Applied Mathematics and Mechanics (English Edition)

Nonlinear effects of line tension in adhesion of small droplets

LV Cun-jing;YIN Ya-jun;ZHENG Quan-shui

2008, 29(10): 1251-1262 . doi:10.1007/s10483-008-1001-7

Abstract ( 2185 )

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hree-phase line tensions may become crucial in the adhesion of micro-nano or small droplets on solid planes. In this paper we study for the first time the nonlinear effects in adhesion spanning the full range of physically possible parameters of surface tension, line tension, and droplet size. It is shown that the nonlinear adhesion solution spaces can be characterized into four regions. Within each region the adhesion behaves essentially the same. Especially, inside the characteristic regions with violent nonlinearities, the co-existence of multiple adhesion states for given materials is disclosed. Besides, two common fixed points in the solution space are revealed. These new results are consistent with numerical analysis and experimental observations reported in the literatures.

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

M. K. Ghosh;M. Kanoria

2008, 29(10): 1263-1278 . doi:10.1007/s10483-008-1002-2

Abstract ( 1622 )

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This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

Dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads

Lü Nian-chunCHENG Yun-hong;LI Xin-gang;CHENG Jin

2008, 29(10): 1279-1290 . doi:10.1007/s10483-008-1003-z

Abstract ( 1617 )

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With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.

A mathematical model for ATP-mediated calcium dynamics in vascular endothelial cells induced by fluid shear stress

HU Xu-qu;XIANG Cheng;CAO Ling-ling;XU Zhe;QIN Kai-rong

2008, 29(10): 1291-1298 . doi:10.1007/s10483-008-1004-4

Abstract ( 1635 )

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In consideration of the mechanism for shear-stress-induced Ca²⁺ influx via ATP(adenosine triphosphate)-gated ion channel P2X₄ in vascular endothelial cells, a modified model is proposed to describe the shear-stress-induced Ca²⁺ influx. It is affected both by the Ca²⁺ gradient across the cell membrane and extracellular ATP concentration on the cell surface. Meanwhile, a new static ATP release model is constructed by using published experimental data. Combining the modified intracellular calcium dynamics model with the new ATP release model, we establish a nonlinear Ca²⁺ dynamic system in vascular endothelial cells. The ATP-mediated calcium response in vascular endothelial cells subjected to shear stresses is analyzed by solving the governing equations of the integrated dynamic system. Numerical results show that the shear-stress-induced calcium response predicted by the proposed model is more consistent with the experimental observations than that predicted by existing models.

Synchronization of N different coupled chaotic systems with ring and chain connections

LIU Yan;Lü Ling

2008, 29(10): 1299-1308 . doi:10.1007/s10483-008-1005-y

Abstract ( 1978 )

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Synchronization of N different coupled chaotic systems with ring and chain connections is investigated. The New system, the Chen system, the Lü system, the Lorenz system, and the Rössler system are used as examples in verifying effectiveness of the method. Based on the Lyapunov stability theory, the form of the controller is designed and the area of the coupling coefficients is determined. Simulations indicate that global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients by using the controller.

Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction

Muhaimin R. Kandasamy;Azme B. Khamis

2008, 29(10): 1309-1317 . doi:10.1007/s10483-008-1006-z

Abstract ( 1383 )

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This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer Equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.

Dynamical response of hyper-elastic cylindrical shells under periodic load

REN Jiu-sheng

2008, 29(10): 1319-1327 . doi:10.1007/s10483-008-1007-x

Abstract ( 1602 )

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Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.

Analytical solution to one-dimensional consolidation in unsaturated soils

QIN Ai-fang;CHEN Guang-jing;TAN Yong-wei;SUN De-an

2008, 29(10): 1329-1340 . doi:10.1007/s10483-008-1008-x

Abstract ( 1816 )

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This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund's one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from analytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.

Hydrodynamic modeling of ferrofluid flow in magnetic targeting drug delivery

LIU Han-dan;XU Wei;WANG Shi-gang;KE Zun-ji

2008, 29(10): 1341-1349 . doi:10.1007/s10483-008-1009-y

Abstract ( 1919 )

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Among the proposed techniques for delivering drugs to specific locations within human body, magnetic drug targeting prevails due to its non-invasive character and its high targeting efficiency. Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a target tissue target under the applied magnetic field. This method increases the drug concentration in the target while reducing the adverse side-effects. Although there have been some theoretical analyses for magnetic drug targeting, very few researchers have addressed the hydrodynamic models of magnetic fluids in the blood vessel. A mathematical model is presented to describe the hydrodynamics of ferrofluids as drug carriers flowing in a blood vessel under the applied magnetic field. In this model, magnetic force and asymmetrical force are added, and an angular momentum equation of magnetic nanoparticles in the applied magnetic field is modeled. Engineering approximations are achieved by retaining the physically most significant items in the model due to the mathematical complexity of the motion equations. Numerical simulations are performed to obtain better insight into the theoretical model with computational fluid dynamics. Simulation results demonstrate the important parameters leading to adequate drug delivery to the target site depending on the magnetic field intensity, which coincident with those of animal experiments. Results of the analysis provide important information and suggest strategies for improving delivery in clinical application.

Improved interpolation method based on singular spectrum analysis iteration and its application to missing data recovery

WANG Hui-zan;ZHANG RenLIU Wei;WANG Gui-hua;JIN Bao-gang;

2008, 29(10): 1351-1361 . doi:10.1007/s10483-008-1010-x

Abstract ( 1617 )

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A novel interval quartering algorithm (IQA) is proposed to overcome insufficiency of the conventional singular spectrum analysis (SSA) iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.

Geometric shapes of the interface surface of bicomponent flows between two concentric rotating cylinders

LI Kai-tai;SHI Feng

2008, 29(10): 1363-1376 . doi:10.1007/s10483-008-1011-y

Abstract ( 1905 )

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In this paper, the shape problem of interface of bicomponent flows between two concentric rotating cylinders is investigated. With tensor analysis, the problem is reduced to an energy functional isoperimetric problem when neglecting the effects of the dissipative energy caused by viscosity. We derive the associated Euler-Lagrangian equation, which is a nonlinear elliptic boundary value problem of the second order. Moreover, by considering the effects of the dissipative energy, we propose another total energy functional to characterize the geometric shape of the interface, and obtain the corresponding Euler-Lagrangian equation, which is also a nonlinear elliptic boundary value problem of the second order. Thus, the problem of the geometric shape is converted into a nonlinear boundary value problem of the second order in both cases.

Nonlinear singularly perturbed problems of ultra parabolic equations

LIN Su-rong;MO Jia-qi;

2008, 29(10): 1377-1381 . doi:10.1007/s10483-008-1012-z

Abstract ( 1634 )

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A class of nonlinear singularly perturbed problem of ultra parabolic equations are considered. Using the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.

Homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations

SHEN Shou-feng;ZHANG Jun

2008, 29(10): 1383-1389 . doi:10.1007/s10483-008-1013-y

Abstract ( 1628 )

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Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations are constructed based on Hirota's bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel'nikov equation, and g-Schrödinger equation are constructed based on Hirota's bilinear method.

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