Noncommutative Geometry and Symplectic Field Theory

In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.Comment: To appear in Physics Letters

NEW SEISMIC SOURCE ZONE MODEL FOR PORTUGAL AND AZORES

The development of seismogenic source models is one of the first steps in seismic hazard assessment. In seismic hazard terminology, seismic source zones (SSZ) are polygons (or volumes) that delineate areas with homogeneous characteristics of seismicity. The importance of using knowledge on geology, seismicity and tectonics in the definition of source zones has been recognized for a long time [1]. However, the definition of SSZ tends to be subjective and controversial. Using SSZ based on broad geology, by spreading the seismicity clusters throughout the areal extent of a zone, provides a way to account for possible long-term non-stationary seismicity behavior [2,3]. This approach effectively increases seismicity rates in regions with no significant historical or instrumental seismicity, while decreasing seismicity rates in regions that display higher rates of seismicity. In contrast, the use of SSZ based on concentrations of seismicity or spatial smoothing results in stationary behavior [4]. In the FP7 Project SHARE (Seismic Hazard Harmonization in Europe), seismic hazard will be assessed with a logic tree approach that allows for three types of branches for seismicity models: a) smoothed seismicity, b) SSZ, c) SSZ and faults. In this context, a large-scale zonation model for use in the smoothed seismicity branch, and a new consensus SSZ model for Portugal and Azores have been developed. The new models were achieved with the participation of regional experts by combining and adapting existing models and incorporating new regional knowledge of the earthquake potential. The main criteria used for delineating the SSZ include distribution of seismicity, broad geological architecture, crustal characteristics (oceanic versus continental, tectonically active versus stable, etc.), historical catalogue completeness, and the characteristics of active or potentially-active faults. This model will be integrated into an Iberian model of SSZ to be used in the Project SHARE seismic hazard assessment

Polyesters with main and side chain phosphoesters as structural motives for biocompatible electrospun fibres

Phosphoester containing polymers are promising materials in biomedical applications due to their biocompatibility and biodegradability. Utilising thiol-ene chemistry, the synthesis of two novel structural polymer motives combining polyesters and phophoester groups was explored. The first polymer was obtained by coupling ene-functional poly(thioether-phosphoester) with thiol functional poly(pentadecalactone). While the coupling reaction was successful, yields remained low presumably due to inadequate endgroup stoichiometry. The second polymer comprised phosphoester side groups conjugated to unsaturated poly(globalide). Double bond conversions up to 84% were achieved depending of the type of phosphoester thiol and relative reactant ratios. The resulting polymers transitioned from solid semicrystaline to liquid amorphous with increasing degree of phosphoester conjugation. Electrospun fibres from polymers with 14% phosphoester conjugation allowed attachment and survival of human dermal fibroblasts, indicating their biocompatibility. These polymers represent a new class of easily accessible biocompatible polyester-phosphoester hybrid materials as potential building blocks for tunable biomaterials

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume-Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature.The obtained results improve over effective field type results.Comment: 13 page

Non-linear Liouville and Shr\"odinger equations in phase space

Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance provides conditions for writing the Liouville operator and Lagrangian for non-linear systems. We analyze, as an example, a generalized kinetic equation where the collision term is local and non-linear. The quantum counter-part of such unitary representations are developed by using the Moyal (or star) product. Then a non-linear Schr\"odinger equation in phase space is derived and analyzed. In this case, an association with the Wigner formalism is established, which provides a physical interpretation for the formalism

Four new coordination polymers involving transition metals with 1,2,4,5-benzenetetracarboxylate and pyridyl-donor ligand di(4-pyridyl) sulfide

AbstractFour new coordination polymers namely {[Mn2(BT)(DPS)2(H2O)6]·10H2O}n (MnBTDPS), {[Co2(BT)(DPS)2(H2O)6]·10H2O}n (CoBTDPS), {[Cu2(BT)(DPS)(H2O)4]·5H2O}n (CuBTDPS) and {[Zn2(BT)(DPS)2]·6H2O}n (ZnBTDPS), where BT=1,2,4,5-benzenetetracarboxylate and DPS=di(4-pyridyl) sulfide, were synthesized and characterized by thermal analysis, vibrational spectroscopy (Raman and infrared) and single crystal X-ray diffraction analysis. In all compounds, the DPS ligands are coordinated to metal sites in a bridging mode and the carboxylate moiety of BT ligands adopts a monodentate coordination mode, as indicated by the Raman spectra data through the Δν (νasym(COO)−ν sym(COO)) value. According to X-ray diffraction analysis, MnBTDPS and CoBTDPS are isostructural and in these cases, the metal centers exhibit a distorted octahedral geometry. In CuBTBPP, the Cu2+ centers geometries are best described as square-pyramids, according to the trigonality index τ=0.14 for Cu1 and τ=0.10 for Cu2. On the other hand, in ZnBTDPS, the Zn2+ sites adopt a tetrahedral geometry. Finally, the four compounds formed two-dimensional sheets that are connected to each other through hydrogen bonding giving rise to three-dimensional supramolecular arrays