M-theory on AdS4 × M: the complete Osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis

We reconsider the Kaluza-Klein compactifications of D = 11 supergravity on AdS₄ × (G/H)₇ manifolds that were classified in the eighties, in the modern perspective of AdS₄/CFT₃ correspondence. We focus on one of the three N = 2 cases: (G/H)₇ = M¹¹¹ = SU(3) × SU(2) × U(1) /SU(2) × U(1)′ × U(1)′'. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fré) with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4) × SU(3) × SU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications. Furthermore, it is a necessary comparison term in the AdS₄/CFT₃ correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the ACS/CFT correspondence than in the S⁷ case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hyperchanges that we obtain in the present article. The investigation of this match is left to future publications. Here we provide an exhaustive construction of the Kaluza-Klein side of our spectroscopy.     

Template burning inside TS-1 and Fe-MFI molecular sieves: an in situ XRPD study

The high X-ray flux available at the European Synchrotron Radiation Facility (ESRF), combined with the use of a suitably designed area detector setup, allowed us to follow in real time the structural changes occurring during the template burning processes inside TS-1 and Fe-silicalite MFI zeolites with a X-ray powder diffraction technique (XRPD). Rietveld analysis of the XRPD patterns collected in the 350-1000 K interval, integrated each 15 K, yields to the determination of the template overall occupancy factor versus T with an accuracy comparable with that obtained by thermogravimetric measurements, routinely employed for this purpose. The evolution of the structural parameters (V, a, b, c, site occupancy factor of the template molecule) vs T has been obtained. These data allow us to have, for the first time, a complete view of the structural rearrangements induced by the template burning process on the zeolitic framework. The differences caused by the different heteroatom inserted in the MFI lattice (Ti or Fe) are discussed. For both TS-1 and Fe-MFI, the kinetics of the reaction were investigated, to obtain the activation energy of the calcinations process employing the nonisothermal data according to the theory recently proposed by Kennedy and Clark [Thermochim. Acta, 1997, 307, 27-35]. For TS-1 only, the time-resolved template burning experiment has been repeated in isothermal conditions at four different temperatures, to obtain the activation energy from isothermal data, according to the standard procedure. Comparison between Arrhenius plots obtained from isothermal and nonisothermal data demonstrates that the Kennedy and Clark method can be also applied to complex materials such as the MFI zeolites. This approach, when applied to time-resolved XRPD studies, is much less time consuming (requesting, in principle, one single nonisothermal run) with respect to the classic approach, which requests at least three isothermal runs. Moreover, it allows a remarkably lower associated error (151 +/- 11 versus 146 +/- 30 kJ mol(-)(1)) due to the much higher number of experimental points employed to perform the linear fit.     

Scaling properties in the production range of shear dominated flows

In large Reynolds number turbulence, isotropy is recovered as the scale is reduced and homogeneous-isotropic scalings are eventually observed. This picture is violated in many cases, e.g., wall bounded flows, where, due to the shear, different scaling laws emerge. This effect has been ascribed to the contamination of the inertial range by the larger anisotropic scales. The issue is addressed here by analyzing both numerical and experimental data for a homogeneous shear flow. In fact, under strong shear, the alteration of the scaling exponents is not induced by the contamination from the anisotropic sectors. Actually, the exponents are universal properties of the isotropic component of the structure functions of shear dominated flows. The implications are discussed in the context of turbulence near solid walls, where improved closure models would be advisable.     

Blowing up generalized Kähler 4-manifolds

We show that the blow-up of a generalized Kähler 4-manifold in a nondegenerate complex point admits a generalized Kähler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a blow-up operation for bi-Hermitian manifolds.     

Generalized Kähler Geometry

Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.     

Hydrodynamic Aspects of Confluence of Rivers with Different Water Densities

Journal of Applied Mechanics and Technical Physics - Confluences of rivers are characterized by highly complex intrabasin processes. The arising hydrodynamic aspects of river confluences have...