Development of an improved three-dimensional rough discrete fracture network model:Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering.Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation.A new 3-dimensional rough discrete fracture network(RDFN3D)model and its modeling method based on the Weierstrass-Mandelbrot(W-M)function were presented in this paper.The RDFN3D model,which improves and unifies the modelling methods for the complex structural planes,has been realized.The influence of fractal dimension,amplitude,and surface precision on the modeling parameters of RDFN3D was discussed.The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed,and the relationship between the mathematical model and the joint characterization was established.The RDFN3D together with the smooth 3-dimensional discrete fracture network(DFN3D)models were successfully exported to the drawing exchange format,which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods.The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code,respectively.The reliability of the RDFN3D model was preliminarily discussed and analyzed.The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns.The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

Stabilization of discrete nonlinear systems based on control Lyapunov functions

The stabilization of discrete nonlinear systems is studied. Based on control Lyapunov functions, a sufficient and necessary condition for a quadratic function to be a control Lyapunov function is given. From this condition, a continuous state feedback law is constructed explicitly. It can globally asymptotically stabilize the equilibrium of the closed-loop system. A simulation example shows the effectiveness of the proposed method.

Dynamics of a Discrete Predator-Prey System with Beddington-DeAngelis Function Response

This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is

Techniques of Discrete Function Transfers into Continuous Function in Practice

One confusing question over a long period of time is how transfer the discrete function transfers into continuous function. Recently the issue has been resolved but some details of the transformation process will be introduced in the paper. The correlation coefficients of 100,000 values are established from the two groups of data with the range between -1 and 1, creating a histogram from these correlation coefficient values known as “the probability mass function.” The coefficient values are brought into the discrete distribution function, so that transfers into the discrete cumulative function, next converted into a continuous cumulative function, next which is differentiated to get the density function, so that it is easy to being research analysis. A model will be established during the process of the conversion what the medium is “the least squares algorithm.” Finally, when the integral of the area within the range of the density function equals to 1, this implies that the transformation complete succeeds from the discrete function to the continuous function.

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

这研究探讨适应控制和函数在 2D Rulkov 分离时间的系统和网络之间的射影的同步问题分离时间的系统。与三个控制器把设计基于背走，一个系统、具体、自动的计划被开发调查功能分离时间的混乱系统的射影的同步。另外，适应控制函数被使用完成二个分离时间的系统的州的同步。数字结果表明建议控制计划的有效性。

Application of Exp-Function Method to Discrete Nonlinear Schrdinger Lattice Equation with Symbolic Computation

In this paper,we present an extended Exp-function method to differential-difference equation(s).Withthe help of symbolic computation,we solve discrete nonlinear Schrdinger lattice as an example,and obtain a series ofgeneral solutions in forms of Exp-function.

ELEMENT FUNCTIONS OF DISCRETE OPERATOR DIFFERENCE METHOD

The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.

The Numerical Integration of Discrete Functions on a Triangular Element

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.

NEW SET OF OPERATOR-VALUED BESSEL FUNCTIONS,THE HOLOMORPHIC DISCRETE SERIES AND ITS ANALYTIC CONTINUATION

ＮＥＷＳＥＴＯＦＯＰＥＲＡＴＯＲ┐ＶＡＬＵＥＤＢＥＳＳＥＬＦＵＮＣＴＩＯＮＳ，ＴＨＥＨＯＬＯＭＯＲＰＨＩＣＤＩＳＣＲＥＴＥＳＥＲＩＥＳＡＮＤＩＴＳＡＮＡＬＹＴＩＣＣＯＮＴＩＮＵＡＴＩＯＮ＊ＤｉｎｇＨｏｎｇｍｉｎｇ（丁鸿明）（Ｓｔ．ＬｏｕｉｓＵｎｉｖｅ...

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.

Constructing exact solutions to discrete systems with the trial function method

Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.

Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.

Reliability Bounds based on Universal Generating Function and Discrete Stress-strength Interference Model

A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method

Function Projective Synchronization of Discrete-Time Chaotic and Hyperchaotic Systems Using Backstepping Method

In this paper,a function projective synchronization scheme is developed to investigate the function projec-tive synchronization between the discrete-time driven chaotic system and the discrete-time response chaotic system.Withthe aid of symbolic-numeric computation,we use the scheme to study the function projective synchronization between2D Lorenz discrete-time system and Hénon discrete-time system,as well as that between 3D discrete-time hyperchaoticsystem and Hénon-like map via three scalar controllers,respectively.Moreover numerical simulations are used to verifythe effectiveness of the proposed scheme.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

功能分离时间的混乱系统的射影的同步被介绍。与三个控制器把设计基于背走，一个系统、具体、自动的计划被开发调查函数有不明确的参数的分离时间的混乱系统的射影的同步(FPS ) 。在符号数字的计算的帮助下，我们使用建议计划与不明确的参数说明在二张相同 3D 象 H é non 一样地图之间的 FPS。数字模拟被用来验证我们的计划的有效性。

Applications of Extended Hyperbolic Function Method for Quintic Discrete Nonlinear SchrSdinger Equation

由使用扩大夸张函数方法，我们学习了 quinticdiscrete 非线性的 Schroedinger 方程并且获得了新准确局部性的解决方案包括分离明亮的 soliton 解决方案，黑暗 soliton 答案，bright 和黑暗 soliton 答案，轮流出现的阶段bright soliton 答案，轮流出现的阶段黑暗 soliton 答案，并且轮流出现阶段bright 和黑暗 soliton 答案，如果一种特殊关系对方程的系数约束力。

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using Backstepping Method

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.