On the Strong Homotopy Lie-Rinehart Algebra of a Foliation

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distribution C of F. Similarly, characteristic cohomologies with local coefficients in the normal bundle TM/C of F may be interpreted as vector fields on P. In particular, they possess a (graded) Lie bracket and act on characteristic cohomology H. In this paper, I discuss how both the Lie bracket and the action on H come from a strong homotopy structure at the level of cochains. Finally, I show that such a strong homotopy structure is canonical up to isomorphisms.Comment: 41 pages, v2: almost completely rewritten, title changed; v3: presentation partly changed after numerous suggestions by Jim Stasheff, mathematical content unchanged; v4: minor revisions, references added. v5: (hopefully) final versio

Entanglement entropy for the long range Ising chain

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi long range order, and one dominated by the long range interaction, with long range N\'eel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central-charges. In the phase with quasi long range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.Comment: 5 pages, all comments welcom

Optical Rogue Waves in Vortex Turbulence

We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg- Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatio-temporal turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability distribution functions with long tails typical of extreme optical events.Comment: 5 pages, 7 figure

Effect of intraoperative constant rate infusion of lidocaine on short-term survival of dogs with septic peritonitis: 75 cases (2007-2011)

OBJECTIVE To investigate whether intraoperative administration of a lidocaine infusion to dogs with septic peritonitis was associated with short-term (48 hours) survival after surgery. DESIGN Retrospective case series. ANIMALS 75 dogs with septic peritonitis. PROCEDURES Medical records of dogs with septic peritonitis that underwent laparotomy between January 2007 and December 2011 at the Royal Veterinary College were reviewed. Select variables during the preoperative, intraoperative, and postoperative periods and short-term survival after surgery were compared between dogs that received an opioid only (group O; n = 33) and dogs that received lidocaine (50 \u3bcg/kg/min [22.7 \u3bcg/kg/min], IV; group L; 42) in addition to an opioid during surgery. RESULTS The proportion of dogs that survived for 48 hours after surgery was significantly greater for group L (35/42) than for group O (20/33). Intraoperative infusion of lidocaine increased the odds of short-term survival (OR, 8.77; 95% CI, 1.94 to 39.57). No significant differences were observed between the 2 treatment groups for variables assessed during the preoperative and postoperative periods. During the intraoperative period, more dogs in group L received an IV bolus of a synthetic colloid than did dogs in group O, but the number of IV boluses administered was not associated with short-term survival. CONCLUSIONS AND CLINICAL RELEVANCE Results indicated that IV infusion of lidocaine might improve the short-term survival of dogs with septic peritonitis. Prospective clinical trials are necessary to determine the efficacy of lidocaine as a supportive treatment for dogs with septic peritonitis

Searching for circumplanetary disks around LkCa 15

We present Karl G. Jansky Very Large Array (VLA) observations of the 7 mm continuum emission from the disk surrounding the young star LkCa 15. The observations achieve an angular resolution of 70 mas and spatially resolve the circumstellar emission on a spatial scale of 9 AU. The continuum emission traces a dusty annulus of 45 AU in radius that is consistent with the dust morphology observed at shorter wavelengths. The VLA observations also reveal a compact source at the center of the disk, possibly due to thermal emission from hot dust or ionized gas located within a few AU from the central star. No emission is observed between the star and the dusty ring, and, in particular, at the position of the candidate protoplanet LkCa 15 b. By comparing the observations with theoretical models for circumplanetary disk emission, we find that if LkCa~15~b is a massive planet (>5 M_J) accreting at a rate greater than 1.e-6 M_J yr^{-1}, then its circumplanetary disk is less massive than 0.1 M_J, or smaller than 0.4 Hill radii. Similar constraints are derived for any possible circumplanetary disk orbiting within 45 AU from the central star. The mass estimate are uncertain by at least one order of magnitude due to the uncertainties on the mass opacity. Future ALMA observations of this system might be able to detect circumplanetary disks down to a mass of 5.e-4 M_J and as small as 0.2 AU, providing crucial constraints on the presence of giant planets in the act of forming around this young star.Comment: Accepted for publication on Ap

B2 and G2 Toda systems on compact surfaces: a variational approach

We consider the B2 and G2 Toda systems on compact surfaces. We attack the problem using variational techniques. We get existence and multiplicity of solutions under a topological assumption on the surface and some generic conditions on the parameters. We also extend some of the results to the case of general systems.Comment: 28 pages, accepted on Journal of Mathematical Physic

Kovacs Effect in a Fragile Glass Model

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs for glassy polymers, is implemented in an exactly solvable dynamical model. This model is characterized by interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property, the model reproduces the characteristic non-monotonic evolution known as the ``Kovacs effect'', observed in polymers, in granular materials and models of molecular liquids, when similar experimental protocols are implemented.Comment: 8 pages, 6 figure

Conformal Gravity with Electrodynamics for Fermion Fields and their Symmetry Breaking Mechanism

In this paper we consider an axial torsion to build metric-compatible connections in conformal gravity, with gauge potentials; the geometric background is filled with Dirac spinors: scalar fields with suitable potentials are added eventually. The system of field equations is worked out to have torsional effects converted into spinorial self-interactions: the massless spinors display self-interactions of a specific form that gives them the features they have in the non-conformal theory but with the additional character of renormalizability, and the mechanisms of generation of mass and cosmological constants become dynamical. As a final step we will address the cosmological constant and coincidence problems.Comment: 13 page