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2014年 第35卷 第1期    刊出日期：2014-01-20

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论文

Water structures inside and outside single-walled carbon nanotubes under perpendicular electric field

徐震 胡国辉 王志亮 周哲玮

2014, 35(1):  1-12.  doi:10.1007/s10483-014-1767-6

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The structures of water inside and outside (6,6), (8,8), and (10,10) singlewalled carbon nanotubes (SWCNTs) under an electric field perpendicular to the tube axis are investigated by molecular dynamics simulations. The results show that dipole reorientation induced by electric field plays a significant role on the structures of confined water inside and outside SWCNTs. Inside SWCNTs, the average water occupancy and the average number of hydrogen bonds (H-bonds) per water molecule decrease as the electric intensity increases. Because the field intensity is sufficiently strong, the initial water structures inside the SWCNTs are destroyed, and the isolated water clusters are found. Outside SWCNTs, the azimuthal distributions of the density and the average number of H-bonds per water molecule around the solid walls become more and more asymmetric as the electric intensity increases. The percentages of water molecules involved in 0–5 H-bonds for all the three types of SWCNTs under different field intensities are displayed. The results show that those water molecules involved with most H-bonds are the most important to hold the original structures. When the electric field direction is parallel with the original preferred orientation, the density and the H-bond connections in water will be increased; when the electric field direction is perpendicular to the original preferred orientation, the density and the H-bond connections in water will be decreased.

Further study of rubber-like elasticity: elastic potentials matching biaxial data

章宇雨 李浩 肖衡

2014, 35(1):  13-24.  doi:10.1007/s10483-014-1768-x

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By virtue of the rational interpolation procedure and logarithmic strain, a direct approach is proposed to obtain elastic potentials that exactly match uniaxial data and shear data for elastomers. This approach reduces the determination of multiaxial elastic potentials to that of two one-dimensional potentials, thus bypassing usual cumbersome procedures of identifying a number of unknown parameters. Predictions of the suggested potential are derived for a general biaxial stretch test and compared with the classical data given by Rivlin and Saunders (Rivlin, R. S. and Saunders, D. W. Large elastic deformation of isotropic materials. VII: experiments on the deformation of rubber. Phill. Trans. Royal Soc. London A, 243, 251–288 (1951)). Good agreement is achieved with these extensive data.

Free torsion of thin-walled structural members of open- and closed-sections

Long-yuan LI D. EASTERBROOK

2014, 35(1):  25-32.  doi:10.1007/s10483-014-1769-6

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Free torsion of thin-walled structures of open- and closed-sections is a classical elastic mechanics problem, which, in literature, is often solved by the method of membrane analogy. The method of membrane analogy, however, can be only applied to structures of a single material. If the structure consists of both open- and closed-sections, the method of membrane analogy is difficult to be applied. In this paper, a new method is presented for solving the free torsion of thin-walled structures of open- and/or closedsections with multiple materials. By utilizing a simple statically indeterminate concept, torsional equations are derived based on the equilibrium and compatibility conditions. The method presented here not only is very simple and easy to understand but also can be applied to thin-walled structures of combined open- and closed-sections with multiple materials.

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method

林治家 庄茁

2014, 35(1):  33-48.  doi:10.1007/s10483-014-1770-8

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An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuumbased shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.

Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

刘小靖 王记增 王晓敏 周又和

2014, 35(1):  49-62.  doi:10.1007/s10483-014-1771-6

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General exact solutions in terms of wavelet expansion are obtained for multiterm time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.

Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature

M. SALARI M. MOHAMMADTABAR A. MOHAMMADTABAR

2014, 35(1):  63-72.  doi:10.1007/s10483-014-1772-8

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The numerical analysis of heat transfer of laminar nanofluid flow over a flat stretching sheet is presented. Two sets of boundary conditions (BCs) are analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanoparticle volume fraction and wall temperature (Case 2). The governing equations and BCs are reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the
increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.

Peristaltic motion of third grade fluid in curved channel

S. HINA M.MUSTAFA T. HAYAT F. E. ALSAADI

2014, 35(1):  73-84.  doi:10.1007/s10483-014-1773-7

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Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems (BVPs) through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.

Impulsive effects on global stability of models based on impulsive differential equations with “supremum” and variable impulsive perturbations

I. M. STAMOVA T.G.STAMOV

2014, 35(1):  85-96.  doi:10.1007/s10483-014-1774-6

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Sufficient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive differential equations with “supremum” and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.

Coupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problems

张文志 黄培彦

2014, 35(1):  97-104.  doi:10.1007/s10483-014-1775-x

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Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value problems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer matrix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

H²-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

郭春晓 郭柏灵 杨慧

2014, 35(1):  105-116.  doi:10.1007/s10483-014-1776-7

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In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H²-regularity random attractor.

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term

李想 张卫国 李正明

2014, 35(1):  117-132.  doi:10.1007/s10483-014-1777-7

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This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing
the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.