Homoclinics and chaotic behaviour for perturbed second order systems

This paper deals with perturbed dynamical systems of the form: $ - \ddot u + u = \nabla V\left( u \right) + \varepsilon \nabla _u W\left( {t,u} \right)$ where u(t)∈Rⁿ(n?1). By means of a variational approach the existence of multibump homoclinics is proved under general assumptions on the Melnikov function. As a particular case, if (W; u) is T-periodic, the existence of approximate and complete Bernoulli shift structures is proved. An application to partial differential equations is also given.     

Electrochemical deposition and structural characterization of Au-Sn alloys

In the present work the electrochemical deposition of Au-Sn alloys is addressed and a cyanide-free process is presented. The electrolyte is an acidic thiourea solution containing gold as a Au[CS(NH₂)₂]⁺ complex and tin as stannous ions. Results concerning the plating process development and deposit characterization are reported. Au-Sn alloy films with a Sn content up to 50 at% and a single-phase structure can be obtained from the acidic thiourea–Au(I) solution under pulsed current plating conditions. Alloy deposits show three main crystal structures: a face centred cubic (fcc) Au(Sn) solid solution, extending up to 7 at% Sn; a hexagonal close-packed structure, of the same type as the metallurgical phase, up to about 18 at% Sn; and a NiAs-type structure, corresponding to the phase of the equilibrium diagram, with an enlarged homogeneity range. Mechanical properties of thin layers of Au-Sn alloys derived from micro-indentation measurements follow the structural modification with the alloy composition. The ordered intermetallic phases occurring in the equilibrium binary system, in particular the and phases at 8 at% and 16 at% Sn, respectively, are not detected in the electrodeposited alloys. The main factors controlling electrochemical phase formation are pointed out, considering the differences between the phase structure of the electrodeposited alloys and the equilibrium phase diagram.Presented at the 3rd International Symposium on Electrochemical Processing of Tailored Materials held at the 53rd Annual Meeting of the International Society of Electrochemistry, 15–20 September 2002, Düsseldorf, Germany     

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.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cantor families of periodic solutions for wave equations via a variational principle

We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities.     

Pedestrian flows and non‐classical shocks

We present a model for the flow of pedestrians that describes features typical of this flow, such as the fall due to panic in the outflow of people through a door. The mathematical techniques essentially depend on the use of non‐classical shocks in scalar conservation laws. Copyright © 2005 John Wiley & Sons, Ltd.     

Reaction diastereoselectivity of chiral aminoalcohols/[Co(II)NO3]+ complexes in evaporating ESI nanodroplets: new insights from a joint experimental and computational investigation

The nature of the ionic species, formed by electrospray ionization (ESI) of Co(NO₃)₂/CH₃OH solutions with a pair of aminoalcohols W and Y, has been investigated by mass spectrometric and computational methods. Collision induced dissociation (CID) of ions, formally corresponding to the [WYCoNO₃]⁺ structures, yields fragmentation patterns which reflect not only the expected [WYCoNO₃]⁺ connectivity but also that of other isomeric structures. Formation of these latter species is observed only in the presence of a tertiary aminoalcohol, like N‐methylpseudoephedrine. The CID patterns are found to be strongly dependent on the chemical form (whether the free aminoalcohol or its hydrochloride), the configuration, and the relative concentration of the W and Y aminoalcohols. This variability parallels the results of classical MD (molecular dynamics) simulations of the [WYCoNO₃]⁺ adducts which show a drastic alteration of the mechanical–dynamical features of the adducts by simply changing the charge state of W and/or Y, their absolute configuration, or by removing the solvent. The present experimental and computational study confirms the observation of fast stereoselective reactions in ESI nanodroplets before their evaporation and warns against any automatic correlation between the ESI spectrum of an analyte and its structure in solution. Copyright © 2009 John Wiley & Sons, Ltd.