On the relation between orbital structure and observed bar morphology

We investigate the morphological relation between the orbits of the central family of periodic orbits ( x ₁ family) and the bar itself using models of test particles moving in a barred potential. We show that different bar morphologies may have as a backbone the same set of x ₁ periodic orbits. We point out that by populating initially axisymmetric stellar discs exponentially with test particles in circular, or almost circular motion, we may end up with a response bar which reveals a shape different in crucial details from that of the individual stable x ₁ orbits. For example, a bar model in which the x ₁ orbits are pure ellipses may have a much more complicated response morphology. This depends on the particular invariant curves around x ₁, which are populated in each model.     

Orbital dynamics of three-dimensional bars – I. The backbone of three-dimensional bars. A fiducial case

In this series of papers we investigate the orbital structure of three-dimensional (3D) models representing barred galaxies. In the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three-dimensional bars. We show that, in a 3D bar, the backbone of the orbital structure is not just the x1 family, as in two-dimensional (2D) models, but a tree of 2D and 3D families bifurcating from x1. Besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance. The families of this group bifurcate from x1 and influence the dynamics of the system only locally. We also find that 3D orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family. They can support 3D bar-like structures along the minor axis of the main bar. Banana-like orbits around the stable Lagrangian points build a forest of 2D and 3D families as well. The importance of the 3D x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in z or in   z˙   .     

Contents to Volume 47

Volume Contents

Contents to Volume 47     

Stormwater control impacts on runoff volume and peak flow: A meta-analysis of watershed modelling studies

Decades of research has concluded that the percent of impervious surface cover in a watershed is strongly linked to negative impacts on urban stream health. Recently, there has been a push by municipalities to offset these effects by installing structural stormwater control measures (SCMs), which are landscape features designed to retain and reduce runoff to mitigate the effects of urbanisation on event hydrology. The goal of this study is to build generalisable relationships between the level of SCM implementation in urban watersheds and resulting changes to hydrology. A literature review of 185 peer-reviewed studies of watershed-scale SCM implementation across the globe was used to identify 52 modelling studies suitable for a meta-analysis to build statistical relationships between SCM implementation and hydrologic change. Hydrologic change is quantified as the percent reduction in storm event runoff volume and peak flow between a watershed with SCMs relative to a (near) identical control watershed without SCMs. Results show that for each additional 1% of SCM-mitigated impervious area in a watershed, there is an additional 0.43% reduction in runoff and a 0.60% reduction in peak flow. Values of SCM implementation required to produce a change in water quantity metrics were identified at varying levels of probability. For example, there is a 90% probability (high confidence) of at least a 1% reduction in peak flow with mitigation of 33% of impervious surfaces. However, as the reduction target increases or mitigated impervious surface decreases, the probability of reaching the reduction target also decreases. These relationships can be used by managers to plan SCM implementation at the watershed scale.     

ELASTOPLASTIC RESPONSE OF PRESSURE SENSITIVE SOLIDS

Tensorially invariant constitutive relations are systematically derived for large strain elastoplastic response of geomaterials. The analysis centres on Mohr–Coulomb (MC) and Drucker–Prager (DP) models with arbitrary hardening and non-associated response. Both flow and deformation theories are constructed for each model with emphasis on linear incremental relations between the Eulerian strain rate tensor and the objective Jaumann stress rate tensor. Specifying the results for plane strain compression we find that deformation theory produces a much smaller tangent instantaneous shear modulus than flow theory. It follows that failure of ellipticity and onset of surface instabilities predicted by deformation theory for associated solids occur at much lower levels of strain than the corresponding flow theory results. On the other hand, flow theory predictions admit a considerable sensitivity to the level of non-associativity. In fact, at high levels of non-associativity flow theory predictions for loss of ellipticity can be at strains below those obtained from deformation theory. © 1997 John Wiley & Sons, Ltd.     

Reionization and the Cosmic Dawn with the Square Kilometre Array

The Square Kilometre Array (SKA) will have a low frequency component (SKA-low) which has as one of its main science goals the study of the redshifted 21 cm line from the earliest phases of star and galaxy formation in the Universe. This 21 cm signal provides a new and unique window both on the time of the formation of the first stars and accreting black holes and the subsequent period of substantial ionization of the intergalactic medium. The signal will teach us fundamental new things about the earliest phases of structure formation, cosmology and even has the potential to lead to the discovery of new physical phenomena. Here we present a white paper with an overview of the science questions that SKA-low can address, how we plan to tackle these questions and what this implies for the basic design of the telescope.     

Inversions for axisymmetric galactic disks

We use two models for the distribution function to solve an inverse problem for axisymmetric disks. These systems may be considered - under certain assumptions - as galactic disks. In some cases the solutions of the resulting integral equations are simple, which allows the determination of the kinematic properties of self-consistent models for these systems. These properties for then = 1 Toomre disk are presented in this study.