Trends and trade-offs in nematicon propagation

We investigate the propagation of nematicons in various nematic liquid crystals. Following some general considerations on the role of material parameters in light self-trapping via a reorientational nonlinear response, we discuss numerical results on light self-action and transverse localization. Finally, we validate our findings with experimental measurements in three liquid crystalline mixtures featuring different amounts of birefringence.     

Methods and evaluation of frequency aging in distributed-feedback laser diodes for rubidium atomic clocks

Distributed-feedback laser diodes emitting at 780?nm have been evaluated, with respect to the aging of the injection current required for reaching the rubidium D2 resonance line. Results obtained for lasers operating in air and in vacuum for 9 months are reported. When operated at constant temperature, the laser current required for emission at the wavelength of the desired atomic resonance is found to decrease by 50 to 80?μA per month. The impact of this result on the lifetime and long-term performances of laser-pumped rubidium atomic clocks is discussed.     

Lagrange solution for three wavelength solitary wave clusters in nematic liquid crystals

We investigate the interaction of three optical solitary waves propagating with angular momentum in bulk nematic liquid crystals. The resulting cluster of solitary waves, or nematicons, is shown to orbit about its common centre of “mass”. An elongated isosceles triangle configuration is derived, this solution being the equivalent of the Lagrange solution of Newtonian gravitation. This triangle solution is found to be stable owing to diffractive radiation. A modulation theory explains the existence of the triangle solution as due to the non-monotonicity of an effective potential for the interaction of the solitary waves. This modulation theory also gives good agreement with numerical solutions for the trajectories of the nematicons in the three colours. Finally, it is shown that a cut-off in the shed diffractive radiation prevents the break-up of the triangle due to radiative losses.     

Heat transfer and crystallization kinetics during fast cooling of thin polymer films

In this work, the heat transfer phenomena taking place during the cooling of thin films of crystallizable polymers were analyzed. The thermal histories, as recorded during experimental cooling runs carried out at various cooling rates, were compared with the predictions of a general purpose numerical code, which was resulted able to capture all the main features of the process. Thus, the conditions which allow homogeneous cooling (negligible temperature gradient within the sample) or homogeneous cooling history (the same cooling history for all the positions within the sample) were predicted by the simulation code.     

Interactions of Type II vectorial spatial solitary waves in materials with quadratic non-linearity

We present analytical, numerical and experimental results of the interactions between Type II vectorial spatial solitary waves (QSSW) in second-order non-linear media. We show that the outcome of the interaction can be changed from beam coalescence to steering, crossing or repulsion through a non-coherent control (i.e. the control does not rely on the relative phase between the interacting QSSW). We also provide experimental evidence that both quasi-elastic and inelastic collision between QSSW are feasible in second order non-linear media, depending on the relative velocity of the interacting QSSW. We determine (analytically, numerically and experimentally) the critical transverse velocity for elastic collision to be observed, when the fundamental frequency component of the two interacting beams are orthogonally polarized at the input face of the non-linear crystal.     

Interaction between light and crystallizing polymer: a simulation study

A study of light transmission through a crystallizing polymer has been carried out by graphic simulations, consisting of sporadic and pre-determinate nucleation and growth of disks (spherulites) in a rectangular area. Interaction between a light beam crossing a sample of polymer has been described by a series of simple graphical rules, accounting for both absorption and scattering. Results of the code well reproduce the experimental behavior observed in the literature of main beam light intensity emerging from a crystallizing polymer sample and allows a better understanding of the interaction between light and nucleating/growing units. Emerging light behavior calculated by the simulation has been adopted as the basis to suggest the dependence of the light scattering coefficient upon crystallization kinetic parameters.     

Nonspecular total internal reflection of spatial solitons at the interface between highly birefringent media

We investigate total internal reflection of nonlocal spatial optical solitons at the interface between two differently oriented regions of a highly birefringent nematic liquid crystal. The solitons survive the interaction with an induced index mismatch and undergo nonspecular reflection, with an emerging angle differing appreciably from the incidence angle.     

Affine representations of $${\ell}$$-groups and MV-algebras

Affine representations for archimedean \({\ell}\)-groups and semisimple MV-algebras via embedding theorems are presented; they are simple to work with but powerful enough to express significant properties of our studied objects. Indeed, we focus on the space of particular homomorphisms between an archimedean \({\ell}\)-group (a semisimple MV-algebra, respectively) and a vector lattice (a Riesz MV-algebra, respectively), i.e., the set of the generalized states, providing a general framework.     

Probable collapse mechanisms in indefinite plates on an elastoplastic continuum

Summary With reference to a theory expounded in a previous note [2] on the limit state behaviour of plates resting on an elastoplastic continuum subject to distributed loads, probable collapse mechanisms are considered in order to supplying more tractable solutions for technical practice. As the case is a general one, it is shown that the results obtained are suitable for following the load carrying capacity of plates and the relative collapse mechanism as the limit resistance of the soil and the spread of the load acting on it vary.Some examples are worked out to illustrate the applicational procedure.

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Sommario Con riferimento ad una teoria esposta in una nota precedente [2] sul comportamento allo stato limite delle piastre su mezzo elasto-plastico continuo soggette a carichi diffusi, si esaminano delle schematizzazioni di probabile collasso allo scopo di fornire soluzioni di più facile impiego nel campo della pratica tecnica.Trattando quindi un caso di carattere generale, si mostra come i risultati ottenuti si prestano ad essere utilizzati per seguire la capacità portante della piastra ed il relativo meccanismo di collasso al variare della resistenza limite del suolo e della estensione del carico su di essa agente.Alla fine, a chiarimento del procedimento applicativo, si sviluppano alcuni esempi.

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This work was supported by CNR (Italian Research Council).     

The inorganic perspective of nerve growth factor: interactions of Cu2+ and Zn2+ with the N-terminus fragment of nerve growth factor encompassing the recognition domain of the TrkA receptor

There is a significant overlap between brain areas with Zn(2+) and Cu(2+) pathological dys-homeostasis and those in which the nerve growth factor (NGF) performs its biological role. The protein NGF is necessary for the development and maintenance of the sympathetic and sensory nervous systems. Its flexible N-terminal region has been shown to be a critical domain for TrkA receptor binding and activation. Computational analyses show that Zn(2+) and Cu(2+) form pentacoordinate complexes involving both the His4 and His8 residues of the N-terminal domain of one monomeric unit and the His84 and Asp105 residues of the other monomeric unit of the NGF active dimer. To date, neither experimental data on the coordination features have been reported, nor has one of the hypotheses according to which Zn(2+) and Cu(2+) may have different binding environments or the Ser1 α-amino group could be involved in coordination been supported. The peptide fragment, encompassing the 1-14 sequence of the human NGF amino-terminal domain (NGF(1-14)), blocked at the C terminus, was synthesised and its Cu(2+) and Zn(2+) complexes characterized by means of potentiometric and spectroscopic (UV/Vis, CD, NMR, and EPR) techniques. The N-terminus-acetylated form of NGF(1-14) was also investigated to evaluate the involvement of the Ser1 α-amino group in metal-ion coordination. Our results demonstrate that the amino group is the first anchoring site for Cu(2+) and is involved in Zn(2+) coordination at physiological pH. Finally, a synergic proliferative activity of both NGF(1-14) and the whole protein on SHSY5Y neuroblastoma cell line was found after treatment in the presence of Cu(2+). This effect was not observed after treatment with the N-acetylated peptide fragment, demonstrating a functional involvement of the N-terminal amino group in metal binding and peptide activity.