Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

Exact General Solutions to Extraordinary N-body Problems

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.Comment: 15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc.

Relaxation to a Perpetually Pulsating Equilibrium

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2 kT, but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale, r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium.Comment: 9 pages including 4 figure

Between social policy and Union citizenship: the Framework Directive on equal treatment in employment

In December 2000, the Council adopted the Framework Directive forbidding discrimination on grounds of religion or belief, disability, age and sexual orientation in the field of employment. The Directive adopted Article 13 EC as its legal basis. However, there are strong arguments suggesting that this was not the correct choice of legal basis; in particular, the Social Chapter of the EC Treaty (Title XI) provided an alternative legal foundation, including different legislative processes (co-decision and the social dialogue). This article first examines the legal grounds requiring a different legal basis for the Directive and then explores the wider political imperatives that may explain the preference of the EU institutions for relying instead on Article 13 EC.</p

Magnetic field amplification by cosmic rays in supernova remnants

Magnetic field amplification is needed to accelerate cosmic cays to PeV energies in supernova remants. Escaping cosmic rays trigger a return current in the plasma that drives a non-resonant hybrid instability. We run simulations in which we represent the escaping cosmic rays with the plasma return current, keeping the maximum cosmic ray energy fixed, and evaluate its effects on the upstream medium. In addition to magnetic field amplification, density perturbations arise that, when passing through the shock, further increase amplification levels downstream. As the growth rate of the instability is most rapid for the smaller scales, the resolution is a limiting factor in the amplification that can be reached with these simulations.Comment: 4 pages, 2 figures, to appear in the proceedings of the conference "370 years of Astronomy in Utrecht", eds. G. Pugliese, A. de Koter and M. Wijbur

Cosmic ray acceleration in young supernova remnants

We investigate the appearance of magnetic field amplification resulting from a cosmic ray escape current in the context of supernova remnant shock waves. The current is inversely proportional to the maximum energy of cosmic rays, and is a strong function of the shock velocity. Depending on the evolution of the shock wave, which is drastically different for different circumstellar environments, the maximum energy of cosmic rays as required to generate enough current to trigger the non-resonant hybrid instability that confines the cosmic rays follows a different evolution and reaches different values. We find that the best candidates to accelerate cosmic rays to ~few PeV energies are young remnants in a dense environment, such as a red supergiant wind, as may be applicable to Cassiopeia A. We also find that for a typical background magnetic field strength of 5 microG the instability is quenched in about 1000 years, making SN1006 just at the border of candidates for cosmic ray acceleration to high energies.Comment: 14 pages, 8 figures. Accepted for publication in MNRA

Developing future energy performance standards for UK housing: The St Nicholas Court project – Part 1

This paper (and Part 2, to appear in the next issue) set out the results of a housing field trial designed to evaluate the impact of an enhanced energy performance standard for dwellings. The project was designed to inform the next review of Part L of the Building Regulations for England and Wales, which, following the publication of the UK government's white paper on energy policy, is expected in 2005. The project explores the implications of an enhanced standard in the context of timber frame construction. Although for programming reasons it was necessary to terminate the research project at the end of the design phase, the results suggest that the standard investigated is well within the capacity of the industry but it was clear that the whole supply chain will need to take a positive approach to the development of new solutions. The secret to a smooth and cost optimised transition is for the necessary development work to begin immediately, not when regulation changes. © 2003, MCB UP Limite

Influence of psychological coping on survival and recurrence in people with cancer: systematic review

OBJECTIVE: To summarise the evidence on the effect of psychological coping styles (including fighting spirit, helplessness/hopelessness, denial, and avoidance) on survival and recurrence in patients with cancer. DESIGN: Systematic review of published and unpublished prospective observational studies. MAIN OUTCOMES MEASURES: Survival from or recurrence of cancer. RESULTS: 26 studies investigated the association between psychological coping styles and survival from cancer, and 11 studies investigated recurrence. Most of the studies that investigated fighting spirit (10 studies) or helplessness/hopelessness (12 studies) found no significant associations with survival or recurrence. The evidence that other coping styles play an important part was also weak. Positive findings tended to be confined to small or methodologically flawed studies; lack of adjustment for potential confounding variables was common. Positive conclusions seemed to be more commonly reported by smaller studies, indicating potential publication bias. CONCLUSION: There is little consistent evidence that psychological coping styles play an important part in survival from or recurrence of cancer. People with cancer should not feel pressured into adopting particular coping styles to improve survival or reduce the risk of recurrence. [References: 42

Confining the high-energy cosmic rays

Diffusive shock acceleration is the prime candidate for efficient acceleration of cosmic rays. Galactic cosmic rays are believed to originate predominantly from this process in supernova remnant shock waves. Confinement of the cosmic rays in the shock region is key in making the mechanism effective. It has been known that on small scales (smaller than the typical gyroradius) high-amplitude non-resonant instabilities arise due to cosmic ray streaming ahead of the shock. For the efficiency of scattering of the highest energy cosmic rays it is of interest to determine the type of instabilities that act on longer length scales, i.e. larger than the cosmic ray gyroradius. We will present the results of our analysis of an instability that acts in this regime and will discuss its driving mechanism and typical growth times.Comment: 4 pages, 1 figure. Proceedings for the conference on Cosmic Rays and the Interstellar Medium (CRISM) in June 2011, Montpellier, France. To appear in MSA