Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a {\it flat parabolic resonance}, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with {\it small} (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed

Tecno-especies: la humanidad que se hace a sí misma y los desechables

Popular culture continues fuelling public imagination with things, human and non-human, that we might beco-me or confront. Besides robots, other significant tropes in popular fiction that generated images include non-human humans and cyborgs, wired into his-torically varying sociocultural realities. Robots and artificial intelligence are re-defining the natural order and its hierar-chical structure. This is not surprising, as natural order is always in flux, shaped by new scientific discoveries, especially the reading of the genetic code, that reveal and redefine relationships between life forms. However, for the first time, a new, artificial, species is being introduced into the existing diagrams, and, for the first time, it appears to hybridise the anthro-pocentric natural world order

Homoclinic orbits and chaos in a second-harmonic generating optical cavity

We present two large families of Silnikov-type homoclinic orbits in a two mode-model that describes second-harmonic generation in a passive optical cavity. These families of homoclinic orbits give rise to chaotic dynamics in the model. 4 refs., 1 fig

Arene oxidation with malonoyl peroxides

Malonoyl peroxide 7, prepared in a single step from the commercially available diacid, is an effective reagent for the oxidation of aromatics. Reaction of an arene with peroxide 7 at room temperature leads to the corresponding protected phenol which can be unmasked by aminolysis. An ionic mechanism consistent with the experimental findings and supported by isotopic labeling, Hammett analysis, EPR investigations and reactivity profile studies is proposed

Non integrability of a self-gravitating Riemann liquid ellipsoid

We prove that the motion of a triaxial Riemann ellipsoid of homogeneous liquid without angular momentum does not possess an additional first integral which is meromorphic in position, impulsions, and the elliptic functions which appear in the potential, and thus is not integrable. We prove moreover that this system is not integrable even on a fixed energy level hypersurface.Comment: 14 pages, 8 reference

On the dynamics of a nonlinear energy harvester with multiple resonant zones

The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is modelled as a Duffing oscillator with linear frequency variation under static, as well as harmonic excitation. Behaviour charts and backbone curves are extracted for the fundamental harmonic response and validated against frequency response curves for selected cases, using direct numerical integration. It is found that variation in stiffness, together with asymmetric forcing, gives rise to a novel structure of multiple resonant zones, incorporating mono-stable and bi-stable dynamics. Contrary to previously considered bi-stable energy harvesters, cross-well oscillations are realized through a transition from single-well potential energy to double-well with forward frequency sweep. Furthermore, in-well_oscillations present a hardening behaviour, unlike the well-known softening in-well response of bi-stable Duffing oscillators. The analysis shows that the proposed system has multiple resonant responses to a frequency sweep, influenced by consecutive interacting backbone curves similar to a multi-modal system. This combined effect of the transition to bi-stable dynamics and the hardening in-well oscillations induces resonant response of the harvester over multiple distinct frequency ranges. Thus, the system exhibits a broadened frequency response, enhancing its energy harvesting potential

Tsetse control and Gambian sleeping sickness ; implications for control strategy

Background Gambian sleeping sickness (human African trypanosomiasis, HAT) outbreaks are brought under control by case detection and treatment although it is recognised that this typically only reaches about 75% of the population. Vector control is capable of completely interrupting HAT transmission but is not used because it is considered too expensive and difficult to organise in resource-poor settings. We conducted a full scale field trial of a refined vector control technology to determine its utility in control of Gambian HAT. Methods and Findings The major vector of Gambian HAT is the tsetse fly Glossina fuscipes which lives in the humid zone immediately adjacent to water bodies. From a series of preliminary trials we determined the number of tiny targets required to reduce G. fuscipes populations by more than 90%. Using these data for model calibration we predicted we needed a target density of 20 per linear km of river in riverine savannah to achieve >90% tsetse control. We then carried out a full scale, 500 km(2) field trial covering two HAT foci in Northern Uganda to determine the efficacy of tiny targets (overall target density 5.7/km(2)). In 12 months, tsetse populations declined by more than 90%. As a guide we used a published HAT transmission model and calculated that a 72% reduction in tsetse population is required to stop transmission in those settings. Interpretation The Ugandan census suggests population density in the HAT foci is approximately 500 per km2. The estimated cost for a single round of active case detection (excluding treatment), covering 80% of the population, is US$433,333 (WHO figures). One year of vector control organised within the country, which can completely stop HAT transmission, would cost US$42,700. The case for adding this method of vector control to case detection and treatment is strong. We outline how such a component could be organised

The Global Dominance of European Competition Law Over American Antitrust Law

The world’s biggest consumer markets – the European Union and the United States – have adopted different approaches to regulating competition. This has not only put the EU and US at odds in high-profile investigations of anticompetitive conduct, but also made them race to spread their regulatory models. Using a novel dataset of competition statutes, we investigate this race to influence the world’s regulatory landscape and find that the EU’s competition laws have been more widely emulated than the US’s competition laws. We then argue that both “push” and “pull” factors explain the appeal of the EU’s competition regime: the EU actively promotes its model through preferential trade agreements and has an administrative template that is easy to emulate. As EU and US regulators offer competing regulatory models in domains as diverse as privacy, finance, and environmental protection, our study sheds light on how global regulatory races are fought and won