聚偏氟乙烯在动载荷作用下压电特性的研究

 本文利用爆炸激波管研究了聚偏氟乙烯（PVF₂）在0.01至1 MPa的冲击波作用下的压电特性。实验发现，大约在0.25 MPa附近，压电灵敏度出现急剧下降，然后很快趋于稳定。本文还利用X射线衍射仪观察了冲击载荷下PVF₂的晶型变化，X射线衍射结果表明，PVF₂在3~4 MPa的冲击波几十次反复作用下晶型不发生明显改变。     

奇异微分方程边值问题的数值解法

本文给出求解奇异微分方程边值问题的正则化方法。解在奇点邻域内展开成级数形式,在余下区间上推导出正则边值问题,应用差分方法求解,并给出收敛结果和数值算例。     

A SYSTEMATIC METHOD OF FINDING LINEARIZING TRANSFORMATIONS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS I: SCALAR CASE

In this paper we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of integrals of motion. The proposed algorithm is simple, straightforward and efficient and helps to unearth several new types of linearizing transformations besides the known ones in the literature. To make our studies systematic we divide our analysis into two parts. In the first part we confine our investigations to the scalar ODEs and in the second part we focus our attention on a system of two coupled second-order ODEs. In the case of scalar ODEs, we consider second and third-order nonlinear ODEs in detail and discuss the method of deriving maximal number of linearizing transformations irrespective of whether it is local or nonlocal type and illustrate the underlying theory with suitable examples. As a by-product of this investigation we unearth a new type of linearizing transformation in third-order nonlinear ODEs. Finally the study is extended to the case of general scalar ODEs. We then move on to the study of two coupled second-order nonlinear ODEs in the next part and show that the algorithm brings out a wide variety of linearization transformations. The extraction of maximal number of linearizing transformations in every case is illustrated with suitable examples.     

改善水下影象衬度方法的研究

光在海水介质中传播时,由于各种因素比起在空气中传播复杂得多,因而影象光信号受到众多因素的干扰,从理论和实验两个方面分析研究表明,采用对称性照明系统是提高影象衬度的一种有效方法,我们作了对称性双光源的实验,与单光源比较影象衬度提高两倍多.     

平均离子模型中束缚能级平衡布居的有效数值计算方法

本文给出求解平衡分布下n壳层电子占据概率P_n^M的方程组和百效的数值方法;对物质Au做了计算,其中包括低温度高密度的计算,计算时间比通常所用方法下降一个量级。     

自相似业务下光缓存设计

提出了在数据包长可变的自相似业务下研究光纤延时线所组成的光缓存问题的解析模型.利用Pareto到达过程来模拟自相似业务.研究表明,缓存深度越大,包丢失率越低,而且存在与业务强度对应的最佳光纤延时线单位,使得在给定的缓存深度下,数据包丢失率最小,在业务强度和缓存深度相同时,Pareto到达比Poisson到达有更大的包丢失率.     

A SYSTEMATIC METHOD OF FINDING LINEARIZING TRANSFORMATIONS FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS II: EXTENSION TO COUPLED ODEs

In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second-order nonlinear ODEs. We show that beside the conventional point, Sundman and generalized linearizing transformations one can also find a large class of mixed or hybrid type linearizing transformations like point-Sundman, point-generalized linearizing transformation and Sundman-generalized linearizing transformation in coupled second-order ODEs using the integrals of motion. We propose suitable algorithms to identify all these transformations (with maximal in number) in a straightforward manner. We illustrate the method of deriving each one of the linearizing transformations with a suitable example.     

模型实验在交通噪声评价中的应用

本文给出了一种简单而经济的用于评价和预测城市建筑群内交通噪声影响的物理模拟实验方案。在1:80的模型中,常规的实时频率分析仪被用于检测电火花所发出的脉冲频谱,使实验得以简单化。将多车道多车种随机的自由车流简化为在平均车道上朝同一方向行驶且有着共同的声影响函数、时距满足负指数分布的数学模型,在微型计算机上进行模拟分析与计算,得出的统计声参量(L_eq和L₁₀)与实测值有较好的吻合。     

普遍情况下阐述动生电动势产生机理的简单方法

本文给出了一种在普遍情况下阐述动生电动势产生机理的简单方法,不仅易于理解,且物理机制明显．     

用Gear方法解一类Stiff常微分方程组

本文利用Gear方法计算了"异形环流器极向场三级电源"中一类Stiff方程组。文中详细叙述了Gear方法的用法及自动调整步长和自动变阶问题,并与单步方法进行了比较,结果表明Gear方法比单步方法省机时。     

OPTIMAL DAMPING OF STAYS IN CABLE-STAYED BRIDGES FOR IN-PLANE VIBRATIONS

Significant vibrations have been reported in stays of recently constructed cable stayed bridges. The vibrations appear as in-plane vibrations that may be caused by rain-wind- induced aeroelastic interaction or by resonance excitation of the cables from the motion of the pylons. The stays of modern cable-stayed bridges are often designed as twin cables with a spacing of, say 1m. In such cases, it is suggested in the paper to suppress the mentioned in-plane types of vibrations by means of a tuned mass-damper (TMD) placed between the twin cables at their midpoints. The TMD divides the stay into four half-cables, and resonance may occur in each of the half-cables as well as in the entire stay. The optimal tuning of the TMD is investigated based on a mathematical model, where the motion of the support points on the pylons is considered to be the main cause of excitation. The indicated motion is modelled as a band-limited Gaussian white noise process. Three load scenarios are considered: narrow-banded excitations, with the central frequency of the autospectrum close to the lowest eigenfrequency of each of the two cables constituting the stay, and a broadbanded excitation which encompasses both of the mentioned frequencies. The spring and the damper constants of the TMD are optimized so that the variances of the displacement of the adjacent four half-cables, the support point of the TMD and the secondary mass are minimized. At optimal design, it is shown that the variances reduce below 14% of those of the unprotected stay.     

一种间接测量圆柱形管内样品冲击波压力的方法

 描述了一种联合使用锰铜计和康铜计间接测量柱对称滑移爆轰条件下，金属管内样品中冲击波压力的方法。给出了冲击压缩方法合成纤锌矿型氮化硼（wBN）时的测量结果。结果表明：管内样品中压力范围大致在11.5~22 GPa范围内，满足冲击波合成wBN所需的压力条件；管内样品压力的发展变化具有不连续性。证明了这种间接测量管内压力的方法是可行的。     

INVARIANT LINEARIZATION CRITERIA FOR SYSTEMS OF CUBICALLY NONLINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Invariant linearization criteria for square systems of second-order quadratically nonlinear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in the first derivatives. It is shown that there are two branches for the linearization problem via point transformations for an arbitrary system of second-order ODEs and its reduction to the simplest system. One is when the system is at most cubic in the first derivatives. One obtains the equivalent of the Lie conditions for such systems. We explicitly solve this branch of the linearization problem by point transformations in the case of a square system of two second-order ODEs. Necessary and sufficient conditions for linearization to the simplest system by means of point transformations are given in terms of coefficient functions of the system of two second-order ODEs cubically nonlinear in the first derivatives. A consequence of our geometric approach of projection is a rederivation of Lie's linearization conditions for a single second-order ODE and sheds light on more recent results for them. In particular we show here how one can construct point transformations for reduction to the simplest linear equation by going to the higher space and just utilizing the coefficients of the original ODE. We also obtain invariant criteria for the reduction of a linear square system to the simplest system. Moreover these results contain the quadratic case as a special case. Examples are given to illustrate our results.     

多车道多车种随机车流量噪声的预报方法

本文将道路中通行的各种车按其发出的噪声级的高低分成四个等级,当车流量较小时,将各等级车,车流量看作复合泊松流,定量地分析出各等级车车流量与路边统计噪声级的关系,推导出相应的公式,给出根据各等级车,车流量对路边L₁₀、L₅₀、L₉₀声级的预报表。这就对多车道多车种随机车流噪声的预报提出一种简便实用的方法。经过北京市九条道路交通噪声的实测检验,证明预报值与实测值能很好地符合。     

STRICT DERIVATION OF MEAN FIELD EQUATION FOR ONE-DIMENSIONAL TRAFFIC FLOW MODEL

A new analysis method is presented for the study of Fukui-Ishibashi deterministic one-dimensional traffic flow cellular automaton model of high speed car on highway. By using this method, the exact mean field equation describing the fundamental diagram curve of average traffic speed versus the car density on highway can be derived strictly.     

一种用于描述多脉冲作用下AX自旋系统演化行为的相干图方法

本文提出了一种用于描述多脉冲作用下AX自旋系统演化行为的相干图方法。它具有简单、易理解等特点,弥补了矢量模型的不足。     

常微分方程边值问题的高阶三对角OCI差分法

本文给出了二阶线性常微分方程两点边值问题(ODETPBVP)的高阶差分格式构造的基本思想,推导出六阶三对角OCI差分格式,并对端点有奇异性的方程进行了极限值处理,消去了奇异性,对边界层问题采用了非均匀网格上的六阶三对角OCI差分格式。通过大量的数值比较实验表明,这种高阶三对角OCI差分格式能很好地求解奇异性问题,固有不稳定性问题,奇异摄动问题,对生不稳定性问题和振荡性问题。     

一维元胞自动机随机交通流模型的理论分析与计算机实验

在一维局部作用元胞自动机(CA)交通流模型中，引入刹车噪声与产生、消失概率，得到一个完全随机的CA交通流模型．利用平衡自旋理论对该模型的研究表明，当P_in＝P_out≠0时，初始密度分布不影响系统的最终状态，求得ρ_ｔ＝0.5；当满足条件P_in＋P_b＝1与P_in＝P_out时，得到简单的“线性”模型，该模型在条件｜1－2P_in｜＝1下，表现出长程相关，导致严重交通“阻塞”的出现．理论结果与计算机实验一致． 关键词：     

二阶常微分方程组边值问题的一种数值解法

本文用压缩变挟方法,求解了函数解随自变量增加而迅速增长的一类常微分方程的边值问题。结果表明,这种方法,可加快收敛速度。在奇点W=0附近,采用局部解析近似处理,得到了比较满意的数值结果。     

非线性迭代解析节块方法的数值稳定方法

针对非线性迭代解析节块方法在特定条件下出现的数值不稳定问题,提出了一种解决方法,并给出了数值结果。