Integrability in Theories with Local U(1) Gauge Symmetry

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.Comment: corrected typos, version accepted in J. Phys.

VLTI/AMBER spectro-interferometry of the late-type supergiants V766 Cen (=HR 5171 A), sigma Oph, BM Sco, and HD 206859

We add four warmer late-type supergiants to our previous spectro-interferometric studies of red giants and supergiants. V766 Cen (=HR 5171 A) is found to be a high-luminosity log(L/L_sun)=5.8+-0.4 source of Teff 4290+-760 K and radius 1490+-540 Rsun located close to both the Hayashi and Eddington limits; this source is consistent with a 40 Msun evolutionary track without rotation and current mass 27-36 Msun. It exhibits NaI in emission arising from a shell of radius 1.5 Rphot and a photocenter displacement of about 0.1 Rphot. V766 Cen shows strong extended molecular (CO) layers and a dusty circumstellar background component. This suggest an optically thick pseudo-photosphere at about 1.5 Rphot at the onset of the wind. V766 Cen is a red supergiant located close to the Hayashi limit instead of a yellow hypergiant already evolving back toward warmer Teff as previously discussed. The stars sigma Oph, BM Sco, and HD 206859 are found to have lower luminosities of about log(L/Lsun)=3.4-3.5 and Teff of 3900-5300 K, corresponding to 5-9 Msun tracks. They do not show extended molecular layers as observed for higher luminosity red supergiants of our sample. BM Sco shows an unusually strong contribution by an over-resolved circumstellar dust component. These stars are more likely high-mass red giants instead of red supergiants. This leaves us with an unsampled locus in the HR diagram corresponding to luminosities log(L/Lsun)~3.8-4.8 or masses 10-13 Msun, possibly corresponding to the mass region where stars explode as type II-P supernovae during the RSG stage. Our previously found relation of increasing strength of extended molecular layers with increasing luminosities is now confirmed to extend to double our previous luminosities and up to the Eddington limit. This might further point to steadily increasing radiative winds with increasing luminosity. [Abridged]Comment: 16 pages, 14 figures, accepted for publication in Astronomy and Astrophysics (A&A

Opening the Rome-Southampton window for operator mixing matrices

We show that the running of operators which mix under renormalization can be computed fully non-perturbatively as a product of continuum step scaling matrices. These step scaling matrices are obtained by taking the "ratio" of Z matrices computed at different energies in an RI-MOM type scheme for which twisted boundary conditions are an essential ingredient. Our method allows us to relax the bounds of the Rome-Southampton window. We also explain why such a method is important in view of the light quark physics program of the RBC-UKQCD collaborations. To illustrate our method, using n_f=2+1 domain-wall fermions, we compute the non-perturbative running matrix of four-quark operators needed in K->pipi decay and neutral kaon mixing. Our results are then compared to perturbation theory.Comment: 8 pages, 7 figures. v2: PRD version, minor changes and few references adde

Expansion around half-integer values, binomial sums and inverse binomial sums

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof.Comment: 21 page

Low--Temperature Series for Renormalized Operators: the Ferromagnetic Square--Lattice Ising Model.

A method for computing low--temperature series for renormalized operators in the two--dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation and decimation for $2 \times 2$ blocks depend on the how we approach the first--order phase--transition line. These Renormalization Group transformations are multi--valued and discontinuous at this first--order transition line when restricted to some finite--dimensional interaction space.Comment: 14 pages, uuencode tar-compressed ps file. Version accepted for publication in J. Stat. Phys. Many changes with respect to the first version

A Rigourous Treatment of the Lattice Renormalization Problem of F_B

The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.Comment: 27 pages, 2 figures (Plain TeX, figures in an appended postscript file

Biomimetic Ca-P coatings Incorporating bisphosphonates produced on starch-based degradable biomaterials

In this study, sodium clodronate, a well-known therapeutic agent from the family of bisphosphonates (BPs), is incorporated in a biomimetic calcium phosphate (CaP) coating, previously formed on the surface of a starch-based biomaterial by a sodium silicate methodology, as a strategy to develop a site-specific drug delivery system for bone tissue regeneration applications. The effects on the resulting CaP coatings were evaluated in terms of morphology, chemistry, and structure. The dissolution of Ca and P from the coating and the release profiles of sodium clodronate was also assessed. As a preliminary approach, this first study also aimed at evaluating the effects of this BP on the viability of a human osteoblastic cell line since there is still little information available on the interaction between BPs and this type of cells. Sodium clodronate was successfully incorporated, at different doses, in the structure of a biomimetic CaP layer previously formed by a sodium silicate process. This type of BPs had a stimulatory effect on osteoblastic activity, particularly at the specific concentration of 0.32 mg/mL. It is foreseen that these coatings can, for instances, be produced on the surface of degradable polymers and then used for regulating the equilibrium on osteoblastic/osteoclastic activity, leading to a controlled regenerative effect at the interface between the biomaterial and bone

Anomalous dimension of the gluon operator in pure Yang-Mills theory

We present new one loop calculations that confirm the theorems of Joglekar and Lee on the renormalization of composite operators. We do this by considering physical matrix elements with the operators inserted at non-zero momentum. The resulting IR singularities are regulated dimensionally. We show that the physical matrix element of the BRST exact gauge variant operator which appears in the energy- momentum tensor is zero. We then show that the physical matrix elements of the classical energy-momentum tensor and the gauge invariant twist two gluon operator are independent of the gauge fixing parameter. A Sudakov factor appears in the latter cases. The universality of this factor and the UV finiteness of the energy-momentum tensor provide another method of finding the anomalous dimension of the gluon operator. We conjecture that this method applies to higher loops and takes full advantage of the triangularity of the mixing matrix.Comment: submitted to Phys. Rev. D, 18 pages LaTEX uses psfig and revtex macros, figures appended as uuencoded Postscript file (complete Postsript version including figures available via anonymous ftp from ftp://max.physics.sunysb.edu/preprints/harris/paper.ps.Z), ITP-SB-94-3

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries