难度系数评分法

本文运用概率统计的理论导出难度系数的计算公式 :D (x) =0 .1Φ- 1(x* ) + 0 .5,进而给出以此公式的计分公式 T =aΦ- 1(x* ) + b。

Rules of distribution in a plastic zone of rocks surrounding a roadway affected by tectonic stress

In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theoretical formula for the plastic zone of rocks surrounding a roadway. We also analyzed the distribution characteristics of the plastic zone under different levels of tectonic stress, vertical pressure, cohesion and friction angle of the surrounding rock. Secondly, we used numerical simulation to analyze the range and shape features of the plastic zone of rocks surrounding the roadway, given different tectonic stress levels. Finally we used a rock drilling detector to carry out field measurements on the broken state of rock surrounding the roadway at the –700 substation and channels in the Xinzhuang mine of the Shenhuo mining area. Given the measured ground stress, we analyzed the relationship between tectonic stress and the distribution of this plastic zone. Our results show that the range of the plastic zone at the top and bottom of the roadway increases with an increase in tectonic stress and this increase is especially obvious at the roadway corner.

A new method determining safe thickness of karst cave roof under pile tip

Cave roofs are used to support pile foundation in many engineering projects. Accurate stability analysis method of cave roof under pile tip is important in order to ensure the safety of the pile foundation structure. Firstly the mechanical model to analysis the stability of cave roof under pile tip is founded aiming to solve the problems that the simplified mechanical model has. Secondly, the boundary of cave roof is simply supposed to be supported according to the integrity of the rock mass in the boundary of cave roof. Thirdly, based on the theory of plates and shells, the simplified model is calculated and the theoretical calculation formula to determine the safe thickness of cave roof under pile tip can be obtained when the edges of the cave roof are simply supported. In the end, the analysis of the practical engineering project proves the feasibility and the rationality of the method which can be a new method to calculate the safe thickness of cave roof under pile tip.

Nonhomogeneous(H,Q)-Process:The Backward and Forward Equations

As for the backward and forward equation of nonhomogeneous(H, Q) -processes,we proof them in a new way. On the base of that, this paper gives the direct computational formalfor one dimensional distribution of the nonhomogeneous(H, Q) -process.

Wind energy input in coastal seas east of China

This study investigates the wind energy input, an important source of mechanical energy, in the coastal seas east of China. Using the wind field from the high-resolution sea surface meteorology dataset in the Bohai Sea, Yellow Sea, and East China Sea, we studied the wind energy input through surface ageostrophic currents and surface waves. Using a simple analytical formula for the Ekman Spiral with time- dependent wind, the wind energy input through ageostrophic currents was estimated at -22 GW averaged from 1960 to 2007, and through use of an empirical formula, the wind energy input through surface waves was estimated at -169 GW. We also examined the seasonal variation and long-term tendency of mechanical energy from wind stress, and found that the wind energy input to the East China Sea decreased before the 1980s, and then subsequently increased, which is contrary to what has been found for the Bohai Sea and Yellow Sea. More complicated physical processes and varying diffusivity need to be taken into account in future studies.

Temperature rise of He Ⅱ forced flow and its negative Joule-Thomson effect

The temperature rise of He Ⅱ transfer system due to the negative Joule-Thomson(JT)effect is one of the major problems in the He Ⅱ forced flow system design.Negative Joule-Thomson effect of the He Ⅱ forced flow was analyzed and calculated in this paper.The temperature rise due to the heat leak along the transfer pipeline was calculated by the simplified equation and was modified by considering the negative Joule-Thomson effect.The modified results were compared with the temperature rise obtained by non-linear differential equations with consideration of the pressure gradient.The results show that the pressure gradient has strong effect on the temperature distribution.The modified results are in good agreement with the values calculated by the complicated equation,which verifies the effectiveness of the simplified equation in calculating the temperature rise when the negative JT effect of He Ⅱ is known.

Distribution of acceleration and empirical formula for calculating maximum acceleration of rockfill dams

To find the distribution patterns of dynamic amplification coefficients for dams subjected to earthquake, 3D seismic responses of concrete-faced rockfill dams with different heights and different shapes of river valley were analyzed by using the equivalent-linear model. Statistical analysis was also made to the seismic coefficient, and an empirical formula for calculating the maximum acceleration was provided. The results indicate that under the condition of the same dam height and the same base acceleration excitations, with the increase of the river valley width, the position of the maximum acceleration on the axis of the top of the dam moves from the center to the riversides symmetrically. For the narrow valleys, the maximum acceleration occurs in the middle of the axis at the top of the dam; for wide valleys the maximum acceleration appears near the riversides. The result negates the application of 2D dynamical computation for wide valleys, and shows that for the seismic response of high concrete-faced rockfill dams, the seismic coefficient along the axis should be given, except for that along the dam height. Seismic stability analysis of rockfill dams using pseudo-static method can be modified according to the formula.

Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs

In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson （C-N） scheme for solving decoupled FBSDEs. Based on the Taylor and ItS-Taylor expansions, the Malliavin calculus theory （e.g., the multiple Malliavin integration-by-parts formula）, and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.

Application of Connection in Molecular Dynamics

The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the former gets analytic expression; the latter depends on heavy numerical calculation,which contains uncertainty.By using connection of fiber bundles,this paper establishes an analytic formula for the latter,and the numerical work is simplified.It shows the mathematical structure of molecule is fiber bundle.