Low frequency noise controls on-off intermittency of bifurcating systems

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative expansion and numerical studies of the probability density function of the unstable mode, we show that intermittency is controlled by the ratio between the departure from onset and the value of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the intermittency regime drastically. This effect also modifies the distribution of the duration that the system spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed

Stability of a nonlinear oscillator with random damping

A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be predicted from the analysis of the moments of the linearized equation. In the case of a white noise, an exact formula for the Lyapunov exponent of the system is derived. We then calculate the critical damping for which the {\em nonlinear} system becomes unstable. We also characterize the intermittent structure of the bifurcated state above threshold and address the effect of temporal correlations of the noise by considering an Ornstein-Uhlenbeck noise

From the SGP to the TSCG through the lenses of European integration theories. Bruges Political Research Papers 67/2018

The Euro crisis has been the biggest shock European economy has been through since the beginning of European integration. It made apparent a series of structural imbalances and failures in the design of the Economic and Monetary Union (EMU), putting into question its own nature and survival. In spite of the doubts that emerged, the response to the crisis eventually led to a deepening of economic integration within the EU. Which were the driving forces and key actors of this deepening in integration? This paper focuses on the strengthening of the fiscal and economic pillars of EMU, using three theories of European integration: Neofunctionalism, Liberal Intergovernmentalism and New Intergovernmentalism. The paper argues that the deepening of integration can be theorized as the result of asymmetrical interdependence and differences in bargaining power among member states, which decide to give up national sovereignty as a tool for reaching credible commitments

Wrinkling in the deflation of elastic bubbles

The protein hydrophobin HFBII self-assembles into very elastic films at the surface of water; these films wrinkle readily upon compression. We demonstrate and study this wrinkling instability in the context of non-planar interfaces by forming HFBII layers at the surface of bubbles; the interfaces are then compressed by deflating the bubble. By varying the initial concentration of the hydrophobin solutions, we are able to show that buckling occurs at a critical packing fraction of protein molecules on the surface. Independent experiments show that at this packing fraction the interface has a finite positive surface tension, and not zero surface tension as is usually assumed at buckling. We attribute this non-zero wrinkling tension to the finite elasticity of these interfaces. We develop a simple geometrical model for the evolution of the wrinkle length with further deflation, and show that wrinkles start close to the needle used for deflation and grow rapidly towards the mid-plane of the bubble. This geometrical model yields predictions for the length of wrinkles in good agreement with experiments, independently of the rheological properties of the adsorbed layer

Elastometry of deflated capsules elastic moduli from shape and wrinkle analysis

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We illustrate this method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having\ud a rigid core surrounded by a softer shell

Photochemical synthesis of p-extended ullazine derivatives as new electron donor for efficient conjugated D–A polymers

We report the synthesis of π-extended ullazine derivatives annulated with either electron-poor pyridine or electron-rich thiophene units through a metal-free, photochemical cyclodehydrochlorination (CDHC) reaction. The strongest electron-donor derivative, 7-tetradecylthieno[3′,2′:7,8]indolizino[6,5,4,3-ija]thieno[2,3-c]quinolone, was copolymerized with electron-deficient thienopyrroledione (TPD), isoindigo (IID), and diketopyrrolopyrrole (DPP) derivatives to provide three donor–acceptor conjugated polymers (D–A CPs). Their photophysical, electrochemical and photovoltaic (PV) properties were investigated. The polymers showed broad UV-vis-NIR absorption bands with λmax values of 612 nm, 698 nm, 788 nm in chloroform and exhibited optical bandgap (Eoptg) of 1.58 eV, 1.41 eV, 1.24 eV measured as films. Inverted bulk heterojunction polymer solar cells (BHJ-PSCs) were fabricated using these polymers as host and light-harvesting materials. The device based on P3:PC70BM blends shows the best power conversion efficiency (PCE) of 2.23% (Voc = 0.55 V, Jsc = 7.86 mA cm−2, FF = 52%). These promising results demonstrate that π-extended ullazine derivatives can be used as electron-rich building blocks for the construction of D–A CPs for efficient PSCs applications