Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic forces. For hard interaction potentials, discrete breathers in this model are known to exist either as ``optic breathers'' with frequencies above the optic band, or as ``acoustic breathers'' with frequencies in the gap between the acoustic and the optic band. In this paper, bifurcations between different types of discrete breathers are found numerically, with the mass ratio m and the breather frequency omega as bifurcation parameters. We identify a period tripling bifurcation around optic breathers, which leads to new breather solutions with frequencies in the gap, and a second local bifurcation around acoustic breathers. These results provide new breather solutions of the FPU system which interpolate between the classical acoustic and optic modes. The two bifurcation lines originate from a particular ``corner'' in parameter space (omega,m). As parameters lie near this corner, we prove by means of a center manifold reduction that small amplitude solutions can be described by a four-dimensional reversible map. This allows us to derive formally a continuum limit differential equation which characterizes at leading order the numerically observed bifurcations.Comment: 30 pages, 10 figure

Riemann solvers and undercompressive shocks of convex FPU chains

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax-shocks are replaced by so called dispersive shocks. For convex-concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave-convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

Relationship between recruitment and mother plant vitality in the alien species Acacia cyclops A. Cunn. ex G. Don

Acacia cyclops is a widespread invader in Mediterranean-climate regions. However, although its naturalization in the Mediterranean Basin dates back only a few years ago, and the invasion process has not been studied hitherto. We investigated seedlings recruitment strategy adopted by A. cyclops in a small island (Lampedusa, Italy) where its natural regeneration was strictly confined under mother plants canopy. Healthy plants (DCP), plants at incipient senescence (SCP) and dead plants (DP) were distinguished according to vitality and canopy status. Living plants were also characterized in relation to leaf C and N isotope composition. Regeneration pattern (seedlings and saplings abundance) was related to the microclimatic differences (soil temperature, air temperature and humidity, soil nutrients, light) observed between canopies and adjacent open areas, and among canopy types. Living canopies ensure milder conditions, reducing extreme values as well as fluctuations between night and day. However, beneath canopies (DP, SCP and DCP) seedlings may benefit from significantly higher soil nutrients content than in the outside, while light availability was much higher under DP. Saplings to seedlings ratio was found to be around 12 under DP, while under SCP it was slightly higher than 1, and just less than 0.5 under DCP. Moreover, saplings growth was significantly higher under SCP and DP, suggesting a prominent role of light in driving seedlings recruitment. Stable isotope analyses of C and N provided ecophysiological information in relation to changes in canopies structure. Thus, while seedling stage appears to be more nutrient-limited, subsequent sapling stage is much more light-limited. Although the species is not yet displaying an invasive spreading on the island, our study provides clear evidence that senescent canopies are better facilitators than healthy in preserving the invasive potential of A. cyclops. This finding suggests some best practices in order to gradually reduce the presence of the alien species within its pristine nuclei of introduction

Ecologia e distribuzione di Chamaerops humilis L. (Arecaceae) nella Sicilia nord-orientale

I settori costieri e collinari della Sicilia nord-orientale e delle Eolie sono stati esplorati ai fini della raccolta di informazioni aggiornate sulla distribuzione dei popolamenti di palma nana e sulle caratteristiche ecologiche delle stazioni che li ospitano. I risultati delle indagini di campo sono stati integrati dalla verifica dei toponimi locali legati ai nomi dialettali della specie. Si con- ferma la totale assenza della palma nana lungo l’intero settore costiero dei Nebrodi. Dei nove popolamenti accertati, quattro si trovano alle Eolie, due sul versante ionico e tre sul versante tir- renico dei Peloritani; uno di questi ultimi, localizzato su Capo Calavà, risulta inedito. La conco- mitanza di diversi fattori di stress e l’impatto plurisecolare dell’uomo è probabilmente responsa- bile del carattere relittuale di gran parte dei popolamenti considerati, che danno vita a consorzi molto discontinui, e sono rappresentati da piccoli nuclei che formano aggruppamenti semplifi- cati sotto un profilo fisionomico e poveri in termini floristici, perlopiù confinati in contesti roc- ciosi costieri. Di contro, la recente espansione della palma nana registrata a Lipari sembra dipen- dere dalla cessazione delle attività agricole. Infine, i casi di naturalizzazione registrati a Milazzo, Tindari, Panarea, Scaletta Zanclea e Taormina derivano dal suo uso come pianta ornamentale e pongono in risalto l’urgente necessità di regolamentare la sua introduzione per evitare l’inquina- mento genetico dei nuclei autoctoni.The coastal and hilly sectors of NE Sicily and the Aeolian Archipelago have been explored, in order to obtain up-to-date information on the distribution of the populations of Chamaerops humilis and on their site conditions. In addition to the field surveys, any local toponym possibly related to the Sicilian vernacular names of the dwarf palm was checked and verified throughout the investigat- ed area. The total absence of the species along the coasts of Nebrodi Massif is confirmed. Of the 9 extant populations, 4 are located on the Aeolian Islands, 2 along the Ionian coast and 3 along the Tyrrhenian coast of Peloritani Mountains: among them, the one of Capo Calavà represents a new record. The co-occurrence of centuries-long human disturbance and several forms of envi- ronmental stresses could be the reason for the relict connotation of most of the considered popu- lations, which also are very discontinuous and consisting of small patches formed by a few indi- viduals, in simplified and species-poor assemblages, mostly found on sea-facing rocky cliffs. On the other hand, the recent spread of Chamaerops humilis in Lipari could be related to the aban- donment of agricultural practices. Finally, the naturalisation cases recorded in Milazzo, Tindari, Panarea, Scaletta Zanclea and Taormina, where the dwarf palm escaped from public and private gardens, point out the urgent need of regulating its introduction, in order to avoid the genetic pol- lution of the autochthonous populations

Preliminary checklist of the Italian gypsophilous flora

The richness and uniqueness of the flora growing on gypsum substrates in Italy is known since the XIX century (Macchiati, 1888). Furthermore, the concept of plant gypsophily can be defined as the exclusiveness (or virtually exclusiveness) for living in gypsum outcropping rocks. Thus only those plant species, which show preference – or even exclusivity - for gypsum substrates, would be classified as gipsophilous (Mota et al., 2011). The main aim of this research has been the elaboration of a checklist of the Italian gypsophilous flora. The study was made possible through international collaboration between the "Mediterranea" University of Reggio Calabria (Italy) and the University of Almería (Spain). During the first step, an extensive literature review has been carried out in order to collect all available information about gypsophilous flora and to compile a preliminary list. Afterwards 18 regional botanists experts on Italian gypsum flora have been asked to rank the preference of these species for gypsum soils. Following the methodology proposed by Mota et al. (2009), the gypsophilous character of more than 100 plant species has been thus ranked on a scale ranging from 1 to 5 (with 5 representing for a total dependence on gypsum substrates). According to the obtained values, all the plant species, ranking between absolute or preferent gypsophytes, will figure in the final checklist of the gypsophytes of the whole Italian territory

A new naturalized alien plant in Sicily: Cotula australis (Sieber ex Spreng.) Hook. f. (Asteraceae) on the Acropolis of Lipari Island (Aeolian Archipelago)

In February 2018 a copious population of Cotula australis Hook f. (Asteraceae, Anthemideae) was found on the cobblestones of the Acropolis of Lipari Island (Aeolian Archipelago, NE Sicily). This population represents the first record in southern Italy and is located at a distance of about 470 km as the crow flies from the nearest neighbour. From the phytosociological point of view, C. aus- tralis dominates a therophytic subnitrophilous dwarf vegetation of trampled sites which can be ascribed to the cosmopolitan class Polygono-Poetea annuae Rivas Mart. 1975. This plant communi- ty is proposed as a new association, Galio muralis-Cotuletum australis, which can be considered a Mediterranean vicariant of the Polycarpo tetraphylli-Cotuletum australis Wildpret, Perez de Paz, Del Arco & Garcia Gallo 1988, recorded from the Canary Islands and Portugal. Some hypotheses on the origin of the Aeolian population in the frame of a documented very fast recent propagation world- wide are discussed

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Site-directed mutations in the C-terminal extension of human aB-Crystalline affect chaperone function and block amyloid fibril formation

Copyright: 2007 Treweek et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Background. Alzheimer’s, Parkinson’s and Creutzfeldt-Jakob disease are associated with inappropriate protein deposition and ordered amyloid fibril assembly. Molecular chaperones, including aB-crystallin, play a role in the prevention of protein deposition. Methodology/Principal Findings. A series of site-directed mutants of the human molecular chaperone, aBcrystallin, were constructed which focused on the flexible C-terminal extension of the protein. We investigated the structural role of this region as well as its role in the chaperone function of aB-crystallin under different types of protein aggregation, i.e. disordered amorphous aggregation and ordered amyloid fibril assembly. It was found that mutation of lysine and glutamic acid residues in the C-terminal extension of aB-crystallin resulted in proteins that had improved chaperone activity against amyloid fibril forming target proteins compared to the wild-type protein. Conclusions/Significance. Together, our results highlight the important role of the C-terminal region of aB-crystallin in regulating its secondary, tertiary and quaternary structure and conferring thermostability to the protein. The capacity to genetically modify aB-crystallin for improved ability to block amyloid fibril formation provides a platform for the future use of such engineered molecules in treatment of diseases caused by amyloid fibril formation