Breakdown of Elasticity in Amorphous Solids

What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the one of disordered magnetic materials. Here we show that in a very large class of amorphous solids this behaviour emerges by decreasing the temperature as a phase transition where standard elastic behaviour breaks down. At the transition all non-linear elastic modulii diverge and standard elasticity theory does not hold anymore. Below the transition the response to deformation becomes history and time-dependent.Comment: 3 figure

Vascular flora of calcareous outcrops in North-Western Sardinia (Italy)

Calcareous outcrops in North-Western Sardinia cover a large area (about 380 Km2) known as "Sassarese". In this study the vascular flora of this area is investigated. The actual flora is checked and, when possible, older references, synonyms and critical notes are given. The floristic list includes 840 entities. Among them, 18 have been cultivated (cultae), 11 are considered erroneously reported and so they are excluded from this area (excludendae) and 81 are in various ways considered not confirmed and to enquiry (inquirendae). The current floristic contingent is therefore reduced to 730 entities, divided into 98 families and 385 genera, many of them here documented for the first time in this area. Among them the more relevant are the Sardinian-Corsican endemic Silene nodulosa Viv. and the Sardinian endemic Hieracium gallurense Arrigoni, previously reported only for granite substrata in North-Eastern Sardinia. The biological spectrum shows a clear dominance of therophytes (41%). The chorological spectrum highlights the dominance of the Tethydic element, in which the dominance of more strictly Mediterranean element emerges. Four entities have in this area their locus classicus: Centaurea corensis Valsecchi et Filigheddu, Limonium racemosum (Lojac.) Diana and Scrophularia morisii Valsecchi, exclusive of the region object of this study, and Ophrys sphegodes Mill. subsp. praecox Corrias. Some entities, though not endemic, have a limited or fragmentary distribution in Sardinia, e.g. Capparis spinosa L. subsp. rupestris (Sm.) Nyman, Coridothymus capitatus (L.) Reichenb. f. and Erica multiflora L., whereas Viola arborescens L.. Borago pygmaea (DC.) Chater et Greuter and Carex panormitana Guss. are included in the Red Book of Italian Plants. Although the area is strongly urbanised and subjected since long time ago to agricultural and pastoral uses, its flora is still rather diversified. The presence of species depending on the existence of hedges, dry-stone walls and other smaller structures belonging to traditional agricultural activities still present, is also substantial, even though their dilapidated state is often high. Finally the presence of floristic elemento of great interest together with small residuals of spontaneous vegetation are of very high value. Indeed, several natural elements from traditionally agricultural activities are present within an area of intense anthropic impact. The indiscriminate building development of the valleys, the reckless exploitation of the water sources and the diffusion of dumps, threaten increasingly some habitats of the region. The improvement of the natural resources could be done through an adeguate ecological net starting from a basic knowledge of the floristic biodiversity, that is the main aim of this work

Lectotypification of <i>Artemisia variabilis</i> Ten. (Compositae)

The name Artemisia variabilis Ten. is here lectotypified. Observations and synonyms are given

Word Sense Disambiguation with LSTM: Do We Really Need 100 Billion Words?

Recently, Yuan et al. (2016) have shown the effectiveness of using Long Short-Term Memory (LSTM) for performing Word Sense Disambiguation (WSD). Their proposed technique outperformed the previous state-of-the-art with several benchmarks, but neither the training data nor the source code was released. This paper presents the results of a reproduction study of this technique using only openly available datasets (GigaWord, SemCore, OMSTI) and software (TensorFlow). From them, it emerged that state-of-the-art results can be obtained with much less data than hinted by Yuan et al. All code and trained models are made freely available

Statistical mechanics of the spherical hierarchical model with random fields

We study analytically the equilibrium properties of the spherical hierarchical model in the presence of random fields. The expression for the critical line separating a paramagnetic from a ferromagnetic phase is derived. The critical exponents characterising this phase transition are computed analytically and compared with those of the corresponding $D$-dimensional short-range model, leading to conclude that the usual mapping between one dimensional long-range models and $D$-dimensional short-range models holds exactly for this system, in contrast to models with Ising spins. Moreover, the critical exponents of the pure model and those of the random field model satisfy a relationship that mimics the dimensional reduction rule. The absence of a spin-glass phase is strongly supported by the local stability analysis of the replica symmetric saddle-point as well as by an independent computation of the free-energy using a renormalization-like approach. This latter result enlarges the class of random field models for which the spin-glass phase has been recently ruled out.Comment: 23 pages, 2 figure

Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis, and a further transition at higher pressures in which a glassy structure of micro-states is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Micro states that are small excitations of an amorphous matrix -- separated by low entropic or energetic barriers -- thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.Comment: 26 pages, 7 figures -- to be published in a Special Issue of The Journal of Physical Chemistry B in honor of Peter G. Wolynes -- paper I is arXiv:1208.042

Following the evolution of glassy states under external perturbations: compression and shear-strain

We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.Comment: 4 pages (3 figures) + 24 pages (5 pages) of appendice

Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.Comment: 6 pages, 3 figures, submitted to PNA