颅内动脉瘤两相血流动力学分析及PIV实验研究

为了探索血液动力学因素对颅内动脉瘤的影响,分析动脉瘤的形成、生长和破裂与血流动力学的关系,为治疗颅内动脉瘤提供技术参考和研究方法.数值模拟部分:依据个体化脑部动脉瘤患者的CT三维重建模型,从计算流体力学的角度出发,将血液假设为血浆和红细胞组成的两相流流体进行瞬态数值模拟.并且与经典牛顿流体与非牛顿流体进行对比.实验部分:利用与数值模拟相同的边界条件进行PIV流场可视化分析.得到一个心跳周期内的血液动力学参数分布情况和相同条件下实验结果.与牛顿流体和非牛顿流体相比,两相流在特征点的血液流速波动更为复杂;在壁面剪切力分布更加不"平滑",红细胞的粒子速率和沉积对颅内动脉瘤有着至关重要的影响,两相流更符合真实血液流动.实验结果证明血液流动会在动脉瘤内部形成低速旋涡区域,并且随着时间的变化旋涡中心不断转移,与数值模拟结果相吻合.     

考虑混凝土材料非均质特性的近场动力学模型

混凝土内部微细观结构影响其损伤和破坏行为.鉴于传统连续介质力学在模拟混凝土损伤累积和渐进破坏过程中存在的问题,基于数值图像技术获得混凝土试件的内部骨料形态,采用键型近场动力学理论,建立了能够考虑混凝土非均质特性的近场动力学模型,并在ABAQUS平台下开发了相应的计算模块,进行了混凝土试样的拉伸和压缩细观破坏分析.结果表明:近场动力学模型和数值方法能够成功模拟混凝土材料的复杂破坏过程,得到的破坏现象与试验结果吻合程度较好,进一步探究了混凝土材料的破坏机制,完善了混凝土结构的破坏分析过程.     

双菌体发酵过程的动力学模型研究

通过双菌体发酵的研究,构建相应的微分方程动力学系统,对双菌体发酵动力学模型的性质进行了初步研究.其次,利用Mathematica软件对菌体的生长、产物和底物消耗模型进行了数值模拟.通过对双菌体发酵模型的初步研究,为将来混合菌体发酵产生皂素提供初步理论依据.     

一类具有非线性发生率和恢复率函数的SIS传染病模型

在传染病模型建模中,采用合理的非线性发生率所得到的动力学性态与实际更加接近,并且在实际的疾病防治过程中,由于受到医院各种医疗资源的影响,染病类的恢复率也会有一定的限制.建立了具有非线性发生率和恢复率函数的SIS传染病模型并分析了其动力学性态,分析这个模型,得到了无病平衡点和地方病平衡点的存在性和稳定性的条件,以及出现Hopf分支的条件.通过数值模拟,给出系统随两个分支参数变化的分支曲线图及系统的相图.     

偏心冲击荷载作用下薄圆板动力学响应的保结构分析

关注动力学系统的局部几何性质,采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上,对动力学控制方程在多辛体系下重新描述,并采用显式中点差分离散方法构造其多辛格式,通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟,研究了相对偏心距对薄圆板振动特性的影响,同时,数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据,而且为偏心冲击动力学问题的研究提供了新的途径.     

离散SCIRS模型在我国流脑中的应用（英文）

本文研究一类离散SCIRS模型的动力学性态,利用再生矩阵的方法得到模型的基本再生数,证明模型无病平衡点的全局渐近稳定性,以及模型地方病平衡点的存在性与一致持续性.数值模拟显示地方病平衡点可能是全局渐近稳定的.最后,把模型应用到我国流脑的传播中,通过数值模拟的结果和法定传染病报告的结果对比,表明该模型在一定程度上可以用来预测流脑在我国的传播.     

两个企业竞争与合作动力学模型的动力学行为

研究了非自治两个企业竞争与合作动力学模型的动力学行为.首先利用微分方程比较原理得到了模型的有界性、持久性和灭绝性的充分条件.然后通过构造Lyapunov函数得到了模型的全局吸引性的充分条件.最后针对所得到的理论结果给出了例子和数值模拟.     

政府调控下的能源供需系统动力学分析

依据一个经济时期内能源需求、能源供应和政府调控之间相互依存、相互制约的演化关系为背景建立了一个新的能源供需模型.模型中引入市场自身调节的闽值,政府调控的阈值,政府调控对能源需求和能源供应的影响系数等参数,通过参数的调整,分析了政府调控在能源供需中的作用.通过平衡点稳定性、系统的耗散性、Lyapunov指数谱等的分析,研究了系统的基本动力学行为,利用数值模拟的方法给出了系统的动力演化行为;给出了模型中参数估计的方式,对模型所反映的现实意义进行了解释,给出了数值模拟结果,验证了理论分析的正确性.     

平面不可压缩磁流体动力学五模类Lorenz方程组的动力学行为及其数值仿真北大核心CSCD

该文研究了平面正方形区域上不可压缩的磁流体动力学方程组五模截断所得到的十维模型的动力学行为问题.首先,利用模式截断方法推导了十模系统,讨论了该方程组定常解及其稳定性,其次,发现了Hopf分叉和混沌,证明了该方程组吸引子的存在性和全局稳定性,最后,给出了系统从分叉到混沌整个过程所呈现的动力学行为演变的详细数值模拟结果,分析了磁性对系统动力学行为的影响.基于分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等数值模拟结果揭示了这个低维系统的动力学行为特征.这个新混沌系统通过周期倍分岔过渡到混沌(费根鲍姆途径).     

一维He与超短强激光脉冲相互作用的经典模型

采用经典理论研究了一维氦原子与超短强激光脉冲相互作用的动力学过程 .利用经典理论中的系综平均方法 ,对氦原子的一阶和二阶电离几率的时间演化进行了数值模拟 .并对模拟结果进行了分析 .     

NaClO3晶体生长过程光学诊断与数值模拟

运用光学干涉诊断方法实时观测NaClO3晶体生长过程，得到晶体生长过程中溶液浓度，晶体尺寸等物理参量．将这些参量与数值模拟得到的结果进行比对，研究重力条件下NaClO3晶体溶液生长过程中速度场、浓度场的分布与演化，尝试提出符合实际情况的晶体生长理论模型,对比两种方法得到的浓度边界层厚度，数值模拟得到了与实验数据相一致的结论.     

Modelling and passive control of flexible guiding hoisting system with time-varying length

ABSTRACT

A coupled dynamic modelling of the flexible guiding hoisting system is established, which includes the transverse-longitudinal-coupled vibration and the rotational vibration. Substituting vibrational energy of the system into Hamilton principle and applying the dynamic constraint, a distributed parameter mathematical model of the multi-rope system is derived. It is governed by coupled partial differential equations and ordinary differential equations (PDEs-ODEs), where the dynamic constraint in the form of an unknown moving force is the only connection between the hoisting conveyance and the guiding ropes. Based on Galerkin method, the dynamic response of the system is validated by numerical calculation and ADAMS simulation. Besides, an absorber with artificial intelligence optimization is proposed to reduce system vibration. The simulation result has demonstrated that a hoisting conveyance resonance can be observed when the external disturbance frequency is close to the system natural frequencies. Moreover, a vibration absorber can effectively diminish the resonant peaks of the first three orders of the guiding rope.     

具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为北大核心CSCD

该文研究了一类具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为,证明了系统全局正解的存在性和唯一性,得到了灭绝性和持久性的充分条件.在此基础上,给出了控制捕食-食饵系统随机持久和灭绝的阈值,并且讨论了系统解的一些渐近性态.最后通过数值模拟,验证了结果的有效性.     

相场方法模拟液滴的动态润湿行为

液滴的动态湿润现象广泛存在于自然界和工业生产中,该现象数值研究的建模需要解决接触线附近的奇异性并引入合理的接触角描述.基于相场方法,结合Yokoi动态接触角模型,建立了考虑动态润湿效应的两相流数值模型,并在OpenFOAM开源平台上实现相应程序.针对液滴撞击壁面的动态湿润过程,数值模拟和对比研究了不同的接触角模型.结果表明:接触角模型的选择对液滴动态润湿过程的模拟结果具有较大的影响,其中基于改进动态接触角模型的结果与文献中的实验结果具有很好的吻合度,反映了提出的数值模型在液滴的动态润湿行为模拟的有效性.     

基于浸入边界-有限元法的流固耦合碰撞数值模拟方法

针对流固耦合碰撞问题,建立了流体中固体与固体碰撞界面解析直接模拟方法,采用清晰界面浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时网格出现负体积的问题,采用基于罚函数的有限元方法对固体的运动和碰撞进行求解,以分域耦合方式实现流体域和固体域的耦合求解.通过与静止流体中球形颗粒与壁面正碰撞和斜碰撞的实验数据对比,验证了建立的数值模拟方法对流体中固体与固体碰撞数值模拟的正确性,获得了流体域流场在碰撞前后随时间的变化,同时通过该文建立的数值模拟方法也获得了固体域中固体的碰撞力和应力.未来,将把该数值模拟方法应用到流体流动环境中,如固体颗粒对管道的冲蚀、流体诱导海洋立管之间的碰撞、坠物对海底管道的撞击等.     

Modeling Optimal Allocation of Deficit Irrigation: Application to Crop Production in Saudi Arabia

We develop an integrated dynamic programming—linear programming (LP) model to solve for optimal land exploitation for a given crop. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing the crop yield per unit area. The dynamic program guarantees that deficit irrigation is considered only when it is economically efficient. Moreover, it provides the best irrigation level for each growth stage of the crop, accounting for the varying impact of water stress overtime. The LP provides the best tradeoff between expanding the irrigated area and decreasing water share per hectare. The model objective is to maximize the total expected crop yield. The model is particularly applicable for regions suffering from irrigation water scarcity, such as Saudi Arabia. The implementation was made for crops in Al-Jouf Region, north of Saudi Arabia     

A Stochastic Model of Sugar Cane Crop Rotation

An identifying model of sugar cane crop rotation has been developed to optimize return to a single sugar cane farm by scheduling harvesting times and implicitly defining the crop growth periods. A Markov decision process is used to provide a simple structure which retains the problem's dynamic nature. Stochastic influence on the system is incorporated within this structure by defining states representing crops at discrete quality levels with probabilistic transitions between states. Non-discounted and discounted versions of the Markov process are solved using a linear programming formulation. Problem formulation and interpretation of the solution is complicated by an extra constraint on the Markov process due to sugar industry restriction. This constraint is treated by two different means and a rule is presented to aid its interpretation.     

Duane-LR模型下复杂系统的动态可靠性增长评定

基于复杂系统可靠性增长试验的特点，运用Duane可靠性增长模型结合数理统计中的线性回归方法对新批次产品的可靠性参数进行预测。结合产品的少量现场试验数据，利用Bayes方法对系统的可靠性增长试验结果进行评定。文中首先给出了可靠性增长分析的模型，然后运用历次阶段试验中的可靠性增长数据建立动态参数的递推估计模型，在此基础上，运用随机变量函数的分布，给出各阶段可靠性增长试验中可靠性参数的Bayes估计。文中对Weibull、指数和二项分布三种试验结果进行分析，给出计算公式。     

Modeling the effects of variable external influences and demographic processes on innovation diffusion

In this paper, a nonlinear mathematical model for innovation diffusion is proposed and analyzed by considering the effects of variable external influences (cumulative marketing efforts) and human population (variable marketing potential) in a society. The change in the population density is caused by various demographic processes such as immigration, emigration, intrinsic growth rate, death rate, etc.Thus, the problem of innovation diffusion is governed by three dynamic variables, namely, non adopters’ density, adopters’ density and the cumulative density of external influences. The model is analyzed by using the stability theory of differential equations and computer simulation.The model analysis shows that the main effect of the increase in cumulative density of external influences is to make the adopter population density reach its equilibrium at a much faster rate. It further shows that the density of adopters’ population increases as the parameters related to increase in non adopters’ population density increase. The effects of various parameters in the model on the nature of existing single equilibrium have also been discussed by using numerical simulation. It is shown that parameters related to the growth of non adopters’ population density have stabilizing effects on the system.     

Dynamic navigation field in the social force model for pedestrian evacuation

This paper presents a generalized walking cost distribution to determine a dynamic navigation field in the social force model for pedestrian evacuation. The local walking cost per unit distance of movement includes the cost associated with travel time and other additional costs incurred by pedestrians to avoid colliding with obstacles in a dynamic environment. In the dynamic navigation field, pedestrians expect to choose an optimal path with the lowest walking cost to reach their target destination reactively based on available instantaneous information. The social force model with the dynamic navigation field is validated by comparing the simulation results with empirical observations. The fundamental diagrams for observations and simulation data agree well, which indicates the effectiveness of the model. Numerical results show that the model with the dynamic navigation field can reproduce typical stages of the dynamics of pedestrian evacuation, such as self-organized arching and queuing phenomena, and can capture the route choice and exit choice behaviors of pedestrians during the evacuation process. Compared to the model with the static navigation field, the model with the dynamic navigation field can reduce the total evacuation time of the room and save the required CPU time for a large group of pedestrians. Furthermore, the strong tendency to avoid local high-density regions (i.e., minimizing collisions) can also reduce the total evacuation time under the same conditions.