Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

alpha-Co(OH)(2)/carbon nanofoam composite as electrochemical capacitor electrode operating at 2 V in aqueous medium

In this work, alpha-Co(OH)(2) is electrodeposited onto carbon nanofoam forming a composite electrode operating in a potential window of 2 V in aqueous medium. Prior to electrodeposition, the carbon nanofoam substrate is subjected to a functionalization process, which leads to an increase of about 40% in its specific capacitance value. Formation of cobalt hydroxide clusters onto the functionalized carbon nanofoam by pulse electrodeposition further enhances the specific capacitance of the electrode. The combination of these factors with an enlarged working potential window, results in a material with specific capacitance close to 300 F g(-1) at current density of 1 A g(-1), considering the total mass loading of the composite. This suggests the potential application of the prepared composites in high energy density electrochemical supercapacitors. (c) 2015 Elsevier B.V. All rights reserved.

Carbon nanotubes as reinforcement of cellulose liquid crystalline responsive networks

The incorporation of small amount of highly anisotropic nanoparticles into liquid crystalline hydroxypropylcellulose (LC-HPC) matrix improves its response when is exposed to humidity gradients due to an anisotropic increment of order in the structure. Dispersed nanoparticles give rise to faster order/disorder transitions when exposed to moisture as it is qualitatively observed and quantified by stress-time measurements. The presence of carbon nanotubes derives in a improvement of the mechanical properties of LC-HPC thin films.