Non-Sobolev modelling of radiation-pressure-driven flows in active galactic nuclei

We present a new general scheme for calculating the structure and dynamics of radiation-pressure-driven photoionized flows. The new method goes one step beyond the Sobolev approximation. It involves a numerical solution of the radiative transfer in absorption lines, including the effects of differential expansion and line interactions such as line locking and blanketing. We also present a new scheme for calculating the radiation pressure due to trapped line photons in finite, differentially expanding flows. We compare our results for the radiation pressure force with those obtained using the Sobolev approximation and show the limitations of the latter. In particular, we demonstrate that the Sobolev method gives a poor approximation near discontinuity surfaces and its neglect of line blanketing can lead to erroneous results in high-velocity flows. We combine the newly calculated radiation pressure force with self-consistent photoionization and thermal calculations to study the dynamics and spectral features of broad absorption-line flows and highly ionized gas flows in active galactic nuclei (AGN). A comparison with Sobolev-type calculations shows that the latter overestimates the terminal velocity of the flow and, conversely, underestimates its opacity. We also show that line locking on broad emission lines can have a significant effect on the dynamics and spectral features of AGN flows.     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave.
Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.     

The characteristics of Asian dust events in Northeast Asia during the springtime from 1993 to 2004

The characteristics of Asian dust events that occurred in Northeast Asia during the springtime from 1993 to 2004 are investigated using 3-hourly SYNOP reports (World Meteorological Organization). Occurrences of blowing sand and dust storm are low in 1997 and 1999, but have increased rapidly since 2000. The maximum occurrence was recorded in 2002. Wind velocity of 6.5 m s^− 1 as a threshold wind velocity is not so exactly consistent with the occurrence of blowing sand. However, wind velocity of 14 m s^− 1 as a strong wind causing dust storm had similar tendency to those of dust storm and Dust Storm Index.Source regions of Asian dust are divided into three regions (A: dry arid, B: semi-arid, and C: cultivated), based upon the occurrence of blowing sand and dust storm. Eight meteorological stations are selected in three regions, which have frequent occurrences of blowing sand. Source regions of Asian dust that affect the Korean peninsula are gradually extending eastward. Positive anomalies of NDVI occurred in 1994, 1995, and 1998 when temperature was high and precipitation was heavy. However, the frequent occurrence of the dust phenomena is not always consistent with lots of vegetation, high temperature, and much precipitation in this study.     

Radiative Transfer in Inhomogeneous Atmospheres. III

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.     

High-resolution calculations of merging neutron stars – II. Neutrino emission

The remnant resulting from the merger of two neutron stars produces neutrinos in copious amounts. In this paper we present the neutrino emission results obtained via Newtonian, high-resolution simulations of the coalescence event. These simulations use three-dimensional smoothed particle hydrodynamics together with a nuclear, temperature-dependent equation of state and a multiflavour neutrino leakage scheme. We present the details of our scheme, discuss the neutrino emission results from a neutron star coalescence and compare them with the core-collapse supernova case where neutrino emission has been studied for several decades. The average neutrino energies are similar to those in the supernova case, but contrary to the latter, the luminosities are dominated by electron-type antineutrinos that are produced in the hot, neutron-rich, thick disc of the merger remnant. The cooler parts of this disc contain substantial fractions of heavy nuclei, which, however, do not influence the overall neutrino emission results significantly. Our total neutrino luminosities from the merger event are considerably lower than those found in previous investigations. This imposes constraints on the ability of neutron star mergers to produce a gamma-ray burst via neutrino annihilation. The neutrinos are emitted preferentially along the initial binary rotation axis, an event seen 'pole-on' would appear much brighter in neutrinos than a similar event seen 'edge-on'.     

The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (ln Λ). We determine the accurate value of this parameter using the direct N -body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that  ln Λ= 6.6 ± 0.6  for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, ln Λ is smaller, with a value of the logarithm argument Λ inversely proportional to the object size.     

Effect of spatial variation characteristics on contouring of design storm depth

The ordinary kriging method, a geostatistical interpolation technique, was applied for developing contour maps of design storm depth in northern Taiwan using intensity–duration–frequency (IDF) data. Results of variogram modelling on design storm depths indicate that the design storms can be categorized into two distinct storm types: (i) storms of short duration and high spatial variation and (ii) storms of long duration and less spatial variation. For storms of the first category, the influence range of rainfall depth decreases when the recurrence interval increases, owing to the increasing degree of their spatial independence. However, for storms of the second category, the influence range of rainfall depth does not change significantly and has an average of approximately 72 km. For very extreme events, such as events of short duration and long recurrence interval, we do not recommend usage of the established design storm contours, because most of the interstation distances exceed the influence ranges. Our study concludes that the influence range of the design storm depth is dependent on the design duration and recurrence interval and is a key factor in developing design storm contours. Copyright © 2003 John Wiley & Sons, Ltd.