The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are gS and gP, respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition gS=gP is the border between two distinctly different conditions: For gS<gP, the P events are attractors of the S events and for gS>gP they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or gP, depending on which is the parameter changed, thereby resulting in a discontinuous transition.     

Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

Sol-Gel Nanosized Semiconducting Titania-Based Powders for Thick-Film Gas Sensors

Pure, 5 at%, and 10 at% Ta- or Nb-doped TiO₂ nanosized powders were prepared by the sol-gel method. The powders heated to 400°C have the crystalline anatase structure. While the pure TiO₂ powder heated to 850°C has the rutile structure, the addition of Ta and Nb inhibited the anatase-to-rutile phase transformation at this temperature. Ta was soluble in the titania lattice up to the concentration of 10 at%, while the solubility of Nb was 5 at%. Thick films were fabricated with these powders by screen printing technology and then fired at 650°C and 850°C for 1 h. SEM observations showed that the anatase-to-rutile phase transformation induces a grain growth of about one order of magnitude for pure TiO₂. The addition of Ta and Nb is effective to keep the TiO₂ grain size at the nanometric level even at 850°C. Conductance measurements showed that a good gas response is observed only for the nanostructured titania-based films. The CO response of these materials is only slightly affected by humidity.     

Chemo- and Stereoselective Coordination of 5,6-Dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene by d8- and d6-Metal Carbonyls. Diels-Alder reactivity of Dienes Perturbed by Remote Olefin Complexation

The endocyclic double bond C(2), C(3) in 5,6-dimethylidene-7-oxabicyclo[2.2.1]-hept-2-ene ( 1 ) can he coordinated selectively on its exo-face before complexation of the exocyclic s-cis-butadiene moiety. Irradiation of Ru₃(CO)₁₂ or Os₃(CO)₁₂ in the presence of 1 gave tetracarbonyl [(1R,2R, 3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]-hept-2-ene)]ruthenium ( 6 ) or -osmium ( 8 ). Similarly, irradiation of Cr(CO)₆ or W(CO)₆ in the presence of 1 gave pentacarbonyl[(1R, 2R, 3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene)]chromium (10) or -tungsten (11) . Irradiation of complexes 6 and 11 in the presence of 1 led to further CO substitution giving bed-tricarbonyl-ae-bis[(1R,2R,3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene)]ruthenium ( 7 ) and trans-tetracarbonyl[(1R,2R,3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo-[2.2.1]hept-2-ene)]tungsten (12) , respectively. The diosmacyclobutane derivative cis-m?-[(1R,3R,3S,4S)-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hepta-2,3-diyl)]bis(tetracarbonyl-osmium) (Os-Os) (9) wa also obtained. The Diels-Alder reactivity of the exocyclic s-cis-butadiene moiety in complexs 7 and 8 was found to be significantly higher than that of the free triene 1 .     

Aromatic substitution in the complexes formed upon addition of gaseous arenium ions to proelectrophiles. A FT-ICR study

Experiments based on FT-ICR mass spectrometry provide conclusive evidence for the operation of an alternative mechanism of electrophilic aromatic substitution occurring within the complex formed upon addition of gaseous arenium ions to a variety of proelectrophiles, including alkyl halides, alcohols, epoxides, esters and diazoalkanes. The factors affecting the efficiency of the unconventional substitution are examined in the light of the kinetic results of the FT-ICR experiments.