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A mathematical model of substantial exchange between three capillaries and the surrounding tissue is presented.We suppose that three capillaries, which are parallel to each other and have the same radius and circular section, are arranged in equilateral triangle.Fluid movement across the capillary walls is assumed to be governed by the generalized Starling's law.The motion of the interstitial fluid obeys Darcy's law.The calculated result obtained in this paper shows that in order to study the effect of capillary networks on the tissue space, as a whole, we have found a concept of equivalent pressure, concentration and source strength for the networks. 相似文献
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有限区间上的分数阶扩散-波方程定解问题与Laplace变换 总被引:6,自引:0,他引:6
求解了如下的分数阶扩散-波方程定解问题0Dαtu=2ux2,00,0<α≤2,u(0,t;α)=0,u(1,t;α)=θ(t),u(x,0+;α)=0,当1<α≤2时,还有ut(x,0+;α)=0.其中θ(t)是Heaviside单位阶跃函数,0Dαt为关于时间t的α阶Caputo分数阶导数算子,u=u(x,t;α)为时间t的因果函数(即t<0时恒为零的函数).利用Laplace变换的复围道积分反演和离散化反演及FoxH函数理论,给出在计算上对大的t和小的t分别适用的解的表达式. 相似文献
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Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion 总被引:1,自引:0,他引:1
The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively
in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this
process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the
solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution;
the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional
motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition
for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second
order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile
at a given point, and the time history can be described by the fractional calculus. 相似文献
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提出广义分数阶单元网络, 取消了Schiessel等人所提出的分数阶单元法对参数的限制, 增加了“协调方程”, 将模型解的构造扩充到广义函数空间, 使其包含更多的具有明显物理意义的解. 应用并发展了离散求逆Laplace变换的方法, 给出了模型方程的广义解. 讨论了广义分数阶单元网络Zener, Poyinting-Thomson模型. 结果表明, 有关黏弹性材料本构方程经典的和前人所得的经典整数阶和分数阶单参数模型的所有结果均可作为本文的特例而被包括. 相似文献
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本文对微循环中最常见的毛细血管网络建立了三管模型。在生理条件下,我们建立了“平均压力”与“平均浓度”的概念,从而给出了间质压力和浓度分布,对三管数学模型求出了近似解。 相似文献
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分数阶扩散方程半无界混合问题的解 总被引:5,自引:1,他引:4
研究了一维半无界分数阶扩散方程具有第三类非齐次边条件的混合问题.分别给出具有第三类齐次边条件的混合问题基本解以及具有零初始条件的混合问题基本解.最后得到分数阶扩散方程半无界混合问题的求解公式. 相似文献
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The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a "compatibility equation" is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper. 相似文献
10.
根据生理学特点,提出管壁由半透膜组成的准单一溶质模型。给出了肾脏Henle氏袢降支(DLH)内水的非等张重吸收与钠离子的稳态分布。 证明了Bossert和Schwartz关于该段肾小管内水的重吸收量所做的推测。计算结果与实验是基本吻合的。 相似文献