Ettore Majorana’s Course on Theoretical Physics: A Recent Discovery

We analyze in some detail the course that Ettore Majorana gave on theoretical physics at the University of Naples between January and March 1938, just prior to his mysterious disappearance. We discuss, in particular, the recently discovered Moreno Lecture Notes, in which all of Majorana’s lectures are recorded, six of which are not present in those that are preserved in the Domus Galilaeana in Pisa, Italy. Antonino Drago is a retired professor of history of physics at the University of Naples “Federico II.” Salvatore Esposito is a researcher on theoretical physics and history of physics at the University of Naples “Federico II.”     

A stochastic lagrangean picture for the three dimensional navier-stokes equation +

We derive a representation formula for the solutions of the navier-Stokes flow in three dimensions in absence of boundary in terms of stochastic current lines. This pictures generalizes an analogous one given in two dimensions and on the other hand the classical Lafrangian picture for the Euler flow. We prove a Vanishing viscosity limit for the whole structure     

Whole-wafer fabrication process for three-terminal double stacked tunnel junctions

A new fabrication process for three-terminal superconducting devices consisting of two Josephson junctions in a stacked configuration is reported. The process is based on the deposition of the whole Nb/Al_xO_y/Nb-Al/Al_xO_y/Nb multilayer on a Si crystalline wafer without any vacuum breaking. Lift-off techniques, anodization processes and a SiO film deposition have been adopted for patterning and insulating the two tunnel stacked junctions. Devices have been characterized in terms of current-voltage (I-V) curves and Josephson critical current vs. the externally applied magnetic field. They show high quality factors (V _m values up to 65 mV at 4.2 K), and good current uniformity. Received 5 June 2001     

Majorana and the Quasi-Stationary States in Nuclear Physics

A complete theoretical model describing artificial disintegration of nuclei by bombardment with α-particles, developed by Majorana as early as 1930, is discussed in detail jointly with the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear process, which is the directly measurable quantity of interest in the experiments. Although this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana work anticipates by several years the related seminal paper by Fano on Atomic Physics.     

Phase-shifted Bragg microstructured optical fiber gratings utilizing infiltrated ferrofluids

Results are presented on the efficient spectral manipulation of uniform and chirped Bragg reflectors inscribed in microstructured optical fibers utilizing short lengths of ferrofluids infiltrated in their capillaries. The infiltrated ferrofluidic defects can generate either parasitic reflection notch features in uniform Bragg reflectors of up to 80% visibility and ~0.1 nm spectral shift or tunability of the bandwidth and strength reflection up to 100% when introduced into chirped gratings. Spectra are presented for different spatial positions and optical characteristics of the ferrofluidic section.     

The effect of linear perturbations on the Yamabe problem

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold $\left( M,g\right) $ is compact. Established in the locally conformally flat case by Schoen (Lecture Notes in Mathematics, vol. 1365, pp. 120–154. Springer, Berlin 1989, Surveys Pure Application and Mathematics, 52 Longman Science, Technology, pp. 311–320. Harlow 1991) and for $n\le 24$ by Khuri–Marques–Schoen (J Differ Geom 81(1):143–196, 2009), it has revealed to be generally false for $n\ge 25$ as shown by Brendle (J Am Math Soc 21(4):951–979, 2008) and Brendle–Marques (J Differ Geom 81(2):225–250, 2009). A stronger version of it, the compactness under perturbations of the Yamabe equation, is addressed here with respect to the linear geometric potential $\frac{n-2}{4(n-1)} {{\mathrm{Scal}}}_g,\, {{\mathrm{Scal}}}_g$ being the Scalar curvature of $\left( M,g\right) $ . We show that a-priori $L^\infty $ –bounds fail for linear perturbations on all manifolds with $n\ge 4$ as well as a-priori gradient $L^2$ –bounds fail for non-locally conformally flat manifolds with $n\ge 6$ and for locally conformally flat manifolds with $n\ge 7$ . In several situations, the results are optimal. Our proof combines a finite dimensional reduction and the construction of a suitable ansatz for the solutions generated by a family of varying metrics in the conformal class of $g$ .