Homogeneous cosmologies and the Maupertuis-Jacobi principle

A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the Maupertuis-Jacobi principle in classical mechanics, such result permits us to infer some dynamical properties of cosmological models from the geometry of the associated effective manifolds, allowing us to go a step further in the study of cosmological dynamics. By means of some explicit examples, we show how the geometrical analysis can simplify considerably the dynamical analysis of cosmological models.Comment: 5 page

Galactic Dark Matter: a Dynamical Consequence of Cosmological Expansion

This work wants to show how standard General Relativity (GR) is able to explain galactic rotation curves without the need for dark matter, this starting from the idea that when Einstein's equations are applied to the dynamics of a galaxy embedded in an expanding universe they do not reduce to Poisson's equation but a generalisation of it taking cosmological expansion into account. A non-linear scheme to perturb Einstein's field equations around the Robertson-Walker (R-W) metric is devised in order to find their non-relativistic limit without losing their characteristic non-linearities. The resulting equation is used to numerically study the gravitational potential of a cosmological perturbation and applied to a simple galactic model with an exponentially decreasing baryonic matter distribution. The non-relativistic limit of GR in a R-W space-time produces a generalised Poisson equation for the gravitational potential which is non-linear, parabolic and heat-like. It is shown how its non-linearities generate an effective "dark matter" distribution caused by both cosmological expansion and the dynamics of the perturbation's gravitational potential. It is also shown how this dynamical effect gets completely lost during a linearisation of Einstein's equations. The equation is then used to successfully fit real galactic rotation curves numerically using a matter distribution following the shape of a simple S\'ersic luminosity profile, common to most galaxies, thus without recourse to dark matter. A relation for the dark to luminous matter ratio is found, explaining the domination of dark matter in low-mass galaxies. A few rotation curves with a faster than Newtonian decrease are also presented and successfully fitted, opening the way to a new possible interpretation of these phenomena in terms of an effective "anti-gravitational" dark matter distribution, purely geometrical in origin.Comment: 8 pages, 18 figures, Research Pape

Loran-C approach guidance project current status

There are four areas of work in the Loran-C flight test project. Current results provide performance data on the effects of Signal Noise Ratio (SNR) on the dynamic performance of the receiver filters for Loran-C data, and data on Loran-C grid deformation at a microscale of 100 meters. The Loran-C receiver provides a line of position (LOP) Master and Slave transmitter at an angle 0 to magnetic north. No transformation to latitude-longitude reference frame is required since this is the major source of Loran-C navigation errors. A local coordinate frame is established centered at touchdown point on the runway with directions along and across the runway. A Loran-C data collection system was set up. The Loran-C data are sent directly to an Apple II computer with a 12 inch monitor. The effect of SNR on Loran-C precision is shown for two receiver filters of different frequency response. A set of ground level static readings of touchdown was taken around Hanscom Field and transferred to an accurate detailed layout drawing; this showed local distortions of the average touchdown values

Entomopathogenic nematodes for biological control of codling moth

Entomopathogenic nematodes are often found naturally infecting codling moth larvae. The effect of an autumn treatment with S. feltiae on the fruit damage in the following summer was evaluated by treating 4 different apple orchards in October 2004 and 2005 at application rates of 3.75; 2 and 1.5 billion nematodes in 4000 l / ha. In three of the treated orchards, one treated with 3.75x109 nematodes/ha the other two treated with 2e9 nematode/ha, reduction in fruit damage was around 50%. In the most heavily infested orchard, which was treated with 1.5x109 nematode/ha only 33% reduction in fruit damage was achieved. Compared to previous studies, this was the first assessing the effect on the fruit damage in the summer following the treatment rather than assessing the mortality of sentinel larvae fixed to the treated tree trunks

Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum

Holography for Lifshitz space-times corresponds to dual field theories on a fixed torsional Newton-Cartan (TNC) background. We examine the coupling of non-relativistic field theories to TNC backgrounds and uncover a novel mechanism by which a global U(1) can become local. This involves the TNC vector $M_\mu$ which sources a particle number current, and which for flat NC space-time satisfies $M_{\mu}=\partial_{\mu}M$ with a Schroedinger symmetry realized on $M$. We discuss various toy model field theories on flat NC space-time for which the new mechanism leads to extra global space-time symmetries beyond the generic Lifshitz symmetry, allowing for an enhancement to Schroedinger symmetry. On the holographic side, the source $M$ also appears in the Lifshitz vacuum with exactly the same properties as for flat NC space-time. In particular, the bulk diffeomorphisms that preserve the boundary conditions realize a Schroedinger algebra on $M$, allowing for a conserved particle number current. Finally, we present a probe action for a complex scalar field on the Lifshitz vacuum, which exhibits Schroedinger invariance in the same manner as seen in the field theory models.Comment: 55 pages + 2 appendice

Incorporation of Spacetime Symmetries in Einstein's Field Equations

In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry. The method is being expressed in a covariant formalism using the framework of a double congruence. The basic notion on which it is based is that of the geometrisation of a general symmetry. As a special application of our general method we consider the case of a spacelike conformal Killing vector field on the spacetime manifold regarding special types of matter fields. New perspectives in General Relativity are discussed.Comment: 41 pages, LaTe