Supersymmetric classical mechanics

The purpose of the paper is to construct a supersymmetric Lagrangian within the framework of classical mechanics which would be regarded as a candidate for passage to supersymmetric quantum mechanics. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Effect of random density irregularities on nonlinear evolution of Langmuir waves in interplanetary medium

The evolution of nonlinear Langmuir waves in the interplanetary medium is investigated by appropriately accounting for the random density irregularities of the medium. A pair of modified Zakharov equations, which describe these waves, is solved numerically as an initial value problem for large scale (≫ 10² km) initial pertubations. For an ion acoustic-Langmuir solitary wave, the random irregularities damp the Langmuir wave by way of scattering and let the ion density perturbation radiate away in a few days. However an initial solitary or shock-like Langmuir wave excites the ion density perturbations within a fraction of a second, and then itself gets damped. These effects will strongly decelerate the collapse of large scale Langmuir waves. The possibility of detecting these processes, by means of interplanetary scintillation, is discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

弹体尾部轴对称干扰流场数值模拟

绕弹体的超声速气流与发动机喷流相互作用,在尾部形成复杂的干扰流场。本文用有限差分法求解全N-S方程,对这一复杂流场进行了数值模拟,得到了实验观察到的各种流场结构及其随喷口压力比的变化规律。外流M_∞=1.94,R_e∞=2.2×10⁵,喷流M_j=3.0,喷口压力比p_j/p_∞分别为1.03,0.527,0.15三种。差分算法为一种改进的Beam-Warming格式。计算底部压力和激波在喷流中心的反射位置与实验数据进行了比较,吻合较好。     

Charateristics of a helical axial flow CO_2 laser

A novel CO_2 laser tube which forms a helical axial gas flow is designed. The influences of such a flow on the output laser beam is discussed.     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

考虑行车状态的一维元胞自动机交通流模型

在Nagel Schrekenberg单车道元胞自动机交通流模型（简称NS模型）的基础上，考虑车辆之间的相对运动薛郁等提出了一种改进的单车道元胞自动机交通流模型（简称改进的NS模型）.通过两种情况列出了改进的NS模型存在不尽周严的地方，随之在新模型中引入了行车状态 变量和反馈规则，从而控制车辆出现倒车和刹车过急等现象.通过计算机对新模型进行模拟 ，发现减速概率和车流密度对车流状态的演化影响很大，当减速概率高（如道路条件差）时 ，即使车流密度低，车流也会出现局部堵塞状态；而当减速概率一定时，随着车流密度增加 ，车流的运动相与堵塞相发生了全局性的交替出现，此时类似于波的波峰和波谷的传播.与 改进的NS模型相比较，新模型模拟的车流量较高，说明新模型减少了车流的总体停滞状态. 关键词： 交通流 元胞自动机 行车状态 反馈规则     

基于Shannon-Cosine小波精细积分法的壁画降噪修复方法

为修复受破损且噪声点众多的壁画图像,提出了用偏微分方程（partial differential equation,PDE）扩散的方法对图像进行降噪修复。针对PDE法求解精度较低的问题,提出了一种Shannon-Cosine小波精细积分法,运用小波数值方法对偏微分方程进行离散处理,降低其方程组规模,并采用精细积分法求解,有效提高了计算速度。试验结果表明,采用该算法对受损壁画降噪处理后,视觉上,图像边界更清晰,且噪声点得到有效减少,达到了保边降噪的效果,更符合人眼的视觉效果;客观上,与中值滤波、均值滤波和维纳滤波方法相比,采用本算法处理后的图像其PSNR值和SSIM值均最大。因此,运用Shannon-Cosine小波精细积分法求解图像的PDE模型是可行的,取得了较好的图像降噪效果。     

时标上二阶广义Emden-Fowler型动态方程的振荡性

研究了时标上的一类具有阻尼项的二阶广义Emden-Fowler型泛函动态方程的振荡性,利用时标上的微积分理论和广义的Riccati变换及不等式技巧,建立了该方程振荡的若干判别准则, 推广且改进了一些已有的结果,并用具体实例来说明本文的主要结论。     

σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性,给出了σ2Hessian方程Pogorelov型C2内估计,进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。