Freezing of a Lennard-Jones fluid: from nucleation to spinodal regime

Using molecular dynamics, we investigate the crystal nucleation in a Lennard-Jones fluid as a function of the degree of supercooling. At moderate supercooling, a nucleation picture applies, while for deeper quenches, the phenomenon progressively acquires a spinodal character. We show that in the nucleation regime, the freezing is a two-step process. The formation of the critical nucleus is indeed preceded by the abrupt formation of a precritical crystallite from a density fluctuation in the fluid. In contrast, as the degree of supercooling is increased, crystallization proceeds in a more continuous and collective fashion and becomes more spatially diffuse, indicating that the liquid is unstable and crystallizes by a spinodal mechanism.     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Diffraction and localization in low-dimensional photonic bandgaps

We show that, in low-dimensional photonic bandgaps, wave diffraction resulting from localization in the translational-invariant directions is strongly influenced by the photonic band structure of the periodic crystal, leading to new kinds of wave localization. In particular, for a periodic layered structure we show that, close to a bandgap edge, diffraction is enhanced, with a transition from a parabolic diffraction curve-typical of isotropic media and supporting Gaussian beams-to hyperbolic or elliptic diffraction curves. In the last two cases localization in the form of stationary X-shaped or sinc-shaped waves is possible.     

Importance of nuclear effects in the measurement of neutrino oscillation parameters

We investigate how models for neutrino–nucleus cross sections based on different assumptions for the nuclear dynamics affect the forecasted sensitivities to neutrino oscillation parameters at future neutrino facilities. We limit ourselves to the quasi-elastic regime, where the neutrino cross sections can be evaluated with less uncertainties, and discuss the sensitivity reach to θ₁₃${\theta }_{13}$ and δ at a prototype low-γ β-beam, mostly sensitive to the quasi-elastic regime.     

Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case

We study the ODE/IM correspondence for ODE associated to \({\widehat{\mathfrak{g}}}\)-valued connections, for a simply-laced Lie algebra \({\mathfrak{g}}\). We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called \({\Psi}\)-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.     

Characterization and Valorization of the Agricultural Waste Obtained from Lavandula Steam Distillation for Its Reuse in the Food and Pharmaceutical Fields

The main focus of the current research was the characterization of the by-products from the steam distillation of Lavandula angustifolia Mill. (LA) and Lavandula x intermedia Emeric ex Loisel (LI) aerial parts, as they are important sources of bioactive compounds suitable for several applications in the food, cosmetic, and pharmaceutical industries. The oil-exhausted biomasses were extracted and the total polyphenol and flavonoid contents were, respectively, 19.22 ± 4.16 and 1.56 ± 0.21 mg/g for LA extract and 17.06 ± 3.31 and 1.41 ± 0.10 mg/g for LI extract. The qualitative analysis by liquid chromatography-electrospray tandem mass spectrometry (HPLC-ESI-MS) revealed that both the extracts were rich in phenolic acids and glycosylated flavonoids. The extracts exhibited radical scavenging, chelating, reducing activities, and inhibitory capacities on acetylcholinesterase and tyrosinase. The IC50 values against acetylcholinesterase and tyrosinase were, respectively, 5.35 ± 0.47 and 5.26 ± 0.02 mg/mL for LA, and 6.67 ± 0.12 and 6.56 ± 0.16 mg/mL for LI extracts. In conclusion, the oil-exhausted biomasses demonstrated to represent important sources of bioactive compounds, suitable for several applications in the food, cosmetic, and pharmaceutical industries.     

Extreme value theory for singular measures

In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and He?non maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.