基于尖点突变的知识应用过程中溢出效应研究

本文引入“知识浓度”和“知识应用速度”两个概念,利用知识稀释效应的系统动力方程解释知识溢出机理。从突变视角分析了知识溢出的突变特性,借鉴尖点突变理论对系统动力方程进行换元变换,建立了知识溢出状态的尖点突变模型,讨论了知识稀释系统控制因子的变化与知识溢出状态间的判定规则,说明了知识应用过程中知识溢出特性如突跳、滞后效应等特性及知识溢出态和接受态之间转化的尖点突变机理。最后,利用我国31个省级行政区面板数据进行实证研究,揭示以省级行政区为对象的知识溢出状态、变化情况及发展趋势,为我国区域经济发展和知识战略提供理论指导。     

煤岩体压裂分形损伤突变演化模型的研究及应用

煤岩与其他普通岩石的力学性能明显不同.为了描述煤岩体压裂岩体突变形成裂缝以及裂缝的扩展问题,基于突变理论定义了损伤变量,并建立了岩体突变过程的能量释放计算模型.基于能量守恒原理,建立了突变后微裂缝扩展的能量方程.通过对黑龙江省鸡西煤矿张晨矿区西三采区3#层右六巷区块煤样在不同压裂阶段缝内流体净压力和微裂缝扩展规律的观察分析,得到由于岩体物性参数不同,微裂缝开始破裂的时间不同,为后续裂缝演化内在混沌特征的研究提供了依据.     

基于突变评价法的研究型大学知识创新综合评价

如何评价研究型大学知识创新是建设创新型国家过程中一个亟待解决的现实问题。本文首先在分析各种评价方法、研究型大学知识创新系统的构成及其特点的基础上，介绍了突变评价法的基本思想和步骤，随后利用突变评价法，建立了研究型大学知识创新综合评价指标体系，并对北京地区的12所大学进行综合评价，得出合理的评价结果，证明突变评价法是一种可行的综合评价方法。     

团队知识共享行为的随机突变模型及仿真

针对团队成员之间的知识共享行为建立一个演化博弈模型,模型中引入监督机制和奖罚机制,并引入白噪声反应博弈过程所受到的随机干扰。借助随机突变理论研究关于团队激励机制、成员自身素质和成员之间交互作用属性参数的连续变化对动力学演化的离散变化的影响即突变性,找到了团队行为发生突变的临界集合。指出演化过程中出现的双模态,反映了团队知识共享行为对外界扰动的敏感性,突跳反映了对参数连续变化的敏感性,而滞后现象反映了管理决策中保持共享行为比治理不共享行为的可靠性。     

Poisson比为1／2材料中球形空穴突变和球形空穴萌生的分岔问题 …

研究Ｐｏｉｓｓｏｎ比为１／２的Ｈｏｏｋｅ材料中,空穴的突变和萌生现象,求解一个球对称几何非线性弹性力学的移动边界问题,空穴为球形,远离空穴处为三向均匀拉伸应力状态,在当前构的列控制方程;在当前构形边界上列边界条件,找到了这个自由边界问题的封闭解并得到空穴半径趋于零时的叉型分岔解,计算结果显示,在位移－载荷曲线上存在一个切分岔型分岔点这个分岔点说明在外力作用下空穴会发生突变,即突然“长大”;当球腔半     

用燕尾突变理论来讨论交通流预测

交通流本身是一个动态过程，运用尖点突变理论来分析交通流的预测时只考虑了流量和密度，而忽视了时间因素，这本身就不是很合理的．基于这个基础之上，采用燕尾突变理论来讨论交通流预测时将时间因素考虑进去，并给出一个算例表明了此方法预测的效果更符合现实。     

害虫种群尖点突变模型的几何分析

基于尖点突变的性质,对修改后的Logistic模型进行变换,并将其化为具有尖点突变的标准模型.利用微分方程定性理论,对模型进行分析,并根据突变理论,给出突变发生的条件.最后利用仿真验证结论的正确性.     

固液两相流中的K－ε双方程湍流模式

建立了固液两相流中更一般的Ｋ－ε双方程湍流模式．模化了固相和液相的连续方程、动量方程及Ｋ方程和ε方程．该湍流模型考虑了固液两相间速度的滑移，颗粒间的作用及相间作用．使用本文所建立的湍流模型，数值预测了一管湍流中的沙水混合流动，其预测结果与实验结果比较一致．     

非对称开采时矿柱失稳的尖点突变模型

针对非对称开采时矿柱稳定性问题建立了一个简化的力学模型．基于势能原理,应用尖点突变理论对矿柱成为非稳定系统进行了探讨,导出了失稳的充要条件、矿柱变形突跳量和能量释放表达式,为定量研究其失稳问题奠定了基础．结果表明:系统的失稳不仅与其所受载荷有关,而且与其内部刚度分配有关,当相对刚度值越大,所承受的临界载荷也越大,越不容易失稳．反之,越容易失稳,且失稳时所释放的能量越大,危害也越大．给出了算例,其计算结果可为安排开采顺序、合理布置采场等提供依据．     

螺旋弹簧临界屈曲失稳的平衡方程

目前,针对螺旋弹簧失稳现象的研究主要基于当量柱模型,将弹簧等效为柱模型,忽略其绕轴线的转动．该文建立了三维螺旋弹簧模型,通过曲线Frenet坐标系和主轴坐标系,建立了描述弹簧螺旋中心线的空间变形和截面扭转变形的平衡方程．采用小变形假设,通过对弹簧挠度变量采用Taylor级数展开,并忽略其高阶小量,平衡方程可以被简化为扭转角和弧长的函数,使获得方程的数值解成为可能．同时,讨论了作用于弹簧圆心位置的轴向力引起的弹簧约束端反作用力,为平衡方程的求解确定了边界载荷条件．该文的研究工作为进一步研究受压螺旋弹簧的后屈曲性奠定了基础．     

A Representation of Virial Coefficients That Avoids the Asymptotic Catastrophe

We investigate the notion of an asymptotic catastrophe in representations of Mayer coefficients. The manifestations of the catastrophe and its formal definition are given. The significance of the definition introduced for an asymptotic catastrophe is clarified. Virial-coefficient representations that are free of the asymptotic catastrophe phenomenon are given. Sets of labeled graphs (blocks) nonseparable in the Harary sense are expanded into classes labeled by cycle ensembles satisfying specific conditions, and the representations are based on these expansions. These cycle ensembles are called frame cycle ensembles. The same classes can be labeled by special blocks, which are called frames. The frames are brought into one-to-one correspondence with the frame cycle ensembles. In the block classification, frames play a role similar to the role of trees in the tree classification of connected labeled graphs. A tree classification of frame cycle ensembles is introduced. We prove that the described virial-coefficient representations are free of the asymptotic catastrophe phenomenon.     

火灾图像的模糊识别探测方法

烟气是火灾过程的重要物理现象,烟气中悬浮的烟气颗粒数目、尺寸分布、烟气浓度及其湍流效应等是火灾图像探测的重要影响因素,本文分析烟气的多参数特征,提出一种基于烟气多参数特征的火灾图像探测方法。     

Continuous compression waves in the two-dimensional Riemann problem

The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.     

Divergence of choices despite similarity of characteristics: An application of catastrophe theory

In this paper we use catastrophe theory to analyse situations in which agents with similar characteristics and objectives and facing identical or similar environments make choices which are considerably different. We first provide two simple analytical examples of this phenomenon and then set up a general framework to which we apply the classification theorem of catastrophe theory.     

分数跳——扩散环境下的巨灾期权定价

在假设巨灾指数服从分数跳-扩散的条件下,利用保险精算方法给出了有N个独立跳跃源的分数跳-扩散过程下巨灾期权的定价.     

Catastrophe risk management with counterparty risk using alternative instruments

Since weather-related disasters have an upward trend-cycle movement and the global financial crisis has revealed the severity of counterparty risk, this study reinvestigates and incorporates the catastrophe characteristics and counterparty risk into the valuation of catastrophe products. First, the excess of loss reinsurance is traditionally used to reduce catastrophe risk. Its premium is estimated under these catastrophe characteristics. Second, this paper looks into the price of catastrophe futures and spread option contracts that are based on a catastrophe index. The (re)insurer can apply these exchange-traded derivatives to reduce catastrophe risk without counterparty risk. Third, this paper takes counterparty risk into account to value catastrophe bonds and catastrophe equity puts. Thus, the fair valuations of these two instruments are revealed to the buyer.     

Numerical computation of nonsimple turning points and cusps

Summary A method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters. An augmented system containing the original equation is introduced, for which the cusp point is an isolated solution. An efficient implementation of Newton's method in the finite-dimensional case is presented. Results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points.     

System catastrophe: A distributive model for collective phenomenon

The phenomenon of system catastrophe often occurs in a system with a network structure. A system's resources can be utilized in two different modes: efficiently or inefficiently. When actions with inefficient mode pose no threat to other users or, in other words, when they employ resources that would otherwise be idle, they do not waste the system's resources at all. But when critical levels of inefficient uses of system's resources are reached, there is a sudden decrease in the capacity of the system due to the multiplication effects of inefficient factors. This collective inefficiency results in everyone getting worse in average. The common theme behind the catastrophe phenomenon demonstrates a possible explanation for the famous question about the choice between market and hierarchy. That is, when all firms pursue their own individual interests, resulting in a collective breakdown, they turn to consolidated ways of carrying out transactions.     

The effects of ridge-top and lee-slope fires upon rotor motions in the lee of a steep ridge

Soon after the outbreak of the South Australian Ash Wednesday I bushfire on a ridge in the Adelaide Hills, fires were observed burning up its lee slope in a direction opposite to that of the main fire. To investigate mathematically why this happened, a simple two-dimensional analytical model of a lee rotor (which occurs when airflow over a ridge separates from the lee slope) is developed by applying the first circulation theorem of physical hydrodynamics to a triangular material curve of air parcels in the lee of a ridge. The resultant equation describes how fire-generated buoyancy, frictional driving from above and lee-slope friction affect the average airspeed around a lee rotor.

A comparison between steady-state solutions of the rotor equation with and without a ridge-top fire indicates that the presence of the latter slightly retards any lee rotor which may have existed under neutral pre-fire conditions. The solution of an initial-value problem simulating the growth and decay of a lee-slope fire is next found and its dependence upon the ratio of the frictional relaxation time to the growth time of maximum fire-induced instability across the rotor is investigated and graphed. For growth times greater than 2.5 minutes and reasonable friction coefficients, it turns out that the response of the rotor to the slope fire is almost instantaneous and its maximum speed is more than twice its pre-fire speed. A halving of the friction coefficients even results in the maximum rotor speed being more than the airspeed above it. It is concluded that buoyant enhancement of lee rotors by fires greatly helps the latter to burn up lee slopes and that lee rotors containing intense fires may sometimes even drive the airflow above them.