应用数学和力学

2008 Vol. 29, No. 10

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Nonlinear Effects of Line Tension in Adhesion of Small Droplets

LÜ Cun-jing, YIN Ya-jun, ZHENG Quan-shui

2008, 29(10): 1135-1146.

Abstract(2942) PDF(678)

Abstract:
Three-phase line tensions may become crucial in the adhesion of micro-nano or small droplets on solid planes.For the first time the nonlinear effects in adhesion spanned the full physically possible parameter ranges of surface tensions,line tensions,and droplet sizes are studied.It is shown that the nonlinear adhesion solution spaces can be characterized into four districts.Within each district the adhesion behaves essentially the same.Especially,inside the characteristic districts 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.The above new results are consistent with numerical analysis and experimental observations 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): 1147-1160.

Abstract(2667) PDF(516)

Abstract:
The determination of thermoelastic displacement,stresses 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 Lind-say theory)are concerned with.The surface of the cavity is stress free and is subjected to a time dependent thermal shock.The basic equations were written in the form of a vecto-rmatrix differential equation in the Laplace transform domain which was then solved by eigenvalue approach.The numerical inversion of the transforms was carried out using Bellman method.The displacement,stresses and temperature were computed and presented graphically.It is found that the variation of thermo-physical properties of a material strongly influences the response to loading.A comparative study with the corresponding homogeneous material has also been made.

Dynamic Propagation Problems Concerning the Surfaces of Asymmetrical Mode Ⅲ Crack Subjected to Moving Loads

LÜ Nian-chun, CHENG Yun-hong, LI Xin-gang, CHENG Jin

2008, 29(10): 1161-1171.

Abstract(2933) PDF(488)

Abstract:
By the measures of the theory of complex functions,dynamic propagation problems concerning the surfaces of asymmetrical mode Ⅲ crack subjected to moving loads were investigated.General representations of analytical solutions were obtained by the approaches of self-similar functions. The problems dealt with can be facilely transformed into Riemann-Hilbert problems by this technique, and analytical solutions of the stress,the displacement and dynamic stress intensity factor under the action of constant moving loads and unit-step moving loads situated at the surfaces of asymmetrical extension crack,respectively,are acquired.By application of those solutions gained and superposition principle,the solutions of discretionarily intricate problems can be attained.

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): 1172-1180.

Abstract(2759) PDF(762)

Abstract:
In consideration of the mechanism for shear-stress-induced calcium influx via ATP(adeno-sine triphosphate)-gated ion channel P2X₄ in vascular endothelial cells,a modified model was proposed to describe the shea-rstress-induced calcium influx,which is considered to be effected not only by the calcium gradient across the cell membrane but also by the extracellular ATP concentration on the cell surface.Meanwhile a new static ATP release model was constructed with published experimental data.Combining the modified intracellular calcium dynamics model with the new ATP release model,a nonlinear calcium dynamic system in vascular endothelial cells was establshed.The ATP- mediated calcium response in vascular endothelial cells subjected to shear stress was analyzed by solving the governing equations of the integrated dynamic system.The numerical results show that the shea-rstress-induced calcium response predicted by the proposed model is more consistent with the experimental observations than that predicted by the existing models in the literature.

Synchronization of N Different Coupled Chaotic Systems With Ring and Chain Connections

LIU Yan, LÜ Ling

2008, 29(10): 1181-1190.

Abstract(2687) PDF(654)

Abstract:
The synchronization of N different coupled chaotic systems with ring and chain connections is investigated.The New system,the Chen system,the L system,the Lorenz system and the Rêssler system were taken as examples to verify the effectiveness of the method.Based on Liapunov stability theory,the form of controller was designed and the area of coupling coefficients were determined.Artificial simulations indicate that the global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients under the function of controller.

Effects of Heat and Mass Transfer on Non-Linear MHD Boundary Layer Flow Over a Shrinking Sheet in the Presence of Suction

Muhaimin R. Kandasamy, Azme B. Khamis

2008, 29(10): 1191-1198.

Abstract(2420) PDF(529)

Abstract:
The magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction is concerned with.The cases of two dimensional and axisymmetric shrinking were discussed.The governing boundary layer equations were written into a dimensionless form by similarity transformations.The transformed coupled nonlinear ordinary differential equations were solved numerically by using the advanced numeric technique.Favorable comparison with previously published work was performed.Numerical results for the dimensionless velocity,temperature and concentration profiles as well as for the skin friction,heat and mass transfer and deposition rate were 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): 1199-1207.

Abstract(2881) PDF(652)

Abstract:
The dynamical response such as the motion and destruction of hyper-elastic cylindrical shells subjected to periodic or a suddenly applied constant load on the inner surface are studied within the framework of finite elasto-dynamics.It was proved that there exists a certain critical value for the internal load through the numerical computing and dynamic qualitative analysis of the nonlinear differential equation that describes the motion of the inner surface of the shell.The motion of the shell is nonlinear periodic or quas-i periodic oscillation when the mean load of the periodic load or the constant load is less than its critical value.But the shell will be destroyed when the load exceeds the critical value.The solution of the static equilibrium problem is the fixed point for the dynamical response of the corresponding system under a suddenly applied constant load.The property of the fixed point is related to the property of the dynamical solution and the motion of the shell.The effects of the thickness and the load parameters on the critical value and the oscillation of the shell were discussed.

Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils

QIN Ai-fang, CHEN Guang-jin, TAN Yong-wei, SUN De-an

2008, 29(10): 1208-1218.

Abstract(3194) PDF(691)

Abstract:
An analytical solution of Fredlund's one-dimensional consolidation equation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions was presented.The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air.The transfer relations between the state vectors at top surface and any depth was gained 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.The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions;by performing the inverse Laplace transforms the analytical solutions were obtained in the time domain.Finally,comparisons between the analytical solutions and the results of the finite difference method indicate that the analytical solution was correct.

Hydrodynamic Modeling of Ferrofluids Flow in Magnetic Targeting Drug Delivery

LIU Han-dan, XU Wei, LIANG Qing-hua, WANG Shi-gang, KE Zun-ji

2008, 29(10): 1219-1226.

Abstract(2803) PDF(878)

Abstract:
Among the proposed techniques for delivering drugs to specific locations within the human body,magnetic drug targeting surpasses 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 tissue target under the applied magnetic field.This method increases the drug concentration in target and reduces the adverse side-effects.Although there have been some analyses theoretically for magnetic drug targeting,very few researchers have addressed the hydrodynamic models of magnetic fluids in the blood vessel of human body.A mathematical model was presented to describe the hydrodynamics of ferrofluids as drug carriers flowing in a blood vessel under the applied magnetic field.In this model,the magnetic force and the asymmetrical force were added and an angular momentum equation of magnetic nanoparticles under the applied magnetic field was modeled.And engineering approximations were achieved by retaining the physically most significant items in the mathematical model due to the mathematical complexity of the motion equations.Numerical simulations were performed to obtain better insight into the theoretical model with computational fluid dynamics(CFD)'simulation results demonstrate the important parameters leading to adequate drug delivery to the target site depending on the magnetic field intensity,which coincide with those animal experiments.Results of the analysis provide important information and can suggest strategies for improving delivery in favor of the clinic application.

Improved Interpolation Method Based on Singular Spectrum Analysis Iteration and Its Application in Missing Data Recovery

WANG Hui-zan, ZHANG Ren, LIU Wei, WANG Gui-hua, JIN Bao-gang

2008, 29(10): 1227-1236.

Abstract(2663) PDF(785)

Abstract:
A novel algorithm called interval quartering algorithm was proposed to improve the insufficiency of the conventional singular spectrum analysis iterative interpolation on parameter selection(including the number K of principal component and the embedding dimension M).Based on the improved singular spectrum analysis iterative interpolation,the interpolated test and comparative analysis was carried out to the outgoing longwave radiation daily data.The results show that interval quartering algorithm can not only find the global optimal parameter to the error curve which has local oscillation effectively but also has the advantage of fast computing speed,and this improved interpolation method is very effective to the interpolation of missing data.

Geometric Shape of Interface Surface of Bicomponent Flows Between Two Concentric Rotating Cylinders

LI Kai-tai, SHI Feng

2008, 29(10): 1237-1248.

Abstract(3039) PDF(694)

Abstract:
The shape problem of interface surface of bicomponent flows between two concentric rotating cylinders is investigated.By the tool of tensor analysis,this problem can be reduced to an isoperimetric problem of energy functional when neglecting the effects of dissipative energy caused by viscosity.The associated Eule-rLagrangian equation,which is a nonlinear elliptic boundary value problem of second order was derived.Moreover,in the case of considering the effects of dissipative energy,another total energy functional with dissipative energy to characterize the geometric shape of interface surface was proposed,and the corresponding Eule-rLagrangian equation which is also a nonlinear elliptic boundary value problem of second order was obtained.Thus,the problem of geometric shape is transformed into the nonlinear boundary value problem of second order in both cases.

Nonlinear Singularly Perturbed Problems of Ultra Parabolic Equations

LIN Su-rong, MO Jia-qi

2008, 29(10): 1249-1253.

Abstract(2780) PDF(647)

Abstract:
A class of nonlinear singularly perturbed problem with ultra parabolic equation 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 Schr^Ldinger-Like Equations

SHEN Shou-feng, ZHANG Jun

2008, 29(10): 1254-1260.

Abstract(2187) PDF(702)

Abstract:
Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. Analytic expressions of homoclinic orbits for some(2+1)-dimensional nonlinear Schr^Ldinge-rlike equations,which include the long wave-short wave resonance interaction equation,generalization of the Zakharov equation,Mel.nikov equation and g-Schr^Ldinger equation,are constructed based on Hirota's bilinear method.