Applied Mathematics and Mechanics (English Edition)

The Riemann problem for nonlinear degenerate wave equations

孙文华盛万成

2010, 31(6): 665-674. doi:10.1007/s10483-010-1301-9

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This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

F.S.IBRAHIM F.M.HADY S.M.ABDEL-GAIED M.R.EID

2010, 31(6): 675-684. doi:10.1007/s10483-010-1302-9

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The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimensionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are presented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ, the order of the chemical reaction parameter m, the Soret number S_r, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

Investigation over the recirculation influence on the combustion of micro organic dust particles

M.BIDABDI A.FANAEE A.RAHBARI

2010, 31(6): 685-696. doi:10.1007/s10483-010-1303-7

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This paper investigates the role of recirculation and non-unity Lewis number on the combustion of organic dust particles. Since recirculation effect is more noticeable in micro-combustors, it is necessary to propose a modeling approach of this phenomenon to better simulate the performance of micro-combustors. In this research, in order to model the combustion of organic dust particles, it is assumed that the dust particles vaporize first to yield a known chemical structure which is oxidized in the gas phase, and the chemical structure of this gaseous fuel is assumed methane. To study the flame structure and solve the governing equations, it is considered that the flame structure consists of three zones titled the preheat-vaporization zone, the narrow reaction zone and finally the post flame zone. The recirculation phenomenon is evaluated by entering the exhausted heat from the post flame zone into the preheat zone. The solution is based on the following approach. First, the governing equations in each zone are nondimensionalized. Then the needed boundary and matching conditions are applied in each zone. After that, these equations and the required boundary and matching conditions are simultaneously solved with the analytical model. Consequently, the remarkable effects of recirculation and nonunity Lewis number on the combustion characteristics of the organic dust particles such as burning velocity and temperature profiles for different particle radii are obtained. The results show reasonable agreement with published experimental data.

Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains

姜金平侯延仁

2010, 31(6): 697-708. doi:10.1007/s10483-010-1304-x

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The existence of the pullback attractor for the 2D non-autonomous g-Navier-Stokes equations on some bounded domains is investigated under the general assumptions of pullback asymptotic compactness. A new method to prove the existence of the pullback attractor for the 2D g-Navier-Stokes equations is given.

Secondary flow coefficient of overbank flow

杨中华高伟槐文信

2010, 31(6): 709-718. doi:10.1007/s10483-010-1305-9

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This paper presents a 2D analytical solution for the transverse velocity distribution in compound open channels based on the Shiono and Knight method (SKM), in which the secondary flow coefficient (K-value) is introduced to take into account the effect of the secondary flow. The modeling results agree well with the experimental results from the Science and Engineering Research Council-Flood Channel Facility (SERC-FCF). Based on the SERC-FCF, the effects of geography on the secondary flow coefficient and the reason for such effects are analyzed. The modeling results show that the intensity of the secondary flow is related to the geometry of the section of the compound channel, and the sign of the K-value is related to the rotating direction of the secondary flow cell. This study provides a scientific reference to the selection of the K-value.

Boundary-layer eigen solutions for multi-field coupled equations in the contact interface

侯磊李涵灵张家健林德志仇璘

2010, 31(6): 719-732. doi:10.1007/s10483-010-1306-z

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The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how constraints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact interface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This paper describes the field affected by the gravity constraints. Applying the multi-scale analysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analysis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic perturbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.

Lag synchronization between discrete chaotic systems with diverse structure

柴元吕翎赵鸿雁

2010, 31(6): 733-738. doi:10.1007/s10483-010-1307-7

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A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda systems. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchronization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.

Dynamic bifurcation of the n-dimensional complex Swift-Hohenberg equation

肖庆坤高洪俊

2010, 31(6): 739-750. doi:10.1007/s10483-010-1308-6

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This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a onedimensional domain (0, L) is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condition when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.

On the stability of equilibria of nonholonomic systems with nonlinear constraints

V.COVIC M.VESKOVIC D.DJURIC A.OBRADOVIC

2010, 31(6): 751-760. doi:10.1007/s10483-010-1309-7

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Lyapunov’s first method, extended by V. V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The motion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin’s series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlinear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.

Weighted estimates for strongly singular integral operators with rough kernels

黄文礼陶祥兴李胜宏

2010, 31(6): 761-768. doi:10.1007/s10483-010-1310-z

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The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

Singularly perturbed reaction diffusion equations with time delay

莫嘉琪温朝晖

2010, 31(6): 769-774. doi:10.1007/s10483-010-1311-6

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A class of initial boundary value problems of differential-difference equations for reaction diffusion with a small time delay is considered. Under suitable conditions and by using the stretched variable method, a formal asymptotic solution is constructed. Then, by use of the theory of differential inequalities, the uniform validity of the solution is proved.

Local Hopf bifurcation and global existence of periodic solutions in TCP system

徐昌进唐先华廖茂新

2010, 31(6): 775-786. doi:10.1007/s10483-010-1312-x

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This paper investigates the dynamics of a TCP system described by a firstorder nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the positive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifurcating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350(12), 4799–4838 (1998)).

Blow-up rate estimate for degenerate parabolic equation with nonlinear gradient term

张正策王彪

2010, 31(6): 787-796. doi:10.1007/s10483-010-1313-6

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In this paper, the blow-up rate is obtained for a porous medium equation with a nonlinear gradient term and a nonlinear boundary flux. By using a scaling method and regularity estimates of parabolic equations, the blow-up rate determined by the interaction between the diffusion and the boundary flux is obtained. Compared with previous results, the gradient term, whose exponent does not exceed two, does not affect the blow-up rate of the solutions.

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