Front propagation in chaotic and noisy reaction-diffusion systems: a discrete-time map approach

We study the front propagation in reaction-diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as t ^1/2 in the pushed case and as t ^1/4 in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes. Received 17 July 2001     

Analytical prediction and experimental validation for longitudinal control of cable oscillations

The paper summarizes the knowledge acquired from the analytical studies and the experimental implementation of a longitudinal non-collocated control strategy for the reduction of cable oscillations. The control is introduced by imposing a longitudinal action at one support based on the knowledge of transverse displacements and velocities of a few selected points. A spatially one-dimensional continuous model of a suspended cable has been used to describe the main features of the non-collocated longitudinal active control strategy. A discrete modal representation has permitted the introduction of suitable non-linear state-feedback controllers. The results have been used to derive an implementable strategy, based on direct output feedback, which preserves the main previous control features. A physical model of an actively controlled cable has been used to demonstrate the control effectiveness of the proposed strategy through a large campaign of experiments, conducted in various frequency ranges and amplitude levels including meaningful external resonance conditions. The responses predicted by the analytical model and the experimental results show good qualitative agreement with one another, in both the uncontrolled and controlled experienced cable dynamics.     

Unveiling the chemistry behind bromination of quercetin: the ‘violet chromogen’

Bromination of quercetin with N-bromosuccinimide in neutral aqueous methanol occurs surprisingly in the electron-deficient A-ring only. Deprotonation of the acidic 7-OH is a major driver of this regioselective reaction. The increase of electron density makes in fact the quercetin anion suitable for an electrophilic attack by bromine at positions 8 and 6. Several pieces of evidence (NMR spectra and H/D exchange) are presented to substantiate the mechanism advanced. Bromoquinones/quinomethides produced in excess of N-bromosuccinimide are responsible for the formation of a stable ‘violet chromogen’.     

Community repeated interaction and strategic delegation

A large population of fixed-type agents engage in exclusive pairwise relationships in a decentralized setting. At the onset, agents randomly meet in pairs under private information of individual time-invariant types. They play a voluntary contribution game. At the end of the first period, members of each pair either stay together in the second period, in which case reported information is common knowledge, or quit and meet randomly new partners, under private information of individual types. Thus, either long-term or short-term relationships may arise. We show that there are values of the parameters such that information extracted in the first period has a positive effect on social efficiency. We give an interpretation of our results in terms of advantageous delegation of decisions to uninformed agents. Finally, we consider several extensions of the model in which our results still hold.     

Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part I: Local Analysis

An experimental model of an elastic cable carrying eight concentrated masses and hanging at in-phase or out-of-phase vertically moving supports is considered. The system parameters are adjusted to approximately realize multiple 1:1 and 2:1 internal resonance conditions involving planar and nonplanar, symmetric and antisymmetric modes. Response measurements are made in various frequency ranges including meaningful external resonance conditions. A local analysis of the system response is made on the basis of numerous amplitude-frequency and amplitude-forcing plots obtained in different ranges of the control parameter space. Attention is mainly devoted to the detection of the main features of the regular motions exhibited by the system, and to the analysis of the relevant phenomena of nonlinear modal interaction, competition, and local bifurcation between planar and nonplanar regular responses. The resulting picture appears very rich and varied.     

Stability and phase transformations of the mesomorphic form of isotactic polypropylene in stereodefective polypropylene

A study of the thermodynamic stability and the related polymorphic transformations induced by thermal treatments of the mesomorphic form that crystallizes in stereodefective metallocene isotactic polypropylene (iPP) is presented. We show that the mesomorphic form of the more isotactic samples is stable at room temperature, whereas the mesomorphic form crystallizing in the more stereoirregular sample is unstable and crystallizes at room temperature in the crystalline α form. In any case, the mesomorphic form transforms during heating or by annealing at temperatures higher than 60–80 °C always in the α form, regardless of the stereoregularity, even in the case of stereoirregular samples generally crystallizing from the melt in the γ form. These data confirm the proposed model of structure of the mesomorphic form as small aggregates of chains in three-fold helical conformation packed with lateral correlations similar to the α form of iPP.     

Synthesis and characterization of sol-gel zirconium phosphate with template surfactants by different methods

Long chain trimethylammonium salts can be successfully used as guest molecules to produce mesoporous layered materials when intercalated in sol-gel zirconium phosphate, an inorganic ion-exchanger. The obtained materials are very similar independently of the chain length and the synthesis method batch (B) or direct intercalation (DI). They show a good thermal stability, and a very high interlayer distance if compared with their precursor. By the thermal characterization it can be observed that the surfactant is lost in two or three steps depending on its position in the host. The layered structure with the expanded interlayer distance is maintained up to 300°C. From the IR spectra the different surfactant release models for (B) and (DI) are confirmed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Advances in microbiology to enhance oil recovery

Applied Biochemistry and Biotechnology - Microbial experiments to study enhanced oil recovery have generally been conducted using vegetative microorganisms and one-dimensional laboratory models....