Multiplicity of layered solutions for Allen–Cahn systems with symmetric double well potential

We study the existence of solutions u:R³→R²$u:{\mathbb{R}}^3\to {\mathbb{R}}^2$ for the semilinear elliptic systems

equation(0.1)

−Δu(x,y,z)+∇W(u(x,y,z))=0,$-\mathrm{\Delta }u(x,y,z)+\mathrm{\nabla }W(u(x,y,z))=0,$

where W:R²→R$W:{\mathbb{R}}^2\to \mathbb{R}$ is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima _a±${\mathbf{a}}_{\pm }$ of W, that (0.1) has infinitely many geometrically distinct solutions u∈C²(R³,R²)$u\in C^2({\mathbb{R}}^3,{\mathbb{R}}^2)$ which satisfy u(x,y,z)→_a±$u(x,y,z)\to {\mathbf{a}}_{\pm }$ as x→±∞$x\to \pm \infty$ uniformly with respect to (y,z)∈R²$(y,z)\in {\mathbb{R}}^2$ and which exhibit dihedral symmetries with respect to the variables y and z  . We also characterize the asymptotic behavior of these solutions as |(y,z)|→+∞$|(y,z)|\to +\infty$.     

Fiber-Drawn Metamaterial for THz Waveguiding and Imaging

In this paper, we review the work of our group in fabricating metamaterials for terahertz (THz) applications by fiber drawing. We discuss the fabrication technique and the structures that can be obtained before focusing on two particular applications of terahertz metamaterials, i.e., waveguiding and sub-diffraction imaging. We show the experimental demonstration of THz radiation guidance through hollow core waveguides with metamaterial cladding, where substantial improvements were realized compared to conventional hollow core waveguides, such as reduction of size, greater flexibility, increased single-mode operating regime, and guiding due to magnetic and electric resonances. We also report recent and new experimental work on near- and far-field THz imaging using wire array metamaterials that are capable of resolving features as small as λ/28.     

Structural and photophysical characterization of multichromophoric pyridylporphyrin-rhenium(i) conjugates

Four porphyrin-Re(I) conjugates, in which a pyridylporphyrin chromophore is directly coordinated to the electron-acceptor fragment [ fac-Re(CO) 3(bipy)] (+), were prepared: the dimeric and pentameric compounds [ fac-Re(CO) 3(bipy)(4'MPyP)](CF 3SO 3) ( 1) (4'MPyP = 4'-monopyridylporphyrin) and [ fac-{Re(CO) 3(bipy)} 4(mu-4'TPyP)](CF 3SO 3) 4 ( 2) (4'TPyP = 4'-tetrapyridylporphyrin), and the corresponding compounds with 3' rather than 4' porphyrins, [ fac-Re(CO) 3(bipy)(3'MPyP)](CF 3SO 3) ( 3) and [ fac-{Re(CO) 3(bipy)} 4(mu-3'TPyP)](CF 3SO 3) 4 ( 4). These adducts proved to be very stable in solution and were also structurally characterized in the solid state by X-ray crystallography. A detailed photophysical study was performed on the zincated adducts of the conjugates 1- 3, labeled 5, 6, and 7, respectively. In all adducts the typical fluorescence of the zinc-porphyrin unit was reduced in intensity and lifetime by the presence of the peripheral rhenium-bipy fragment(s) (heavy-atom effect). For the dyads 5 and 7 the photoinduced charge transfer process from the zinc-porphyrin to the Re(I)-bipy unit is only slightly exoergonic. Ultrafast spectroscopy experiments showed no evidence for electron transfer quenching in the dyads as such, whereas the addition of pyridine (that binds axially to zinc and thus affects the porphyrin redox potential) led to a moderately efficient photoinduced electron transfer process. In perspective, an appropriate functionalization of the bipy ligand and/or of the porphyrin chromophore might improve the thermodynamics and, thus the efficiency, of the photoinduced electron transfer process.     

Validation of a new reversed-phase high-performance liquid chromatography method for separation and quantification of bovine milk protein genetic variants

A new RP-HPLC method for the separation and quantification of the most common genetic variants of bovine milk proteins is described. A reversed-phase analytical column C8 (Zorbax 300SB-C8 RP, 3.5 microm, 300A, 150 x 4.6 I.D.) was used. All the most common casein (CN) and whey protein genetic variants, including beta-CN(I) were detected and separated simultaneously in less then 40 min, with the exception of alpha(S1)-CN(B) and CN(C) variants. Purified protein genetic variants were employed in calibration and showed different absorbances at 214 nm. The procedure was developed using 40 raw individual milk samples of cows belonging to four different breeds and certified skim milk powder BCR-063R. Method validation consisted in testing linearity, repeatability, reproducibility and accuracy. A linear relationship (R(2)>0.99) between the concentrations of proteins and peak areas was observed over the concentration range, with low detection limits. Repeatability and reproducibility were satisfactory for both retention times and peak areas. The RSD of peak areas ranged from 0.92 to 4.32% within analytical day and from 0.85 to 9.52% across analytical days. The recoveries, calculated using mixtures of samples previously quantified, ranged from 98.1 to 103.7%.     

Phyllostictines A-D, oxazatricycloalkenones produced by Phyllosticta cirsii, a potential mycoherbicide for Cirsium arvense biocontrol

Phyllosticta cirsii, a fungal pathogen isolated from Cirsium arvense and proposed as biocontrol agent of this noxious perennial weed, produces in liquid cultures different phytotoxic metabolites with potential herbicidal activity. Four new oxazatricycloalkenones, named phyllostictines A-D, were isolated and characterized using essentially spectroscopic and chemical methods. Tested by leaf-puncture assay on the fungal host plant phyllostictine A proved to be highly toxic. The phytotoxicity decreases when both the dimension and the conformational freedom of the macrocyclic ring change, as in phyllostictines B and D, and it is totally lost when also the functionalization of the same ring is modified, as in phyllostictine C. Beside its phytotoxic properties, phyllostictine A has no antifungal activity, an interesting antibiotic activity only against Gram+ bacteria, and a noticeable zootoxic activity when tested at high concentrations. The integrity of the oxazatricycloalkenone system appears to be an important feature to preserve these activities.     

Spectral multipliers on 2-step groups: topological versus homogeneous dimension

Let G be a 2-step stratified group of topological dimension d and homogeneous dimension Q. Let \({\mathcal{L}}\) be a homogeneous sub-Laplacian on G. By a theorem due to Christ and to Mauceri and Meda, an operator of the form \({F(\mathcal{L})}\) is of weak type (1, 1) and bounded on L ^p (G) for all p ∈ (1, ∞) whenever the multiplier F satisfies a scale-invariant smoothness condition of order s > Q/2. It is known that, for several 2-step groups and sub-Laplacians, the threshold Q/2 in the smoothness condition is not sharp and in many cases it is possible to push it down to d/2. Here we show that, for all 2-step groups and sub-Laplacians, the sharp threshold is strictly less than Q/2, but not less than d/2.     

Study on the shear viscosity behavior of keratin/PEO blends for nanofibre electrospinning

Graessley's theory has been applied to keratin/PEO concentrated aqueous solutions giving qualitative insight to the rheology of these polymer blends in electrospinning. The shear rate dependent viscosity of different blends was compared with that of pure polymer solutions. The characteristic time τ_η was calculated by the minimum value of at the beginning of the non‐Newtonian viscosity behavior. Flow curves of PEO (at concentration from 1.0 to 7.0 wt %) reduce to a single curve by plotting η/η₀ against . Moreover, PEO solutions exhibit a linear proportionality between zero‐shear viscosity and the characteristic time η₀ ∝ τ_η. Keratin/PEO blend solutions follow the same proportionality at very high and low keratin content, whereas linearity drops when the keratin content range from 50 to 70%. The departure from the theory has been interpreted as a sign of some interaction between the macromolecules of keratin and PEO. It was supposed that keratin displaces solvent molecules and expands the PEO chain coils increasing the relaxation time of the polymer solution. This behavior was correlated with changes in the morphology of the nanofibres produced by electrospinning from these polymer blends. Finally, additive rules to zero‐shear viscosity were applied to keratin and PEO solutions, indicating that the experimental η₀ values were higher than the theoretical ones for all the proportions of the blends, especially for high keratin amount. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1193–1201, 2008     

A theoretical study of AmOn and CmOn (n = 1, 2)

Americium and curium oxides AmOn and CmOn (n = 1, 2) were studied using state-of-the-art multiconfigurational, relativistic, quantum chemical methods. Spectroscopic properties for the ground state and several excited states of the four target compounds were determined. The computed dissociation energy of AmO (4.6 eV) agrees fairly well with estimates derived from experimental studies (5.73 +/- 0.37 eV) while the computed dissociation energy of CmO (7.1 eV) agrees well with the experimental value (7.5 eV). The computed ionization energy of AmO (6.3 eV) is in good agreement with the current experimental value (5.9 +/- 0.2 eV).     

Correlation between colloidal stability and surfactant adsorption/association phenomena studied by light scattering

The stability of a colloidal system composed of styrene-acrylate copolymer particles and potassium stearate (KS) anionic surfactant molecules has been determined in terms of the Fuchs stability ratio, W, as a function of the surfactant concentration, by measuring the initial aggregation kinetics using the small-angle light scattering (SALS) technique. The structure of the particle surface is peculiar, being irregularly patterned, and thus represents a model system to investigate colloidal stability of nonsmooth colloidal particles. From the SALS kinetic experiments, it is found that the stability increases dramatically with KS concentration until the saturation of the available surface occurs. At concentrations higher than the saturation concentration, the W value decreases markedly with KS, as a consequence of attractive depletion forces induced by formation of micelles in the water phase. The adsorption isotherm, determined through the surface tension technique, agrees with the W vs KS behavior, with respect to the onset of saturation and the surface-per-molecule value, and it can be described by the two-step Langmuir isotherm. Static light scattering spectra of the particles at different adsorbed amounts of KS have been fitted by means of the Lorenz-Mie theory and accounting for the experimentally determined particle size distribution. The increase in the particle diameter imputable to KS adsorption is sizable. Stability data measured under high fluid shear in a turbulent capillary (in the absence of any screening salt) fit well into this scenario. However, depletion forces are shown to be noncooperative with turbulent shear in the absence of screening electrolytes.