation is derived and solved numerically to obtain the shape of the interface, and to predict the critical hydrostatic pressure at which the superhydrophobicity vanishes in a submersed surface. Two examples are given for demonstration of the method’s capabilities and accuracy

Effect of fiber orientation on shape and stability of air-water interface on submerged superhydrophobic electrospun thin coatings

To better understand the role of fiber orientation on the stability of superhydrophobicelectrospun coatings under hydrostaticpressures, an integro-differential equation is developed from the balance of forces across the air–water interface between the fibers. This equation is solved numerically for a series of superhydrophobicelectrospun coatings comprised of random and orthogonal fiber orientations to obtain the exact 3D shape of the air–water interface as a function of hydrostaticpressure. More important, this information is used to predict the pressure at which the coatings start to transition from the Cassie state to the Wenzel state, i.e., the so-called critical transition pressure. Our results indicate that coatings composed of orthogonal fibers can withstand higher elevated hydrostaticpressures than those made up of randomly orientated fibers. Our results also prove that thin superhydrophobic coatings can better resist the elevated pressures. The modeling methodology presented here can be used to design nanofibrous superhydrophobic coatings for underwater applications

Predicting shape and stability of air–water interface on superhydrophobic surfaces comprised of pores with arbitrary shapes and depths

An integro-differential equation for the three dimensional shape of air–water interface on superhydrophobicsurfaces comprised of pores with arbitrary shapes and depths is developed and used to predict the static critical pressure under which such surfaces depart from the non-wetting state. Our equation balances the capillary forces with the pressure of the air entrapped in the pores and that of the water over the interface. Stability of shallow and deep circular, elliptical, and polygonal pores is compared with one another and a general conclusion is drawn for designing pore shapes for superhydrophobicsurfaces with maximum stability