Universal amplitude ratios and Coxeter geometry in the dilute A model

The leading excitations of the dilute $A_L$ model in regime 2 are considered using analytic arguments. The model can be identified with the integrable $\phi_{1,2}$ perturbation of the unitary minimal series $M_{L,L+1}$. It is demonstrated that the excitation spectrum of the transfer matrix satisfies the same functional equations in terms of elliptic functions as the exact S-matrices of the $\phi_{1,2}$ perturbation do in terms of trigonometric functions. In particular, the bootstrap equation corresponding to a self-fusing process is recovered. For the special cases $L=3,4,6$ corresponding to the Ising model in a magnetic field, and the leading thermal perturbations of the tricritical Ising and three-state Potts model, as well as for the unrestricted model, $L=\infty$, we relate the structure of the Bethe roots to the Lie algebras $E_{8,7,6}$ and $D_4$ using Coxeter geometry. In these cases Coxeter geometry also allows for a single formula in generic Lie algebraic terms describing all four cases. For general $L$ we calculate the spectral gaps associated with the leading excitation which allows us to compute universal amplitude ratios characteristic of the universality class. The ratios are of field theoretic importance as they enter the bulk vacuum expectation value of the energy momentum tensor associated with the corresponding integrable quantum field theories.Comment: 32 pages (tcilatex

Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model

The exact perturbation approach is used to derive the elementary correlation lengths $\xi_i$ and related mass gaps $m_i$ of the two-dimensional dilute A_L lattice model in regimes 1 and 2 for L odd from the Bethe Ansatz solution. In regime 2 the A_3 model is the E_8 lattice realisation of the two-dimensional Ising model in a magnetic field at T=T_c. The calculations for the A_3 model in regime 2 start from the eight thermodynamically significant string types found in previous numerical studies. These string types are seen to be consistent in the ordered high field limit. The eight masses obtained reduce with the approach to criticality to the E_8 masses predicted by Zamolodchikov, thus providing a further direct lattice determination of the E_8 mass spectrum.Comment: 57 pages, Latex, Elsevier style file

A New Approach to Systematic Uncertainties and Self-Consistency in Helium Abundance Determinations

Tests of big bang nucleosynthesis and early universe cosmology require precision measurements for helium abundance determinations. However, efforts to determine the primordial helium abundance via observations of metal poor H II regions have been limited by significant uncertainties. This work builds upon previous work by providing an updated and extended program in evaluating these uncertainties. Procedural consistency is achieved by integrating the hydrogen based reddening correction with the helium based abundance calculation, i.e., all physical parameters are solved for simultaneously. We include new atomic data for helium recombination and collisional emission based upon recent work by Porter et al. and wavelength dependent corrections to underlying absorption are investigated. The set of physical parameters has been expanded here to include the effects of neutral hydrogen collisional emission. Because of a degeneracy between the solutions for density and temperature, the precision of the helium abundance determinations is limited. Also, at lower temperatures (T \lesssim 13,000 K) the neutral hydrogen fraction is poorly constrained resulting in a larger uncertainty in the helium abundances. Thus the derived errors on the helium abundances for individual objects are larger than those typical of previous studies. The updated emissivities and neutral hydrogen correction generally raise the abundance. From a regression to zero metallicity, we find Y_p as 0.2561 \pm 0.0108, in broad agreement with the WMAP result. Tests with synthetic data show a potential for distinct improvement, via removal of underlying absorption, using higher resolution spectra. A small bias in the abundance determination can be reduced significantly and the calculated helium abundance error can be reduced by \sim 25%.Comment: 51 pages, 13 figure

Thermal radiation processes

We discuss the different physical processes that are important to understand the thermal X-ray emission and absorption spectra of the diffuse gas in clusters of galaxies and the warm-hot intergalactic medium. The ionisation balance, line and continuum emission and absorption properties are reviewed and several practical examples are given that illustrate the most important diagnostic features in the X-ray spectra.Comment: 37 pages, 16 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 9; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

Relativistic close coupling calculations for photoionization and recombination of Ne-like Fe XVII

Relativistic and channel coupling effects in photoionization and unified electronic recombination of Fe XVII are demonstrated with an extensive 60-level close coupling calculation using the Breit-Pauli R-matrix method. Photoionization and (e + ion) recombination calculations are carried out for the total and the level-specific cross sections, including the ground and several hundred excited bound levels of Fe XVII (up to fine structure levels with n = 10). The unified (e + ion) recombination calculations for (e + Fe XVIII --> Fe XVII) include both the non-resonant and resonant recombination (`radiative' and `dielectronic recombination' -- RR and DR). The low-energy and the high energy cross sections are compared from: (i) a 3-level calculation with 2s^2p^5 (^2P^o_{1/2,3/2}) and 2s2p^6 (^2S_{1/2}), and (ii) the first 60-level calculation with \Delta n > 0 coupled channels with spectroscopic 2s^2p^5, 2s2p^6, 2s^22p^4 3s, 3p, 3d, configurations, and a number of correlation configurations. Strong channel coupling effects are demonstrated throughout the energy ranges considered, in particular via giant photoexcitation-of-core (PEC) resonances due to L-M shell dipole transition arrays 2p^5 --> 2p^4 3s, 3d in Fe XIII that enhance effective cross sections by orders of magnitude. Comparison is made with previous theoretical and experimental works on photoionization and recombination that considered the relatively small low-energy region (i), and the weaker \Delta n = 0 couplings. While the 3-level results are inadequate, the present 60-level results should provide reasonably complete and accurate datasets for both photoionization and (e + ion) recombination of Fe~XVII in laboratory and astrophysical plasmas.Comment: 19 pages, 8 figures, Phys. Rev. A (submitted

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Urban road networks -- Spatial networks with universal geometric features? A case study on Germany's largest cities

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for in time evolution of urban road networks.Comment: 16 pages; 8 figure

AN UPDATE OF OSCILLATOR STRENGTHS AND PHOTOIONISATION CROSS SECTIONS FOR THE Be ISOELECTRONIC SEQUENCE

Nous présentons une synthèse des travaux récemment publiés pour la photoabsorption par les ions berylliumoïdes, en soulignant notre propre étude des transitions lié-lié et lié-libre dans 15 membres de la séquence : Be à Si+10, S+12, A+14, Ca+16 et Fe+22. Nos calculs sont basés sur l'approximation quantique du couplage fort ('close coupling') dans laquelle on tient compte seulement des interactions électrostatiques. Nous avons identifié 1814 termes LS et nous avons déterminé leurs énergies. Les forces d'oscillateur pondérées (valeurs g f) pour 33030 transitions dipolaires électriques ont été évaluées. D'autre part nous avons calculé 1554 sections efficaces de photoionisation à partir des niveaux au-dessous du premier seuil d'ionisation. Des pas d'énergie suffisament petits ont été utilisés pour pouvoir délinéer la plupart des résonances d'autoionisation qui perturbent les sections. La photoexcitation du coeur produit de grandes résonances d'autoionisation du type PEC ; celles-ci dominent beaucoup de sections efficaces pour Be et les ions faiblement ionisés. Nous donnons des exemples sélectionnés parmi nos données et nous les comparons avec les travaux d'autres chercheurs.We summarise recent work for photoabsorption by beryllium-like ions, giving particular emphasis to our own study of bound-bound and bound-free transitions in the following members of the sequence : Be to Si+10, S+12, A+14, Ca+16 and Fe+22. Our calculations are based on the quantal close-coupling approximation in which only electrostatic interactions are taken into account. A total of 1814 LS terms have been identified and their energies determined. Weighted oscillator strengths (g f values) for 33030 electric dipole transitions amongst these levels have been evaluated. We have also calculated cross sections for photoionisation from 1554 levels lying below the first ionisation threshold. Photoexcitation of the core produces large PEC resonances ; these dominate many of the cross sections for Be and the less highly ionised ions. We give selected samples of our data and make comparisons with the work of other investigators