Quasi-linear Schrödinger–Poisson system under an exponential critical nonlinearity: existence and asymptotic behaviour of solutions

We prove the generalized $$L^p$$ -Poincaré inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.     

Interaction of the Fungal Metabolite Harzianic Acid with Rare-Earth Cations (Pr3+, Eu3+, Ho3+, Tm3+)

Rare-earth elements (REEs) are in all respect a class of new contaminants that may have toxic effects on organisms and microorganisms and information on their interactions with natural ligands should be of value to predict and control their diffusion in natural environments. In the current study, we investigate interactions of tripositive cations of praseodymium, europium, holmium, and thulium with harzianic acid (H₂L), a secondary metabolite produced by selected strains of fungi belonging to the Trichoderma genus. We applied the same techniques and workflow previously employed in an analogous study concerning lanthanum, neodymium, samarium, and gadolinium tripositive cations. Therefore, in the current study, HPLC-ESI-HRMS experiments, circular dichroism (CD), and UV-Vis spectrophotometric absorption data, as well as accurate pH measurements, were applied to characterize bonding interactions between harzianic acid and Pr³⁺, Eu³⁺, Ho³⁺, and Tm³⁺ cations. Problems connected to the low solubility of harzianic acid in water were overcome by employing a 0.1 M NaClO₄/(CH₃OH + H₂O 50/50 w/w) mixed solvent. For Pr³⁺, Ho³⁺, and Tm³⁺, only the mono complexes PrL⁺, HoL⁺, and TmL⁺ were detected and their formation constant determined. Eu³⁺ forms almost exclusively the bis complex EuL2− for which the corresponding formation constant is reported; under our experimental conditions, the mono complex EuL⁺ is irrelevant. Combining the results of the present and previous studies, a picture of interactions of harzianic acid with rare-earth cations extending over 8 of the 17 REEs can be composed. In order to complement chemical information with toxicological information, a battery of bioassays was applied to evaluate the effects of praseodymium, europium, holmium, and thulium tripositive cations on a suite of bioindicators including Aliivibrio fischeri (Gram-negative bacterium), Raphidocelis subcapitata (green alga), and Daphnia magna (microcrustacean), and median effective concentration (EC50) values of Pr³⁺, Eu³⁺, Ho³⁺, and Tm³⁺ for the tested species were assessed.     

Effect of wall slip on the viscoelastic particle ordering in a microfluidic channel

The formation of a line of equally spaced particles at the centerline of a microchannel, referred as “particle ordering,” is desired in several microfluidic applications. Recent experiments and simulations highlighted the capability of viscoelastic fluids to form a row of particles characterized by a preferential spacing. When dealing with non-Newtonian fluids in microfluidics, the adherence condition of the liquid at the channel wall may be violated and the liquid can slip over the surface, possibly affecting the ordering efficiency. In this work, we investigate the effect of wall slip on the ordering of particles suspended in a viscoelastic liquid by numerical simulations. The dynamics of a triplet of particles in an infinite cylindrical channel is first addressed by solving the fluid and particle governing equations. The relative velocities computed for the three-particle system are used to predict the dynamics of a train of particles flowing in a long microchannel. The distributions of the interparticle spacing evaluated at different slip coefficients, linear particle concentrations, and distances from the channel inlet show that wall slip slows down the self-assembly mechanism. For strong slipping surfaces, no significant change of the initial microstructure is observed at low particle concentrations, whereas strings of particles in contact form at higher concentrations. The detrimental effect of wall slip on viscoelastic ordering suggests care when designing microdevices, especially in case of hydrophobic surfaces that may enhance the slipping phenomenon.     

Dynamic convexity for natural thermostatted systems

Natural thermostatted systems are mechanical systems whose Lagrangian is the difference of a kinetic and a potential energy, subjected to the nonholonomic constraint of a constant kinetic energy. When any two points of the configuration space are joined by a thermostatted motion, we say that the system is dynamically convex. A thermostatted charged particle on the plane with a constant electric field is not a dynamically convex system. We prove a general sufficient condition for dynamic convexity, from which whole classes of examples are easily constructed.     

Manganese dioxide oxidation of 3,4,4a,5-tetrahydro[1,2,4]triazino[6,1-c][1,4]benzoxazines

Since we developed [1] a synthetic entry to 3,4,4a,5-tetrahydro[1,2,4]triazino[6,1-c][1,4]benzoxazines 1 , we decided to explore the chemistry of this novel ring system. Its behaviour towards manganese dioxide is here described.     

Improved coupled-mode analysis of nonlinear distributed feedback structures

Coupled-mode theory is employed to describe the nonlinear behaviour of a distributed feedback grating, including intensity-dependent terms resulting from the periodic variations in the nonlinearity. The improved coupled-mode analysis leads to modified values for the on and off-switching intensities, as demonstrated numerically.On leave from Dpto. Tecnologia Fotónica, Universidad Politécnica de Madrid, Ciudad Universitaria, 28040 Madrid, Spain.     

Photoelectron diffraction study of ultrathin film growth of Ni on Pt(111)

X-ray photoelectron diffraction (PD) based on a forward scattering approach (FS-PD) has been used to study the growth mode of the first few Ni monolayers deposited on the Pt(111) surface, with a particular attention to the initial stages of epitaxy, i.e. the formation of the first atomic layer. Strong evidences for a layer-by-layer (or Frank-Van der Merwe) growth mode are reported, substantiated also by theoretical simulations carried out with the single scattering cluster-spherical wave (SSC-SW) framework. The first Ni monolayer grows strained in-plane to match the substrate pseudomorphically even if there is a 10% mismatch between the lattice parameters of Ni and Pt. The multilayer (up at least to six monolayers) maintains the horizontal strain and consequently shows a vertical spacing contraction (tetragonal distorsion). It retains the overall threefold symmetry and azimuthal orientation of the substrate, indicative of a single-domain epitaxial fcc stacking. There is also some evidence (even if it is not conclusive) for the fact that the Ni atoms of the first monolayer occupy hcp sites of the substrate surface.     

Coumarin as dipolarophile towards 3,5-dichloro-2,4,6-trimethylbenzonitrile oxide

The reaction of coumarin with the title nitrile oxide gives a single regioisomer in high yield. This result is compared with the dipolarophilic behavior of cinnamic acid esters.     

Steiner systems andn −1-isomorphisms

In this work we introduce the concept of n ^–1-isomorphism between Steiner systems (this coincides with the concept of isomorphism whenever n=1).Precisely two Steiner systems S₁ and S₂ are said to be n^–1-isomorphic if there exist n partial systems S _i ⁽¹⁾ ,...,S _i ⁽ⁿ⁾ contained in Si, i.{1,2},such that S ₁ ^(k) and S ₂ ^(k) are isomorphic for each k{1,..., n}.The n^–1-isomorphisms are also used to study nets replacements, see Ostrom [8], and to study the transformation methods of designs and other incidence structures introduced in [9] and generalized in [1] and [10].Work done under the auspicies of G.N.S.A.G.A. supported by 40% grants of M.U.R.S.T.     

Excitation of self-transparency Bragg solitons in quadratic media

We show that self-transparent or gap solitons with leading-order components at fundamental frequency can be generated in a singly resonant Bragg grating by second-harmonic generation. We discuss the conditions required for exciting these localized waves.