Chord diagrams and BPHZ subtractions

The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three point vertex in $\phi^3$ theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections). The resolution of the singular crossings using the equivalence relations in these examples provides confirmation of a proposed fundamental relationship between knot theory and renormalization in perturbative quantum field theory.Comment: 12 pages, 5 Postscript figures, LaTex 2

Local structure of Liquid-Vapour Interfaces

The structure of a simple liquid may be characterised in terms of ground state clusters of small numbers of atoms of that same liquid. Here we use this sensitive structural probe to consider the effect of a liquid-vapour interface upon the liquid structure. At higher temperatures (above around half the critical temperature) we find that the predominant effect of the interface is to reduce the local density, which significantly suppresses the local cluster populations. At lower temperatures, however, pronounced interfacial layering is found. This appears to be connected with significant orientational ordering of clusters based on 3- and 5-membered rings, with the rings aligning perpendicular and parallel to the interface respectively. At all temperatures, we find that the population of five-fold symmetric structures is suppressed, rather than enhanced, close to the interface.Comment: 10 pages, 8 figures, accepted for publication by Molecular Physic

Increasing concentrations of dichloromethane, CH2Cl2, inferred from CARIBIC air samples collected 1998–2012

Atmospheric concentrations of dichloromethane, CH2Cl2, a regulated toxic air pollutant and minor contributor to stratospheric ozone depletion, were reported to have peaked around 1990 and to be declining in the early part of the 21st century. Recent observations suggest this trend has reversed and that CH2Cl2 is once again increasing in the atmosphere. Despite the importance of ongoing monitoring and reporting of atmospheric CH2Cl2, no time series has been discussed in detail since 2006. The CARIBIC project (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container) has analysed the halocarbon content of whole-air samples collected at altitudes of between ~10–12 km via a custom-built container installed on commercial passenger aircraft since 1998, providing a long-term record of CH2Cl2 observations. In this paper we present this unique CH2Cl2 time series, discussing key flight routes which have been used at various times over the past 15 years. Between 1998 and 2012 increases were seen in all northern hemispheric regions and at different altitudes, ranging from ~7–10 ppt in background air to ~13–15 ppt in regions with stronger emissions (equating to a 38–69% increase). Of particular interest is the rising importance of India as a source of atmospheric CH2Cl2: based on CARIBIC data we provide regional emission estimates for the Indian subcontinent and show that regional emissions have increased from 3–14 Gg yr^-1 (1998–2000) to 16–25 Gg yr^-1 (2008). Potential causes of the increasing atmospheric burden of CH2Cl2 are discussed. One possible source is the increased use of CH2Cl2 as a feedstock for the production of HFC-32, a chemical used predominantly as a replacement for ozone-depleting substances in a variety of applications including air conditioners and refrigeration