滑坡速度计算及涌浪预测方法探讨

滑坡滑动速度的计算是涌浪预测的基础。在考虑滑坡入水条块受水阻力的基础上,对计算滑速的美国土木工程师协会推荐公式和运动方程方法进行改进,并以三峡库区秭归县下土地岭滑坡为例,计算了滑坡下滑过程中的平均速度及各条块的加速度、速度,对比分析了考虑水阻力前后加速度、速度大小、变化规律,并计算了滑坡下滑激起的初始涌浪高度。结果表明,考虑滑坡入水条块所受的水阻力,更符合滑坡运动过程中的实际受力情况。且水阻力对于滑坡运动的加速度、速度有较大影响,没有考虑水的阻力时,随着入水条块的增多,加速度先增大后减小,且变化趋势不会反弹;考虑水阻力后,由于水阻力大小和滑坡速度及坡面的迎水面积均相关,在两种因素综合作用下,加速度有可能在出现减小趋势后再增大。

AuX(X=O,S)低电子态的理论研究

通常要用多参考态方法才能合理处理需考虑旋轨耦合(SOC)效应的开壳层分子如AuO和AuS的低电子态.事实上,通过选取合适的参考态,采用运动方程耦合簇方法(EOM-CC)也能计算这些分子的一些低电子态,而且EOM-CC方法是单参考态方法,使用起来比多参考态方法更加简单.本文采用最近发展的含旋轨耦合的EOM-CC计算电离能的方法(EOMIP-CC),选取对应的负离子为参考态,在CCSD级别上计算了AuO和AuS低电子态的性质.在不考虑旋轨耦合时,通过比较EOMIP-CCSD和EOMIP-CCSDT的结果考察EOMIPCCSD的精度.此外,与EOMIP-CCSDT结果相比,如果自旋污染较为显著而且T1的模较大时,UCCSD(T)方法对能量最低的某一特定对称性的电子态的所对应的电离能误差约为0.1-0.15 eV.在考虑了旋轨耦合效应后,我们的方法得到的键长和振动频率与实验值吻合较好.另一方面,虽然EOMIP-SOC-CCSD高估了能量较高的2Δ3/2态、2Σ+1/2态和2Π1/2态的能量,但是对于其它能量更低的电子态,它们的能量与已有实验值误差在0.2 eV左右.这显示我们所用的含SOC的EOMIP-CCSD方法对原本需要用多参考态方法才能处理的AuO和AuS低电子态能给出可靠的结果.

NSPMF-EB耦合模型及其在近岸波浪计算中的应用

提出通过耦合透水介质的流体运动方程(NSPMF模型)和改良Boussinesq方程(EB模型)来描述近岸水波现象的数学模型。NSPMF模型的优越性在于它能描述波浪破碎、越浪以及波浪和各种结构物(包括透水性结构物)之间的相互作用等伴随着复杂流动结构的局部波动现象;EB模型则可用于求解广阔海域内非线性不规则波浪的运动和变形过程。耦合模型兼有二者的优势,具有广阔的应用前景。验证计算的结果表明本文建议的耦合方法是有效的。

硫族铅化物阳离子低电子态的理论研究

采用我们最近发展的含旋轨耦合的运动方程耦合簇计算电离能(EOMIP-CC)方法,在CCSD级别上计算了硫族铅化物PbS、PbSe、PbTe阳离子低电子态的平衡键长和谐振频率以及绝热和垂直电离能,得到的结果与已有的实验值吻合较好.不考虑旋轨耦合(SOC)的情况下通过与CCSD(T)的计算结果比较,考察了三重激发对计算结果的影响,结果显示考虑三重激发的贡献后得到的键长和频率结果与实验值吻合更好.计算结果表明PbTe+中2Π态的能量分裂明显大于PbS+和PbSe+中2Π态的能量分裂,但是PbTe+中2Π1/2和2Σ1/2态之间的相互耦合则明显弱于PbS+和PbSe+中这两个态之间的耦合.PbTe+中2Π1/2和2Σ1/2态之间耦合很弱,一方面是因为2Σ+态和2Π态的能量差比PbS+和PbSe+中2Σ+态和2Π态的能量差大,另一方面还由于PbTe+中2Π1/2和2Σ1/2态之间的旋轨耦合矩阵元只是PbS+和PbSe+中2Π1/2和2Σ1/2态之间的旋轨耦合矩阵元的一半.这些计算结果为PbS+、PbSe+、PbTe+阳离子的低电子态性质提供了新的理论数据,可以为将来的实验数据提供参考.

含旋轨耦合的运动方程耦合簇理论计算闭壳层原子激发能

本文采用X2C(exact two-component)哈密顿量,结合我们最近发展的含旋轨耦合的运动方程耦合簇方法,在EOM-CCSD级别上,用接近完备的基函数计算了一系列闭壳层原子体系的最低单重和三重激发能以及激发态的旋轨耦合分裂能.结果显示,对于IIA族原子、IIB族原子、IIIA族阳离子以及稀有气体原子,本文计算得到的激发能与实验值差别通常在0.1 e V以内.对于IB族正离子,由于CCSD方法对其基态存在较大误差,因此激发能被显著高估.对于激发态的旋轨耦合分裂能,前五周期IIA族原子、IIB族原子、IIIA族阳离子计算结果与实验结果吻合非常好,差别通常在1%以内.对于第六周期体系,这个方法得到的激发态旋轨耦合分裂能与实验比有一定误差,这可能是由于求解Hartree-Fock方程时忽略了旋轨耦合所导致.对惰性气体原子,即使是较轻元素,这个方法给出的旋轨耦合分裂能与实验值也有一定差别.

Quantum Entanglement of Parallel-Coupled Double Quantum Dots:a Theoretical Study Using the Hierarchical Equations of Motion Approach

Quantum dots comprise a type of quantum impurity system. The entanglement and co- herence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-rnotion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.

Inverse kinematics of a heavy duty manipulator with 6-DOF based on dual quaternion

An iterative method is introduced successfully to solve the inverse kinematics of a 6-DOF manipulator of a tunnel drilling rig based on dual quaternion, which is difficult to get the solution by Denavit-Hartenberg(D-H) based methods. By the intuitive expression of dual quaternion to the orientation of rigid body, the coordinate frames assigned to each joint are established all in the same orientation, which does not need to use the D-H procedure. The compact and simple form of kinematic equations, consisting of position equations and orientation equations, is also the consequence of dual quaternion calculations. The iterative process is basically of two steps which are related to solving the position equations and orientation equations correspondingly. First, assume an initial value of the iterative variable; then, the position equations can be solved because of the reduced number of unknown variables in the position equations and the orientation equations can be solved by applying the solution from the position equations, which obtains an updated value for the iterative variable; finally, repeat the procedure by using the updated iterative variable to the position equations till the prescribed accuracy is obtained. The method proposed has a clear geometric meaning, and the algorithm is simple and direct. Simulation for 100 poses of the end frame shows that the average running time of inverse kinematics calculation for each demanded pose of end-effector is 7.2 ms on an ordinary laptop, which is good enough for practical use. The iteration counts 2-4 cycles generally, which is a quick convergence. The method proposed here has been successfully used in the project of automating a hydraulic rig.

SA METHOD FOR PREDICTING THE PERFORMANCE OF DASH STOP MANEUVER OF HELICOPTER

The Dash Stop flight at the extreme condition is the primary interest of this study. This paper describes some research on the flight characteristics of helicopter in Dash Stop. A set of equations which govern the Dash Stop is developed. A method which determines the acceleration and deceleration is proposed. Formulas are then developed which relate the aircraft angular rates and attitudes to flight speed, angle of attack and acceleration or deceleration. Finally the DOLPHIN helicopter is taken as an example to calculate its acceleration/deceleration capability, pilot control and aircraft attitudes in space. It is found that the results are reasonable.

Moving collocation methods for time fractional differential equations and simulation of blowup

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.