A Rigid-Field Hydrodynamics approach to modelling the magnetospheres of massive stars

We introduce a new Rigid-Field Hydrodynamics approach to modelling the magnetospheres of massive stars in the limit of very strong magnetic fields. Treating the field lines as effectively rigid, we develop hydrodynamical equations describing the one-dimensional flow along each, subject to pressure, radiative, gravitational and centrifugal forces. We solve these equations numerically for a large ensemble of field lines to build up a three-dimensional time-dependent simulation of a model star with parameters similar to the archetypal Bp star σ Ori E. Since the flow along each field line can be solved independently of other field lines, the computational cost of this approach is a fraction of an equivalent magnetohydrodynamical treatment.
The simulations confirm many of the predictions of previous analytical and numerical studies. Collisions between wind streams from opposing magnetic hemispheres lead to strong shock heating. The post-shock plasma cools initially via X-ray emission, and eventually accumulates into a warped, rigidly rotating disc defined by the locus of minima of the effective (gravitational plus centrifugal) potential. However, a number of novel results also emerge. For field lines extending far from the star, the rapid area divergence enhances the radiative acceleration of the wind, resulting in high shock velocities (up to  ∼3000 km s⁻¹  ) and hard X-rays. Moreover, the release of centrifugal potential energy continues to heat the wind plasma after the shocks, up to temperatures around twice those achieved at the shocks themselves. Finally, in some circumstances the cool plasma in the accumulating disc can oscillate about its equilibrium position, possibly due to radiative cooling instabilities in the adjacent post-shock regions.     

Virialization of cosmological structures in models with time-varying equation of state

We study the virialization of the cosmic structures in the framework of flat cosmological models where the dark energy component plays an important role in the global dynamics of the Universe. In particular, our analysis focuses on the study of the spherical matter perturbations, as the latter decouple from the background expansion, start to 'turn around' and finally collapse. We generalize this procedure, taking into account models with an equation of state which vary with time, and provide a complete formulation of the cluster virialization attempting to address the non-linear regime of structure formation. In particular, assuming that clusters have collapsed prior to the epoch of z _f≃ 1.4, in which the most distant cluster has been found, we show that the behaviour of the spherical collapse model depends on the functional form of the equation of state.     

Statistical analysis of galaxy surveys – III. The non-linear clustering of red and blue galaxies in the 2dFGRS

We present measurements of the higher order clustering of red and blue galaxies as a function of scale and luminosity made from the two-degree field galaxy redshift survey (2dFGRS). We use a counts-in-cells analysis to estimate the volume-averaged correlation functions,     , as a function of scale up to the order of   p = 5  , and also the reduced void probability function. Hierarchical amplitudes are constructed using the estimates of the correlation functions:     . We find that (i) red galaxies display stronger clustering than blue galaxies at all orders measured; (ii) red galaxies show values of   S _p   that are strongly dependent on luminosity whereas blue galaxies show no segregation in   S _p   within the errors; this is remarkable given the segregation in the variance; (iii) the linear relative bias shows the opposite trend to the hierarchical amplitudes, with little segregation for the red sequence and some segregation for the blue; (iv) faint red galaxies deviate significantly from the 'universal' negative binomial reduced void probabilities followed by all other galaxy populations. Our results show that the characteristic colour of a galaxy population reveals a unique signature in its spatial distribution. Such signatures will hopefully further elucidate the physics responsible for shaping the cosmological evolution of galaxies.     

Five dimensional universe model with variable cosmological term Λ and a big bounce

We assume the four dimensional induced matter of the 5D Ricci flat bouncing cosmological solution contains a perfect fluid. The big bounce singularity of simple 5D cosmological model is studied with the cosmological term Λ=α ρ and Λ=β H ² where α and β are constants and ρ and H are respectively energy density and Hubble parameter. This big bounce singularity is found to be an event horizon at which the scale factor and mass density of the universe are finite, while the pressure is infinite.      

Some remarks on the Gaussian beam summation method

Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high-frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the 'free' complex parameter ε which specifies the initial widths and phases of the Gaussian beams.
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means.     

新四面体理论与磁极倒转

本文以最新修正了的新四面体理论模型来解释地球磁极倒转现象及其规律性。文章简要回顾了依附于收缩说的地球四面体理论的兴衰,接着简述了应归属于脉动说范畴的新四面体理论研究的最新进展——地球多级驻波(式)脉动演化模型。新模型可概括为:地球的形态在演化过程中呈“准球体→负准四面体→准球体→正准四面体→准球体→…”的驻波脉动;在呈每种形体的大阶段中,又包含着次级、更次级的驻波脉动。然后论述了地磁极性倒转的规律性(即多变→固定[正向]→多变→固定[反向] →多变→…)以及新模型对其所做的解释(即固定正向和固定反向阶段分别为负和正准四面体阶段,多变阶段为准球体阶段)。