Rigorous Generalization of Young's Law for Heterogeneous and Rough Substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameters.     

Photochromic reverse mode polymer dispersed liquid crystals

Control of light intensity and colour are two of the major features required in the realization of smart windows. We designed a bi-functional polymer dispersed liquid crystal (PDLC) film in order to satisfy such requirements, i.e. it is able both to modulate the optical transmission, if an external electric field is applied, and to change colour if exposed to sunlight. A monomer/liquid crystal mixture was doped with a small amount of photochromic material and homeotropically aligned by means of rough surfaces. A transparent and pale pink coloured film was achieved after photopolymerization. Such a film changes colour upon exposure for some seconds to sunlight or ultraviolet radiation in a persistent but reversible manner. In addition, the film appears transparent without the application of an electric field (OFF state) and becomes opaque on application of a driving voltage of about 75 V (ON state), and thus the film operates in reverse mode with respect to conventional PDLCs.     

Some classes of non general type codimension two subvarieties inP n

We classify smooth subvarieties of codimension twoX⊂P ⁿ , 4≤n≤5, which are arithmetically Cohen-Macaulay and of non general type. By the way we exhibit some classes of non extendable subvarieties. Then we give new proofs of the classification of scrolls inP ⁴; finally we consider smooth surfaces of non general type inP ⁴ arising from rank three vector bundles.

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Sunto Classifichiamo le sottovarietà lisce di codimensione dueX⊂P ⁿ , 4≤n≤5, aritmeticamente Cohen-Macaulay e non di tipo generale. Nel contempo descriviamo alcune classi di sottovarietà non estendibili. Diamo poi due nuove dimostrazioni della classificazione degli scrolls inP ⁴; infine consideriamo superfici lisce inP ⁴, non di tipo generale, associate a fibrati di rango tre.

     

Mechanosynthesis of YIG and GdIG: A Structural and Mössbauer Study

We have investigated the mechanosynthesis of gadolinium and yttrium iron garnets by high-energy ball-milling of α-Fe₂O₃ and Gd₂O₃ or α-Fe₂O₃ and Y₂O₃, respectively, followed by short thermal annealings conducted at moderate temperatures. The samples were characterized by X-ray diffraction and Mössbauer spectroscopy, in order to determine the influence of the milling time and annealing conditions on the final products. For as-milled samples of each rare-earth system, the results revealed the formation of perovskite phases, in relative amounts that depend on the milling time. The formation of garnet phases was observed in as-annealed samples treated at 1000°C for 2 h or 1100°C for 3 h, i.e., at very modest annealing requirements when compared with ordinary solid-state-reaction processes performed without previous high-energy milling. Also, the occurrence was verified of a milling time for which the relative amount of garnet phases formed by annealing was maximized. This time depends on the rare-earth composing the garnet phase and on the annealing temperature.     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001