On the geometry of Abel maps for nodal curves

In this paper we give local conditions to the existence of Abel maps for nodal curves that are limits of Abel maps for smooth curves. We use this result to construct Abel maps for any degree for nodal curves with two components.Comment: 30 pages, 1 figur

A Torelli theorem for graphs via quasistable divisors

The Torelli theorem establishes that the Jacobian of a smooth projective curve, together with the polarization provided by the theta divisor, fully characterizes the curve. In the case of nodal curves, there exists a concept known as fine compactified Jacobian. The fine compactified Jacobian of a curve comes with a natural stratification that can be regarded as a poset. Furthermore, this poset is entirely determined by the dual graph of the curve and is referred to as the poset of quasistable divisors on the graph. We present a combinatorial version of the Torelli theorem, which demonstrates that the poset of quasistable divisors of a graph completely determines the biconnected components of the graph (up to contracting separating edges). Moreover, we achieve a natural extension of this theorem to tropical curves.Comment: MSC: 05Cxx, 14Hxx. 22 page

Enriched curves and their tropical counterpart

In her Ph.D. thesis, Main\`o introduced the notion of enriched structure on stable curves and constructed their moduli space. In this paper we give a tropical notion of enriched structure on tropical curves and construct a moduli space parametrizing these objects. Moreover, we use this construction to give a toric description of the scheme parametrizing enriched structures on a fixed stable curve.Comment: 41 pages, 13 figures; final version, to appear in Ann. Inst. Fourie

A theoretical and numerical approach for selecting miniaturized antenna topologies on magneto-dielectric substrates

An increasing interest is arising in developing miniaturized antennas in the microwave range. However, even when the adopted antennas dimensions are small compared with the wavelength, radiation performances have to be preserved to keep the system-operating conditions. For this purpose, magneto-dielectric materials are currently exploited as promising substrates, which allows us to reduce antenna dimensions by exploiting both relative permittivity and permeability. In this paper, we address generic antennas in resonant conditions and we develop a general theoretical approach, not based on simplified equivalent models, to establish topologies most suitable for exploiting high permeability and/or high-permittivity substrates, for miniaturization purposes. A novel definition of the region pertaining to the antenna near-field and of the associated field strength is proposed. It is then showed that radiation efficiency and bandwidth can be preserved only by a selected combinations of antenna topologies and substrate characteristics. Indeed, by the proposed independent approach, we confirm that non-dispersive magneto-dielectric materials with relative permeability greater than unit, can be efficiently adopted only by antennas that are mainly represented by equivalent magnetic sources. Conversely, if equivalent electric sources are involved, the antenna performances are significantly degraded. The theoretical results are validated by full-wave numerical simulations of reference topologies

Design of Novel Systems for Position Independent Energy and Data Transfer

This thesis proposes a theoretical and experimental framework for the modeling, analysis and design of a complete energy and data transfer system, which provides constant performances independently of the receiver position. The energy transfer is considered for industrial scenarios, which require high powers and efficiencies, as well as for biomedical implants, which have high distances but do not require necessarily high efficiency. In the former, the method provides a constant received voltage, independent of the load and position in one direction of the receiver and without any feedback loop. It is based on a geometrical optimization of an inductive link composed of three coils and on resonant inverters and rectifier, respectively in class EF and E, operating at 6.78MHz. Furthermore, it enables to passively localize the receiver, without requiring its involvement. In the latter, the proposed solution enables to power small implants without knowing their orientation. The high throughput data transfer is intended for the industrial scenario, where it integrates in a single system with the power link and enables every part to connect and cooperate with each other. It employs consumer hardware and provides bandwidths of over 100Mb/s, independently of the position and with high resistance to interference.Questa tesi propone un quadro teorico e pratico per la modellazione, l'analisi e il progetto di un sistema completo per il trasferimento di energia e dati indipendente dalla posizione del ricevitore. Il trasferimento di energia è trattato sia per scenari industriali, che richiedono alte potenze ed efficienze, sia per quelli di impianti biomedicali, che presentano distanze significative ma non necessitano di particolari efficienze. Nel primo caso, il metodo proposto consente una tensione al ricevitore costante, indipendente dalla posizione, in una direzione, e dal carico del ricevitore, senza nessuna necessità di controllo in retroazione. Si basa sulla ottimizzazione geometrica di un link induttivo composto da tre spire e su inverter e rettificatore risonanti, in classe EF ed E, rispettivamente, funzionanti a 6.78MHz. Consente inoltre di localizzare il ricevitore in maniera passiva e indipendente dal ricevitore. Nel secondo caso, la soluzione proposta consente di alimentare dispositivi impiantabili indipendentemente dalla loro rotazione. Il trasferimento dei dati a banda larga si inserisce nello scenario industriale, integrandosi in un unico sistema di potenza e dati, con la possibilità anche di interagire tra loro. Attraverso l'uso di hardware di consumo, consente bande superiori a 100Mb/s, indipendentemente dalla posizione, con ottima resistenza alle interferenze