Unstable Disk Galaxies. II. the Origin of Growing and Stationary Modes

I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a non-uniform function of the orbital angular momentum, the capture of stars into the corotation resonance imbalances the disk angular momentum and triggers growing bar and spiral modes. The stellar disk can then recover its angular momentum balance through the response of non-resonant stars. I carry out a complete analysis of orbital structure corresponding to each Fourier component in the radial angle, and present a mathematical condition for the occurrence of van Kampen modes, which constitute a continuous family. I discuss on the discreteness and allowable pattern speeds of unstable modes and argue that the mode growth is saturated due to the resonance overlapping mechanism. An individually growing mode can also be suppressed if the corotation and inner Lindblad resonances coexist and compete to capture a group of stars. Based on this mechanism, I show that self-consistent scale-free disks with a sufficient distribution of non-circular orbits should be stable under perturbations of angular wavenumber $m>1$. I also derive a criterion for the stability of stellar disks against non-axisymmetric excitations.Comment: 15 Pages (emulateapj), 7 Figures, Accepted for Publication in The Astrophysical Journa

Analytic Central Orbits and their Transformation Group

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are generalisations of the semi-latus-rectum and the eccentricity. 'm' is given as a function of 'eccentricity'. For nearly circular orbits 'm' is sqrt{k}, while the above orbit becomes exact at the energy of escape where 'e' is one and 'm' is 'k'. Orbits in the logarithmic potential that gives rise to a constant circular velocity are derived via the limit of small alpha. For such orbits, r^2 vibrates almost harmonically whatever the 'eccentricity'. Unbound orbits in power-law potentials are given in an appendix. The transformation of orbits in one potential to give orbits in a different potential is used to determine orbits in potentials that are positive powers of r. These transformations are extended to form a group which associates orbits in sets of six potentials, e.g. there are corresponding orbits in the potentials proportional to r, r^{-2/3}, r^{-3}, r^{-6}, r^{4/3} and r^{-4}. A degeneracy reduces this to three, which are r^{-1}, r^2 and r^{-4} for the Keplerian case. A generalisation of this group includes the isochrone with the Kepler set.Comment: 12 pages, 8 figures; updated version with minor typographical corrections; published in MNRA

Seasonality and predictability shape temporal species diversity

Temporal environmental fluctuations, such as seasonality, exert strong controls on biodiversity. While the effects of seasonality are well known, the predictability of fluctuations across years may influence seasonality in ways that are less well understood. The ability of a habitat to support unique, non‐nested assemblages of species at different times of the year should depend on both seasonality (occurrence of events at specific periods of the year) and predictability (the reliability of event recurrence) of characteristic ecological conditions. Drawing on tools from wavelet analysis and information theory, we developed a framework for quantifying both seasonality and predictability of habitats, and applied this using global long‐term rainfall data. Our analysis predicted that temporal beta diversity should be maximized in highly predictable and highly seasonal climates, and that low degrees of seasonality, predictability, or both would lower diversity in characteristic ways. Using stream invertebrate communities as a case study, we demonstrated that temporal species diversity, as exhibited by community turnover, was determined by a balance between temporal environmental variability (seasonality) and the reliability of this variability (predictability). Communities in highly seasonal mediterranean environments exhibited strong oscillations in community structure, with turnover from one unique community type to another across seasons, whereas communities in aseasonal New Zealand environments fluctuated randomly. Understanding the influence of seasonal and other temporal scales of environmental oscillations on diversity is not complete without a clear understanding of their predictability, and our framework provides tools for examining these trends at a variety of temporal scales, seasonal and beyond. Given the uncertainty of future climates, seasonality and predictability are critical considerations for both basic science and management of ecosystems (e.g., dam operations, bioassessment) spanning gradients of climatic variability

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay theory, operates with nonosculating Andoyer elements. This situation parallels a similar phenomenon that often happens (but seldom gets noticed) in orbital dynamics, when the standard Lagrange-type or Delaunay-type planetary equations unexpectedly render nonosculating orbital elements. In orbital mechanics, osculation loss happens when a velocity-dependent perturbation is plugged into the standard planetary equations. In attitude mechanics, osculation is lost when an angular-velocity-dependent disturbance is plugged in the standard dynamical equations for the Andoyer elements. We encounter exactly this situation in the theory of Earth rotation, because this theory contains an angular-velocity-dependent perturbation (the switch from an inertial frame to that associated with the precessing ecliptic of date). While the osculation loss does not influence the predictions for the figure axis of the planet, it considerably alters the predictions for the instantaneous spin-axis' orientation. We explore this issue in great detail

Unaccompanied & Denied: Regional Legal Framework for Unaccompanied Minors Asylum Seekers (UMAS)

Unaccompanied minor asylum seekers are vulnerable and thus, provided special International law protections. However, in reality, they are being mistreated as illegal immigrants and on thereceiving end of ethnic violence, discrimination, restrictions in enjoyment of their rights duly recognised by International human rights law. This article identifies legislative, policy and supportmechanisms which encompass the minimum UMAS guardianship standards at International law and which are evidence-based from best practice models for the provision of guardians for UMASinternationally. It presents situation of UMAS in relation to human rights violations with emphasis on the legal framework and practices in Australia and five ASEAN State Members. This article also highlights the various stands taken by various countries providing better legal framework and practices regarding the terms for protection and enforcement of human rights for UMAS. Finally, this article provides recommendations for Australia and ASEAN Member States to adopt in order to realise the International human rights of UMAS with respect to guardianship

A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores

Enhanced Thermal Performance of Mosques in Qatar

Qatar has an abundance of mosques that significantly contribute to the increasing energy consumption in the country. Little attention has been given to providing mitigation methods that limit the energy demands of mosques without violating the worshippers' thermal comfort. Most of these researches dealt with enhancing the mosque envelope through the addition of insulation layers. Since most mosque walls in Qatar are mostly already insulated, this study proposes the installation of shading on the mosque roof that is anticipated to yield similar energy savings in comparison with insulated roofs. An actual mosque in Qatar, which is a combination of six different spaces consisting of men and women's prayer rooms, ablutions and toilets, was simulated and yielded a total annual energy demand of 619.55 kWh/m2. The mosque, whose walls are already insulated, yielded 9.1% energy savings when an insulation layer was added to its roof whereas it produced 6.2% energy savings when a shading layer was added above this roof. As the reconstruction of the roof envelope is practically unrealistic in existing mosques, the addition of shading to the roof was found to produce comparable energy savings. Lastly, it was found that new mosques with thin-roof insulation and shading tend to be more energy-efficient than those with thick-roof insulation. Published under licence by IOP Publishing Ltd.The authors would like to acknowledge Qatar University for their support in providing the necessary tools for the completion of this study.Scopu

The role of chaotic resonances in the solar system

Our understanding of the Solar System has been revolutionized over the past decade by the finding that the orbits of the planets are inherently chaotic. In extreme cases, chaotic motions can change the relative positions of the planets around stars, and even eject a planet from a system. Moreover, the spin axis of a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with adverse effects on the climates of otherwise biologically interesting planets. Some of the recently discovered extrasolar planetary systems contain multiple planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure

To understand climate change adaptation, we must characterize climate variability: Here's how

Climate change adaptation involves the management of climate-related risks, and the Intergovernmental Panel on Climate Change says we must prioritize adaptation immediately. However, researchers and policymakers have little systematic understanding of which adaptations are effective at reducing risks, including under different climate conditions. Drawing on data from human communities past and present, we review how features of climate variability—temporal autocorrelation, frequency, and severity—may predict which candidate climate change adaptations communities innovate or adopt. Using a case study of climate and remittances in Africa, we outline how researchers can characterize features of climate data relevant to adaptation—autocorrelation, frequency, and severity—and then qualitatively compare these data to candidate adaptations. We include suggestions for how to involve communities in these explorations, from setting climate thresholds to identifying impactful hazards. By better understanding the relationship between climate variability and common solutions used by communities, researchers and policymakers can better support communities as they adapt to contemporary climate change