Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Evaluating the performance of external fault ridethrough solutions used in wind farms with fixed speed induction generators when facing unbalanced faults

Na sequência da integração da energia eólica em larga escala foram estabelecidos códigos de rede pelos vários operadores de sistema, exigindo que os parques eólicos permaneçam em serviço durante e após a ocorrência de defeitos na rede a montante. Nos parques eólicos equipados com sistemas de velocidade constante este requisito pode ser assegurado pela instalação, no ponto de interligação à rede, de equipamento de compensação dinâmica de potência reactiva, controlado como fonte de tensão, sendo as funções de controlo baseadas em medidas efectuadas no ponto de interligação relativamente às componentes directas da tensão e da corrente. Como a adopção deste tipo de soluções externas é adequada ao funcionamento do sistema em regime equilibrado, este artigo foca a avaliação do desempenho da solução no caso da ocorrência de defeitos assimétricos. Os resultados obtidos através das simulações dinâmicas evidenciam o aparecimento de sobre tensões nas fases não afectadas pelo defeito que poderão colocar o parque eólico fora de serviço.

Aviation solutions

Overview Some of the Challenges - Future Technology - Capacity - Safety Working with Airports, Air Traffic Service Providers and Airlines The Role of the Regulator Air Traffic Service Providers

Technological Solutions Potentially Influencing the Future of Long-Term Care. ENEPRI Research Report No. 114, April 2012

This report provides a forecast of the potential direct and indirect influences of various kinds of technologies on the LTC milieu, answering the following question: from a technology-driven perspective: “Consider each technological solution. What could be its future usage in the LTC sector?” Future technological deployments will induce changes in the respective roles of the care recipient and of the formal and informal carers, with an impact on three major concerns: the transformation of the care recipient into a proactive subject, the augmented potentiality for home care and the new functions that informal carers could assume.

The euro crisis: ten roots, but fewer solutions. Bruegel Policy Contribution 2012/17, October 2012

Many factors have contributed to the euro crisis. Some have been addressed by policymakers, even if belatedly, and European Union member states have been willing to improve the functioning of the euro area by agreeing to relinquish national sovereignty in some important areas. However, the most pressing issue threatening the integrity, even the existence, of the euro, has not been addressed: the deepening economic contraction in southern euro-area member states. The common interest lies in preserving the integrity of the euro area and in offering these countries improved prospects. Domestic structural reform and appropriate fiscal consolidation, wage increases and slower fiscal consolidation in economically stronger euro-area countries, a weaker euro exchange rate, debt restructuring and an investment programme should be part of the arsenal. In the medium term, more institutional change will be necessary to complement the planned overhaul of the euro area institutional framework. This will include the deployment of a euro-area economic stabilising tool, managing the overall fiscal stance of the euro area, some form of Eurobonds and measures to make euro-area level decision making bodies more effective and democratically legitimate.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.