A two band model for Superconductivity: Probing interband pair formation

We propose a two band model for superconductivity. It turns out that the simplest nontrivial case considers solely interband scattering, and both bands can be modeled as symmetric (around the Fermi level) and flat, thus each band is completely characterized by its half-band width $W_{n}$ (n=1,2). A useful dimensionless parameter is $\delta$, proportional to $W_{2}-W_{1}$. The case $\delta =0$ retrieves the conventional BCS model. We probe the specific heat, the ratio gap over critical temperature, the thermodynamic critical field and tunneling conductance as functions of $\delta$ and temperature (from zero to $T_{c}$). We compare our results with experimental results for $MgB_{2}$ and good quantitative agreement is obtained, indicating the relevance of interband coupling. Work in progress also considers the inclusion of band hybridization and general interband as well as intra-band scattering mechanisms.Comment: 7 pages, 5 figures (in postscript format). PACS numbers: 74.20.-z, 74.20.Fg, 74.70.A

A general theory of linear cosmological perturbations: bimetric theories

We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.Comment: Published version with extra comments in conclusio

Present and potential land use mapping in Mexico

The Mexican Water Plan (MWP) conducted studies of present and potential land use in Mexico using LANDSAT-1 satellite imagery. Present land use studies were carried out all over the country (197 million hectares); nine soil uses were mapped according to the first classification level recommended by the U.S. Geological Survey. Also 6.3 million hectares of land with advanced erosion were detected. Work was executed at a rate of 8 million hectares per month; reliability was 90% and the cost of only 0.1 cents/hectare. The potential land use study was performed in 45 million hectares at a rate of 4 million hectares per month and at a cost of 0.33 cents/hectare. Soil units according to FAO classification were delineated scale 1:1 million; interpretative maps were also prepared dealing with potential agricultural productivity carrying capacity for cattle, water, erosion risk, and slope ranges

A covariant approach to parameterised cosmological perturbations

We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyse scalar, vector and tensor perturbations at the same time in a straightforward manner. We apply the procedure to diffeomorphism invariant single-tensor, scalar-tensor and vector-tensor theories and show explicitly the full covariant form of the quadratic actions in such cases, in addition to the actions determining the evolution of vector and tensor perturbations. We also discuss the role of the symmetry of the background in identifying the set of cosmologically relevant free parameters describing these classes of theories, including calculating the relevant free parameters for an axisymmetric Bianchi-I vacuum universe.Comment: Updated to match published versio

Measuring the growth rate of structure with Type IA Supernovae from LSST

We investigate measuring the peculiar motions of galaxies up to $z=0.5$ using Type Ia supernovae (SNe Ia) from LSST, and predict the subsequent constraints on the growth rate of structure. We consider two cases. Our first is based on measurements of the volumetric SNe Ia rate and assumes we can obtain spectroscopic redshifts and light curves for varying fractions of objects that are detected pre-peak luminosity by LSST (some of which may be obtained by LSST itself and others which would require additional follow-up). We find that these measurements could produce growth rate constraints at $z<0.5$ that significantly outperform those using Redshift Space Distortions (RSD) with DESI or 4MOST, even though there are $\sim4\times$ fewer objects. For our second case, we use semi-analytic simulations and a prescription for the SNe Ia rate as a function of stellar mass and star formation rate to predict the number of LSST SNe IA whose host redshifts may already have been obtained with the Taipan+WALLABY surveys, or with a future multi-object spectroscopic survey. We find $\sim 18,000$ and $\sim 160,000$ SN Ia with host redshifts for these cases respectively. Whilst this is only a fraction of the total LSST-detected SNe Ia, they could be used to significantly augment and improve the growth rate constraints compared to only RSD. Ultimately, we find that combining LSST SNe Ia with large numbers of galaxy redshifts will provide the most powerful probe of large scale gravity in the $z<0.5$ regime over the coming decades.Comment: 12 pages, 1 table, 5 figures. Accepted for publication in ApJ. The Fisher matrix forecast code used in this paper can be found at: https://github.com/CullanHowlett/PV_fisher. Updated to fix error in Eq. 1 (thanks to Eric Linder for pointing this out

A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers