As the generalized stability theory has demonstrated, linear stability produces misleading predictions for the response of nonlinear systems to small but non-infinitesimal noise when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is generally found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find however that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition.

Jens H.M. Fransson, Alessandro Talamelli, Luca Brandt, Carlo Cossu. Reducing skin friction is important in nature and in many technological applications. This reduction may be achieved by reducing stresses in turbulent boundary layers, for instance tailoring biomimetic rough skins. Here we take a second approach consisting in keeping the boundary layer laminar as long as possible by forcing small optimal perturbations. Due to the highly non-normal nature of the underlying linearized operator, these perturbations are highly amplified and able to modify the mean velocity profiles at leading order. We report results of wind-tunnel experiments in which we implement this concept by using suitably designed roughness elements placed on the skin to enforce nearly optimal perturbations. We show that using this passive control technique it is possible to sensibly delay transition to turbulence. PRL 96, 064501 (2006)

Authors: A. Grabowski and R. A. Kosiski We present a simple deterministic and based on local rules model of evolving social network, which leads to a network with the properties of a real social system, e.g., small-world topology and assortative mixing. The state of an individual S_{i} is characterized by the values of Q cultural feat... [Phys. Rev. E 73, 016135] Published Fri Jan 27, 2006

Authors: Wei Li, Li Xi, Michael D. Graham Comments: 17 Pages, 4 figures, Submitted to Journal of Fluid Mechanics Subj-class: Fluid Dynamics; Chaotic Dynamics Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect of polymer additives on these "exact coherent states" (ECS), in the plane Poiseuille geometry. Many key aspects of the turbulent drag reduction phenomenon are found, including: delay in transition to turbulence; drag reduction onset threshold; diameter and concentration effects. Furthermore, examination of the ECS existence region leads to a distinct prediction, consistent with experiments, regarding the nature of the maximum drag reduction regime. Specifically, at sufficiently high wall shear rates, viscoelasticity is found to completely suppress the normal (i.e. streamwise-vortex-dominated) dynamics of the near wall region, indicating that the maximum drag reduction regime is dominated by a distinct class of flow structures.

Authors: Ronald Suryo and Osman A. Basaran. In zero gravity, liquid does not drip from a tube but hangs from it for all time as a pendant drop. It is shown that a drop can be made to fall off a tube by heating the contact line (CL), which causes a temperature gradient between the drop's CL and its tip.

Authors: Romain Bachelard (CPT), Cristel Chandre (CPT), Xavier Leoncini (CPT, PIIM). A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.