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We construct stationary global configurations of both aligned and unaligned logarithmic spiral perturbations in a composite disc system of stellar and isopedically magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. Earlier models are generalized to a more general theoretical framework. The thin gaseous SID is threaded across by a vertical magnetic field B z with a constant ratio of the surface gas mass density to B z . In reference to SID models of there exist two classes of stationary magnetohydrodynamic (MHD) solutions with in-phase and out-of-phase density perturbations here. Relevant parameter regimes are explored numerically. For both aligned and unaligned cases with azimuthal periodicities |m| 2 (m is an integer), there may be two, one and no solution situations, depending on the chosen parameters. For the transition criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities, the corresponding T /|W| ratio can be much lower than the oft-quoted value of T /|W| ∼ 0.14, where T is the total rotational kinetic energy and W is the total gravitational potential energy plus the magnetic energy. The T /|W| ratios for the two sets of solutions in different ranges are separated by m/(4m + 4). For the unaligned cases, we study marginal stabilities for axisymmetric (m = 0) and non-axisymmetric (m = 0) disturbances. By including the gravitational influence of an axisymmetric dark matter halo on the background, the case of a composite partial magnetized singular isothermal discs (MSID) system is also examined. The global analytical solutions and their properties are valuable for testing and benchmarking numerical MHD codes. For astrophysical applications to large-scale galactic dynamics, our model analysis contains more realistic elements and offers useful insights into the structures and dynamics of disc galaxies consisting of stars and magnetized interstellar medium (ISM). In particular, in the presence of star burst activities, supernovae, hypernovae, superbubbles etc., our open magnetic field geometry in disc galaxies bears strong implications on circumnuclear and spiral galactic winds.

Global stationary configurations of both aligned and logarithmic spiral magnetohydrodynamic (MHD) perturbations are constructed analytically within an axisymmetric background of razorthin scale-free gas disc, which is embedded in an axisymmetric gravitational potential of a dark matter halo and involves an isopedic magnetic field almost vertically threaded through the disc plane. The scale-free index β of the disc rotation speed v θ ∝ R −β falls in the range of (−1/2, 1/2) where R is the cylindrical radius. With the holding-back of a deep background dark matter halo potential, the isopedic magnetic field may be strong enough to allow for the magnetic tension force overtaking the disc self-gravity, which can significantly influence global stationary MHD perturbation configurations and stability properties of the scale-free disc system. Only for stationary logarithmic spiral MHD perturbations with a perturbation scalefree index β 1 = 1/4 or for aligned stationary MHD perturbations, can the MHD disc maintain a constant radial flux of angular momentum. The variable radial flux of angular momentum in the radial direction corresponds to a complex dispersion relation. The marginal instabilities for axisymmetric MHD disturbances are also examined for a special case as an example. When the magnetic tension force overtakes the disc self-gravity, the scale-free disc can be completely stable against axisymmetric MHD disturbances of all wavelengths. We predict the possible existence of an isopedically magnetized gas disc system in rotation primarily confined by a massive dark matter halo potential.

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Tourism and recreational second-home development has increased rapidly in peripheral and lower tier cities of China in recent years. While tourism-led real estate development has been widely accepted as an effective investment opportunity, it can increase urban segregation and stratification. This pattern is seen in the resort city of Sanya on Hainan Island, China. Sanya's recreational second homes vary in form and can be categorized into (1) elite-vacation second homes (short stay, private homes), (2) lifestyle-migration second homes (short stay, commercial homes), and (3) retirement-migration second homes (longer term, seasonal homes). Unlike the segregated cities formed by displaced labor migrants in many of China's cities, seasonal recreational migrants are both economically better-off and are emerging as a dominant political force. The segregated residential spaces created by Sanya's second-home development landscape further limits interaction and social network building between indigenous local residents and part-time recreational migrants. The perceived home space and feelings of place attachment towards Sanya is under drastic change, with locals feeling increasingly displaced. The new mosaic of consumption-led amenity cities in developing economies is one where traditional models of migration-based segregation are reversed. Wealthier second-home migrants have the capacity for more political power than local residents, as well as relying more on non-localized social networks and multi-nodal home spaces. Consumption-led mobility is an important determinant in building explanations of socio-spatial segregation and stratification in global cities that are undergoing dramatic development change.