瓶颈中颗粒流动的堵塞行为

颗粒物质流经瓶颈时难以预知的堵塞现象是1个古老且令人困惑的难题。本文选取3种球形颗粒,统计分析颗粒流出小于临界开口尺寸锥形瓶颈的颗粒数,探讨堵塞转变的概率分布特征和物理机制。结果显示:(1)堵塞前流出瓶颈的颗粒数概率分布存在1个峰值,峰值前概率呈幂函数增长,峰值后概率为指数衰减;(2)颗粒的密度、弹性系数及表面摩擦等因素影响颗粒间的接触时间、堵塞结构稳定性和堵塞概率分布。当瓶颈开口尺寸低于临界尺寸,且颗粒流态由稀疏流转变为密集流后,堵塞转变必将发生。     

A nonlinear model for myogenic regulation of blood flow to bone: equilibrium states and stability characteristics

A simple compartmental model for myogenic regulation of interstitial pressure in bone is developed, and the interaction between changes in interstitial pressure and changes in arterial and venous resistance is studied. The arterial resistance is modeled by a myogenic model that depends on transmural pressure, and the venous resistance is modeled by using a vascular waterfall. Two series capacitances model blood storage in the vascular system and interstitial fluid storage in the extravascular space. The static results mimic the observed effect that vasodilators work less well in bone than do vasoconstrictors. The static results also show that the model gives constant flow rates over a limited range of arterial pressure. The dynamic model shows unstable behavior at small values of bony capacitance and at high enough myogenic gain. At low myogenic gain, only a single equilibrium state is present, but a high enough myogenic gain, two new equilibrium states appear. At additional increases in gain, one of the two new states merges with and then separates from the original state, and the original state becomes a saddle point. The appearance of the new states and the transition of the original state to a saddle point do not depend on the bony capacitance, and these results are relevant to general fluid compartments. Numerical integration of the rate equations confirms the stability calculations and shows limit cycling behavior in several situations. The relevance of this model to circulation in bone and to other compartments is discussed.     

一类非线性波动方程局部解的存在性

通过对一类具非线性阻尼项的波动方程的初边值问题的研究,在非线性阻尼项及源项的指数不加限制的情况下,应用压缩映射原理,结合内插定理和嵌入定理,证明了该问题局部广义解的存在性和唯一性.