Crises in a dissipative Bouncing ball model

The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the basins of the attracting fixed points is characterized, as we vary the control parameters. Crises between the attractors and their boundaries are observed. We found that the multiple attractors are intertwined, and when the boundary crisis between their stable and unstable manifolds occur, it creates a successive mechanism of destruction for all attractors originated by the sinks. Also, an impact physical crises is setup, and it may be useful as a mechanism to reduce the number of attractors in the system

Escape through a time-dependent hole in the doubling map

We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the sides of the hole are moving in or out of phase respectively. We find out that the escape rate is well described by the overlap of the hole with its images, for holes centred at periodic orbits.Comment: 9 pages, 7 figures. To appear in Physical Review E in 201

Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard

A competition between decay and growth of energy in a time-dependent stadium billiard is discussed giving emphasis in the decay of energy mechanism. A critical resonance velocity is identified for causing of separation between ensembles of high and low energy and a statistical investigation is made using ensembles of initial conditions both above and below the resonance velocity. For high initial velocity, Fermi acceleration is inherent in the system. However for low initial velocity, the resonance allies with stickiness hold the particles in a regular or quasi-regular regime near the fixed points, preventing them from exhibiting Fermi acceleration. Also, a transport analysis along the velocity axis is discussed to quantify the competition of growth and decay of energy and making use distributions of histograms of frequency, and we set that the causes of the decay of energy are due to the capture of the orbits by the resonant fixed points

Engineering America's Future in Space: Systems Engineering Innovations for Sustainable Exploration

The National Aeronautics and Space Administration (NASA) delivers space transportation solutions for America's complex missions, ranging from scientific payloads that expand knowledge, such as the Hubble Space Telescope, to astronauts and lunar rovers destined for voyages to the Moon. Currently, the venerable Space Shuttle, which has been in service since 1981, provides U.S. capability for both crew and cargo to low-Earth orbit to construct the International Space Station, before the Shuttle is retired in 2010, as outlined in the 2006 NASA Strategic Plan. I In the next decade, NASA will replace this system with a duo of launch vehicles: the Ares I Crew Launch Vehicle/Orion Crew Exploration Vehicle and the Ares V Cargo Launch Vehicle/Altair Lunar Lander. The goals for this new system include increased safety and reliability, coupled with lower operations costs that promote sustainable space exploration over a multi-decade schedule. This paper will provide details of the in-house systems engineering and vehicle integration work now being performed for the Ares I and planned for the Ares V. It will give an overview of the Ares I system-level test activities, such as the ground vibration testing that will be conducted in the Marshall Center's Dynamic Test Stand to verify the integrated vehicle stack's structural integrity against predictions made by modern modeling and simulation analysis. It also will give information about the work in progress for the Ares I-X developmental test flight planned in 2009 to provide key data before the Ares I Critical Design Review. Activities such as these will help prove and refine mission concepts of operation, while supporting the spectrum of design and development tasks being performed by Marshall's Engineering Directorate, ranging from launch vehicles and lunar rovers to scientific spacecraft and associated experiments. Ultimately, the work performed will lead to the fielding of a robust space transportation solution that will carry international explorers and essential payloads for sustainable scientific discovery beyond planet Earth

Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes

Gravitational waves from coalescences of neutron stars or stellar-mass black holes into intermediate-mass black holes (IMBHs) of $\gtrsim 100$ solar masses represent one of the exciting possible sources for advanced gravitational-wave detectors. These sources can provide definitive evidence for the existence of IMBHs, probe globular-cluster dynamics, and potentially serve as tests of general relativity. We analyse the accuracy with which we can measure the masses and spins of the IMBH and its companion in intermediate-mass ratio coalescences. We find that we can identify an IMBH with a mass above $100 ~ M_\odot$ with $95\%$ confidence provided the massive body exceeds $130 ~ M_\odot$. For source masses above $\sim200 ~ M_\odot$, the best measured parameter is the frequency of the quasi-normal ringdown. Consequently, the total mass is measured better than the chirp mass for massive binaries, but the total mass is still partly degenerate with spin, which cannot be accurately measured. Low-frequency detector sensitivity is particularly important for massive sources, since sensitivity to the inspiral phase is critical for measuring the mass of the stellar-mass companion. We show that we can accurately infer source parameters for cosmologically redshifted signals by applying appropriate corrections. We investigate the impact of uncertainty in the model gravitational waveforms and conclude that our main results are likely robust to systematics.Comment: 9 pages, 11 figure

Reflection as learning about the self in context: mentoring as catalyst for reflective development in pre-service teachers

Establishing a close alignment between teacher education programmes and the realities of the actual classroom remains a challenge in preparing pre-service teachers at higher education institutions. The literature indicates that reflection is a core quality of effective teachers. We investigate how the development of reflective practice through mentoring programmes can facilitate the inevitable transitions that students have to make to the professional sector. Through a narrative analysis, we report on the insights of a selected group of Postgraduate Certificate in Education (PGCE) students participating in the initial development phase of a mentoring system during their practice teaching in schools guiding them to reflect critically on their learning and practice. The data suggest that mentoring can act as a catalyst to enhance reflection.The development of reflection as praxis can assist in bridging the gap between theory and practice.Keywords: mentoring; pre-service teacher development; reflection;teacher identit

The Human Transformation of Rapa Nui (Easter Island, Pacific Ocean)

Rapa Nui (Easter Island) has become widely known as a case study of human-induced environmental catastrophe resulting in cultural collapse. The island\u27s alleged ecocide is offered as a cautionary tale of our own environmental recklessness. The actual archaeological and historical record for the island reveals that while biodiversity loss unfolded, the ancient Polynesians persisted and succeeded. Demographic collapse came with epidemics of Old World diseases introduced by European visitors. In this paper, we outline the process of prehistoric landscape transformation that took place on Rapa Nui. This process includes the role of humans using fire to remove forest and convert to land for agricultural use as well as the impact of introduced rats (Rattus exulans) as agents that depressed recruitment of native vegetation and contributed to the island\u27s deforestation. For humans, the transformation of the landscape improved productivity. Burning of palms and other trees provided a short-term addition of nutrients to poor soils. Rock mulch and agricultural enclosures solved problems of cultivation and mitigated risk in an uncertain environment. The environmental transformation of Rapa Nui, while a tragedy in terms of biodiversity, was a success for a sustainable Polynesian subsistence economy

Abstract Interpretation of Supermodular Games

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework