Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime

The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-MHD effects should be considered in studies of magnetic energy release in this environment. This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection. A Lagrangian remap shock-capturing code (Lare2d) is used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth in resistive Hall MHD. A magnetic null-point finding algorithm is also used to locate and track the evolution of the multiple null-points that are formed in the system. Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null, (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.Comment: 13 pages, 10 figure

Alfv\`en wave phase-mixing and damping in the ion cyclotron range of frequencies

Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k^2di^2 where k is wavenumber and di is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k^2di^2>>1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits

Generalized Chaplygin gas model, supernovae and cosmic topology

In this work we study to which extent the knowledge of spatial topology may place constraints on the parameters of the generalized Chaplygin gas (GCG) model for unification of dark energy and dark matter. By using both the Poincar\'e dodecahedral and binary octahedral spaces as the observable spatial topologies, we examine the current type Ia supernovae (SNe Ia) constraints on the GCG model parameters. We show that the knowledge of spatial topology does provide additional constraints on the $A_s$ parameter of the GCG model but does not lift the degeneracy of the $\alpha$ parameter.Comment: Revtex 4, 8 pages, 10 figures, 1 table; version to match the published on

Topological Lensing in Spherical Spaces

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.Comment: 32 pages, 26 figure

Constraints on the cosmological density parameters and cosmic topology

A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can use this observable to set constraints on the density parameters of the Universe by using a specific spatial topology along with type Ia supenovae and X-ray gas mass fraction data sets.Comment: 11 pages, 4 figures. To appear in Int. J. Mod. Phys. D (2006). Invited talk delivered at the 2nd International Workshop on Astronomy and Relativistic Astrophysic

Green roof and ground-level invertebrate communities are similar and are driven by building height and landscape context

Green roofs are increasingly promoted for urban biodiversity conservation, but the value of these novel habitats is uncertain. We aimed to test two hypotheses: (i) green roofs can support comparable invertebrate family and order richness, composition and abundances to ground-level habitats and (ii) green roofs planted with native species from local habitats will support a richer invertebrate community at family and order level than other green roofs. We sampled the invertebrate community on green roofs dominated by native grassland or introduced succulent species in Melbourne, Australia, and compared these to the invertebrate community in ground-level sites close by, and sites with similar vegetation types. The only significant differences between the invertebrate communities sampled on green roofs and ground-level habitats were total abundance and fly family richness, which were higher in ground-level habitats. Second hypothesis was not supported as invertebrate communities on green roofs supporting a local vegetation community and those planted with introduced Sedum and other succulents were not detectably different at family level. The per cent cover of green space surrounding each site was consistently important in predicting the richness and abundance of the invertebrate families we focussed on, while roof height, site age and size were influential for some taxa. Our results suggest that invertebrate communities of green roofs in Melbourne are driven largely by their surrounding environment and consequently the effectiveness of green roofs as invertebrate habitat is highly dependent on location and their horizontal and vertical connection to other habitats.City of Melbourne for funds that enabled Nathan Brown to identify the Diptera, Hemiptera and Hymenoptera families. C.G.T. received support from Australia Research Council Linkage Grant LP0990383 and the Clean Air and Urban Landscapes Hub, which was funded by the Australian Government’s National Environmental Science Program. B.N. received support from the Natural Environment Research Council (grant number NE/J015067/1)