Numerical continuation for fractional PDEs: sharp teeth and bloated snakes

Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical and numerical approaches. The purpose of this work is to study the effects of the spectral fractional Laplacian on the bifurcation structure of reaction-diffusion systems on bounded domains. In order to do this we use advanced numerical continuation techniques to compute the solution branches. Since current available continuation packages only support systems involving the standard Laplacian, we first extend the pde2path software to treat fractional PDEs. The new capabilities are then applied to the study of the Allen-Cahn equation, the Swift-Hohenberg equation and the Schnakenberg system (in which the standard Laplacian is each replaced by the spectral fractional Laplacian). Our study reveals some common effects, which contributes to a better understanding of fractional diffusion in generic reaction-diffusion systems. In particular, we investigate the changes in snaking bifurcation diagrams and also study the spatial structure of non-trivial steady states upon variation of the order of the fractional Laplacian. Our results show that the fractional order can induce very significant qualitative and quantitative changes in global bifurcation structures

The effects of fecundity, mortality and distribution of the initial condition in phenological models

Pest phenological models describe the cumulative flux of the individuals into each stage of the life cycle of a stage-structured population. Phenological models are widely used tools in pest control decision making. Despite the fact that these models do not provide information on population abundance, they share some advantages with respect to the more sophisticated and complex demographic models. The main advantage is that they do not require data collection to define the initial conditions of model simulation, reducing the effort for field sampling and the high uncertainty affecting sample estimates. Phenological models are often built considering the developmental rate function only. To the aim of adding more realism to phenological models, in this paper we explore the consequences of improving these models taking into consideration three additional elements: the age distribution of individuals which exit from the overwintering phase, the age- and temperature-dependent profile of the fecundity rate function and the consideration of a temperature-dependent mortality rate function. Numerical simulations are performed to investigate the effect of these elements with respect to phenological models considering development rate functions only. To further test the implications of different models formulation, we compare results obtained from different phenological models to the case study of the codling moth (Cydia pomonella) a primary pest of the apple orchard. The results obtained from model comparison are discussed in view of their potential application in pest control decision support

Trivulzio, Gian Giacomo

voce biografic

The «little history» of an Italian murdered in Rio Grande do Sul

Il saggio racconta la storia di un migrante italiano nel territorio gaucho tra Argentina e Rio Grande del Sud brutalmente assassinato nel 1892. Fu un episodio che accadde a poche settimane dallo scoppio della revolu\ue7\ue3o federalista (1893-95), e che negli anni successivi non rimase isolato. Simili eventi contribuirono a complicare i rapporti diplomatici tra Italia e Brasile, ma anche ad avviare accordi tra i due Stati per indennizzare le numerose vittime innocenti della guerra civile. Sulla base di documentazione di archivi pubblici e privati italiani si seguono poi le vicende di alcuni altri migranti italiani, omonimi dello sfortunato protagonista. I parenti avevano perso le loro tracce e si rivolsero al Ministero degli Esteri per sperare di essere inclusi nei programmi di risarcimento previsti dagli accordi bilaterali italo-brasilianiThis article gives the account of an Italian immigrant in gaucho territory and his brutal murder, which took place in 1892 in the Rio Grande do Sul (Brazil). His murder occurred a matter of weeks from the outbreak of the revolu\ue7\ue3o federalista (1893-1895), and, in the years that followed, it was not to be an isolated incident. Similar events contributed to complications in diplomatic relations between Italy and Brazil, but also to paving the way for agreements between the two states in order to compensate the numerous innocent victims of the civil war. The stories of Italian emigrants, analogous to the unfortunate protagonist, that are recounted in this article, are based on documentation from public and private archives in Italy. Their relatives had lost all trace of them and turned to the Italian Foreign Ministry hoping to be included in the compensation programmes agreed upon in the bilateral agreements established between Italy and Brazil.L\u2019essai raconte l\u2019histoire d\u2019un migrant italien, qui fut brutalement assassin\ue9 dans le territoire gaucho entre l\u2019Argentine et le Rio Grande Sud en 1892. Ce fut un \ue9pisode qui eut lieu quelques semaines apr\ue8s le d\ue9clenchement de la revolu\ue7\ue3o f\ue9d\ue9raliste (1893-1895) et que n\u2019est pas rest\ue9s isol\ue9s dans les ann\ue9es suivantes. De tels \ue9v\ue9nements ont contribu\ue9 \ue0 compliquer les relations diplomatiques entre l\u2019Italie et le Br\ue9sil, mais aussi \ue0 lancer des accords entre les deux \uc9tats pour indemniser les nombreuses victimes innocentes de la guerre civile. Sur la base de la documentation des archives publiques et priv\ue9es italiennes, suivent les histoires de quelques autres migrants italiens homonymies du malchanceux protagoniste. Leurs parents avaient perdu leurs traces et ont tourn\ue9 vers le minist\ue8re des Affaires \ue9trang\ue8res dans l\u2019espoir d\u2019\ueatre inclus dans les programmes d\u2019indemnisation pr\ue9vus dans les accords bilat\ue9raux italo-br\ue9siliens.El ensayo cuenta la historia de un inmigrante italiano en el territorio gaucho entre Argentina y Rio Grande do Sul, donde fue brutalmente asesinado en 1892. Fue un episodio que ocurre pocas semanas despu\ue9s del estallido de la revolu\ue7\ue3o federalista (1893-1895), y que en los a\uf1os siguientes fue un hecho que no permaneci\uf3 aislado. Eventos similares contribuyeron a complicar las relaciones diplom\ue1ticas entre Italia y Brasil, y tambi\ue9n a iniciar acuerdos entre los dos estados para indemnizar las numerosas v\uedctimas inocentes de la guerra civil. Bas\ue1ndose en la documentaci\uf3n de los archivos p\ufablicos y privados italianos, se da seguimiento a acontecimientos de algunos otros inmigrantes italianos, hom\uf3nimos del desafortunado protagonista. De ellos, los familiares hab\uedan perdido rastro y se dirigieron al Ministerio de Relaciones Exteriores con la esperanza de ser incluidos en los programas de indemnizaci\uf3n previstos en los acuerdos bilaterales de Italobrasilianos