The Riemannian manifold of all Riemannian metrics

The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric which is invariant under the action of the diffeomorphism group. We determine its geodesics, exponential mapping, curvature, and Jacobi fields in a very explicit manner

Pseudoriemannian metrics on spaces of bilinear structures

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation explicitly. Each space of pseudo Riemannian metrics with fixed signature is a geodesically closed submanifold. The space of non degenerate 2-forms is also a geodesically closed submanifold. Then we show that, if we fix a distribution on $M$, the space of all Riemannia metrics splits as the product of three spaces which are everywhere mutually orthogonal, for the usual metric. We investigate this situation in detail

Non-lethal PCR genotyping of single Drosophila

In Drosophila, genetic techniques relying on stochastic chromosomal rearrangements involve the generation and screening of a large number of fly stocks to isolate a few lines of interest. Here, we describe a PCR-based method allowing non-lethal molecular characterization of single flies. Using this procedure, individual candidate recombinant animals can be genotyped and selected one generation earlier than with extant methodology and, importantly, before stocks are established. This advance should significantly facilitate several of the most fundamental and routine techniques in Drosophila genetics

Linear magnetoresistance in metals: guiding center diffusion in a smooth random potential

We predict that guiding center (GC) diffusion yields a linear and non-saturating (transverse) magnetoresistance in 3D metals. Our theory is semi-classical and applies in the regime where the transport time is much greater than the cyclotron period, and for weak disorder potentials which are slowly varying on a length scale much greater than the cyclotron radius. Under these conditions, orbits with small momenta along magnetic field $B$ are squeezed and dominate the transverse conductivity. When disorder potentials are stronger than the Debye frequency, linear magnetoresistance is predicted to survive up to room temperature and beyond. We argue that magnetoresistance from GC diffusion explains the recently observed giant linear magnetoresistance in 3D Dirac materials

Spark Model for Pulsar Radiation Modulation Patterns

A non-stationary polar gap model first proposed by Ruderman & Sutherland (1975) is modified and applied to spark-associated pulsar emission at radio wave-lengths. It is argued that under physical and geometrical conditions prevailing above pulsar polar cap, highly non-stationary spark discharges do not occur at random positions. Instead, sparks should tend to operate in well determined preferred regions. At any instant the polar cap is populated as densely as possible with a number of two-dimensional sparks with a characteristic dimension as well as a typical distance between adjacent sparks being about the polar gap height. Our model differs, however, markedly from its original 'hollow cone' version. The key feature is the quasi-central spark driven by pair production process and anchored to the local pole of a sunspot-like surface magnetic field. This fixed spark prevents the motion of other sparks towards the pole, restricting it to slow circumferential drift across the planes of field lines converging at the local pole. We argue that the polar spark constitutes the core pulsar emission, and that the annular rings of drifting sparks contribute to conal components of the pulsar beam. We found that the number of nested cones in the beam of typical pulsar should not excced three; a number also found by Mitra & Deshpande (1999) using a completely different analysis.Comment: 31 pages, 8 figures, accepted by Ap

World Agriculture Organization (WAO): New Global Governance for Agricultural Trade

It is increasingly questionable whether the WTO regime is the most appropriate form of governance for addressing global problems related to agriculture. In particular, climate change, sustainability, hunger/poverty in developing countries, and expected imbalance in food demand-supply by 2050 are emerging as grave challenges to humanity and the WTO is still struggling to resolve issues (related to the multifunctional roles of agriculture) of the 20th century while completely lacking the capacity to tackle such new global issues of the 21st century. Given this outmoded institution, the primary objective of this article is to propose that a new system of governance is needed so as to exclusively and effectively deal with problems arising from the interactions among climate change, agricultural sustainability, food security, and trade.Global public goods, climate change, sustainable agriculture, food security, WTO, agricultural trade, International Relations/Trade,