应用数学和力学

2004 Vol. 25, No. 6

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Study on Prediction Methods for Dynamic Systems of Nonlinear Chaotic Time Series

MA Jun-hai, CHEN Yu-shu, XIN Bao-gui

2004, 25(6): 551-557.

Abstract(2683) PDF(644)

Abstract:
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached: High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.

Stress Field at a Tip of a Prefabricated Spiral V-Notch

ZHENG Zhou-lian, CHEN Shan-lin, YE Xiao-ming

2004, 25(6): 558-562.

Abstract(2388) PDF(498)

Abstract:
Based on the tranditional V-notched blasting, a technique of spirally V-notched blasting to loosen earth and rock was presented. Fracture mechanics and Westergaard stress function were adopted to build a complex stress function to derive the plane stress and strain fields at one tip of the crack under a quasi-static pressure. An expression was formulated to define the stress intensity factor of spiral V-notch loosen blasting. Factors that have effects on the stress intensity factor were studied. It is demonstrated that spiral V-notch loosen blasting is an extension of vertical V-notch blasting, straight cracking, and alike theories.

Nonempty Intersection Theorems and System of Generalized Vector Equilibrium Problems in Product G-Convex Spaces

DING Xie-ping

2004, 25(6): 563-571.

Abstract(2393) PDF(739)

Abstract:
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Multi-Valued Quasi Variational Inclusions in Banach Spaces

ZHANG Shi-sheng

2004, 25(6): 572-580.

Abstract(2428) PDF(689)

Abstract:
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces. By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established. The results generalize, improve and unify a number of Noor's and others' recent results.

Study on the Adjoint Method in Data Assimilation and the Related Problems

LÜ Xian-qing, WU Zi-ku, GU Yi, TIAN Ji-wei

2004, 25(6): 581-590.

Abstract(2549) PDF(861)

Abstract:
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M₂ tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M₂ tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.

Interaction of Viscous Wakes With a Free Surface

LU Dong-qiang

2004, 25(6): 591-598.

Abstract(2961) PDF(696)

Abstract:
The interaction of laminar wakes with free-surface waves generated by a moving body beneath the surface of an incompressible viscous fluid of infinite depth was investigated analytically. The analysis was based on the steady Oseen equations for disturbed flows. The kinematic and dynamic boundary conditions were linearized for the small-amplitude free-surface waves. The effect of the moving body was mathematically modeled as an Oseenlet. The disturbed flow was regarded as the sum of an unbounded singular Oseen flow which represents the effect of the viscous wake and a bounded regular Oseen flow which represents the influence of the free surface. The exact solution for the free-surface waves was obtained by the method of integral transforms. The asymptotic representation with additive corrections for the free-surface waves was derived by means of Lighthill's two-stage scheme. The symmetric solution obtained shows that the amplitudes of the free-surface waves are exponentially damped by the presences of viscosity and submergence depth.

Characteristic Analysis for Stress Wave Propagation in Transversely Isotropic Fluid-Saturated Porous Media

LIU Ying, LIU Kai-xin

2004, 25(6): 599-606.

Abstract(2556) PDF(721)

Abstract:
According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.

Nonlinear Transient Response of Stay Cable With Viscoelasticity Damper in Cable-Stayed Bridge

CHEN Shui-sheng, SUN Bing-nan, FENG Yi-qing

2004, 25(6): 607-613.

Abstract(2571) PDF(593)

Abstract:
Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.

Theoretical Analysis on Hydraulic Transient Resulted by Sudden Increase of Inlet Pressure for Laminar Pipeline Flow

DENG Song-sheng, ZHOU Shao-qi, LIAO Zhen-fang, QIU Zheng-yang, ZENG Shun-peng

2004, 25(6): 614-620.

Abstract(2659) PDF(527)

Abstract:
Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.

Mid-Facets of a Simplex

LI Xiao-yan, HE Bin-wu, LENG Gang-song

2004, 25(6): 621-626.

Abstract(2090) PDF(797)

Abstract:
The mid-facet of a simplex in n-dimensional Euclidean space which was introduced quite recently is an important geometric element. An analytic expression for the mid-facet area of a simplex is firstly given. In order to obtain the expression, the exterior differential method was presented. Furthermore, the properties of the mid-facets of a simplex analogous to median lines of a triangle (such as for all mid-facets of a simplex, there exists another simplex such that its edge-lengths equal to these mid-facets area respectively, and all of the mid-facets of a simplex have a common point) were proved. Finally, by applying the analytic expression, a number of inequalities which combine edge- lengths, circumradius, median line, bisection area and facet area with the mid-facet area for a simplex were established.

Global Stability Analysis in Cellular Neural Networks With Unbounded Time Delays

ZHANG Ji-ye

2004, 25(6): 627-634.

Abstract(2181) PDF(718)

Abstract:
Without assuming the boundedness and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of cellular neural networks with unbounded time delays and variable delays were studied. Using the idea of vector Liapunov method, the intero-differential inequalities with unbounded delay and variable delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions for global asymptotic stability of cellular neural networks were obtained.

Streamline-Based Mathematical Model for CO₂ Miscible Flooding

HOU Jian

2004, 25(6): 635-642.

Abstract(2824) PDF(686)

Abstract:
According to the research theory of improved black oil simulator, a practical mathematical model for CO₂ miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO₂ drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO₂ drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening and reservoir dynamic management of the CO₂ miscible oil field.

Global Existence and Blow-up Phenomena of Classical Solutions for the System of Compressible Adiabatic Flow Through Porous Media

LIU Fa-gui, KONG De-xing

2004, 25(6): 643-652.

Abstract(2862) PDF(844)

Abstract:
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small' solution.

Prediction of Mode Ⅰ Crack Propagation Direction in Carbon-Fiber Reinforced Composite Plate

ZHANG Shao-qin, YANG Wei-yang

2004, 25(6): 653-660.

Abstract(2271) PDF(586)

Abstract:
A newly developed Z fracture criterion for the composite materials was introduced, the new concepts of in-plane average strain, in-plane dilatational strain energy density factor and reciprocal characteristic function were presented. Many experimental results show that the Z fracture criterion can be well used to predict the crack propagating direction for mode crack in carbon-fiber reinforced composite laminates.