Analytic Central Orbits and their Transformation Group

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are generalisations of the semi-latus-rectum and the eccentricity. 'm' is given as a function of 'eccentricity'. For nearly circular orbits 'm' is sqrt{k}, while the above orbit becomes exact at the energy of escape where 'e' is one and 'm' is 'k'. Orbits in the logarithmic potential that gives rise to a constant circular velocity are derived via the limit of small alpha. For such orbits, r^2 vibrates almost harmonically whatever the 'eccentricity'. Unbound orbits in power-law potentials are given in an appendix. The transformation of orbits in one potential to give orbits in a different potential is used to determine orbits in potentials that are positive powers of r. These transformations are extended to form a group which associates orbits in sets of six potentials, e.g. there are corresponding orbits in the potentials proportional to r, r^{-2/3}, r^{-3}, r^{-6}, r^{4/3} and r^{-4}. A degeneracy reduces this to three, which are r^{-1}, r^2 and r^{-4} for the Keplerian case. A generalisation of this group includes the isochrone with the Kepler set.Comment: 12 pages, 8 figures; updated version with minor typographical corrections; published in MNRA

Spatial Regulation of Membrane Fusion Controlled by Modification of Phosphoinositides

Membrane fusion plays a central role in many cell processes from vesicular transport to nuclear envelope reconstitution at mitosis but the mechanisms that underlie fusion of natural membranes are not well understood. Studies with synthetic membranes and theoretical considerations indicate that accumulation of lipids characterised by negative curvature such as diacylglycerol (DAG) facilitate fusion. However, the specific role of lipids in membrane fusion of natural membranes is not well established. Nuclear envelope (NE) assembly was used as a model for membrane fusion. A natural membrane population highly enriched in the enzyme and substrate needed to produce DAG has been isolated and is required for fusions leading to nuclear envelope formation, although it contributes only a small amount of the membrane eventually incorporated into the NE. It was postulated to initiate and regulate membrane fusion. Here we use a multidisciplinary approach including subcellular membrane purification, fluorescence spectroscopy and Förster resonance energy transfer (FRET)/two-photon fluorescence lifetime imaging microscopy (FLIM) to demonstrate that initiation of vesicle fusion arises from two unique sites where these vesicles bind to chromatin. Fusion is subsequently propagated to the endoplasmic reticulum-derived membranes that make up the bulk of the NE to ultimately enclose the chromatin. We show how initiation of multiple vesicle fusions can be controlled by localised production of DAG and propagated bidirectionally. Phospholipase C (PLCγ), GTP hydrolysis and (phosphatidylinsositol-(4,5)-bisphosphate (PtdIns(4,5)P2) are required for the latter process. We discuss the general implications of membrane fusion regulation and spatial control utilising such a mechanism

Duality properties of Gorringe-Leach equations

In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe

General Transformation Formulas for Fermi-Walker Coordinates

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.Comment: 23 pages. Corrected typos in the last two equations. Accepted for publication in Classical and Quantum Gravit

A Statistical Mechanical Problem in Schwarzschild Spacetime

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief comments on the system's center of mass and the thermodynamic limi

Absorption Enhancement in Organic-Inorganic Halide Perovskite Films with Embedded Plasmonic Gold Nanoparticles

We report on the numerical analysis of solar absorption enhancement in organic-inorganic halide perovskite films embedding plasmonic gold nanoparticles. The effect of particle size and concentration is analyzed in realistic systems in which random particle location within the perovskite film and the eventual formation of dimers are also taken into account. We find a maximum integrated solar absorption enhancement of ∼10% in perovskite films of 200 nm thickness and ∼6% in 300 nm films, with spheres of radii 60 and 90 nm, respectively, in volume concentrations of around 10% in both cases. We show that the presence of dimers boosts the absorption enhancement up to ∼12% in the thinnest films considered. Absorption reinforcement arises from a double contribution of plasmonic near-field and scattering effects, whose respective weight can be discriminated and evaluated from the simulations.Peer Reviewe

Extended Fermi coordinates

We extend the notion of Fermi coordinates to a generalized definition in which the highest orders are described by arbitrary functions. From this definition rises a formalism that naturally gives coordinate transformation formulae. Some examples are developped in which the extended Fermi coordinates simplify the metric components.Comment: 16 pages, 1 figur

Timelike Killing Fields and Relativistic Statistical Mechanics

For spacetimes with timelike Killing fields, we introduce a "Fermi-Walker-Killing" coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, derived both independently and as the Newtonian limit of our formula. We also find the relativistic thermodynamic equation of state. Specific examples are given in Kerr spacetime.Comment: This version contains minor corrections, additional discussion, and will appear in Classical and Quantum Gravit

DEVELOPING NEW APPROACHES TO GLOBAL STOCK STATUS ASSESSMENT AND FISHERY PRODUCTION POTENTIAL OF THE SEAS

Stock status is a key parameter for evaluating the sustainability of fishery resources and developing corresponding management plans. However, the majority of stocks are not assessed, often as a result of insufficient data and a lack of resources needed to execute formal stock assessments. The working group involved in this publication focused on two approaches to estimating fisheries status: one based on single-stock status, and the other based on ecosystem production.JRC.G.4-Maritime affair