广义特征坐标系计算膨胀波与激波优越性的数值验证

最近提出的以流体速度和声速的线性组合为速度而运动的广义特征坐标系,是-个更为-般的坐标系统,当参数取不同特殊值的时候,就可以得到其他经典的坐标系统.这种坐标系的最大特点是,它能跟随膨胀波(当然也可以跟随激波和接触间断)运动,从而在使用同-计算格式的前提下,使得膨胀波的计算精度更高.对膨胀波和激波进行数值试验,结果显示广义特征坐标系在计算膨胀波和激波时明显优于传统的坐标系.     

有关傅科摆的一种解法

本文对傅科摆运动规律的研究与一般书中处理方法不同，不是直接选用固定在地球上的固定坐标系来研究，而是选用相对地球有特定转动的半固定坐标系求解．结果是傅科摆在这个特定的半固定坐标系中轨道稳定，物理图象直观，使学生易于加深理解傅科摆对地球的运动规律．     

三维线性谐振子量子性运动图像的可视化探究

本文从量子力学中三维线性谐振子在直角坐标和球坐标系下的波函数出发，采用蒙特卡罗方法对空间概率函数进行了抽样，并采用Mathmatica软件对不同坐标系下谐振子运动的概率云图像进行了可视化呈现，进一步结合可视化图像对两种坐标系下不同量子数分解方式下得到的系统量子性运动特征进行了详细的对比研究，并从量子力学理论角度分析了对应的物理意义.     

灵活选择坐标系解答一道物理竞赛题

在同一参照系中，描述物体运动可以运用不同的坐标系．在不同坐标系中，描述物体运动量的变量虽然不同，但是它们相对同一参照系的速度、加速度等物理量是相同的．在解答力学问题时，正确灵活变换坐标系，常能揭示物体速度、加速度等运动量间的约束关系，突破解题难     

非紧凑低马赫数运动边界散射流动噪声的预测

提出了一种求解非紧凑低马赫数运动边界散射流动诱发噪声的预测方法。该方法首先基于运动坐标系下的连续性方程和动量方程推导得到该坐标系下的波动方程及其积分解,然后在该坐标系下采用边界元方法求解得到非紧凑运动边界表面的声压,最后将求解得到的壁面声压回代到静止或运动坐标系下的积分方程中实现对远场噪声的预测。推导得到的积分方程适用于流体与飞机机身、高速列车车身及旋转叶片等非紧凑结构边界作用诱发噪声的预测。     

也谈正则动量算符之争

讨论了平直空间曲线坐标系中质点运动的两种不同的量子化假设，比较了它们在物理思想和实际操作上的区别和优劣。     

对称陀螺运动的简明分析方法

本文就对称则体的情况提出一种求解刚体定点运动（即对称陀螺运动）的新方法．即，用节线坐标系代替固定在刚体上的主轴坐标系作为角动量定理的投影坐标系；在重力陀螺运动的分析中，用等效势分析代替解三次方程．此法较之通行的解欧勒动力学方程的方法，在计算方面明显简化，且更具直观性．     

关于质速关系m=m_0/{(1-v~2/c~2)1/2}的一个简单证明

狭义相对论的一个重要关系式 ,在非物理专业的普通物理教材中,一般并没有加以证明;即使少数教材给出了证明,其过程也很复杂.本文介绍一种简易的证明方法,可使初学者在较短时间内尽快地掌握这一公式的来龙去脉. 动量守恒定律在自然界中是普遍成立的,不同惯性系的观察者测量的物体相对于同一惯性系的动量应相等.这就是本文证明的出发点. 为简单起见,假设K'坐标系相对于K坐标系作匀速。运动,其运动方向沿x轴正方向,并且在两坐标系重合时;双方的钟都指向0(即t=t'=0),有一静止质量为m0的质点在其中运动,运动方向沿x(或x')轴,如图所示. 由K'系中…     

一个自动跟踪问题的轨道与追及时间

本文讨论一个有实际意义的自动跟踪问题，在固定参照系和运动参照系的不同坐标系中计算了跟踪的轨道，并求出了从开始跟踪到命中目标的时间．     

引入牵连微商讨论相对运动的方法

本文指出,在讨论相对运动时如引进一种新的时间微商,即所谓牵连微商,就可简化相对运动中速度和加速度的计算,并便于从物理上说明牵连加速度和柯赖奥来加速度的含义。文中得到了绝对微商、相对微商和牵连微商这三种算符之间的关系式,用这种算符关系式讨论相对运动是十分方便的。 一、引言 一质点M相对于基本坐标系Ω的运动称为绝对运动,相对于动坐标系Oxyz的运动称为相对运动。理论力学中一个重要的问题是,如已知质点M在动坐标系K中的位置和速度,如何由动坐标系K相对于基本坐标系K’的运动,求出质点M在K’中的速度和加速度,即求出其绝对…     

二维三温能量方程的差分格式及平面靶数值模拟

通过统一二维直角坐标与柱坐标下三温能量方程的差分格式,实现了LARED-H(laser radiationelectron dynamic holehurm)程序既可以模拟正入射激光平面靶过程,也可模拟斜入射平面靶问题,从而扩展了LARED-H程序的功能.使用发展后的LARED-H程序进行了直角坐标系下线聚焦打靶耦合过程数值模拟,给出了不同入射角度下靶等离子体的膨胀过程.     

Kinemaitcs in spatially flat FLRW spacetimes

The kinematics on spatially flat FLRW spacetimes is presented for the first time in local charts with physical coordinates, i.e., the cosmic time and proper Cartesian space coordinates of Painlevé-type. It is shown that there exists a conserved momentum that determines the form of the covariant four-momentum on geodesics in terms of physical coordinates. Moreover, with the help of this conserved momentum, the peculiar momentum can be defined, thus separating the peculiar and recessional motions without ambiguity. It is shown that the energy and peculiar momentum satisfy the mass-shell condition of special relativity while the recessional momentum does not produce energy. In this framework, the measurements of the kinetic quantities along geodesics performed by different observers are analyzed, pointing out an energy loss of the massive particles similar to that producing the photon redshift. The examples of the kinematics on the de Sitter expanding universe and a new Milne-type spacetime are extensively analyzed.     

New theoretical approach concerning the physical phenomena in space and time,and the action principle

The unity of physical nature is advanced. A primordial continuum with geometric character is assumed to exist; its coordinates are the elements generating the physical magnitudes. The relation between these primordial coordinates and the physical magnitudes is established. Starting from the condition of minimum path in the primordial continuum, an explanation of the action principle is given. In sequence the equations for the four-dimensional space-time are obtained, and with some specializations the equation of gravity is derived.     

对气象常用坐标系中位涡形式的探讨

气象常用垂直坐标系中的位涡方程及位涡形式是位涡理论及位涡诊断技术的基础.本文依据坐标转换的观点,分别用两种不同的方法推导出等压坐标和等熵坐标中的位涡方程及相应的位涡表达式.一是从三维矢量运动方程出发,由三维涡度方程、连续方程和热力学方程推导位涡方程;二是直接从等压坐标和等熵坐标中的标量运动方程组出发推导位涡方程.结果表明,用两种方法所得到的等压坐标中的位涡方程和位涡表达式形式有所不同,而等熵坐标中用两种方法所得到的位涡方程和位涡形式相同.对垂直坐标系的物理本质分析表明,采用第一种方法时尽管矢量运动方程中的 关键词： 位涡 坐标转换 等压坐标 等熵坐标     

The physical meaning of Fermi coordinates

Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space or even in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. A proposal for a modification is made and applied to the observer with constant acceleration in the two- and four-dimensional Minkowski space. The two-dimensional case shows some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification also leads to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.     

Testing whether two chaotic one dimensional processes are dynamically identical

Consider the situation where two individuals observe the same chaotic physical process but through time series of different measured variables (e.g., one individual measures a temperature and the other measures a voltage). If the two individuals now use their data to reconstruct (e.g., via delay coordinates) a map, the maps they obtain may appear quite different. In the case where the resulting maps appear one dimensional, we introduce a method to test consistency with the hypothesis that they represent the same physical process. We illustrate this method using experimental data from an electric circuit.     

Spin Hall effect in noncommutative coordinates

A semiclassical constrained Hamiltonian system which was established to study dynamical systems of matrix valued non-Abelian gauge fields is employed to formulate spin Hall effect in noncommuting coordinates at the first order in the constant noncommutativity parameter θ. The method is first illustrated by studying the Hall effect on the noncommutative plane in a gauge independent fashion. Then, the Drude model type and the Hall effect type formulations of spin Hall effect are considered in noncommuting coordinates and θ deformed spin Hall conductivities which they provide are acquired. It is shown that by adjusting θ different formulations of spin Hall conductivity are accomplished. Hence, the noncommutative theory can be envisaged as an effective theory which unifies different approaches to similar physical phenomena.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

Instantons in non-Cartesian coordinates

The multi-instanton solutions of ’t Hooft and of Jackiw, Nohl, and Rebbi are generalized to the case of curvilinear coordinates. The resulting formulas are considerably simplified if the transformation of coordinates is supplemented with a gauge transformation. As a result, the gauge field develops a term that has the same form as in Cartesian coordinates and which describes pseudoparticles and a compensating addition of a geometric origin (it is determined by the coordinate frame used). The singularities of the compensating field are irrelevant to physical quantities, but they can affect gauge-dependent quantities.     

New interpolation technique for the CIP method on curvilinear coordinates

We propose a new interpolation technique for the CIP method applied to curvilinear coordinates. The CIP method can hardly maintain third-order accuracy on curvilinear coordinates. The reason for the degeneracy in accuracies has not been discussed in detail. This paper reveals the problems of the CIP method on curvilinear coordinates and presents an improved CIP method to solve the advection equation accurately. The features of the presented method are: (1) the metric computation on the upwind stencil is defined in the same manner as in the advection phase of the CIP method; and (2) gradient values in the physical domain in the computation on the curvilinear coordinates are used. Various test problems show that the improved CIP method has approximate third-order accuracy.