Conjugate two-dimensional electric potential maps

Two dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on `capacitor-like' geometries with current flowing between two opposite electrodes. A `topographical' investigation across the embedding medium (map of equipotential curves) allows to reassure a number of physical properties. This paper focuses on some less common configurations that bear pedagogical interest. We analyze `open-geometries' with electrodes in the form of long strips with slits. They provide a natural groundwork to bring the student to complex variable methods. Aided by this, we show that shaping the conducting paper board one may analyze finite size effects, as well as some meaningful discontinuities in the measured potential. The concept of conjugate electric potentials is exploited. Equipotentials and electric field lines acquire interchangeable roles and may be obtained in complementary `dual' experiments. A feasible theoretical analysis based on introductory complex variables and standardized numerics gives a remarkable quantification of the experimental results.Comment: 15 pages, 8 figure

Explaining exchange rate dynamics: the uncovered equity return parity condition

By employing Lucas’ (1982) model, this study proposes an arbitrage relationship – the Uncovered Equity Return Parity (URP) condition – to explain the dynamics of exchange rates. When expected equity returns in a country/region are lower than expected equity returns in another country/region, the currency associated with the market offering lower returns is expected to appreciate. First, we test the URP assuming that investors are risk neutral and next we relax this hypothesis. The resulting risk premia are proxied by economic variables, which are related to the business cycle. We employ differentials in corporate earnings’ growth rates, short-term interest rate changes, annual inflation rates, and net equity flows. The URP explains a large fraction of the variability of some European currencies vis-à-vis the US dollar. When confronted with the naïve random walk model, the URP for the EUR/USD performs better in terms of forecasts for a set of alternative statistics. JEL Classification: D82, G14, G15asset pricing, foreign exchange markets, GMM, random walk, UIP

The uncovered return parity condition

This paper proposes an equilibrium relationship between expected exchange rate changes and differentials in expected returns on risky assets. We show that when expected returns on a risky asset in a certain economy are higher than the returns that are expected from investing in a risky asset in another economy, then the currency corresponding to the economy whose asset offers higher returns is expected to depreciate. Due to its similarity with Uncovered Interest Parity (UIP), we call this equilibrium condition “Uncovered Return Parity” (URP). However, in the URP condition returns’ differentials are not known ex ante, while in the UIP they are. The paper finds empirical support in favour of URP for certain markets over some sample periods. JEL Classification: F30, F31, G12, C32GMM, stochastic discount factor, Uncovered interest parity, Uncovered Return Parity

Robust strategies for lossy quantum interferometry

We give a simple multiround strategy that permits to beat the shot noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.Comment: 4 pages, 3 figure

Deconstructing double-barred galaxies in 2D and 3D. II. Two distinct groups of inner bars

The intrinsic photometric properties of inner and outer stellar bars within 17 double-barred galaxies are thoroughly studied through a photometric analysis consisting of: i) two-dimensional multi-component photometric decompositions, and ii) three-dimensional statistical deprojections for measuring the thickening of bars, thus retrieving their 3D shape. The results are compared with previous measurements obtained with the widely used analysis of integrated light. Large-scale bars in single- and double-barred systems show similar sizes, and inner bars may be longer than outer bars in different galaxies. We find two distinct groups of inner bars attending to their in-plane length and ellipticity, resulting in a bimodal behaviour for the inner/outer bar length ratio. Such bimodality is related neither to the properties of the host galaxy nor the dominant bulge, and it does not show a counterpart in the dimension off the disc plane. The group of long inner bars lays at the lower end of the outer bar length vs. ellipticity correlation, whereas the short inner bars are out of that relation. We suggest that this behaviour could be due to either a different nature of the inner discs from which the inner bars are dynamically formed, or a different assembly stage for the inner bars. This last possibility would imply that the dynamical assembly of inner bars is a slow process taking several Gyr to happen. We have also explored whether all large-scale bars are prone to develop an inner bar at some stage of their lives, possibility we cannot fully confirm or discard.Comment: 14 pages, 8 figures, 1 table. Accepted for publication in MNRA

The intrinsic three-dimensional shape of galactic bars

We present the first statistical study on the intrinsic three-dimensional (3D) shape of a sample of 83 galactic bars extracted from the CALIFA survey. We use the galaXYZ code to derive the bar intrinsic shape with a statistical approach. The method uses only the geometric information (ellipticities and position angles) of bars and discs obtained from a multi-component photometric decomposition of the galaxy surface-brightness distributions. We find that bars are predominantly prolate-triaxial ellipsoids (68%), with a small fraction of oblate-triaxial ellipsoids (32%). The typical flattening (intrinsic C/A semiaxis ratio) of the bars in our sample is 0.34, which matches well the typical intrinsic flattening of stellar discs at these galaxy masses. We demonstrate that, for prolate-triaxial bars, the intrinsic shape of bars depends on the galaxy Hubble type and stellar mass (bars in massive S0 galaxies are thicker and more circular than those in less massive spirals). The bar intrinsic shape correlates with bulge, disc, and bar parameters. In particular with the bulge-to-total (B/T) luminosity ratio, disc g-r color, and central surface brightness of the bar, confirming the tight link between bars and their host galaxies. Combining the probability distributions of the intrinsic shape of bulges and bars in our sample we show that 52% (16%) of bulges are thicker (flatter) than the surrounding bar at 1$\sigma$ level. We suggest that these percentages might be representative of the fraction of classical and disc-like bulges in our sample, respectively.Comment: 18 pages, 11 figures, accepted for publication in MNRA