On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

The Akhmediev breather is unstable

In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in Muñoz (Proyecciones (Antofagasta) 36(4):653–683, 2017), in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space

Commons Organizing: Embedding Common Good and Institutions for Collective Action. Insights from Ethics and Economics

In recent years, business ethics and economic scholars have been paying greater attention to the development of commons organizing. The latter refers to the processes by which communities of people work in common in the pursuit of the common good. In turn, this promotes commons organizational designs based on collective forms of common goods production, distribution, management and ownership. In this paper, we build on two main literature streams: (1) the ethical approach based on the theory of the common good of the frm in virtue ethics and (2) the economic approach based on the theory of institutions for collective action developed by Ostrom’s research on common-pool resources to avert the tragedy of the commons. The latter expands to include the novel concepts of new commons, “commoning” and polycentric governance. Drawing on the analysis of what is new in these forms of organizing, we propose a comprehensive model, highlighting the integration of two sets of organizing principles—common good and collective action – and fve problem-solving processes to explain the main dimensions of commons organizing. We contribute to business ethics literature by exploring the convergence between the ethical and economic approaches in the development of a commons organizing view

Review on the Stability of the Peregrine and Related Breathers

In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned

Small-Molecule Photostabilizing Agents are Modifiers of Lipid Bilayer Properties

AbstractSmall-molecule photostabilizing or protective agents (PAs) provide essential support for the stability demands on fluorescent dyes in single-molecule spectroscopy and fluorescence microscopy. These agents are employed also in studies of cell membranes and model systems mimicking lipid bilayer environments, but there is little information about their possible effects on membrane structure and physical properties. Given the impact of amphipathic small molecules on bilayer properties such as elasticity and intrinsic curvature, we investigated the effects of six commonly used PAs—cyclooctatetraene (COT), para-nitrobenzyl alcohol (NBA), Trolox (TX), 1,4-diazabicyclo[2.2.2]octane (DABCO), para-nitrobenzoic acid (pNBA), and n-propyl gallate (nPG)—on bilayer properties using a gramicidin A (gA)-based fluorescence quench assay to probe for PA-induced changes in the gramicidin monomer↔dimer equilibrium. The experiments were done using fluorophore-loaded large unilamellar vesicles that had been doped with gA, and changes in the gA monomer↔dimer equilibrium were assayed using a gA channel-permeable fluorescence quencher (Tl+). Changes in bilayer properties caused by, e.g., PA adsorption at the bilayer/solution interface that alter the equilibrium constant for gA channel formation, and thus the number of conducting gA channels in the large unilamellar vesicle membrane, will be detectable as changes in the rate of Tl+ influx—the fluorescence quench rate. Over the experimentally relevant millimolar concentration range, TX, NBA, and pNBA, caused comparable increases in gA channel activity. COT, also in the millimolar range, caused a slight decrease in gA channel activity. nPG increased channel activity at submillimolar concentrations. DABCO did not alter gA activity. Five of the six tested PAs thus alter lipid bilayer properties at experimentally relevant concentrations, which becomes important for the design and analysis of fluorescence studies in cells and model membrane systems. We therefore tested combinations of COT, NBA, and TX; the combinations altered the fluorescence quench rate less than would be predicted assuming their effects on bilayer properties were additive. The combination of equimolar concentrations of COT and NBA caused minimal changes in the fluorescence quench rate

Path and trajectory planning of a tethered UAV-UGV marsupial robotics system

This paper addresses the problem of trajectory planning in a marsupial robotic system consisting of an unmanned aerial vehicle (UAV) linked to an unmanned ground vehicle (UGV) through a non-taut tether that has a controllable length. The objective is to determine a synchronized collision-free trajectory for the three marsupial system agents: UAV, UGV, and tether. First, we present a path planning solution based on optimal Rapidly exploring Random Trees (RRT*) that takes into account constraints related to the positions of UAV, UGV, tether and the 3D environment. The specialization of the main RRT* methods allows us to obtain feasible solutions in short times. Then, the paper presents a trajectory planner based on non-linear least squares. The optimizer takes into account aspects not considered in the path planning, like temporal constraints of the motion that impose limits on the velocities and accelerations of the robots. Results from simulated scenarios demonstrate that the approach is able to generate obstacle-free and smooth trajectories for the UAV, UGV, and tether.Comment: 8 pages, 4 figures, 2 table

Plasmonics Devoted to Photocatalytic Applications in Liquid, Gas, and Biological Environments

Plasmonic nanomaterials have emerged in the last years as a very interesting option for many photocatalytic processes. Their localized surface plasmon resonance (LSPR) brings in some unique properties that overcome some of the drawbacks associated with traditional photocatalysis based on semiconductors. Even when in its infancy, many advances have been made in the field, mainly related to the synthesis of new structures with the capabilities of light absorption in the whole solar spectrum. A great number of reactions have been attempted using nanoplasmonic materials. In this chapter, we present the most recent advances made in the field of plasmonic photocatalysis comprising an introductory section to define the main types of plasmonic nanomaterials available, including the most recently labeled alternatives. Following with the major areas of catalytic application, a second section of the chapter has been devoted to liquid-phase reactions for the treatment of pollutants and a selection of organic reactions to render added-value to chemicals under mild conditions. The third part of the chapter addresses two specific applications of nanoplasmonic photocatalysts in gas-phase reactions involving the remediation of volatile organic compounds and the transformation of carbon dioxide into valuable energy-related chemicals. Finally, a fourth section of the chapter introduces the most recent applications of plasmonics in biochemical processes involving the regulation of cofactor molecules and their mimetic behavior as potential enzyme-like surrogates

Concentration of trace elements in raw milk from cows in the southeast of Córdoba province, Argentina

International audienceAbstractIn recent years, trace elements in cow milk have been considered good bioindicators of pollution in the agricultural environment. The aim of the study was to analyze the correlation between trace element content in livestock drinking water and cow milk from dairy farms located in the southeast of Córdoba province, Argentina. Groundwater is the main source of livestock drinking water. According to the results, trace elements were grouped in three categories: (a) those that were in high concentration in phreatic water and in low concentration in deep wells (As, V); (b) those which showed the opposite trend (Cu, Fe, Mn, Zn); and (c) those that were in very low concentrations in all water samples (Cd, Cr, Ni, Pb, and Se). In elements from group (a), a positive correlation between As content in water and in milk was observed. For elements included in group (b), it was observed a higher concentration in milk samples from farms that use deep wells, related with their higher concentrations in water. Cr, Ni, Pb, and Se milk contents are within the ranges reported in other areas. Soil and forage trace element content may contribute to their presence in milk. Since information about transference of trace elements from environmental matrices to milk is very scarce, at national and international levels, further studies are necessary, including speciation in milk and dairy products, to guarantee food safety