A note on the Petri loci

Let \M_g be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\rho(g,r,n)$ is non-negative every component of the Petri locus P^r_{g,n}\subset \M_g whose general member is a curve $C$ such that $W^{r+1}_n(C) = \emptyset$, has codimension one in \M_g.Comment: Final version, to appear on Manuscripta Mathematic

Purcell Effect in the Stimulated and Spontaneous Emission Rates of Nanoscale Semiconductor Lasers

Nanoscale semiconductor lasers have been developed recently using either metal, metallo-dielectric or photonic crystal nanocavities. While the technology of nanolasers is steadily being deployed, their expected performance for on-chip optical interconnects is still largely unknown due to a limited understanding of some of their key features. Specifically, as the cavity size is reduced with respect to the emission wavelength, the stimulated and the spontaneous emission rates are modified, which is known as the Purcell effect in the context of cavity quantum electrodynamics. This effect is expected to have a major impact in the 'threshold-less' behavior of nanolasers and in their modulation speed, but its role is poorly understood in practical laser structures, characterized by significant homogeneous and inhomogeneous broadening and by a complex spatial distribution of the active material and cavity field. In this work, we investigate the role of Purcell effect in the stimulated and spontaneous emission rates of semiconductor lasers taking into account the carriers' spatial distribution in the volume of the active region over a wide range of cavity dimensions and emitter/cavity linewidths, enabling the detailed modeling of the static and dynamic characteristics of either micro- or nano-scale lasers using single-mode rate-equations analysis. The ultimate limits of scaling down these nanoscale light sources in terms of Purcell enhancement and modulation speed are also discussed showing that the ultrafast modulation properties predicted in nanolasers are a direct consequence of the enhancement of the stimulated emission rate via reduction of the mode volume.Comment: 12 pages, 5 figure

Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves

A genus-g du Val curve is a degree-3g plane curve having 8 points of multiplicity g, one point of multiplicity g-1, and no other singularity. We prove that the corank of the Gauss-Wahl map of a general du Val curve of odd genus (>11) is equal to one. This, together with the results of [1], shows that the characterisation of Brill-Noether-Petri curves with non-surjective Gauss-Wahl map as hyperplane sections of K3 surfaces and limits thereof, obtained in [3], is optimal

A characterization of bielliptic curves via syzygy schemes

We prove that a canonical curve $C$ of genus $\ge 11$ is bielliptic if and only if its second syzygy scheme $\mathrm{Syz}_2(C)$ is different from $C$

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries, and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed and a solution strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201

Mukai's program for curves on a K3 surface

Let C be a general element in the locus of curves in M_g lying on some K3 surface, where g is congruent to 3 mod 4 and greater than or equal to 15. Following Mukai's ideas, we show how to reconstruct the K3 surface as a Fourier-Mukai transform of a Brill-Noether locus of rank two vector bundles on C.Comment: Final version. To appear in "Algebraic Geometry

A New Approach to the Link Budget Concept for an OAM Communication Link

Following on from the increasing interest for electromagnetic waves carrying Orbital Angular Momentum (OAM), different configurations of antenna systems able to generate such beams have been proposed. However, in our opinion, a traditional radiation pattern approach does not provide the right picture of an OAM-based communication link. For this reason we propose a new general concept, the "OAM-link pattern", which takes into account the peculiar phase structure characterizing these waves. Focusing on OAM transmissions between antenna arrays, we introduce a formula for the link budget evaluation which describes the whole communication link and directly leads to a "classically shaped" main lobe pattern for a proper rephased reception in the case of uniform circular arrays.Comment: 4 pages, 3 figure

OAM multiple transmission using uniform circular arrays: numerical modeling and experimental verification with two digital television signals

In this work we present the outcomes of a radio-frequency OAM transmission between two antenna arrays performed in a real-world context. The analysis is supplemented by deep simulative investigations able to provide both a preliminary overview of the experimental scenario and a posteriori validation of the achieved results. As a first step, the far-field OAM communication link is tested at various frequencies and the corresponding link budget is studied by means of an angular scan generated by the rotation of the receiving system. Then, on the same site, two digital television signals encoded as OAM modes ($\ell$=1 and $\ell$=-1) are simultaneously transmitted at a common frequency of 198.5 MHz with good mode insulation.Comment: 16 pages, 14 figure