Deformations with a resonant irregular singularity

I review topics of my talk in Alcal\ue1, inspired by the paper [1]. An isomonodromic system with irregular singularity at z= 1e (and Fuchsian at z=0) is considered, such that z= 1e becomes resonant for some values of the deformation parameters. Namely, the eigenvalues of the leading matrix at z= 1e coalesce along a locus in the space of deformation parameters. I give a complete extension of the isomonodromy deformation theory in this case

Effects of thermohaline instability and rotation-induced mixing on the evolution of light elements in the Galaxy : D, 3He and 4He

Recent studies of low- and intermediate-mass stars show that the evolution of the chemical elements in these stars is very different from that proposed by standard stellar models. Rotation-induced mixing modifies the internal chemical structure of main sequence stars, although its signatures are revealed only later in the evolution when the first dredge-up occurs. Thermohaline mixing is likely the dominating process that governs the photospheric composition of low-mass red giant branch stars and has been shown to drastically reduce the net 3He production in these stars. The predictions of these new stellar models need to be tested against galaxy evolution. In particular, the resulting evolution of the light elements D, 3He and 4He should be compared with their primordial values inferred from the Wilkinson Microwave Anisotropy Probe data and with the abundances derived from observations of different Galactic regions. We study the effects of thermohaline mixing and rotation-induced mixing on the evolution of the light elements in the Milky Way. We compute Galactic evolutionary models including new yields from stellar models computed with thermohaline instability and rotation-induced mixing. We discuss the effects of these important physical processes acting in stars on the evolution of the light elements D, 3He, and 4He in the Galaxy. Galactic chemical evolution models computed with stellar yields including thermohaline mixing and rotation fit better observations of 3He and 4He in the Galaxy than models computed with standard stellar yields. The inclusion of thermohaline mixing in stellar models provides a solution to the long-standing "3He problem" on a Galactic scale. Stellar models including rotation-induced mixing and thermohaline instability reproduce also the observations of D and 4He.Comment: 12 pages, 9 figures, accepted for publication in A&

Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the Gaussian symplectic ensemble is demonstrated. A duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Herschel Observations of the W43 "mini-starburst"

Aims: To explore the infrared and radio properties of one of the closest Galactic starburst regions. Methods: Images obtained with the Herschel Space Observatory at wavelengths of 70, 160, 250, 350, and 500 microns using the PACS and SPIRE arrays are analyzed and compared with radio continuum VLA data and 8 micron images from the Spitzer Space Telescope. The morphology of the far-infrared emission is combined with radial velocity measurements of millimeter and centimeter wavelength transitions to identify features likely to be associated with the W43 complex. Results: The W43 star-forming complex is resolved into a dense cluster of protostars, infrared dark clouds, and ridges of warm dust heated by massive stars. The 4 brightest compact sources with L > 1.5 x 10^4 Lsun embedded within the Z-shaped ridge of bright dust emission in W43 remain single at 4" (0.1 pc) resolution. These objects, likely to be massive protostars or compact clusters in early stages of evolution are embedded in clumps with masses of 10^3 to 10^4 Msun, but contribute only 2% to the 3.6 x 10^6 Lsun far-IR luminosity of W43 measured in a 16 by 16 pc box. The total mass of gas derived from the far-IR dust emission inside this region is ~10^6 Msun. Cometary dust clouds, compact 6 cm radio sources, and warm dust mark the locations of older populations of massive stars. Energy release has created a cavity blowing-out below the Galactic plane. Compression of molecular gas in the plane by the older HII region near G30.684-0.260 and the bipolar structure of the resulting younger W43 HII region may have triggered the current mini-star burst.Comment: 5 pages, 3 figures, accepted for A&A Special Issu

Radio Recombination Lines in Galactic HII Regions

We report radio recombination line (RRL) and continuum observations of a sample of 106 Galactic HII regions made with the NRAO 140 Foot radio telescope in Green Bank, WV. We believe this to be the most sensitive RRL survey ever made for a sample this large. Most of our source integration times range between 6 and 90 hours which yield typical r.m.s. noise levels of 1.0--3.5 milliKelvins. Our data result from two different experiments performed, calibrated, and analyzed in similar ways. A CII survey was made at 3.5 cm wavelength to obtain accurate measurements of carbon radio recombination lines. When combined with atomic (CI) and molecular (CO) data, these measurements will constrain the composition, structure, kinematics, and physical properties of the photodissociation regions that lie on the edges of HII regions. A second survey was made at 3.5 cm wavelength to determine the abundance of 3He in the interstellar medium of the Milky Way. Together with measurements of the 3He+ hyperfine line we get high precision RRL parameters for H, 4He, and C. Here we discuss significant improvements in these data, with both longer integrations and newly observed sources.Comment: LaTeX, 50 pages with 11 figures. Accepted for publication in The Astrophysical Journal Supplement Serie

3-He in the Milky Way Interstellar Medium: Ionization Structure

The cosmic abundance of the 3-He isotope has important implications for many fields of astrophysics. We are using the 8.665 GHz hyperfine transition of 3-He+ to determine the 3-He/H abundance in Milky Way HII regions and planetary nebulae. This is one in a series of papers in which we discuss issues involved in deriving accurate 3-He/H abundance ratios from the available measurements. Here we describe the ionization correction we use to convert the 3-He+/H+ abundance, y3+, to the 3-He/H abundance, y3. In principle the nebular ionization structure can significantly influence the y3 derived for individual sources. We find that in general there is insufficient information available to make a detailed ionization correction. Here we make a simple correction and assess its validity. The correction is based on radio recombination line measurements of H+ and 4-He+, together with simple core-halo source models. We use these models to establish criteria that allow us to identify sources that can be accurately corrected for ionization and those that cannot. We argue that this effect cannot be very large for most of the sources in our observational sample. For a wide range of models of nebular ionization structure we find that the ionization correction factor varies from 1 to 1.8. Although large corrections are possible, there would have to be a conspiracy between the density and ionization structure for us to underestimate the ionization correction by a substantial amount.Comment: 36 pages, 4 figures To appear Astrophysical Journal, 20 August 2007, vol 665, no

On the S-matrix renormalization in effective theories

This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal -- needed to fix the S-matrix, and non-minimal -- for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that in theories with the amplitudes which asymptotic behavior is governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with $n \leq 3$ lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for $n \leq 3$ cannot be taken arbitrary: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative QFT. We discuss this point and, finally, compare the corner stones of our approach with the philosophy known as ``analytic S-matrix''.Comment: 28 pages, 10 Postscript figures, REVTeX4, submitted to Phys. Rev.

On the bound states of the Dirac equation in the extreme Kerr metric

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. To this purpose a self-adjoint holomorphic operator family associated to this eigenvalue problem is considered. We show that the eigenvalues satisfy a first order nonlinear differential equation with respect to the black hole mass and we solve it. Finally, we prove that there exist no bound states for the Dirac equation in the aforementioned metric.Comment: 13 page

The Chemical Evolution Carousel of Spiral Galaxies : Azimuthal Variations of Oxygen Abundance in NGC1365

19 pages, 13 figures. Accepted to ApJThe spatial distribution of oxygen in the interstellar medium of galaxies is the key to understanding how efficiently metals that are synthesized in massive stars can be redistributed across a galaxy. We present here a case study in the nearby spiral galaxy NGC1365 using 3D optical data obtained in the TYPHOON Program. We find systematic azimuthal variations of the HII region oxygen abundance imprinted on a negative radial gradient. The 0.2 dex azimuthal variations occur over a wide radial range of 0.3 to 0.7 R25 and peak at the two spiral arms in NGC1365. We show that the azimuthal variations can be explained by two physical processes: gas undergoes localized, sub-kpc scale self-enrichment when orbiting in the inter-arm region, and experiences efficient, kpc scale mixing-induced dilution when spiral density waves pass through. We construct a simple chemical evolution model to quantitatively test this picture and find that our toy model can reproduce the observations. This result suggests that the observed abundance variations in NGC1365 are a snapshot of the dynamical local enrichment of oxygen modulated by spiral-driven, periodic mixing and dilution.Peer reviewedFinal Published versio