On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

Separation of Variables for Bi-Hamiltonian Systems

We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand–Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.     

Iron–cobalt nanocrystalline alloy supported on a cubic mesostructured silica matrix: FeCo/SBA-16 porous nanocomposites

A series of novel nanocomposites constituted of FeCo nanoparticles dispersed in an ordered cubic Im3m mesoporous silica matrix (SBA-16) have been successfully synthesized using the wet impregnation method. SBA-16, prepared using the non-ionic Pluronic 127 triblock copolymer as a structure-directing agent, is an excellent support for catalytic nanoparticles because of its peculiar three-dimensional cage-like structure, high surface area, thick walls, and high thermal stability. Low-angle X-ray diffraction, N₂ physisorption, and transmission electron microscopy analyses show that after metal loading, calcination at 500 °C, and reduction in H₂ flux at 800 °C, the nanocomposites retain the well-ordered structure of the matrix with cubic symmetry of pores. FeCo alloy nanoparticles with spherical shape and narrow size distribution (4–8 nm) are homogeneoulsy distributed throughout the matrix and they seem in a large extent to be allocated inside the pores.     

Poisson pencils, algebraic integrability, and separation of variables

In this paper we review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the bihamiltonian structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.     

Dipolar Rotors Orderly Aligned in Mesoporous Fluorinated Organosilica Architectures

New mesoporous covalent frameworks, based on hybrid fluorinated organosilicas, were prepared to realize a periodic architecture of fast molecular rotors containing dynamic dipoles in their structure. The mobile elements, designed on the basis of fluorinated p‐divinylbenzene moieties, were integrated into the robust covalent structure through siloxane bonds, and showed not only the rapid dynamics of the aromatic rings (ca. 10⁸ Hz at 325 K), as detected by solid‐state NMR spectroscopy, but also a dielectric response typical of a fast dipole reorientation under the stimuli of an applied electric field. Furthermore, the mesochannels are open and accessible to diffusing in gas molecules, and rotor mobility could be individually regulated by I₂ vapors. The iodine enters the channels of the periodic structure and reacts with the pivotal double bonds of the divinyl‐fluoro‐phenylene rotors, affecting their motion and the dielectric properties.     

Reversible tunability of the near-infrared valence band plasmon resonance in Cu(2-x)Se nanocrystals

We demonstrate that colloidal Cu(2-x)Se nanocrystals exhibit a well-defined infrared absorption band due to the excitation of positive charge carrier oscillations (i.e., a valence band plasmon mode), which can be tuned reversibly in width and position by varying the copper stoichiometry. The value of x could be incrementally varied from 0 (no plasmon absorption, then a broad peak at 1700 nm) to 0.4 (narrow plasmon band at 1100 nm) by oxidizing Cu(2)Se nanocrystals (upon exposure either to oxygen or to a Ce(IV) complex), and it could be incrementally restored back to zero by the addition of a Cu(I) complex. The experimentally observed plasmonic behavior is in good agreement with calculations based on the electrostatic approximation.     

CoFe2O4 nanocrystalline powders prepared by citrate-gel methods: Synthesis, structure and magnetic properties

Nanocrystalline CoFe₂O₄ powders were prepared by decomposition of metal ion citrate precursors. Four samples were synthesized from precursor solutions having different pH values in the range <1–7.0. The powders were characterized by X-ray Diffraction, Thermogravimetry, Differential Thermal Analysis, N₂ physisorption and Transmission Electron Microscopy. Magnetic properties were explored by a SQUID magnetometer. Three out of the four samples, coming from solutions of pH 2, 4 and 7, were produced by an autocombustion reaction and are very similar as regards average size of the nanoparticles (about 20 nm), their morphology and the magnetic properties, while the fourth sample was produced by a slower thermal decomposition and is composed of smaller nanoparticles (about 10 nm).     

Magnetic pH-responsive nanogels as multifunctional delivery tools for small interfering RNA (siRNA) molecules and iron oxide nanoparticles (IONPs)

We here exploit pH-responsive nanogels as carriers to deliver functional anti-GFP siRNA and superparamagnetic IONPs to HeLa-GFP cells. The siRNA release via pH-mediated endosomal escape is shown. The IONPs act first as magnetofection agents to boost cellular uptake and then as probes to track the release mechanism by electron microscopy.