应用数学和力学

2001 Vol. 22, No. 5

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Study on the Prediction Method of Low-Dimension Time Series That Arise From the Intrinsic Nonlinear Dynamics

MA Jun-hai, CHEN Yu-shu

2001, 22(5): 441-448.

Abstract(2552) PDF(701)

Abstract:
The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low dimension are discussed mainly.Based on the work of the foreign researchers,the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed.At first,the model parameters were estimated by using the improved least square method.Then as the precision was satisfied,the optimization method was used to estimate these parameters.At the end by using the obtained chaotic model,the future data of the chaotic time series in the phase space was predicted.Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper.The results show that if the algorithms developed here are adopted,the parameters of the corresponding chaotic model will be easily calculated well and true.Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations.And if the optimal model rank is chosen,the prediction precision will increase notably.Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable.

Influences of Slope Gradient on Soil Erosion

LIU Qing-quan, CHEN LI, LI Jia-chun

2001, 22(5): 449-457.

Abstract(2514) PDF(817)

Abstract:
The main factors influencing soil erosion include the net rain excess,the water depth,the velocity,the shear stress of overland flows,and the erosion-resisting capacity of soil.The laws of these factors varying with the slope gradient were investigated by using the kinematic wave theory.Furthermore,the critical slope gradient of erosion was driven.The analysis shows that the critical slope gradient of soil erosion is dependent on grain size,soil bulk density,surface roughness,runoff length,net rain excess,and the friction coefficient of soil,etc.The critical slope gradient has been estimated theoretically with its range between 41.5°~50°.

A New Completely Integrable Liouville’s System, Its Lax Representation and Bi-Hamiltonian Structure

FAN En-gui, ZHANG Hong-qing

2001, 22(5): 458-464.

Abstract(2388) PDF(1292)

Abstract:
A new isospectral problem and the corresponding hierarchy of nonlinear evolution equations is presented.As a reduction,the well-known MKdV equation is obtained.It is shown that the hierarchy of equations is integrable in Liouville's sense and possesses Bi-Hamiltonian structure.Under the constraint between the potentials and eigenfunctions,the eigenvalue problem can be nonlinearized as a finite dimensional completely integrable system.

Forces and Moments of the Liquid Finite Amplitude Sloshing in a Liquid-Solid Coupled System

GOU Xing-yu, LI Tie-shou, MA Xing-rui, WANG Ben-li

2001, 22(5): 465-476.

Abstract(2605) PDF(593)

Abstract:
Nonlinear coupling dynamics between a spring-mass system and a finite amplitude sloshing system with liquid in a cylindrical tank is investigated.Based on a group of nonlinear coupling equations of six degrees of freedoms,analytical formulae of forces and moments of the liquid large amplitude sloshing were obtained.Nonlinearity of the forces and moments of the sloshing was induced by integrating on final configuration of liquid sloshing and the nonlinear terms in the liquid pressure formula.The symmetry between the formula of ox and oy direction proves that the derivation is correct.According to the coupled mechanism,the formulae are available in other liquid-solid coupled systems.Simulations and corresponding experimental results arecompared.It is shown that the forces and moments formulae by integrating on the final sloshing configuration are more reasonable.The omitted high-dimensional modal bases and high-order nonlinear terms and the complexity of sloshing damping are main sources of errors.

Auto-Darboux Transformation and Exact Solutions of the Brusselator Reaction Diffusion

YAN Zhen-ya, ZHANG Hong-qing

2001, 22(5): 477-482.

Abstract(2480) PDF(827)

Abstract:
Firstly,using the improved homogeneous balance method,an auto-Darboux transformation(ADT) for the Brusselator reaction diffusion model is found.Based on the ADT,several exact solutions are obtained which contain some authors.results known.Secondly,by using a series of transformations,the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method,more exact solutions are found which contain soliton solutions.

The Crack-Inclusion Interaction and the Analysis of Singularity for the Horizontal Contact

TAO Fang-ming, TANG Ren-ji

2001, 22(5): 483-492.

Abstract(2539) PDF(519)

Abstract:
Using the basic solutions of a single crack and a single inclusion,and making use of the principle of linear superposition of elastic mechanics,the interaction problem between a planar crack and a flat inclusion in an elastic solid is studied.The problem is reduced to solve a set of standard Cauchy-type singular equations.And the stress intensity factors at points of crack and inclusion were obtained.Besides,the singularity for the horizontal contact of crack and inclusion was analyzed.The calculating model put forward can be regarded as a new technique for studying the crack and its expanding caused by inclusion tip.Then several numerical examples are given.

A Computational Method for Interval Mixed Variable Energy Matrices in Precise Integration

GAO Suo-wen, WU Zhi-gang, WANG Ben-li, MA Xing-rui

2001, 22(5): 493-498.

Abstract(2237) PDF(502)

Abstract:
To solve the Riccati equation of LQ control problem,the computation of interval mixed variable energy matrices is the first step.Taylor expansion can be used to compute the matrices.According to the analogy between structural mechanics and optimal control and the mechanical implication of the matrices,a computational method using state transition matrix of differential equation was presented.Numerical examples are provided to show the effectiveness of the present approach.

Fixed Points on Two Complete and Compact Metric Spaces

M. Telci

2001, 22(5): 499-503.

Abstract(2210) PDF(937)

Abstract:
By using functions,some related fixed point theorems on two metric spaces are established.These results generalize some theorems of Fisher.

Uniform Analytic Construction of Wavelet Analysis Filters Based on Sine and Cosine Trigonometric Functions

LI Jian-ping, TANG Yuan-yan, YAN Zhong-hong, ZHANG Wan-ping

2001, 22(5): 504-518.

Abstract(2531) PDF(868)

Abstract:
Based on sine and cosine functions,the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time.When N=2^k-1 and N=2k,the unified analytic constructions of orthogonal wavelet filters are put forward,respectively.The famous Daubechies filter and some other well known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.

A 1/3 Pure Subharmonic Solution and Transient Process for the Duffing’s Equation

XU Yu-xiu, BAO Wen-bo, W.Schiehlen, HU Hai-yan

2001, 22(5): 519-524.

Abstract(2089) PDF(564)

Abstract:
The 1/3 subharmonic solution for the Duffing s equation is investigated by using the methods of harmonic balance and numerical integration.The sensitivity of parameter variation for the transient process and the transient process for the perturbance initial conditions are studied.Over and above,the precision of numerical integration method is discussed and the numerical integration method is compared with the harmonic balance method.Finally,asymptotical stability of the pure subharmonic oscillations element is inspected.

[0,k_i]₁^m-Factorizations Orthogonal to a Subgraph

MA Run-nian, XU Jin, GAO Hang-shan

2001, 22(5): 525-528.

Abstract(1704) PDF(562)

Abstract:
Let G be a graph,k₁,…,k_m be positive integers.If the edges of graph G can be decom- posed into some edge disjoint [0,k₁]-factor F₁…,[0,k_m]-factor F_m then we can say F={F₁,…,F_m},is a [0,k_i]₁^m-factorization of G.If H is a subgraph with m edges in graph G and |E(H)∩E(F_i)|=1 for all 1≤i≤m,then we can call that F is orthogonal to H.It is proved that if G is a[0,k₁+… +k_m-m+1]-graph,H is a subgraph with m edges in G,then graph G has a [0,k_i]₁^m-factorization orthogonal to H.

Probability Inequalities for Sums of Independent Unbounded Random Variables

ZHANG Di-xin, WANG Zhi-cheng

2001, 22(5): 529-533.

Abstract(2302) PDF(942)

Abstract:
The tail probability inequalities for the sum of independent undbounded random variables on a probability space(Ω,T,P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space(Ω,T,P).The probability exponential inequalities for sums of independent unbounded random variables were given.As applications of the results,some interesting examples were given.The examples show that the method proposed in the paper and the results of the paper are guite useful in the study of the large sample properties of the sums of independent unbounded random variables.

Convergence of a Modified SLP Algorithm for the Extended Linear Complementarity Problem

XIU Nai-hua, GAO Zi-you

2001, 22(5): 534-540.

Abstract(2116) PDF(568)

Abstract:
A modified sequential linear programming algorithm is presented,whose subproblem is always solvable,for the extended linear complementarity problem(XLCP),the global convergence of the algorithm under assumption of X-row sufficiency or X-column monotonicity is proved.As a result,a sufficient condition for existence and boundedness of solution to the XLCP are obtained.

Locking-Free Degenerated Isoparametric Shell Element

ZHANG Xiang-ming, WANG An-wen, HE Han-lin

2001, 22(5): 541-549.

Abstract(2443) PDF(522)

Abstract:
An 8-noded locking-free degenerated isoparametric shell element is presented.A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation,rotation and constant curvature) are preserved,which can be used to eliminate shear locking.A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior.The new 8-noded element has the proper rank,with the requisite number of zero eigenvalues each associated with a rigid mode.The element does not exhibit membrane or shear locking for large span-thickness ratio.The element does not form element mechanisms or extra spurious zero energy modes.Therefore,it can be used for both thin and thick shells.

2001, 22(5): 550-550.

Abstract(1506) PDF(426)

Abstract: