On simultaneous arithmetic progressions on elliptic curves

In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open questions which focus on the most interesting aspects of the problem for us.Comment: 22 page

Theoretical study of loss compensation in long-range dielectric loaded surface plasmon polariton waveguides

In this paper, a theoretical study of loss compensation in long-range dielectric loaded surface plasmon waveguides (LR-DLSPPs) is presented. Although extendable to other gain materials, rare-earth doped double tungstates are used as gain material in this work. Two different structures are studied and the effect of the different waveguide geometrical parameters on the material gain required to fully compensate the propagation losses are reported. The simulations were performed at 1.55 micrometer wavelength. A material gain as low as 12.5 dB/cm was determined as sufficient to obtain complete loss compensation in one of the proposed waveguide structures supporting sub-micron lateral mode dimension

OB stars at the lowest Local Group metallicity: GTC-OSIRIS observations of Sextans A

Our aim is to find and classify OB stars in Sextans A, to later determine accurate stellar parameters of these blue massive stars in this low metallicity region $(Z \sim 0.1 \rm Z_{\odot})$. Using UBV photometry, the reddening-free index Q and GALEX imaging, we built a list of blue massive star candidates in Sextans A. We obtained low resolution (R $\sim$ 1000) GTC-OSIRIS spectra for a fraction of them and carried out spectral classification. For the confirmed O-stars we derive preliminary stellar parameters. The target selection criteria and observations were successful and have produced the first spectroscopic atlas of OB-type stars in Sextans A. From the whole sample of 18 observed stars, 12 were classified as early OB-types, including 5 O-stars. The radial velocities of all target stars are in agreement with their Sextans A membership, although three of them show significant deviations. We determined the stellar parameters of the O-type stars using the stellar atmosphere code FASTWIND, and revisited the sub-SMC temperature scale. Two of the O-stars are consistent with relatively strong winds and enhanced helium abundances, although results are not conclusive. We discuss the position of the OB stars in the HRD. Initial stellar masses run from slightly below 20 up to 40 solar masses. The target selection method worked well for Sextans A, confirming the procedure developed in Garcia \& Herrero (2013). The stellar temperatures are consistent with findings in other galaxies. Some of the targets deserve follow-up spectroscopy because of indications of a runaway nature, an enhanced helium abundance or a relatively strong wind. We observe a correlation between HI and OB associations similar to the irregular galaxy IC1613, confirming the previous result that the most recent star formation of Sextans A is currently on-going near the rim of the H\,{\sc I} cavity

Unbounded violations of bipartite Bell Inequalities via Operator Space theory

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise

Matrix Product State Representations

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.Comment: Minor changes. To appear in QI

Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas

The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled

Dependence of the drag over super hydrophobic and liquid infused surfaces on the textured surface and Weber number

Direct Numerical Simulations of a turbulent channel flow have been performed. The lower wall of the channel is made of staggered cubes with a second fluid locked in the cavities. Two viscosity ratios have been considered, m=μ1/μ2=0.02 and 0.4 (the subscript 1 indicates the fluid in the cavities and 2 the overlying fluid) mimicking the viscosity ratio in super–hydrophobic surfaces (SHS) and liquid infused surfaces (LIS) respectively. A first set of simulations with a slippery interface has been performed and results agree well with those in literature for perfect slip conditions and Stokes approximations. To assess how the dynamics of the interface affects the drag, a second set of DNS has been carried out at We=40 and 400 corresponding to We+≃10−3 and 10−2. The deformation of the interface is fully coupled to the Navier-Stokes equation and tracked in time using a Level Set Method. Two gas fractions, GF=0.5 and 0.875, have been considered to assess how the spacing between the cubes affects the deformation of the interface and therefore the drag. For the dimensions of the substrate here considered, under the ideal assumption of flat interface, staggered cubes with GF=0.875 provide about 20% drag reduction for We=0. However, a rapid degradation of the performances is observed when the dynamics of the interface is considered, and the same geometry increases the drag of about 40% with respect to a smooth wall. On the other hand, the detrimental effect of the dynamics of the interface is much weaker for GF=0.5 because of the reduced pitch between the cubes

Internal energy fluctuations of a granular gas under steady uniform shear flow

The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy with molecular systems. The theoretical predictions are compared with molecular dynamics simulation results. Good agreement is found in the limit of weak inelasticity, while systematic and relevant discrepancies are observed when the inelasticity increases. The origin of this behavior is discussed