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1.
一类时滞差分方程的全局吸引性及其应用   总被引:3,自引:0,他引:3  
刘玉记 《应用数学》2001,14(2):28-33
研究一类广泛的时滞差分方程的全局吸引性 ,在较弱的前提下给出其零解全局吸引的充分条件 .将定理应用于红血球增长差分模型及广义 L ogistic差分模型 ,所得定理推广和改进了已有的结果  相似文献
2.
微通道液体流动双电层阻力效应   总被引:2,自引:0,他引:2  
龚磊  吴健康 《应用数学和力学》2006,27(10):1219-1225
采用数值方法求解双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程,研究微通道双电层对压强梯度液体流动的阻力效应。量纲分析表明,双电层阻力大小可以用一个无量纲的电阻力数表示,它与液体的介电系数、固体表面的zeta电位平方成正比,与液体的动力粘性系数、电导率以及微通道的宽度平方成反比,在计算流动诱导的流动电位势和电阻力时,提出电流密度平衡条件,可以消除传统电流平衡条件导致的固壁附近产生局部回流的不合理物理现象,还给出不同电阻力数的微通道流量、流量损失率、速度剖面的数值结果,合理解释了双电层对微通道液体流动的阻力效应。  相似文献
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4.
刘玉记 《数学季刊》2000,15(4):55-60
采用一种新方法研究时滞泛函微分方程x(t) a(t) (1 x(t) )ln(1 x(t) ) (1 x(t) )F(t,x(·) ) =0 ,的全局吸引性 ,并将所得结果应用于动物体内红血球生长模型 ,得到的全局吸引的充分条件 ,推广和改进了已有的结果  相似文献
5.
In this paper, we deal with a model for the survival of red blood cells with periodic coefficients x'(g)=-μ(t)x(t)+P(t)e^-γ(t)x(t-τ(t)),t≥0.(*)A new sufficient condition for global attractivity of positive periodic solutions of Eq. (*) is obtained. Our criterion improves corresponding result obtained by Li and Wang in 2005.  相似文献
6.
The bundling and tumbling behavior of bacterial flagella in a viscous fluid has got immense significance in the field of biological fluid dynamics. In this paper we investigate the hydrodynamic interaction among two and more than two flagella in a viscous fluid based on an immersed boundary method. We model each helical flagellum by a number of triangular cross-sections with three immersed boundary (IB) points on each cross-section. Three types of elastic links are generated from each IB point to create an elastic network model of the flagellum and the first cross-section is modeled as the flagellar motor. The elastic forces are computed based on the elastic energy approach and the motor forces are obtained from the applied angular frequency of rotation of the motor. The Stokes equations governing the flow are solved on a staggered Cartesian grid system using a fractional-step based finite-volume method. It is observed that when two left-handed helical flagella rotate in the counter-clockwise direction, the resulting hydrodynamic interaction leads to bundling. When one of the flagella reverses the direction of rotation to clockwise the hydrodynamic interaction results in tumbling. During the bundling, the flagella wrap and intertwine each other, whereas during the tumbling they separate in an erratic way. There exists an exact combination of the handedness and rotational direction of the flagella to achieve the bundling. The bundling-to-tumbling behavior of the flagella is studied and it is concluded that the tumbling occurs faster than the bundling. Further, the hydrodynamic interaction among three flagella in a viscous fluid is studied for the cases of rotation in the same direction and in different directions. The bundling and tumbling behavior is well captured even for the case of multiple (more than two) flagella using the developed model.  相似文献
7.
This paper analyzes the electroosmotic flow fields in heterogeneous microchannels by applying the lattice Poisson–Boltzmann equation. The influences of surface potential, ionic molar concentration, channel height, and driving force fields on fluid velocity are discussed in detail. A scheme for producing vortexes in a straight channel by adjusting the heterogeneous surface potentials and phase angles of the periodic driving force fields is introduced. By distributing the heterogeneous surface potentials at particular positions, we can create vortexes near walls or in the center of the channel. The size, strength, and rotational direction of vortexes are further variable by introducing appropriate phase angles for a single driving force field or for the phase differences between combined driving force fields, such as electric/pressure fields. These obstacle-like vortexes perturb fluids and hinder flow, and thus, may be useful for enhancing micromixer performance.  相似文献
8.
High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. In this paper, we model the malaria-infected RBCs (pRBCs) as paramagnetic particles suspended in a Newtonian fluid. Trajectories of the infected cells are numerically calculated inside a micro-channel exposed to a periodic magnetic field gradient. First-order stiff ordinary differential equations (ODEs) governing the trajectory of particles under periodic magnetic fields due to an array of wires are solved numerically using the 1st to 5th order adaptive step Runge-Kutta solver. The numerical experiments show that in order to achieve a capture efficiency of 99% for the pRBCs it is required to have a longer length than 80 mm; this implies that in principle, using optimization techniques the length could be adjusted, i.e., shortened to achieve 99% capture efficiency of the pRBCs.  相似文献
9.
The behaviour of a fluid, which may contain particle suspensions, flowing in micro-dimensional channels is governed by both viscous and surface tension forces as well as high shear rates and geometric effects such as bifurcations, constriction, and high surface-to-volume ratio. This paper discusses some of the key design factors affecting fluid behaviour in micro-engineered products containing a main channel, constriction and side channel bifurcations. Differences in fluid behaviour at the macro and micro-scales are discussed. The dynamic bulk fluid behaviour is characterised in terms of: (i) fluid properties, (ii) governing physics and (iii) microchannel geometric features.At this stage of the analysis the fluids are assumed to be Newtonian and single phase, where any particle suspension is represented through a bulk density and viscosity. Based on these assumptions Computational Fluid Dynamics (CFD) is used to investigate the effect of both product inlet and outlet boundary conditions on the bulk flow behaviour. Discussions are provided on how these boundary conditions can affect particle separation efficiency. In particular, the so called pull-design whereby the fluid is pulled out of the device at the outlet, is shown to offer better performance compared to the mode of operation where the fluid is pushed into the device at the inlet. It is also observed that increasing the pressure at the outlet of the main channel can achieve a balanced flow rate ratio which leads to a uniform separation performance among all bifurcations.  相似文献
10.
In this paper, deformation of a mass-less elastic fiber with a fixed end, immersed in a two-dimensional viscous channel flow, is simulated numerically. The lattice-Boltzmann method (LBM) is used to solve the Newtonian flow field and the immersed-boundary method (IBM) is employed to simulate the deformation of the flexible fiber interacting with the flow. The results of this unsteady simulation including fiber deformation, fluid velocity field, and variations of the fiber length are depicted in different time-steps through the simulation time. Similar trends are observed in plots representing length change of fibers with different values of stretching constant. Also, the numerical solution reaches a steady state equivalent to the fluid channel flow over a flat plate.  相似文献
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