Gravitational lenses in the dark Universe

We discuss how different cosmological models of the Universe affect the probability that a background source has multiple images related by an angular distance $\theta_E$ of the line of sight, \textit{i. e.}, the optical depth of gravitational lensing. We examine some cosmological models for different values of the density parameter $\Omega_i$: i) the cold dark matter model, ii) the $\Lambda$CDM model, iii) the Bose-Einstein condensate dark matter model, iv) the Chaplygin gas model, v) the viscous fluid cosmological model and vi) the holographic dark energy model. We note that the dependence of the energy-matter content of the universe profoundly alters the frequency of multiple quasar image.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics and Space Scienc

Bound state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

In this work, we study of the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the $left$-$handed$ and $right$-$handed$ projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency $\omega_c$ and on the parameters $Z$ and $\Phi_{AB}$ that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state ($n=1$) and the first excited state ($n=2$). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with $\omega_{c}$.Comment: 13 pages, no figur

Exact solutions of the Dirac oscillator under the influence of the Aharonov-Casher effect in the cosmic string background

In this work, we study the Aharonov-Casher effect in the $(2+1)$-dimensional Dirac oscillator coupled to an external electromagnetic field. We set up our system in two different scenarios: in the Minkowski spacetime and the cosmic string spacetime. In both cases, we solve exactly the Dirac oscillator and we determine the energy spectrum and the eigenfunctions for the bound states. We verify that in the Minkowski spacetime, the Dirac oscillator spectrum depends linearly on the strength of the magnetic field $B$, and on the Aharonov-Casher phase. In addition, we explicitly obtain the corrections on the Dirac spinors and the energy levels due to the curvature effects in the cosmic string background. Finally, we investigate the nonrelativistic limit and compare our results with those found in the literature.Comment: 15 pages, no figur

Substrate effects and diffusion dominated roughening in Cu2O electrodeposition

Cuprous oxide (Cu2O) films from 25 nm to 1500 nm were electrodeposited on n-Si(100) and Ni/n-Si(100) substrates from aqueous solution at room temperature. X-ray diffraction and transmission electron microscopy imaging show that the Cu2O structure and morphology is strongly affected by the substrate choice, with V shape and U shape columnar growth on n-Si(100) and Ni/n-Si(100), respectively. Atomic force microscopy reveals the presence of rounded grains at the surface in both cases. Anomalous and normal roughening are observed in films grown on n-Si and Ni, respectively, but estimates of scaling exponents are not conclusive. On the other hand, the distributions of local heights, roughness, and extremal heights show good agreement with those of the fourth order linear stochastic equation of Mullins and Herring (MH). Thus, surface dynamics in both systems is dominated by diffusion of adsorbed molecules, with no large scale effect of possible inhomogeneities in mass flux from the solution or in reaction and adsorption rates. In growth on n-Si substrates, the noise amplitude of the MH equation increases in time as t^{0.8}, while the coefficient of the curvature-related term is time-independent. Step edge energy barriers restrict the mass flux across grain boundaries, thus a broad size distribution of initial grains leads to coarsening of the larger ones. This explains their V shape in the thickest films and establishes a connection with the anomalous roughening. These effects are reduced in films grown on Ni/n-Si, which initially have much larger grains with narrower size distributions and, consequently, smaller fluctuations in coarse grained growth rates.Comment: 11 pages, 9 figure

Prompt emission from GRB 150915A in the GeV energy range detected at ground by the New-Tupi detector: A review

Since 2014, a new detector (New-Tupi) consisting of four plastic scintillators ($150 \times 75 \times 5 cm^3$) placed in pairs and located in Niteroi, Rio de Janeiro, Brazil, has been used for the search of transient solar events and photomuons from gamma-ray bursts (GRBs). On September 15, 2015, at 21:18:24 UT, the Swift Burst Alert Telescope (BAT) triggered and located GRB 150915A (trigger 655721). The GRB light curve shows a weak complex structure of long duration $T_{90}=164.7 \pm 49.7$ s, and a fluence in the 15-150 keV band of $8.0 \pm 1.8 \times 10^{-7}erg/cm^2$. GRB 150915A was fortuitously located in the field of view of the New-Tupi detector, and a search for prompt emission in the GeV energy range is presented here. The analysis was made using the "scaler" or "single-particle" technique. The New-Tupi detector registered a counting rate excess peak of duration $T_{90}=(6.1\pm 0.6)$ s with a signal significance $(4.4\pm 0.5)\sigma$, (and not $6.9\sigma$ as reported in the previous version). The signal is within the T90 duration of the Swift BAT GRB, with an estimated "excess" fluence of $F_S(E>0.1 GeV)=1.3 \pm 0.3 \times 10^{-6} erg/cm^2$. This value can be considered the lower limit of the gamma ray fluence in the GeV energy region. However, the Poisson probability of the event to be a background fluctuation is $5.0 \times 10^{-6}$ and it appears in the counting rate of the New-Tupi detector with an annual rate $\sim 76$. In addition, the signal has a significance of only $2\sigma$ in the time profiles with a bin above 2 seconds. Thus we conclude that the event has a high probability to be background fluctuation.Comment: 11 pages, 9 figure

The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass

In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, $\Phi_{AB}$ and $\kappa$. We notice that the parameter $\kappa$ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass ($\kappa\to{0}$). Moreover, also we note that even in the absence of ABC system ($Z=\Phi_{AB}=0$), the particle with PDM still has a discrete energy spectrum.Comment: 9 page

A Forward Electricity Contract Price Projection: A Market Equilibrium Approach

This work presents a methodology for forward electricity contract price projection based on market equilibrium and social welfare optimization. In the methodology supply and demand for forward contracts are produced in such a way that each agent (generator/load/trader) optimizes a risk adjusted expected value of its revenue/cost. When uncertainties are represented by a discrete number of scenarios, a key result in the paper is that contract price corresponds to the dual variable of the equilibrium constraints in the linear programming problem associated to the optimization of total agents' welfare. Besides computing an equilibrium contract price for a given year, the methodology can also be used to compute the evolution of the probability distribution associated to a contract price with a future delivery period; this an import issue in quantifying forward contract risks. Examples of the methodology application are presented and discusse

Muon Excess at Sea Level during the Progress of a Geomagnetic Storm and High Speed Stream Impact Near the Time of Eath's Heliospheric Sheet Crossing

In this article we present results of the study on the association between the muon flux variation at ground level, registered by the \textit{\textit{New-Tupi}} muon telescopes ($22^0 53'00''S,\; 43^0 06'13'W$; 3 m above sea level) and a geomagnetic storm of 25\,--\,29 August 2015 that has raged for several days as a result of a coronal mass ejection (CME) impact on Earth's magnetosphere. A sequence of events started with an M3.5 X-ray class flare on 22 August 2015 at 21:19 UTC. The \textit{\textit{New-Tupi}} muon telescopes observed a Forbush decrease (FD) triggered by this geomagnetic storm, with onset on 26 August 2015. After the Earth crossed a heliospheric current sheet (HCS), an increase in the particle flux was observed on 28 August 2015 by spacecrafts and ground level detectors. The observed peak was in temporal coincidence with the impact of a high speed stream (HSS). We study this increase, that has been observed with a significance above 1.5\% by ground level detectors in different rigidity regimes. We also estimate the lower limit of the energy fluence injected on Earth. In addition, we consider the origin of this increase, such as acceleration of particles by shock waves on the front of the HSS and the focusing effect of the HCS crossing. Our results show possible evidence of a prolonged energetic (up to GeV energies) particle injection within the Earth atmosphere system, driven by the HSS. In most cases these injected particles are directed to polar regions. However, the particles from the high energy tail of the spectrum can reach middle latitudes, and that could have consequences for the atmospheric chemistry, for instance, the creation of NOx species may be enhanced and can lead to increased ozone depletion. This topic requires further study.Comment: 20 pages, 8 figures. Accepted in Solar Physic

Duality considerations about the Maxwell-Podolsky theory through the symplectic embedding formalism and spectrum analysis

We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and preserve the gauge symmetry. We also furnish an investigation of the pole structure of the vector propagator by the residue matrix which considers the eventual existence of the negative-norm of the theory.Comment: 7 pages. Revtex

Hidden symmetries in the two-dimensional isotropic antiferromagnet

We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex physical systesm in arbitrary sequences of reference frames. All theories of the fundamental interactions rely on gauge invariance. In Dirac's approach, the two-dimensional isotropic antiferromagnet is subject to second class constraints, which are independent of the Hamiltonian symmetries and can be used to eliminate certain canonical variables from the theory. We have used the symplectic embedding formalism developed by a few of us to make the system under study gauge-invariant. After carrying out the embedding and Dirac analysis, we systematically show how second class constraints can generate hidden symmetries. We obtain the invariant second-order Lagrangian and the gauge-invariant model Hamiltonian. Finally, for a particular choice of factor ordering, we derive the functional Schr\"odinger equations for the original Hamiltonian and for the first class Hamiltonian and show them to be identical, which justifies our choice of factor ordering.Comment: To appear in Volume 43 of the Brazilian Journal of Physic