The effect on Fisher-KPP propagation in a cylinder with fast diffusion on the boundary

In this paper we consider a reaction-diffusion equation of Fisher-KPP type inside an infinite cylindrical domain in $\mathbb{R}^{N+1}$, coupled with a reaction-diffusion equation on the boundary of the domain, where potentially fast diffusion is allowed. We will study the existence of an asymptotic speed of propagation for solutions of the Cauchy problem associated with such system, as well as the dependence of this speed on the diffusivity at the boundary and the amplitude of the cylinder. When $N=1$ the domain reduces to a strip between two straight lines. This models the effect of two roads with fast diffusion on a strip-shaped field bounded by them.Comment: 31 pages, 3 figure

Set Unification

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature--and properly revisited and analyzed--and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI1 unification and a new simpler algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of Logic Programming (TPLP

Stochastic learning in co-ordination games : a simulation approach

In the presence of externalities, consumption behaviour depends on the solution of a co-ordination problem. In our paper we suggest a learning approach to the study of co-ordination in consumption contexts where agents adjust their choices on the basis of the reinforcement (payoff) they receive during the game. The results of simulations allowed us to distinguish the roles of different aspects of learning in enabling co-ordination within a population of agents. Our main results highlight: 1. the role played by the speed of learning in determining failures of the co-ordination process; 2. the effect of forgetting past experiences on the speed of the co-ordination process; 3. the role of experimentation in bringing the process of co-ordination into an efficient equilibrium

Progetto dell'interramento della linea ferroviaria Pistoia-Lucca in corrispondenza di Altopascio

E' stata studiata la realizzazione del raddopio della linea ferroviaria Lucca Pistoia prevedendo l'interramento della stessa in corrispondenza del centro abitato di Altopascio senza causare interruzzioni alla circolazione viaria e ferroviaria

Reconsidering the dual nature of property rights: personal property and capital in the law and economics of property rights

In the last two decades, a renewed interest in property rights have challenged the accepted interpretation of property rights as “bundle of rights” over the use of things and have rehabilitated the old classical interpretation of property rights as exclusive (absolute) dominium over things rooted in the right to exclude. This paper provides a three-dimensional framework for the study of property rights and shows that, historically, the reason for this dual nature of property rights derives from the fact that properties can either be treated as personal property, or capital. While the classical approach is consistent with the former interpretation, the neoclassical (“bundle of right”) approach is consistent with the latter. By reinterpreting the dual nature of property rights as a dichotomy between capital and personal property the work makes two main contributions to the debates in the legal and economic literature. First, it re-evaluates and justifies the interpretation of property rights as a “politically-embedded” bundle of right provided by legal realist, old progressive and institutional economists at the turn of the twentieth century. Second, it reassesses the conclusions reached by the Coasean legacy in law and economics; the paper shows that transaction costs are necessary and sufficient to explain the emergence and the form of legal institutions only in pure capitalistic societies, but cannot explain the emergence and the nature of legal institutions whenever personal properties are involved. Additional normative assumptions explaining the origin and the legitimacy of value judgments are needed to understand and explain the dual nature of property rights and to make sense of the decisions to employ personal properties as capital (or vice versa). This highlights the often neglected (but decisive) role played by the rationality assumption in legitimizing the normative conclusions reached by Coasean law and economics (and welfare economics more generally). It also highlights that the normative power of transaction costs is always institution determined (socially-embedded), never institution-determinin

Zinc oxide nanowires decorated with gold nanorods for photovoltaic applications

Le celle solari plasmoniche utilizzano il fenomeno della LSPR (Localized Surface Plasmon Resonance) per aumentare l'assorbimento di luce. Effetti legati alla LSPR consentono di creare un maggior numero di coppie elettrone-lacuna nel semiconduttore. Nanorods di oro con comportamento plasmonico sono stati depositati su nanowires di ossido di zinco. Un aumento dell'assorbimento di luce dovuto a bande plasmoniche è stato identificato, cosଠcome un effetto sulla fotoluminescenza.ope

Ground-state of graphene in the presence of random charged impurities

We calculate the carrier density dependent ground state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects non-perturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low ($\lesssim 10^{12}$ cm$^{-2}$) carrier density with the density fluctuations becoming larger than the average density.Comment: Final version, accepted for publication in Phys. Rev. Let

Spatially dependent Kondo effect in Quantum Corrals

We study the Kondo screening of a single magnetic impurity inside a non-magnetic quantum corral located on the surface of a metallic host system. We show that the spatial structure of the corral's eigenmodes lead to a spatially dependent Kondo effect whose signatures are spatial variations of the Kondo temperature, $T_K$. Moreover, we predict that the Kondo screening is accompanied by the formation of multiple Kondo resonances with characteristic spatial patterns. Our results open new possibilities to manipulate and explore the Kondo effect by using quantum corrals.Comment: 4 pages 5 figure

Spontaneous interlayer superfluidity in bilayer systems of cold polar molecules

Quantum degenerate cold-atom gases provide a remarkable opportunity to study strongly interacting systems. Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up new possibilities to realize novel quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable novel broken-symmetry states with spontaneous interlayer coherence in cold polar molecules. These exotic states appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets and excitonic condensates.Comment: 7 pages, 5 figures, final versio