Dirac operator on spinors and diffeomorphisms

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$ and a Hilbert space \HH_{\sigma, g}= L^2(S_{\sigma, g},\vol{M}{g}) of $L^2$-spinors of $S_{\sigma, g}$. The group \diff{M} of orientation-preserving diffeomorphisms of $M$ acts both on $g$ (by pullback) and on $[\sigma]$ (by a suitably defined pullback $f^*\sigma$). Any f\in \diff{M} lifts in exactly two ways to a unitary operator $U$ from \HH_{\sigma, g} to \HH_{f^*\sigma,f^*g}. The canonically defined Dirac operator is shown to be equivariant with respect to the action of $U$, so in particular its spectrum is invariant under the diffeomorphisms.Comment: 13 page

Some results on the Zeeman topology

In a 1967 paper, Zeeman proposed a new topology for Minkowski spacetime, physically motivated but much more complicated than the standard one. Here a detailed study is given of some properties of the Zeeman topology which had not been considered at the time. The general setting refers to Minkowski spacetime of any dimension k+1. In the special case k=1, a full characterization is obtained for the compact subsets of spacetime; moreover, the first homotopy group is shown to be nontrivial.Comment: Part of my Laurea thesis. REVTeX4. Minor changes from previous versio

Optimal Aerodynamic Design of a Transonic Centrifugal Turbine Stage for Organic Rankine Cycle Applications

This paper presents the results of the application of a shape-optimization technique to the design of the stator and the rotor of a centrifugal turbine conceived for Organic Rankine Cycle (ORC) applications. Centrifugal turbines have the potential to compete with axial or radial-inflow turbines in a relevant range of applications, and are now receiving scientific as well as industrial recognition. However, the non-conventional character of the centrifugal turbine layout, combined with the typical effects induced by the use of organic fluids, leads to challenging design difficulties. For this reason, the design of optimal blades for centrifugal ORC turbines demands the application of high-fidelity computational tools. In this work, the optimal aerodynamic design is achieved by applying a non-intrusive, gradient-free, CFD-based method implemented in the in-house software FORMA (Fluid-dynamic Opti-mizeR for turboMachinery Aerofoils), specifically developed for the shape optimization of turbomachinery profiles. FORMA was applied to optimize the shape of the stator and the rotor of a transonic centrifugal turbine stage, which exhibits a significant radial effect, high aerodynamic loading, and severe non-ideal gas effects. The optimization of the single blade rows allows improving considerably the stage performance, with respect to a baseline geometric configuration constructed with classical aerodynamic methods. Furthermore, time-resolved simulations of the coupled stator-rotor configuration shows that the optimization allows to reduce considerably the unsteady stator-rotor interaction and, thus, the aerodynamic forcing acting on the blades