Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.     

非线性Rossby波所满足的三阶Zakharov方程与低频振荡

本文在基本气流具有水平切变的情况下,利用摄动法导出了非线性Rossby波所满足的三阶Zakharov方程,然后,考虑了基流具有弱切变的情况,通过使用三阶Zakharov方程研究了Rossby波列的第一类不稳定性问题。结果表明:通过非线性作用,大气中的Rossby波列可产生调制不稳定。同时,本文对这种不稳定的区域,增长率和周期进行了详细的计算,并讨论了波振幅、波数、纬度和基流切变对它们的影响,指出Rossby波列的调制不稳定可以激发30～60天的低频振荡。     

Cosmic structure growth and dark energy

Dark energy has a dramatic effect on the dynamics of the Universe, causing the recently discovered acceleration of the expansion. The dynamics are also central to the behaviour of the growth of large-scale structure, offering the possibility that observations of structure formation provide a sensitive probe of the cosmology and dark energy characteristics. In particular, dark energy with a time-varying equation of state can have an influence on structure formation stretching back well into the matter-dominated epoch. We analyse this impact, first calculating the linear perturbation results, including those for weak gravitational lensing. These dynamical models possess definite observable differences from constant equation of state models. Then we present a large-scale numerical simulation of structure formation, including the largest volume to date involving a time-varying equation of state. We find the halo mass function is well described by the Jenkins et al. mass function formula. We also show how to interpret modifications of the Friedmann equation in terms of a time-variable equation of state. The results presented here provide steps toward realistic computation of the effect of dark energy in cosmological probes involving large-scale structure, such as cluster counts, the Sunyaev–Zel'dovich effect or weak gravitational lensing.     

Numerical Stabilization of Orbital Motion

Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders.     

Coronal Holes and Icosahedral Symmetry

The study of the expansion of the solar wind out of a system of coronal holes is continued. To this end, we consider the numerical integration of partial differential equations for problems with icosahedral symmetry, in general. First, employing Weyl theory, orbifold coordinates are introduced. Second, the icosahedral coordinates are discussed in detail. Third, following an analysis of the properties of these coordinates and the derivation of a few expressions useful for grid construction, various alternatives for the distribution of lattice points required for numerical integration are considered. A comparison of these numerical grids motivates the choice of a specific grid optimized for the numerical integration carried out in the accompanying paper by Kalish et al.(2002). This revised version was published online in July 2006 with corrections to the Cover Date.     

介质横向不均匀对震后地表位移场的影响

利用三维有限元模拟两层地球模型(包括弹性层和粘弹性层)介质的横向不均匀和断层错动的复杂性对震后地表位移场的影响，其数值结果包括弹性解和粘弹性解。结果表明，震后位移场的分布特征不仅与粘弹性层的流变特性有关，还与弹性层介质的剪切模量以及断层的同震错动有关。     

Seismic rays in an ellipsoidal earth model: theoretical analysis and estimation of deviations due to the ellipticity

Summary. A first-order form of the Euler's equations for rays in an ellipsoidal model of the Earth is obtained. The conditions affecting the velocity law for a monotonic increase, with respect to the arc length, in the angular distance to the epicentre, and in the angle of incidence, are the same in the ellipsoidal and spherical models. It is therefore possible to trace rays and to compute travel times directly in an ellipsoidal earth as in the spherical model. Thus comparison with the rays of the same coordinates in a spherical earth provides an estimate of the various deviations of these rays due to the Earth's flattening, and the corresponding travel-time differences, for mantle P -waves and for shallow earthquakes. All these deviations are functions both of the latitude and of the epicentral distance. The difference in the distance to the Earth's centre at points with the same geocentric latitude on rays in the ellipsoidal and in the spherical model may reach several kilometres. Directly related to the deformation of the isovelocity surfaces, this difference is the only cause of significant perturbation in travel times. Other differences, such as that corresponding to the ray torsion, are of the first order in ellipticity, and may exceed 1 km. They induce only small differences in travel time, less than 0.01s. Thus, we show that the ellipticity correction obtained by Jeffreys (1935) and Bullen (1937) by a perturbational method can be recovered by a direct evaluation of the travel times in an ellipsoidal model of the Earth. Moreover, as stated by Dziewonski & Gilbert (1976), we verify the non-dependence of this correction on the choice of the velocity law.     

首都圈地区现今断层活动的数学模拟及地震危险性讨论

以首都圈地区现今活动断层上近２０年的位移测量资料为依据，用二维线弹性有限元对该区断层的活动特征进行了拟合，并结合有关资料讨论了该区的地震危险性。结果表明：１９７７－１９８６年间该区主压应力优势方位与华北较一致，约为Ｎ４５°－８０°Ｅ；１９８６－１９９０年其主压应力方向向北偏转，约为Ｎ５°－６０°Ｅ；１９９０年至现在其主压应力又向东偏转，角度大于第一阶段，约为Ｎ８０°－９５°Ｅ。该区的张家口－延庆一带近期有发生中强震的可能；丰镇－阳高－大同地区和凉城－古营盘地区应力较高，也应引起注意。