应用数学和力学

2001 Vol. 22, No. 4

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Moving Boundary Problem for Diffusion Release of Drug From a Cylinder Polymeric Matrix

TAN Wen-chang, WU Wang-yi, YAN Zong-yi, WEN Gong-bi

2001, 22(4): 331-336.

Abstract(2407) PDF(572)

Abstract:
An approximate analytical solution of moving boundary problem for diffusion release of drug from a cylinder polymeric matrix was obtained by use of refined integral method.The release kinetics has been analyzed for non-erodible matrices with perfect sink condition.The formulas of the moving boundary and the fractional drug release were given.The moving boundary and the fractional drug release have been calculated at various drug loading levels,and the calculated results were in good agreement with those of experiments.The comparison of the moving boundary in spherical, cylinder,planar matrices has been completed.An approximate formula for estimating the available release time was presented.These results are useful for the clinic experiments.This investigation provides a new theoretical tool for studying the diffusion release of drug from a cylinder polymeric matrix and designing the controlled released drug.

3D Fracture Propagation Simulation and Production Prediction in Coalbed

GUO Da-li, Ji Lu-jun, ZHAO Jin-zhou, LIU Ci-qun

2001, 22(4): 337-344.

Abstract(2362) PDF(709)

Abstract:
In accordance with the fracturing and producing mechanism in coalbed methane well,and combining the knowledge of fluid mechanics,linear elastic fracture mechanics,thermal transfer, computing mathematics and software engineering,the three-dimensional hydraulic fracture propagating and dynamical production predicting models for coalbed methane well is put forward.The fracture propagation model takes the variation of rock mechanical properties and in-situ stress distribution into consideration.The dynamic performance prediction model takes the gas production mechanism into consideration.With these models,a three-dimensional hydraulic fracturing optimum design software for coalbed methane well is developed,and its practicality and reliability have been proved by example computation.

Asymptotic Solutions of Boundary Value Problems for Third Order Ordinary Differential Equations With Turning Points

JIANG Fu-ru, JIN Qi-nian

2001, 22(4): 345-353.

Abstract(2481) PDF(741)

Abstract:
Boundary value problems for third order ordinary differential equations with turning points are studied as follows: , where f(x;0) has several multiple zero points in(-a,b).The necessary conditions for exhibiting resonance is given,and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.

The Analytical Solution for Sediment Reaction and Diffusion Equation With Generalized Initial-Boundary Conditions

XIONG Yue-shan, Onyx Wai Wing hong

2001, 22(4): 354-358.

Abstract(2292) PDF(499)

Abstract:
The sediment reaction and diffusion equation with generalized initial and boundary condition is studied.By using Laplace transform and Jordan lemma,an analytical solution is got,which is an extension of analytical solution provided by Cheng Kwokming James(only diffusion was considered in analytical solution of Cheng).Some problems arisen in the computation of analytical solution formula are also analysed.

Computer Simulation of Non-Newtonian Flow and Mass Transport Through Coronary Arterial Stenosis

LI Xin-yu, WEN Gong-bi, LI Ding

2001, 22(4): 359-372.

Abstract(2297) PDF(715)

Abstract:
A numerical analysis of Newtonian and non-Newtonian flow in an axi-symmetric tube with a local constriction simulating a stenosed artery under steady and pulsatile flow conditions was carried out.Based on these results,the concentration fields of LDL(low-density lipoprotein)and Albumin were discussed.According to the results,in great details the macromolecule transport influences of wall shear stress,non-Newtonian fluid character and the scale of the molecule etc are given.The results of Newtonian fluid flow and non-Newtonian fluid flow,steady flow and pulsatile flow are compared.These investigations can provide much valuable information about the correlation between the flow properties,the macromolecule transport and the development of atherosclerosis.

Dynamics in Newtonian-Riemannian Space-Time (Ⅱ)

ZHANG Rong-ye

2001, 22(4): 373-381.

Abstract(2326) PDF(660)

Abstract:
The relativity of motion and covariance of equation of motion in Newtonian-Riemannian space-time,some relationship between Newton.s mechanics in N-R space-time and the general relativity,their difference and identity are discussed.

Dynamics in Newtonian-Riemannian Space-Time(Ⅲ)

ZHANG Rong-ye

2001, 22(4): 382-392.

Abstract(2096) PDF(701)

Abstract:
The Hamiltonian mechanics in Newt onian-Riemannian space-time and its application to hydromechanics are discussed.

Dynamics in Newtonian-Riemannian Space-Time(Ⅳ)

ZHANG Rong-ye

2001, 22(4): 393-403.

Abstract(2105) PDF(586)

Abstract:
Lagrangian mechanics in Newtonian-Riemannian space-time and relationship between Lagrangian mechanics and Newtonian mechanics,and between Lagrangian mechanics and Hamiltonian mechanics in N-R space-time are discussed.

Study on the Fuel Air Mixing Induced by a Shock Wave Propagating Into a H₂-Air Interface

XU Sheng-li, YUE Peng-tao, HAN Zhao-yuan

2001, 22(4): 404-410.

Abstract(2422) PDF(643)

Abstract:
2nd order upwind TVD scheme was used to solve the laminar,fully Navier-Stokes equations.The numerical simulations were done on the propagation of a shock wave with Ma_S=2 and 4 into a hydrogen and air mixture in a duct and a duct with a rearward step.The results indicate that a swirling vortex may be generated in the lopsided interface behind the moving shock.Meanwhile,the complex shock system is also formed in this shear flow region.A large swirling vortex is produced and the fuel mixing can be enhanced by a shock wave at low Mach number.But in a duct with a rearward step,the shock almost disappears in hydrogen for Ma_S=2.The shock in hydrogen will become strong if MaS is large.Similar to the condition of a shock moving in a duct full of hydrogen and air,a large vortex can be formed in the shear flow region.The large swirling vortex even gets through the reflected shock and impacts on the lower wall.Then,the distribution of hydrogen behind the rearward step is divided into two regions.The transition from regular reflection to Mach reflection was observed as well in case Ma_S=4.

Numerical Studies on the Mixing of CH₄ and Kerosene Injected Into a Supersonic Flow With H₂ Pilot Injection

XU Sheng-li, YUE Peng-tao, HAN Zhao-yuan

2001, 22(4): 411-419.

Abstract(2217) PDF(606)

Abstract:
Two-fluid model and divisional computation techniques were used.The multi-species gas fully N-S equations were solved by upwind TVD scheme.Liquid phase equations were solved by NND scheme.The phases-interaction ODE equations were solved by 2nd Runge-Kutta approach.The favorable agreement is obtained between computational results and PLIF experimental results of iodized air injected into a supersonic flow.Then,the numerical studies were carried out on the mixing of CH₄ and kerosene injected into a supersonic flow with H₂ pilot injection.The results indicate that the penetration of kerosene approaches maximum when it is injected from the second injector.But the kerosene is less diffused compared with the gas fuels.The droplet free region appears in the flow-field.The mixing mechanism of CH₄ with H₂ pilot injection is different from that of kerosene.In the staged duct,H₂ can be entrained into both recirculation zones produced by the step and injectors.But CH₄ can only be carried into the recirculation between the injectors.Therefore,initiations of H₂ and CH₄ can occur in those regions.The staged duct is better in enhancing mixing and initiation with H₂ pilot flame.

On the Problem of Dissipative Perturbations of Nonexpansive Mappings

LUO Yuan-song

2001, 22(4): 420-424.

Abstract(2386) PDF(674)

Abstract:
Some fixed point theorems for mappings of the type-A+T are established,where P is a cone in a Hilbert space,A:P→2^P is an accretive mappings and T:P→P is a nonexpansive mappings.In application,the results presented in the paper are used to study the existence problem of solutions for a class of nonlinear integral equations in L²(Ω).

Studies on Stress Transference Mechanism of Steel Fibre Reinforced Concrete

YANG You-fa, XU Shao-qian, ZHONG Zheng-hua

2001, 22(4): 425-434.

Abstract(2204) PDF(605)

Abstract:
The stress transfer mechanism of steel fibre reinforced concrete is studied.The solutions for the stress and displacement were regarded as the superposition of "the elementary solutions" and "the improved solutions".The elementary solutions were found by using two dimensional elastic theory and the improved solutions were found by using the Love displacement function method.The calculated results indicate that the solutions possess good convergence.By comparing the three-dimensional solutions with the shear-lag solutions,evident difference may be found.

Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations

LI Ren-gui, LIU Li-shan

2001, 22(4): 435-440.

Abstract(2397) PDF(833)

Abstract:
New existence results are presented for the singular second order nonlinear boundary value problems u″+g(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0 under the conditions 0≤f₀⁺<M₁,m₁<f_∞^-≤∞ or 0≤f_∞⁺<M₁,m₁<f₀^-≤∞,where f₀⁺=₀f(u)/u,f_∞^-=_∞f(u)/u,f₀^-=₀f(u)/u,f_∞⁺=_∞f(u)/u,g may be singular at t=0 and/or t=1.The proof uses a fixed point theorem in cone theory.