Applied Mathematics and Mechanics (English Edition)

Constraint-induced restriction and extension operators with applications

陈波李孝伟刘高联

2009, 30(11): 1345-1352. doi:10.1007/s10483-009-1101-x

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The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.

Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction

I.Muhaimin R.Kandasamy Azme B. Khamis

2009, 30(11): 1353-1364. doi:10.1007/s10483-009-1102-6

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An analysis is presented to investigate the effects of variable viscosities and thermal stratification on the MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of a chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically with finite difference methods. Numerical calculations up to the thirdorder level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and show that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those available in literature, and show excellent agreement.

Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

袁益让李长峰杨成顺韩玉笈

2009, 30(11): 1365-1378. doi:10.1007/s10483-009-1103-x

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The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the twodimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal order l2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.

Large eddy simulation of hot and cold fluids mixing in a T-junction for predicting thermal fluctuations

朱维宇卢涛姜培学郭志军王奎升

2009, 30(11): 1379-1392. doi:10.1007/s10483-009-1104-7

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Temperature fluctuations in a mixing T-junction have been simulated on the FLUENT platform using the large eddy simulation (LES) turbulent flow model and a sub-grid scale Smagorinsky-Lilly model. The normalized mean and root mean square temperatures for describing time-averaged temperature and temperature fluctuation intensity, and the velocity are obtained. The power spectrum densities of temperature fluctuations, which are key parameters for thermal fatigue analysis and lifetime evaluation, are analyzed. Simulation results are consistent with experimental data published in the literature, showing that the LES is reliable. Several mixing processes under different conditions are simulated in order to analyze the effects of varying Reynolds number and Richardson number on the mixing course and thermal fluctuations.

Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach

Zafar Iqbal Muhammad Nawaz Naeem Nazra Sultana Shahid Hussain Arshad Abdul Ghafar Shah

2009, 30(11): 1393-1404. doi:10.1007/s10483-009-1105-x

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The vibration characteristics of a functionally graded material circular cylindrical shell filled with fluid are examined with a wave propagation approach. The shell is filled with an incompressible non-viscous fluid. Axial modal dependence is approximated by exponential functions. A theoretical study of shell vibration frequencies is analyzed for simply supported-simply supported, clamped-simply supported, and clamped-clamped boundary conditions with the fluid effect. The validity and the accuracy of the present method are confirmed by comparing the present results with those available in the literature. Good agreement is observed between the two sets of results.

Design method of multiple time-delay controller for active structural vibration control

陈龙祥蔡国平

2009, 30(11): 1405-1414. doi:10.1007/s10483-009-1106-z

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An optimal control method for seismic-excited building structures with multiple time delays is investigated in this paper. The system state equation with multiple time delays is discretized and transformed into a standard discrete form without any explicit time delay by a particular augmenting for state variables. A time-delay controller is then designed based on this standard equation using the discrete optimal control method. Effectiveness of the proposed controller is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in the instability of the control system if it is not compensated in the control design. Time delay may be compensated effectively by the proposed controller, in the mean time, an effective control may be obtained. The proposed controller is valid for both small and large time delays.

Neurodynamics analysis of brain information transmission

王如彬张志康 Chi K. Tse

2009, 30(11): 1415-1428. doi:10.1007/s10483-009-1107-y

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This paper proposes a model of neural networks consisting of populations of perceptive neurons, inter-neurons, and motor neurons according to the theory of stochastic phase resetting dynamics. According to this model, the dynamical characteristics of neural networks are studied in three coupling cases, namely, series and parallel coupling, series coupling, and unilateral coupling. The results show that the indentified structure of neural networks enables the basic characteristics of neural information processing to be described in terms of the actions of both the optional motor and the reflected motor. The excitation of local neural networks is caused by the action of the optional motor. In particular, the excitation of the neural population caused by the action of the optional motor in the motor cortex is larger than that caused by the action of the reflected motor. This phenomenon indicates that there are more neurons participating in the neural information processing and the excited synchronization motion under the action of the optional motor.

First fundamental problems of anisotropic elastic plane weakened by periodic collinear cracks

蔡海涛路见可

2009, 30(11): 1429-1436. doi:10.1007/s10483-009-1108-3

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Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46(1), 133–142 (1993)]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.

Plane strain consolidation of soil layer with anisotropic permeability

艾智勇吴超

2009, 30(11): 1437-1444. doi:10.1007/s10483-009-1109-7

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This paper presents an alternative analytical technique to study a plane strain consolidation of a poroelastic soil by taking into account the anisotropy of permeability. From the governing equations of a saturated poroelastic soil, the relationship of basic variables for a point of a soil layer is established between the ground surface (z = 0) and the depth z in the Laplace-Fourier transform domain. Combined with the boundary conditions, an exact solution is derived for plane strain Biot’s consolidation of a finite soil layer with anisotropic permeability in the transform domain. Numerical inversions of the Laplace transform and the Fourier transform are adopted to obtain the actual solution in the physical domain. Numerical results of plane strain Biot’s consolidation for a single soil layer show that the anisotropic of permeability has a great influence on the consolidation behavior of the soils.

Propagation of plane waves at the imperfect boundary of elastic and electro-microstretch generalized thermoelastic solids

Rajneesh Kumar Rupender

2009, 30(11): 1445-1454. doi:10.1007/s10483-009-1110-6

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The problem of reflection and transmission of plane waves incident on the contact surface of an elastic solid and an electro-microstretch generalized thermoelastic solid is discussed. It is found that there exist five reflected waves, i.e., longitudinal displacement (LD) wave, thermal (T) wave, longitudinal microstretch (LM) wave and two coupled transverse displacement and microrotational (CD(I) and CD(II)) waves in the electro-microstretch generalized thermoelastic solid, and two transmitted waves, i.e., longitudinal (P) and transverse (SV) waves in the elastic solid. The amplitude ratios of different reflected and transmitted waves are obtained for an imperfect boundary and deduced for normal force stiffness, transverse force stiffness, and perfect bonding. The variations of amplitude ratios with incidence angles have been depicted graphically for
the LD wave and the CD(I) wave. It is noticed that the amplitude ratios of reflected and transmitted waves are affected by the stiffness, electric field, stretch, and thermal properties of the media. Some particular interest cases have been deduced from the present investigations.

A class of singular perturbation solutions to semilinear equations of fourth order

莫嘉琪

2009, 30(11): 1455-1460. doi:10.1007/s10483-009-1111-x

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A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied. In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

刘冠琦王玉文史峻平

2009, 30(11): 1461-1468. doi:10.1007/s10483-009-1112-z

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In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.

Stability of Schrödinger-Poisson type equations

黄娟张健陈光淦

2009, 30(11): 1469-1474. doi:10.1007/s10483-009-1113-y

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Variational methods are used to study the nonlinear Schr¨odinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.

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