A method to improve first order approximation of smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) is a useful meshless method. The first and second orders are the most popular derivatives of the field function in the mechanical governing equations. New methods were proposed to improve accuracy of SPH approximation by the lemma proved. The lemma describes the relationship of functions and their SPH approximation. Finally, the error comparison of SPH method with or without our improvement was carried out. Foundation item: The National Natural Science Foundation of China (No. 50778111); The Key Project of Fund of Science and Technology Development of Shanghai (No. 07JC14023)     

Improvement of the second order approximation of the smoothed particle hydrodynamics

The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been successfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics.High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high.A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpolation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.     

SPH法模拟立面二维溃坝流动应用研究

光滑离子流体动力学(SPH)法是一种纯拉格朗日(Lagrange)无网格方法,近年来发展日趋成熟。对SPH法的基本原理、核函数及控制方程离散格式、边界处理方法等进行了介绍。在此基础上建立了数值水槽模型,模拟了立面二维溃坝流动问题,并将所得结果与VOF法及模型试验得到的结果进行比较,结果表明:SPH法能够捕捉到流体的飞溅及融合现象,适于模拟具有瞬时极大变形等物理力学问题。     

Bounded Real Lemma for Generalized Linear System with Finite Discrete Jumps

Introduction In the past decade, research interests on sam-pled-data systems are increasing with the wide ap-plication of digital control in the industry. Tradi-tional discretization technique is limited since failedto take into account intersample behavi…     

On sequential composition of precise zero-knowledge

Precise zero-knowledge was introduced by Micali and Pass in STOC'06.This notion captures the idea that the view of any verifier in interaction can be reconstructed in almost time.Pass also obtained a sequential composition lemma for precise zero-knowledge protocols.However,this lemma doesn't provide tight precisions for composed protocols.In this paper we further obtain a sequential composition lemma for a subclass of precise zero-knowledge protocols,which all satisfy a property:their simulators use the cod...     

Characteristics of new-type energy absorber for vehicle collision

A new type energy absorber was introduced, which is composed of thousands of thin ring plates with different diameters. Because it can switch the impact to thousands of shearing actions among thin ring plates inside the absorber, the impact energy is decentralized and dissipated gradually, the impact acting time is extended and the peak of acceleration is reduced obviously. Numerical simulations by finite element method (FEM) coupled with smoothed particle hydrodynamics (SPH) method were preformed to predict the energy absorption characteristics. Energy absorption ability with different impact velocities was studied and the effects of thickness and material of ring plates were discussed. The sled crash test was carried out to validate the result of simulations. The new type absorber is effective for collision that impact velocity is lower than 40 km/h.     

伸缩步长法在数控加工中的应用

非圆曲线轮廓是机械零件常见的轮廓要素之一，但大多数数控机床加工非圆曲线只能用很多直线段或圆弧段来逼近非圆曲线，本文从数学的角度详细地介绍了伸缩步长法的基本原理及其在数控加工中的具体应用。     

直径为5的树的优美性

本文利用移边定理（引理1）,对星型树进行移边操作,针对不同情况,得到了相应特殊标号点分布的双星型树,再技巧性地移边,最终得到一组具体的优美标号,证明了任一直径为5的树的优美性．     

初探WKB近似法中波函数的选择

本文分析了教科书中利用WKB近似法求解势垒贯穿几率时选择波函数的方法,讨论了该方法的局限性.并通过对典型问题的处理,说明了在利用此近似法处理量子力学问题时,正确选取波函数的基本准则.     

Re-parameterization of Bézier Curves by Square Approximation with Endpoint Constraints

In order to get an approximation with better effect of parameterization of Bozier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete even de-parameterization of the curves. This method is simple and easy to implement, and the property of the approximation has no change compared with the original curve. A quantitative criterion for estimating the effect of parameterization is also built to quantitatively characterize the parameterization effect of the algorithms. As a result, the nearly arc-length parameterized curve has a smaller relative deviation using either the algorithm with point constraint at endpoints or the algorithm with point constraint plus the first derivative constraint at endpoints. Experiments show that after re-parameterization with our algorithms, the relative deviation will have at least a 20% reduction.     

带时变时滞细胞神经网络的全局渐近稳定性

研究了带时变时滞的细胞神经网络的全局渐近稳定性问题,给出了带时变时滞细胞神经网络平衡点全局渐近稳定的新充分判定准则。首先,提出所研究的时滞细胞神经网络模型、系统激活函数所需满足的条件及需要的引理。然后,将所研究的系统通过一个等式进行线性变换,在定义一个与系统相关的映射操作基础上,基于Lya-punov-Krasovskii稳定性定理和线性矩阵不等式技术来讨论时滞细胞神经网络的全局渐近稳定性。所得条件是时滞相关的。最后,用一个数值例子验证所得的稳定性条件是有效的。     

基于多种方位角计算方法的超短波AOA定位比较

考虑到方位角计算是AOA （angle of arrival）定位的基础之一，首先，提出了以大地坐标计算方位角的球面近似法和正轴圆柱投影-平面法；进而，建立了球面精确AOA定位方程、球面近似AOA定位方程和正轴圆柱投影-平面AOA定位方程；最后，采用无约束非线性规划方法建立了基于大地坐标的分别与上述方程相对应的3个最优化AOA定位模型，并以网格逐点搜索求解法进行了模型验证. 验证结果的分析表明:在不考虑测向误差时，球面精确AOA定位模型的精度最高，且与纬度无关，但其定位运算时间最长；球面近似AOA定位模型和正轴圆柱投影-平面AOA定位模型的精度均较高，后者的定位误差略大于前者，定位运算时间也长于前者；要提高AOA定位网的定位精度，既可提高各站点的测向精度，也可增加测向站点数，并应综合考虑定位时效性要求和精度要求选择合适的AOA定位模型.      

高维欧氏空间上无界连续函数逼近的渐近公式

利用扩展乘数法讨论了高维氏空间上线性正算子改造为逼近多元无界连续函数的渐近估计，给出了具有一般性的渐近公式，作为实例研究了多元非乘积型的Landau多项算子逼近多元无界连续函数的渐近估计式，推广了前人的若干结论。     

Beta算子的导数对一类函数的逼近速度

利用渐近分析的方法讨论了Beta算子的导数对一类函数的逼近速度,获得了类似函燮华的结果。     

混合法研究水下刚性目标全波数散射特性

通过构建油港储运系统评估指标体系,建立多层次灰色变权综合安全评价模型对研究对象进行评价,并且在评价过程采用层次分析方法确定权重.实例结果表明,多层次灰色综合评价结果具有较强的客观性,能给决策者提供比较可靠的判断依据.     

遗传算法在估计瞬时单位线参数中的应用

以m atlab为平台,应用遗传算法和m atlab工具箱中的统计函数,通过求解还原洪水过程与实测洪水过程之差绝对值的加权之和最小化问题来优化估计瞬时单位线的参数,避免了用近似公式法求解带来的方法误差.实例研究表明该方法是有效的,其精度明显高于矩法,也较近似公式法高.     

基于2D弹性理论的船舶板结构无网格技术

应用无网格局部Petrov-Galerkin法对船舶平直板结构进行了研究。运用最小二乘法和加权余量法来求解结构位移场量的逼近函数,给出了问题的控制方程和刚度方程。通过算例与有限元法计算结果进行了比较分析,验证了文章提出方法的正确性。文章研究对于分析船舶结构变形和应力具有良好的适用性。     

小底坡梯形明渠临界水深的加权逼近法

用两小加权迭代法计算小底坡梯形明渠的临界水深，计算简便，而精度很高；迭代两步所得结果的相对误差为１０＾－５数量级，迭代三步为１０＾－６数量级，适用范围也较宽，能满足一般水利工程的需要。     

无网格对称粒子法中两类热边界条件的处理

第二、三类边界条件对无网格对称粒子法求解瞬态热传导问题的计算精度和稳定性有重要影响。提出一种有效的方法来处理这两类边界条件。该方法采用统一表达式描述两类边界条件,并将边界粒子分为光滑域内的边界粒子和非光滑域的边界粒子。对于前者,在温度导数的对称粒子近似中引入边界条件方程,精确地施加边界条件;对于后者,根据其相邻粒子的温度导数,采用具有一阶连续性的粒子近似,计算出其温度导数。应用该方法计算了一个数值算例。计算结果与解析解和有限元法的计算结果符合良好,且计算误差随时间呈下降趋势,说明该方法具有良好的精度和稳定性。     

Interval Bézier Surfaces Approximation of Rational Surfaces

On the basis of the perturbation, we present an approach to approximating rational surfaces by the interval Bézier surfaces using energy minimization method. The approach makes the perturbation surfaces have more restrictions than the original surfaces. It could be combined with subdivision method to obtain a piecewise interval polynomial approximation for a rational surface. The applications of this approach are illustrated too.