The group of causal automorphisms

The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed

Microlensing path parametrization for Earth-like Exoplanet detection around solar mass stars

We propose a new parametrization of the impact parameter u0 and impact angle {\alpha} for microlensing systems composed by an Earth-like Exoplanet around a Solar mass Star at 1 AU. We present the caustic topology of such system, as well as the related light curves generated by using such a new parametrization. Based on the same density of points and accuracy of regular methods, we obtain results 5 times faster for discovering Earth-like exoplanet. In this big data revolution of photometric astronomy, our method will impact future missions like WFIRST (NASA) and Euclid (ESA) and they data pipelines, providing a rapid and deep detection of exoplanets for this specific class of microlensing event that might otherwise be lost.Comment: 8 pages, 7 figures, accepted to be published in The Astronomical Journa

Minimal resonances in annular non-Euclidean strips

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. Within this class of strips, we derive a condition under which a strip can have vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added 2 figure