重建极性连续统理论的基本定律和原理(Ⅳ)——表面守恒定律

从普遍均衡定律的平移和转动的不变性出发来重新建立较为完整的微极热力连续统的表面守恒定律,提出了广义的能量动量和能量动量矩张量.给出了Piola型、Cauchy型和Kirchhoff型微极热力连续统的表面守恒定律的具体形式.现有的结果都可以当做是特殊情形从该结果自然地推导出来,并可从归结过程中清楚地看出现有理论的不完整性程度.非局部微极热力连续统的表面守恒定律可通过局部化得到.     

Characteristic-based finite volume scheme for 1D Euler equations

In this paper, a high-order finite-volume scheme is presented for the one- dimensional scalar and inviscid Euler conservation laws. The Simpson＇s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson＇s quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory （CWENO） reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.     

关于《对一道典型物理错题的分析》的补充

《物理通报》2011年第4期的封三上发表的文章《对一道典型物理错题的分析》,我读过后有些补充意见陈述如下.(1)文中指出的(2)、(3)、(4)、(5)诸式是错的,并说明物体的运动应遵守角动量守恒定律.下面根据角动量守恒和匀速圆周运动向心力公式导出(9)式是对的,只是(6)式错了——v少个平方.最     

力场与时间有关系统的功能定理及其应用

与时间有关的有势力场与其他力共同作用系统的功能定理具有比普通的功能定理更为强大的应用价值,本文介绍这一功能定理,并应用于不同参考系观察同一系统的机械能如何变化的两个简单实例:在地面上和升降机中观察地面附近同一质点的机械能变化,在地面上和在运动车厢里看一端固定于车厢壁的弹簧振子的机械能变化.指出了有些文献的有关错误.     

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.     

验证动量守恒定律实验的探究

1问题的引出验证"碰撞中的动量守恒"实验课的分组实验中,一位学生发现了问题:如图1所示中,在等位板处释放小球a,去碰撞放在水平轨道的另外一个完全相同的小球b时,不能出现小球a静止,小球b获     

“守株待兔”测算当地重力加速度

一.引言重力加速度g值,是我们初高中都一直离不开的简单而又重要的物理量,在初高中我们都会用不同的方法来测算它。而在这里,我们将应用高中的相关物理知识,融合出有一种更加另类、更加有趣的测算方法,并利用数字实验仪器和电子计算机测算出相关的数值,进而求出当地重力加速度。     

变质量非完整力学系统的Noether定理及其逆定理

1 引言动力学系统的守恒定律或运动积分是满足运动微分方程的物理量和几何量之间的某种确定的函数关系;动力学系统的对称性或不变性是指表征系统的某个特征对某个变换在某种意义下是不变的.1918年,A E Nocther 提出的Noether 定理,首先把动力学系统     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

对一道中学生物理竞赛试题答案的商榷

重新解答了第26届全国中学生物理竞赛复赛第3题第1小题,指明了该题的参考解答(标准答案)错误.