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.     

Infiltration at the Tai rain forest (Ivory Coast): Measurements and modelling

Infiltration experiments have been performed at three sites along a well-known catena under virgin tropical rain forest using a portable sprinkling infiltrometer. Experimentally determined infiltration curves are presented. Infiltration curves are also simulated on the basis of the Mein-Larson equation. The parameters for this model have been obtained from the infiltration curves (saturated conductivity) and simple soil moisture determinations (fillable porosity). The agreement between experimentally determined and modelled infiltration is reasonable, provided (a) saturated conductivity as derived from the experimental data is corrected, (b) a storage parameter, also derived from the experimental data, is added to the Mein-Larson model, and (c) the decline in soil porosity with depth is either small or occurs abruptly at shallow depth. Comparison of observed infiltration rates with rainfall intensity shows that Horton Overland Flow has to occur naturally at least on the middle and lower section of the catena. Despite the fact that most parameters can be estimated in principle from basic soil data, it remains advisable to obtain sprinkling infiltrometer field measurements, because of soil variability due to dynamic surface conditions, macroporosity, air entrapment, and irregularity of the wetting front.     

关于具二次约束最小二乘问题的敏度分析

本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。     

Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures

A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers.To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed.     

任意曲线曲面上重磁位场转换的B样条函数法

提出用B样条函数求解曲线、曲面上重磁位场的向上延拓,水平、垂向导数计算,磁异常分量互换的方法。该方法的特点是:原理简明,程序通用性强,计算精度高。     

In situ and satellite observations of the eastward migration of the Western Alboran Sea Gyre

During October 2003 an intensive oceanographic survey (BIOMEGA) was carried out in the Alboran Sea, coinciding with a migration event of the Western Alboran Sea Gyre (WAG). The observations gathered during that cruise constitute the first field evidence of a migrated stage of the WAG. In this work we present the main differences between the 3D hydrodynamic fields observed during BIOMEGA and those corresponding to a WAG located at its usual position. The migration of the gyre was followed by satellite (altimetry and sea surface temperature) imagery. The causes of the gyre migration are explored in terms of the quasi-geostrophic tendency equation, in particular of the dynamics governing scales larger than the Rossby radius of deformation. It is shown that the steady state gyre must be almost equivalent barotropic and that the key process to break down the stationarity would be a density advection at gyre scale. The mechanisms to explain the migration of the WAG proposed by previous authors are discussed in light of the explanation proposed in this work.     

On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

On the periodic solutions of a particular Lame equation

We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t).     

共线条件方程式教学中的几个问题

指出了共线条件方程式教学中应注意的一些问题：共线条件方程式是联立的两个平面方程式，存在双主距（fx,fy)时的几何概念，以及它的变换式与直接线性变换关系式的异同点。     

Formation of Concentric Rings Around Sources

Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings.