Structure and evolution of strange attractors in non-elastic triangular billiards

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter λ is varied. For λ∈(0,1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of λ gaps arise in the Cantor structure. For λ close to 1, the attractor splits into three transitive components, whose basins of attraction have fractal boundaries.     

Minimising movements for the motion of discrete screw dislocations along glide directions

In Alicandro et al. (J Mech Phys Solids 92:87–104, 2016) a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in Cermelli and Gurtin (Arch Ration Mech Anal 148, 1999) and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in [3], and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on \(\Gamma \)-convergence techniques.     

Effect of the alkylaluminum cocatalyst on ethylene polymerization by a nickel–diimine complex

Different chlorine-free alkylaluminum compounds were active cocatalysts for ethylene polymerization in the presence of 1,4-bis(2,6-diisopropylphenyl)-acenaphthenediimine-dichloronickel (II) (1). The combination of 1 with trimethylaluminum or triisobutylaluminum produced catalytically active species that polymerized ethylene with productivities up to 469 kg_polymer/(mol_Ni · h). The activity of the catalytic system and the properties of the polymeric materials were influenced strongly by the reaction temperature. The polymers had a high molecular weight (up to 642 × 10³ g · mol⁻¹), and the molecular weight increased with the reaction time. The polyethylenes were branched, and the branching could be modulated by the proper choice of reaction parameters. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4656–4663, 1999     

Nitrogen‐Doped Ordered Mesoporous Carbon Supported Bimetallic PtCo Nanoparticles for Upgrading of Biophenolics

Hydrodeoxygenation (HDO) is an attractive route for the upgrading of bio‐oils produced from lignocellulose. Current catalysts require harsh conditions to effect HDO, decreasing the process efficiency in terms of energy and carbon balance. Herein we report a novel and facile method for synthesizing bimetallic PtCo nanoparticle catalysts (ca. 1.5 nm) highly dispersed in the framework of nitrogen‐doped ordered mesoporous carbon (NOMC) for this reaction. We demonstrate that NOMC with either 2D hexagonal (p6m) or 3D cubic (Im m) structure can be easily synthesized by simply adjusting the polymerization temperature. We also demonstrate that PtCo/NOMC (metal loading: Pt 9.90 wt %; Co 3.31 wt %) is a highly effective catalyst for HDO of phenolic compounds and “real‐world” biomass‐derived phenolic streams. In the presence of PtCo/NOMC, full deoxygenation of phenolic compounds and a biomass‐derived phenolic stream is achieved under conditions of low severity.     

Cloud point extraction for cobalt preconcentration with on-line phase separation in a knotted reactor followed by ETAAS determination in drinking waters

A novel method for cobalt preconcentration by cloud point extraction with on-line phase separation in a PTFE knotted reactor and further determination by electrothermal atomic absorption spectrometry (ETAAS) is proposed. The cloud point system was formed in the presence of non-ionic micelles of polyethyleneglycolmono-p-nonylphenylether (PONPE 7.5) and it was retained on the inner walls of a knotted reactor (KR). The surfactant rich-phase was removed from the knotted reactor with 75 microL of methanol acidified with 0.8 mol L(-1) nitric acid, directly into the dosing hole of the L'Vov graphite tube. An enrichment factor of 15 was obtained with a preconcentration time of 60 s, with respect to the direct determination of cobalt by ETAAS in aqueous solutions. The value of the detection limit for the preconcentration of 5 mL of sample solution was 10 ng L(-1). The precision, expressed as the relative standard deviation (R.S.D.), for 10 replicate determinations at 0.5 microg L(-1) Co level was 4.5%. Verification of the accuracy was carried out by analysis of a standard reference material (NIST SRM 1640e "Trace elements in natural water"). The method was successfully applied to the determination of cobalt in drinking water samples.     

How deeply are core electrons perturbed when valence electrons are spin polarized? The case study of transition metal compounds

The ferromagnetic and antiferromagnetic wave functions of the KMnF₃ perovskite have been evaluated quantum-mechanically by using an all electron approach and, for comparison, pseudopotentials on the transition metal and the fluorine ions. It is shown that the different number of α and β electrons in the d shell of Mn perturbs the inner shells, with shifts between the α and β eigenvalues that can be as large as 6 eV for the 3s level, and is far from negligible also for the 2s and 2p states. The valence electrons of F are polarized by the majority spin electrons of Mn, and in turn, spin polarize their 1s electrons. When a pseudopotential is used, such a spin polarization of the core functions of Mn and F can obviously not take place. The importance of such a spin polarization can be appreciated by comparing (i) the spin density at the Mn and F nuclear position, and then the Fermi contact constant, a crucial quantity for the hyperfine coupling, and (ii) the ferromagnetic–antiferromagnetic energy difference, when obtained with an all electron or a pseudopotential scheme, and exploring how the latter varies with pressure. This difference is as large as 50% of the all electron datum, and is mainly due to the rigid treatment of the F ion core. The effect of five different functionals on the core spin polarization is documented.     

Protease Production by Different Thermophilic Fungi

A comparative study was carried out to evaluate protease production in solid-state fermentation (SSF) and submerged fermentation (SmF) by nine different thermophilic fungi – Thermoascus aurantiacus Miehe, Thermomyces lanuginosus, T. lanuginosus TO.03, Aspergillus flavus 1.2, Aspergillus sp. 13.33, Aspergillus sp. 13.34, Aspergillus sp. 13.35, Rhizomucor pusillus 13.36 and Rhizomucor sp. 13.37 – using substrates containing proteins to induce enzyme secretion. Soybean extract (soybean milk), soybean flour, milk powder, rice, and wheat bran were tested. The most satisfactory results were obtained when using wheat bran in SSF. The fungi that stood out in SSF were T. lanuginosus, T. lanuginosus TO.03, Aspergillus sp. 13.34, Aspergillus sp. 13.35, and Rhizomucor sp. 13.37, and those in SmF were T. aurantiacus, T. lanuginosus TO.03, and 13.37. In both fermentation systems, A. flavus 1.2 and R. pusillus 13.36 presented the lowest levels of proteolytic activity.     

Uncatalyzed, anti-Michael addition of amines to β-nitroacrylates: practical, eco-friendly synthesis of β-nitro-α-amino esters

A variety of primary and secondary amines give the conjugate reaction with β-nitroacrylates, via an anti-Michael addition, without any catalyst and/or solvent, allowing good yields of β-nitro-α-amino esters.     

Solid-state NMR studies of weak interactions in supramolecular systems

The field of application of solid-state NMR to the study of supramolecular systems is growing rapidly, with many research groups involved in the development of techniques for the study of crystalline and amorphous phases. This Feature Article aims to provide an overview of the recent contributions of our research group to this field, paying particular attention to the study of the weak interactions such as hydrogen bonds in supramolecular systems through solid-state NMR investigations. The structure and dynamic behaviour of selected host-guest systems will be also discussed.