带有交叉扩散项的捕食-食饵模型的全局分歧

讨论了一类带有交叉扩散项的捕食模型在齐次Dirichlet边界条件下正解的存在性.利用极大值原理得到正解的先验估计;借助Crandall-Rabinowitz分歧理论,得出局部分歧正解的存在性;最后,将局部分歧延拓为全局分歧,得到正解存在的充分条件.从而给出捕食者与食饵在一定条件下可以共存的结果.     

（2＋1）维Broer-Kaup-Kupershmidt方程的行波解及其分岔

利用平面动力系统的分岔理论研究了（2＋1）维Broer-Kaup-Kupershmidt （BKK ）方程。给出了方程在不同的参数区域所对应的所有可能存在的行波解,并得到了方程在一些特殊的参数条件下的显式精确孤立波解及周期波解的表达式。     

一类非自治食物链模型的局部分歧

研究了一类具Beddington-DeAngelis(B-D)反应函数非自治的食物链模型.以确定时变环境的参数b为分歧参数.用单特征值分歧理论得到了周期解存在的条件,并运用Crandall-Rabinowitz定理证明了单种群分歧解的稳定性.     

峰值电流模式控制Boost PFC变换器斜波补偿设计

峰值电流模式控制Boost PFC变换器中存在着丰富的菲线性行为,为了控制以削弱不稳定现象的范围,工程上通常采用斜波补偿的方法,但完全靠设计经验.以非线性系统理论的分叉控制观点给出了系统稳定性的临界参数条件及判据,推导了斜波补偿法的参数选择公式,为设计电路时的参数选择提供了理论依据,对实际产品开发具有一定的指导意义.     

一类竞争模型正平衡解的分支和稳定性

讨论了一类推广的竞争生态模型的平衡态系统在第三边界条件下正解的存在性和稳定性.利用极值原理得到半平凡解(u0,0),(0,v0)的存在惟一性,利用局部分歧的技巧证明了系统在(u0,0)(0,v0)处出现分歧现象,从而得到正解分支.然后利用线性算子扰动理论和分支解的稳定性理论得到这类正解的稳定性.     

A numerical study of crack shielding and deflection under extensive plasticity

Experimentally observed crack deflection events in multi-layered material systems, occurring even under pure mode-I loading, are here simulated and explained through elasto-plastic finite element modelling. The crack tip opening displacement is adopted as the crack driving force and estimated along crack paths whose deflection is predicted using the maximum tangential strain criterion. Shielding conditions that promote deflection and bifurcation are evaluated. It is shown that, under conditions of extended plasticity, CTOD evolution as a crack approaches an interface can reveal crack shielding and amplification, and that crack deflection and growth can be assessed from the variation of tangential strains around the crack tip.     

THE EFFECTS OF PHYSIOLOGICAL FLOW WAVEFORM ON WALL SHEAR STRESS IN CAROTID BIFURCATION MODEL

Numerical models of carotid bifurcation were constructed using a combination of tuning-fork bifurcation and straight or curved common carotid. The different inlet velocity profiles of the common carotid were generated for Bloch flow waveform and Holdsworth flow waveform, respectively. The effects of the different flow waveform for the common carotid on Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI) of carotid bifurcation were studied by CFD method. The results show that the physiological flow waveform of curved common carotid has a significant effect on OSI. In particular, the OSI on the outer walls of carotid sinus and external carotid becomes higher in the inward-curved common carotid for Holdsworth flow waveform. But, in both cases of low WSS and high OSI, the effects of flow waveforms are smaller than those of the curved common carotid. The study reveals that the exact knowledge of the physiological flow waveform, vascular geometry and inlet velocity profile is important for hemodynamic numerical simulation of artery bifurcation.     

Dynamics of premixed flames in a narrow channel with a step-wise wall temperature

The effect of channel height, inflow velocity and wall temperature on the dynamics and stability of unity Lewis number premixed flames in channels with specified wall temperature is investigated with steady and transient numerical simulations using a two-dimensional thermo-diffusive model. The simplified model is capable of capturing many of the transitions and the combustion modes observed experimentally and in direct numerical simulations in micro- and meso-scale channels, and indicates that the thermal flame/wall interaction is the mechanism leading to the observed flame instabilities. Finally, an ad-hoc one-dimensional model based on the flame-sheet approximation is tested in its capacity to reproduce some of the flame dynamics of the two-dimensional thermo-diffusive model.     

顶板断裂瞬间煤体稳定性的动力学分析及数值模拟

为了研究顶板突然性断裂诱发煤层失稳的致灾条件,本文采用动力学方法分析了顶板断裂瞬间煤岩系统的受力状态和力学响应。首先推导了顶板断裂时惯性力、惯性力矩的计算公式,进而得到顶板断裂瞬时转动加速度与惯性力、惯性力矩的关系,利用数值模拟计算了顶板断裂前后以及不同转动角加速度条件下的煤岩体应力、变形和两帮位移。计算结果显示:当顶板断裂瞬时转动角加速度较小,即顶板断裂释放能量较小时,工作面煤壁两帮移近量随顶板瞬时转动角加速度的增大而增大;当顶板断裂瞬间转动加速度达到某临界值时,煤岩系统出现失稳分支点,具体体现为工作面处煤体的应力基本不变,煤壁顶部竖向下沉激增,煤岩系统的平衡须依靠煤壁回缩方可维持。因此顶板断裂可以诱发煤岩体系统的失稳,但并非失稳的充分条件。     

收缩—扩散型喷嘴长度影响空化效果的数值分析

喷嘴长度是影响收缩—扩散型喷嘴空化效果的重要参数。运用连续方程、动量方程和Rayleigh-Plesset方程,对流经收缩—扩散型喷嘴的泡液流进行稳态求解。计算结果表明泡液流中很小的入口空隙率对流动特性有强烈影响,并随着无量纲喷嘴长度的变化对流动特性的影响有着显著的相似性。随着喷嘴长度的增长,喷嘴入口空隙率临界值以指数规律下降,气泡半径呈线性增长。