The low dimensional dynamical system approach in General Relativity: an example

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of Robinson-Trautman spacetimes.Comment: 7 pages, 5 figure

Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterised by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. Apparent enhancement of piezoelectric coefficient $d_{33}$ is observed in an optimally oriented BaTiO$_3$ single crystal. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO$_{3}$ is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centred around ${45^\circ}$. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal.Comment: 11 pages, 7 figure

Structural and insulator-to-metal phase transition at 50 GPa in GdMnO3

We present a study of the effect of very high pressure on the orthorhombic perovskite GdMnO3 by Raman spectroscopy and synchrotron x-ray diffraction up to 53.2 GPa. The experimental results yield a structural and insulator-to-metal phase transition close to 50 GPa, from an orthorhombic to a metrically cubic structure. The phase transition is of first order with a pressure hysteresis of about 6 GPa. The observed behavior under very high pressure might well be a general feature in rare-earth manganites.Comment: 4 pages, 3 figures and 2 table

Time Dependent Current Oscillations Through a Quantum Dot

Time dependent phenomena associated to charge transport along a quantum dot in the charge quantization regime is studied. Superimposed to the Coulomb blockade behaviour the current has novel non-linear properties. Together with static multistabilities in the negative resistance region of the I-V characteristic curve, strong correlations at the dot give rise to self-sustained current and charge oscillations. Their properties depend upon the parameters of the quantum dot and the external applied voltages.Comment: 4 pages, 3 figures; to appear in PR

On the Formation of Copper Linear Atomic Suspended Chains

We report high resolution transmission electron microscopy and classical molecular dynamics simulation results of mechanically stretching copper nanowires conducting to linear atomic suspended chains (LACs) formation. In contrast with some previous experimental and theoretical work in literature that stated that the formation of LACs for copper should not exist our results showed the existence of LAC for the [111], [110], and [100] crystallographic directions, being thus the sequence of most probable occurence.Comment: 4 pages, 3 figure

Bacterial cellulose as a support for the growth of retinal pigment epithelium

The feasibility of bacterial cellulose (BC) as a novel substrate for retinal pigment epithelium (RPE) culture was evaluated. Thin (41.6 ± 2.2 m of average thickness) and heatdried BC substrates were surface modified via acetylation and polysaccharide adsorption, using chitosan and carboxymethyl cellulose. All substrates were characterized according to their surface chemistry, wettability, energy, topography and also regarding their permeability, dimensional stability, mechanical properties and endotoxin content. Then, their ability to promote RPE cell adhesion and proliferation in vitro was assessed. All surface-modified BC substrates presented similar permeation coefficients with solutes of up to 300 kDa. Acetylation of BC decreased its swelling and the amount of endotoxins. Surface modification of BC greatly enhanced the adhesion and proliferation of RPE cells. All samples showed similar stress-strain behavior; BC and acetylated BC showed the highest elastic modulus, but the latter exhibited a slightly smaller tensile strength and elongation at break as compared to pristine BC. Although similar proliferation rates were observed among the modified substrates, the acetylated ones showed higher initial cell adhesion. This difference may be mainly due to the moderately hydrophilic surface obtained after acetylation.The authors acknowledge the Portuguese Foundation for Science and Technology (FCT, Portugal) for the financial support provided by the Research Grants SERH/BD/63578/2009, SFRH/BD/64901/2009, SFRH/BPD/64958/2009, and SFRH/BPD/63148/2009 for S.G., J.P., J.P.S., and V.S., respectively. The authors also acknowledge the Projects PEst-OE/EQB/LA0004/2013, PEst-OE/EQB/LA0023/2013, PTDC/BBB-BQB/2450/2012, and RECI/BBB-EBI/0179/2012 (Number: FCOMP-01-0124-FEDER-027462), cofunded by QREN, FEDER

Dotted and Undotted Algebraic Spinor Fields in General Relativity

We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor fields. We found that some ad hoc rules postulated for the covariant derivatives of Pauli sigma matrices and also for the Dirac gamma matrices in General Relativity cover important physical meaning, which is not apparent in the usual matrix presentation of the theory of two components dotted and undotted spinor fields. We also discuss some issues related to the the previous one and which appear in a proposed "unified" theory of gravitation and electromagnetism which use two components dotted and undotted spinor fields and also paravector fields, which are particular sections of the even subundle of the Clifford bundle of spacetime.Comment: some new misprints have been correcte

A Kolmogorov-Zakharov Spectrum in AdSAdS Gravitational Collapse

We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically $AdS_D$ spacetimes for $D=4,5$. We conclude that spherically symmetric gravitational collapse in asymptotically $AdS$ spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as $\omega^{-s}$ with the frequency, $\omega$, and $s\approx 1.7\pm 0.1$.Comment: 5 pages, 4 figures. v2: Typos, other initial profile considered for universality, error analysis, close to PRL versio