分形方法在洪涝灾害预测中的应用——以广西梧州为例

洪涝灾害是由暴雨洪水形成的一种突发性、最常见的自然灾害,它的发生在时间序列上具有分形特征.以广西梧州解放以来发生的特大洪涝灾害年份建立灾变日期序列,运用分式布朗运动模型中的R/S分析对洪涝灾害发生的时间序列进行模拟,计算了H指数值,建立R(t)/S(t)的幂函数关系式等,并以此为依据,预测下次灾年将在1999年出现.

Fractal evolution mechanism of rock fracture in undersea metal mining

Through rock mechanics test, similar simulation experiment, borehole photographic observation of rock fissure, numerical simulation calculation of plastic zone distribution and deformation monitoring of rock mass during undersea mining, the fractal evolution mechanisms of rock fracture in undersea metallic deposits of Sanshandao Gold Mine were studied by fractal theory. The experimental researches on granite mechanics test in undersea deposit indicate that with the increase of load, the granite deformation energy and the fractal dimension of acoustic emission(FDAE) increase gradually. However, after reaching the peak stress of specimen, the fractal dimensions of acoustic emission(FDAEs) decrease and the granite specimen fails. Therefore, the fractal dimension evolution of rock failure can be divided into four stages, which are fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, respectively. By calculating and analyzing the damage photographs of rock specimens in Sanshandao Gold Mine, the fractal dimension of rock fissure is 1.4514, which is close to the average value of FDAE during granite destruction, i.e., 1.4693. Similar simulation experiments of undersea mining show that with the excavation proceeding, the FDAE in rock stratum increases gradually, and when the thickness of the isolation roof is less than 40 m, the FDAE begins to decrease, and meanwhile the sign of water inrush emerges. The numerical simulation researches on the plastic zone distribution of undersea mining in Sanshandao Gold Mine indicate that the fractal dimension of plastic zone(FDPZ) where the failure characteristics occur is 1.4598, close to the result of similar simulation experiment of 1.4364, which shows the sign of water inrush. Meanwhile, the thickness of the isolation roof for undersea mining should be more than 40 m, which is consistent with the results of similar simulation experiment. In Sanshandao Gold Mine, the rock fissures in undersea mining were observed by borehole photography and the rock mass deformation was monitored by multi-point displacement meters, and at the same time the fractal dimensions of strata borehole fissure distribution and energy release ratio(ERR) of rock mass were calculated by fractal principle, which are 1.2328 and 1.2685, respectively. The results demonstrate that rock deformation and fissure propagation are both in the second stage of fissure growth, and have not reached the fourth stage of fracture instability. Therefore, the conclusion can be obtained that the undersea mining in Sanshandao Gold Mine is safe at present.

Low-Bias Conductance Mechanism of Diarylethene Isomers:a First-Principle Study

The structure-property relationship of diarylethene(DAE)-derivative molecular isomers,which involve ring-closed and ring-open forms,is investigated by employing the nonequilibrium Green’s function formalism combined with density functional theory.Molecular junctions are formed by the isomers connecting to Au(111)electrodes through flanked pyridine groups.The difference in electronic structures caused by different geometry structures for the two isomers,particularly the interatomic alternative single bond and double bond of the ring-closed molecule,contributes to the vastly different low-bias conductance values.The lowest unoccupied molecular orbital(LUMO)of the isomers is the main channel for electron transport.In addition,more electrons transferred to the ring-closed molecular junction in the equilibrium condition,thereby decreasing the LUMO energy to near the Fermi energy,which may contribute to a larger conductance value at the Fermi level.Our findings are helpful for understanding the mechanism of low-bias conductance and are conducive to the design of high-performance molecular switching based on diarylethene or diarylethene-derivative molecules.

(G′/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.

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.