Y型分叉冠状动脉血管中血液流动对血栓形成的影响

为研究Y型分叉血管中血液流动对血栓形成的影响,根据黏性流体稳定流动的Navier-Stokes方程,建立了冠状动脉分叉血管中血液流动的数学模型,并采用计算流体力学(computational fluid dynamics,CFD)的方法,数值模拟了不同Y型分叉冠状动脉血管中血液流动情况,并考虑了分叉角度、血液黏度、入口血流初始速度对血流速度场、壁面剪应力、壁面压强的影响.结果表明:分叉角度越小成栓可能性越大,存在最易成栓的血流速度,但血液黏度对血柱形成的影响不大.     

Bifurcation analysis for an SMIB power system with series capacitor compensation associated with sub-synchronous resonance

In this paper,an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.     

A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems

A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturba- tion and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of t...     

Hot-spot combustion of heterogeneous condensed mixtures. Thermal percolation

A model of combustion of heterogeneous condensed mixtures composed of reactive particles separated by an inert heat-conducting substance is considered. Propagation of the reaction in a one-dimensional periodic system of point reaction cells connected by inert thermal bridges is examined. The burning rate is determined as a function of the basic parameters of the system, and stability of the steady combustion mode is studied. It is shown that there exists a range of parameters in which the reaction propagates in an unstable manner. Combustion of the system in the instability domain is examined. It is shown that the reaction propagation loses its stability many times as the adiabatic temperature of the system decreases; in this case, the existing unsteady mode is replaced by another, more complicated mode, and the alteration of the regimes in the examined systems always proceeds as a period-doubling bifurcation. Beginning from a certain value of adiabatic temperature, the reaction-propagation process becomes stochastic. In the systems examined, there exists an ultimate adiabatic temperature, below which self-sustained propagation of the reaction in the system becomes impossible.Translated from Fizika Goreniya i Vzryva, Vol. 41, No. 1, pp. 41–54, January–February, 2005.     

一类非多项式微分系统的定性分析

利用常微分方程定性理论方法,借助函数的Taylor展开,对一类非多项式微分系统进行定性分析;利用基于H.Poincaré思想的形式级数法,对系统的细焦点进行分析,并根据对称原理对系统进行中心的判定;借助Dulac函数讨论了闭轨的不存在性;利用Hopf分支理论根据参数变化时焦点稳定性的变化,分析得到极限环存在的若干充分条件。     

扩展BVP振子弱周期扰动下的振荡与同步

针对扩展bonhoeffer-van der pol(BVP)振子易受不确定因素影响的问题,提出了将非线性动力学分析与数值模拟相结合的方法,并考察了弱扰动对混合模式振荡类型和同步行为的影响.根据模拟结果得知,多种类型的混合模式振荡受弱扰动的影响出现了坍塌现象,且从理论上证明了两个耦合bonhoeffer-van der pol振子的膜电压比慢变量到达完全同步时所需的耦合强度要大,在二维参数平面上,膜电压到达同步时所取参数范围应小些.结果表明,与膜电压相比,慢变量更容易达到同步,且变量之间呈现一种线性关系.     

重访Duffing系统中的对称破裂分岔与激变

借Duffing系统在简谐激励下发生的对称破裂分岔与激变的实例分析,推介对称系统非线性动力学现象的特色及其研究对策;解释了混沌鞍在混沌动力学分析中的作用。研究表明:周期解的对称破裂分岔只需通过一次鞍结分岔就可直接实现。而混沌吸引子的对称破裂激变往往需要通过边界激变、内部激变与吸引子融合激变等组合手段方能实现。     

医院内抗生素耐药性传染的稳定性与Hopf分支

研究了医院内感染的带有非线性发生率的抗生素耐药性的时滞传染病模型的稳定性.确定了疾病暴发的阈值R0,运用Lasalle-Liapunov不变集原理和Routh-Hurwitz判据得到了,当R01时无病平衡点是全局稳定的;当R01时,地方病平衡点存在且唯一,对于任意的τ≠0,总能得到在地方病平衡点处的Hopf分支存在的条件.最后通过数值模拟验证了结论的正确性.     

各向异性砂土剪切带角度的理论分析

针对平面应变条件下各向异性砂土剪切带角度的试验规律,采用传统的3种理论和分叉理论进行对比分析。将平面应变条件下剪切带角度的试验结果按照传统3种理论整理发现,尽管传统3种理论可以估算同种砂剪切带角度的极小、中间和极大值,但无法解释其各向异性规律。砂土在平面应变条件下破坏时会产生明显的剪切带,当剪切带方向和砂土沉积面方向接近时,会较早诱发剪切带的产生,使材料强度降低,造成了平面应变条件下各向异性强度规律明显不同于常规三轴条件下的试验规律,采用分叉理论结合各向异性模型则可以有效解释这个规律。随砂土沉积面角度的变化,模型可以从细观角度解释常规三轴条件下剪切带角度的单调变化的试验规律,结合分叉理论可以描述平面应变条件下其先减小然后增大的规律。通过几种理论对比分析表明,模型结合分叉理论不但能够描述多种应力状态下的平面应变和常规三轴应力条件下剪切带角度表现的不同规律,而且能够从细观角度解释其各向异性成因。     

具时滞物价瑞利方程的Neimark-Sacker分支

研究了以滞量为参数的具时滞物价瑞利方程的数值Hopf分支问题。首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其数值逼近间的关系,最后证明了当连续系统产生Hopf分支时,其Euler离散将产生Neimark-Sacker分支,进而得到结论：Euler离散使得方程的Hopf分支性质得以保持。