Exact Fermi coordinates for a class of spacetimes

We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative cosmological constant, and the Einstein static universe. Maximal charts for Fermi coordinates are discussed.Comment: 15 page

2-(4-Formyl-2,6-dimeth­oxy­phenoxy)­acetic acid

In the title compound, C11H12O6, the aldehyde group is disordered over two sites in a 0.79:0.21 ratio. The carb­oxy­lic acid chain is found in the [ap,ap] conformation due to two intramolecular O—H⋯O hydrogen bonds

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

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

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

Urban development, land sharing and land sparing: the importance of considering restoration

1. At present, there is limited knowledge of how best to reconcile urban development with biodiversity conservation, and in particular whether populations of wild species would be greater under low-density housing (with larger gardens), or high-density housing (allowing more area to be left as undeveloped green spaces). The land sharing/sparing framework – originally developed in the context of farming – can be applied to address this question. 2. We sampled the abundance of trees in the city of Cambridge, UK, along a gradient of human density. We designed different scenarios of urban growth to accommodate the human population predicted in 2031. For each scenario, we projected the future city-wide tree population size and quantified its carbon sequestration potential. We also considered, for the first time in an urban sharing-sparing context, the implications of habitat restoration on degraded urban green space. 3. We found that the density of most native and non-native tree species is presently highest in areas of low human density, compared to both higher density areas and green space (which is largely maintained with few trees). However, restoring woodland in green spaces would lead to far greater densities of native trees than on any existing land use. Hence, provided >2% of green space is restored, native tree population sizes would be larger if urban growth followed a land-sparing approach. Likewise, carbon sequestration would be maximised under land sparing coupled with restoration, but even so only a maximum of 2·5% of the city's annual greenhouse gas emissions could be offset. 4. Although both tree populations and carbon storage thus appear to benefit from land-sparing development, the risk that this might widen the existing disconnect between people and nature must also be addressed – perhaps through a combination of adding housing in low-density areas while ensuring these are in close proximity to high-quality green space. 5. Synthesis and applications. In regions which have already been cleared of intact habitat, a combination of land-sparing urban development with the restoration of green space could accommodate urban population growth whilst dramatically improving the existing status of local tree populations. Where cities are expanding into intact habitat, the merits of urban development by land sparing may be even more pronounced. Studies in such regions are urgently needed

3-(2-Formyl­phen­oxy)propanoic acid

In the structure of the title compound, C10H10O4, the carboxyl group forms a catemer motif in the [100] direction instead of the expected dimeric structures. The carboxylic acid group is found in the syn conformation and the three-dimensional organization in the crystal is based on C—H⋯O and O—H⋯O interactions

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