Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Links in a thickened surface

For a given two-dimensional surface μ, we studi invariants for oriented links in μ×[0,1] which generalize the two-variable HOMFLY polynomials when μ is the 2-disk. These invariants are connected to multiparameter quantum groups whose special properties are discussed. Si studiano gli invarianti dei nodi in spazi del tipo μ×[0,1], dove μ è una superficie. Questi invarianti generalizzano gli invarianti di HOMFLY.

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(Conferenza tenuta dal Prof. P. Cotta-Ramusino il 16 maggio 1991)     

An optical bridge reflectometer for sensitive measurement of ion implantation dose

An instrument is described that can be used to monitor, with unprecedented sensitivity, changes in the optical reflectivity due to crystailine damage incurred during ion implantation. It is shown that at the shot-noise limit, changes in the optical reflectivity of silicon as small as 5·10^–7 can be measured in a 10 Hz bandwidth with a signal-to-noise ratio of 100, corresponding to an extrapolated uniform implantation dose of 5·10⁸ cm^–2 for ¹¹B⁺ at 50 keV in silicon.     

2D Ising Model with Layers of Quenched Spins

The model considered is a d=2 disordered Ising system on a square lattice with nearest neighbor interaction. The disorder is induced by layers (rows) of spins, randomly located, which are frozen in an antiferromagnetic order. It is assumed that all the vertical couplings take the same positive value J _v, while all the horizontal couplings take the same positive value J _h. The model can be exactly solved and the free energy is given as a simple explicit expression. The zero-temperature entropy can be positive because of the frustration due to the competition between antiferromagnetic alignment induced by the quenched layers and ferromagnetic alignment due to the positive couplings. No phase transition is found at finite temperature if the layers of frozen spins are independently distributed, while for correlated disorder one finds a low-temperature phase with some glassy properties.     

FLUORESCENCE OF Euglena gracilis PHOTORECEPTOR PIGMENT: AN in vivo MICROSPECTROFLUOROMETRIC STUDY

Abstract— The spectroscopic characterization of the photoreceptor pigment is one of the main questions in the study of the photosensory transduction chains in photomotile microorganisms. One of the possible techniques that can be used is in vivo microspectrofluorometry. By means of a tunable dye-laser microspectrofiuorometer developed by us, we have investigated some of the spectroscopic properties of the photoreceptor pigment of the green flagellate Euglena gracilis. The in vivo fluorescence excitation spectrum has been determined and the fluorescence quantum yield has been measured. The results show that flavins are indeed present in the paraflagellar body of E. gracilis and that their fluorescence quantum yield is much lower than that of a free flavin. An estimate of the order of magnitude of the rate constants for primary molecular reactions is tentatively given.