Hamiltonians of Spherically Symmetric, Scale-Free Galaxies in Action-Angle Coordinates

We present a simple formula for the Hamiltonian in terms of the actions for spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or logarithmic function of a linear combination of the actions. Our expression reduces to the well-known results for the familiar cases of the harmonic oscillator and the Kepler potential. For other power-laws, as well as for the singular isothermal sphere, it is exact for the radial and circular orbits, and very accurate for general orbits. Numerical tests show that the errors are always small, with mean errors across a grid of actions always less than 1 % and maximum errors less than 2.5 %. Simple first-order corrections can reduce mean errors to less than 0.6 % and maximum errors to less than 1 %. We use our new result to show that :[1] the misalignment angle between debris in a stream and a progenitor is always very nearly zero in spherical scale-free potentials, demonstrating that streams can be sometimes well approximated by orbits, [2] the effects of an adiabatic change in the stellar density profile in the inner regions of a galaxy weaken any existing 1/r density cusp, which is reduced to $1/r^{1/3}$. More generally, we derive the full range of adiabatic cusp transformations and show how to relate the starting cusp index to the final cusp index. It follows that adiabatic transformations can never erase a dark matter cusp.Comment: 6 pages, MNRAS, in pres

Promoting sustainable Indian textiles: final report to the Department for Environment, Food and Rural Affairs (Defra), London, UK

In 2009, the Department for Environment, Food and Rural Affairs (Defra), through the Sustainable Development Dialogue (SDD) fund, backed the Centre for Sustainable Fashion (CSF) at London College of Fashion and Pearl Academy of Fashion (PAF), New Delhi to run a project to promote Indian sustainable textiles. Improving patterns of sustainable consumption and production (SCP) in India and the UK is one of the agreed areas for collaboration under the UK-India Sustainable Development Dialogue. The project is also part of a body of work taking place under the Defra Sustainable Clothing Roadmap, which aims to improve the sustainability of clothing. Defra has identified that ‘while an economic success story (globally worth over £500 billion) the industry has a significant environmental and social footprint across its supply chain.’ The Roadmap aims to improve the sustainability of clothing by gathering a robust evidence base of impacts and working with a wide range of stakeholders, to build on existing interventions. For more details on the roadmap see: http://www.defra.gov.uk/environment/business/products/roadmaps/clothing/index.htm This report is only one of the dissemination tools associated with the project. The project film, images and website should be viewed in conjunction with this report

HEALTH AND SAFETY REGULATION OF SMALL, HIGH-RISK SUBPOPULATIONS

The choice of decision framework used to set regulatory tolerance levels for hazardous substances can be divided into rigid and flexible tolerance levels. Rigid decision frameworks include zero or deminimis that fix risk levels for some subpopulation. and/or highly tolerances The accelerating identification of highly sensitive exposed individuals and the division of the population into ever smaller subpopulations at higher risk could prove to be tremendously burdensome on regulatory systems, particularly for rigid decision frameworks. Rigid tolerance levels, philosophically based on "rights" to zero or arbitrarily low excess risks for individuals, do not contain sufficient flexibility to account for small high-risk subpopulations. Furthermore, the equal protection for all such groups is an illusion, mainly because of the potentially large number of such subgroups and the relatively fixed regulatory resources. Thus, deminimis regulation is seen as a minimal but inadequate improvement over zero risk regulation. with improved measures of the heterogeneous demand for risk reduction by various high-risk subpopulations, augmented cost-benefit analyses leading to flexible tolEr2.nces could provide a richer analytic framework for more efficient regulatory decisions. Additionally, it may be useful to attempt to c2.tegorize hazards and subpopulations on the basis of the ability to self-protect.De minimis, sensitive, decision framework, cost benefit, Food Consumption/Nutrition/Food Safety, Health Economics and Policy,

Heat and electricity from the Sun using parabolic dish collector systems

Point focus distributed receiver solar thermal technology for the production of electric power and of industrial process heat is addressed. The thermal power systems project which emphasizes the development of cost effective systems which will accelerate the commercialization and industrialization of plants up to 10 MWe, using parabolic dish collectors is described. The projected size of the isolated load market in the 1990-2000 time period is 300 to 1000 MW/year. Although this market is small in comparison to the grid connected utility market, it is indicated that by assuming only a 20 percent market penetration, up to 10,000 power modules per year would be required to meet this need. At a production rate of 25,000 units/year and assuming no energy storage, levelized bus bar energy costs of 75 mills/kWeh are projected. These numbers are based on what is believed to be a conservative estimate regarding engine-generator conversion efficiency (40 percent) for the 1990 time period. With a more optimistic estimate of efficiency (i.e., 45 percent), the bus bar cost decreases to about 67 mills/kWeh. At very large production rates (400,000 modules/years), the costs decrease to 58 mills/kWeh. Finally, the present status of the technology development effort is discussed

Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors

The distribution of thermally excited vortex loops near a superfluid phase transition is calculated from a renormalized theory. The number density of loops with a given perimeter is found to change from exponential decay with increasing perimeter to algebraic decay as T_c is approached, in agreement with recent simulations of both cosmic strings and high-T_c superconductors. Predictions of the value of the exponent of the algebraic decay at T_c and of critical behavior in the vortex density are confirmed by the simulations, giving strong support to the vortex-folding model proposed by Shenoy.Comment: Version to appear in Phys. Rev. Lett, with a number of corrections and addition