一种从经纬度网格资料获得正方形网格资料的插值方案

本文提出了一种把经纬度网格点上的气象要素值转化到正方形网格点上的多项式插值方案。对插值方案作了稳定性讨论和定量及定性分析。结果表明,这种插值方案方便可行,而且有广泛适用性。     

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd     

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 calculations in the orbital determination of an artificial satellite for a long arc

Numerical methods are usually used for the computation of ephemerides with perturbations for the precise orbital determination of an artificial satellite. But their numerical stability will be encountered in a long arc. In this case the use the improved Encke special perturbation methods has been suggested. The results of this paper show that Encke's method does indeed have a certain effectiveness, but cannot yet completely resolve the numerical stability, and the more efficient method is to use the energy integral or its variational relation to control the growth of the along-track error in general numerical calculations so that the aim of stabilization can be achieved.     

A numerical method for differential equations of second order

A new algorithm of order five is presented for the solution of the initial value problem where the system of ordinary differential equations is of second order and does not contain the first derivative.     

Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target

2D numerical modelling of impact cratering has been utilized to quantify an important depth-diameter relationship for different crater morphologies, simple and complex. It is generally accepted that the final crater shape is the result of a gravity-driven collapse of the transient crater, which is formed immediately after the impact. Numerical models allow a quantification of the formation of simple craters, which are bowl-shaped depressions with a lens of rock debris inside, and complex craters, which are characterized by a structural uplift. The computation of the cratering process starts with the first contact of the impactor and the planetary surface and ends with the morphology of the final crater. Using different rheological models for the sub-crater rocks, we quantify the influence on crater mechanics. To explain the formation of complex craters in accordance to the threshold diameter between simple and complex craters, we utilize the Acoustic Fluidization model. We carried out a series of simulations over a broad parameter range with the goal to fit the observed depth/diameter relationships as well as the observed threshold diameters on the Moon, Earth and Venus.     

Studying Hydrodynamic Instability Using Shock-Tube Experiments

The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.     

Numerical modeling for analyzing thermal surface anomalies induced by underground coal fires

Coal seams burning underneath the surface are recognized all over the world and have drawn increasing public attention in the past years. Frequently, such fires are analyzed by detecting anomalies like increased exhaust gas concentrations and soil temperatures at the surface. A proper analysis presumes the understanding of involved processes, which determine the spatial distribution and dynamic behavior of the anomalies.In this paper, we explain the relevance of mechanical and energy transport processes with respect to the occurrence of temperature anomalies at the surface. Two approaches are presented, aiming to obtain insight into the underground coal fire situation: In-situ temperature mapping and numerical simulation. In 2000 to 2005, annual temperature mapping in the Wuda (Inner Mongolia, PR China) coal fire area showed that most thermal anomalies on the surface are closely related to fractures, where hot exhaust gases from the coal fire are released. Those fractures develop due to rock mechanical failure after volume reduction in the seams. The measured signals at the surface are therefore strongly affected by mechanical processes.More insight into causes and effects of involved energy transport processes is obtained by numerical simulation of the dynamic behavior of coal fires. Simulations show the inter-relation between release and transport of thermal energy in and around underground coal fires. Our simulation results show a time delay between the coal fire propagation and the observed appearance of the surface temperature signal. Additionally, the overall energy flux away from the burning coal seam into the surrounding bedrock is about 30-times higher than the flux through the surface. This is of particular importance for an estimation of the energy released based on surface temperature measurements. Finally, the simulation results also prove that a fire propagation rate estimated from the interpretation of surface anomalies can differ from the actual rate in the seam.     

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC⁺⁺. Examples are provided to demonstrate the new contact rule between two blocks.     

Experimental solidification of anhydrous latitic and trachytic melts at different cooling rates: The role of nucleation kinetics

Two sets of cooling experiments were run at atmospheric conditions for two anhydrous starting latitic and trachytic melts: 1) five cooling rates (25, 12.5, 3, 0.5, and 0.125 °C/min) between 1300° and 800 °C, and 2) a 0.5 °C/min cooling rate from 1300 °C with quench temperatures at 1200°, 1100°, 1000° and 900 °C. Trachytic run-products are invariably glassy. Nucleation is also suppressed in the latitic run-products at the three highest cooling rates. Conversely, in the 0.5 and 0.125 °C/min runs, latites have a crystal content of  90 vol.%. The phases are: plagioclase, clinopyroxene, glass and iron-bearing oxide (in order of abundance). The variable quench temperatures, investigated by coupling experiments with Pt wire and Pt capsule sample containers in set 2, again did not produce crystallization of trachyte, whereas latitic samples are characterized by  10 vol.% of oxides, pyroxenes and plagioclase (in order of appearance), at temperature < 1000 °C. Effects of (preferential) heterogeneous nucleation on sample holders, of superheating degree, and chemical species loss during cooling are absent for both melt compositions. The difference of solidification paths between these two silicate melts can be ascribed only to their small chemical differences. In comparison with calculated equilibrium conditions all the experimental latitic and trachytic run-products revealed strong kinetic effects, interpretable in the light of the nucleation theory. The glass-forming ability (GFA) of trachyte is higher, whereas their critical cooling rate (Rc) is lower (< 0.125 °C/min), in comparison to latitic melts (Rc > 0.5 °C/min). The experimental results carried out in this study can be applied to lava flows and domes; trachytic lavas are able to flow for longer period with respect to latitic ones in a metastable condition. Glass-rich terrestrial lavas, i.e. obsidians, can be the result of sluggish nucleation kinetics due to the relative high polymerisation of evolved silicate melts.