一组适合快速计算的氨热力性质方程

经分析计算，本文给出了一套形式简单，使用方便的氨热力性质计算方程，其中状态方程选用２舍项维里方程。在工程应用的温度、压力范围内使用，计算精度很好。由于计算比容及由压力计算饱和温度时无须迭代运算，方程适合用于对氨热力性质进行快速计算的场合，也很适合工程设计使用。     

阶梯梁位移方程间的普遍关系

基于梁性变曲基本理论，论证了梁在任意复杂载荷作用下，不同梁段位移方程之间存在的普遍关系。这一关系说明，不同梁段位移方程之间仅相差一个已知函数该结论使位移方程的求解得以简化，同时在《材料力学》基础理论研究及教学上均有其实用价值。     

非定常射流泵性能方程的推导

根据流体力学的基本原理，利用准二维分析方法导出了非定常情况下射流泵的性能方程，并与定常情况下的性能方程进行了分析对比，为进一步分析非定常射流泵的机理奠定了基础。     

求刚性中子动力学方程数值解的新方法

中子动力学方程是刚性方程，数值计算很费机时，为减少计算机时提出了许多算法，常用的有隐式差分法、多步法和自动变步长法等，著名的方法有吉尔方法和埃米特方法，但这些方法的计算程序复杂且总计算时间减少不明显，消去刚性法是一个全新的算法，稳定步长可达到20s，计算时间大大下降。     

刚柔耦合系统动力学建模新方法

作高速大范围运动的机械系统，由于运动和变形的耦合将产生动力刚化现象，传统动力学理论难以计及这种影响。通过Kane方程在保证变形广义坐标完全精确到一阶项的前提下建立了系统一阶完备动力学方程。通过与传统动力学方程的对比分析，揭示了传统建模方法不仅遗失了动力刚度项。同时遗失了某些刚柔耦合惯性项。本文提出了一种通过对传统非完备动力学方程的修正以获得一阶完备动力学方程的新方法。     

探讨计算标准曲线方程的一种新方法——斜率平均法

本文力求探索一种求标准曲线方程的新的计算方法，通过计算标准的斜率，相加后平均即为所求标准曲线方程的斜率，首先从数学上进行了证明，又列举了计算实例，并与回归方程法作了比较，通过探讨，寻求一个简便，易行，准确地计算标准曲线方程的新方法。     

三点法测量圆弧半径的数据处理

介绍了在圆弧上测得任意三点的坐标值，通过建立直线方程和圆方程以及通过算得测点间的坐标距离求得圆弧半径的三种数据处理方法。     

空气调节一般性能量方程的探讨

本文首先提出了热、湿调节过程理想化物理模型，进而建立了空气能量变化的一般性能量方程和空调负荷分析的一般性能量方程，揭示了空气得热和空调系统需热量之间的区别，最后讨论了一般性能量和方程在几种特殊情况下的应用。     

求解不规则区域上椭圆方程的一种Cartesian网格方法及其在Navier-Stokes方程中的应用

提出了一种求解不规则边界上有Robin边界条件的椭圆方程的Cartesian网格方法。该椭圆方程经重写后转化为定义在矩形区域上的椭圆界面问题，进而采用水平集浸入界面方法 (IIM)对其进行求解。特别地，Robin边界条件采用单边三次插值离散。随后，利用该方法求解定义在不规则区域上的Navier-Stokes程。Navier-Stokes方程的解法器由求解速度方程的虚拟流体方法 (GFM)和辅助变量方程的IIM耦合而成。数值测试表明，椭圆方程的解法器能够产生二阶精度的数值解和梯度，而且能够快速收敛，Navier-Stokes方程的解法器产生了二阶精度的速度及一阶精度的压力。圆柱绕流的仿真验证了Navier-Stokes方程解法器的鲁棒性。     

流体力学理论在流量计量中的应用

文章介绍了流体力学理论如何和流量计量结合，给出连续性方程和伯努利方程在流量上的推导和经典的应用。     

时滞微分方程特征值的近似求解方法

通过将时滞微分方程变换为积分方程后并进行离散,得到相应的差分方程,从理论上建立了差分方程的系统矩阵的特征值与原线性时滞微分系统的特征值之间的关系,从而得到了一种求解时滞微分方程特征值的新方法。作为算例,计算了时滞的Logistic方程的前10阶特征值。误差分析表明,提出的近似方法不但简单,并且有很高的精度。     

The Gibbs equation versus the Kelvin and the Gibbs-Thomson equations to describe nucleation and equilibrium of nano-materials

The Kelvin equation, the Gibbs equation and the Gibbs-Thomson equation are compared. It is shown that the Kelvin equation (on equilibrium vapor pressure above nano-droplets) can be derived if the inner pressure due to the curvature (from the Laplace equation) is substituted incorrectly into the external pressure term of the Gibbs equation. Thus, the Kelvin equation is excluded in its present form. The Gibbs-Thomson equation (on so-called equilibrium melting point of a nano-crystal) is an analog of the Kelvin equation, and thus it is also excluded in its present form. The contradiction between the critical nucleus size (from the Gibbs equation) and the so-called equilibrium melting point of nano-crystals (from the Gibbs-Thomson equation) is explained. The contradiction is resolved if the Gibbs equation is applied to study both nucleation and equilibrium of nano-crystals. Thus, the difference in the behavior of nano-systems compared to macro-systems is due to their high specific surface area (Gibbs) and not to the high curvature of their interface (Kelvin). Modified versions of the Kelvin equation and the Gibbs-Thomson equation are derived from the Gibbs equation for phases with a general shape and for a spherical phase.     

Invalidity of the spectral Fokker–Planck equation for Cauchy noise driven Langevin equation

The standard Langevin equation is a first order stochastic differential equation where the driving noise term is a Brownian motion. The marginal probability density is a solution to a linear partial differential equation called the Fokker–Planck equation. If the Brownian motion is replaced by so-called -stable noise (or Lévy noise) the Fokker–Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. Instead it has been attempted to formulate an equation for the characteristic function (the Fourier transform) corresponding to the density function. This equation is frequently called the spectral Fokker–Planck equation.

This paper raises doubt about the validity of the spectral Fokker–Planck equation in its standard formulation. The equation can be solved with respect to stationary solutions in the particular case where the noise is Cauchy noise and the drift function is a polynomial that allows the existence of a stationary probability density solution. The solution shows paradoxic properties by not being unique and only in particular cases having one of its solutions closely approximating the solutions to a corresponding Langevin difference equation. Similar doubt can be traced Grigoriu's work [Stochastic Calculus (2002)].     

一种新的散射电子空间输运坐标转换方法

提出一种新的随动坐标系矢量转换方法，给出用于转换散射电子空间输运坐标的矩阵方程，该方程具有递推的形式，计算方便，并且只涉及乘法运算，不会引起计算上的困难，将其用于PMMA－Si中电子散射过程的Monte Carlo模拟，结果表明可以有效节约机时，提高模拟效率，明显优于习惯上使用的静态坐标系方程。     

Solution of mode coupling in step-index optical fibers by the Fokker-Planck equation and the Langevin equation

The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based on the computer-simulated Langevin force. The solution matches the solution of the power-flow equation reported previously. Conceptually important steps of this work include (i) the expression of the power-flow equation in a form of the diffusion equation that is known to represent the solution of the stochastic differential equation describing processes with random perturbations and (ii) the recognition that mode coupling in multimode optical fibers is caused by random perturbations.     

Wave equation model for solving advection–diffusion equation

This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator-splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first-order advection equation, the present wave equation model solves a second-order equivalent wave equation whose solution is identical to that of the first-order advection equation. Numerical examples of 1-D and 2-D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1-D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.     

Numerical method of inertance tube pulse tube refrigerator

A nodal analysis method for simulating inertance tube pulse tube refrigerators is introduced. The energy equation, continuity equation, momentum equation of gas, energy equation of solid are included in this model. Boundary condition can be easily changed to enable the numerical program calculate thermal acoustic engines, inertance tube pulse tube refrigerators, double inlet pulse tube refrigerators, and others. Implicit control volume method is used to solve these equations. In order to increase the calculation speed, the continuity equation is changed to pressure equation with ideal gas assumption, and merged with momentum equation. Then the algebraic equation group from continuity and momentum equation becomes one group. With this numerical method, an example calculation of a large scale inertance tube pulse tube refrigerator is shown.     

脉冲源反演介质参数的近似波前法

在时域内对弹性波动方程退化的非均匀介质声波方程，引入背景场参数与扰动参数，并化为积分方程形式；针对脉冲源情况，根据射线理论中的传递方程和程函方程，对非均匀介质中的波场形式引入一种波前近似形式，得到波散射点满足散射关系曲线及散射波幅值与介质参数扰动比的代数关系方程式；为求解非均匀介质中散射波场及反演介质参数提供了一种方法，通过对一个完整算例全部过程的模拟，验证了此方法的正确性。     

Evaluation of the T-stress in branch crack problem

This paper investigates the T-stress in the branch crack problem. The problem is modeled by a continuous distribution of dislocation along branches, and the relevant singular integral equation is obtained accordingly. After discretization of the singular integral equation, the balance for the number of equations and unknowns is well designed. After the singular integral equation is solved, the equation for evaluating the T-stress is derived. The merit of present study is to provide necessary equation for evaluating T-stress, rather than to provide the integral equation. Many computed results for T-stress under different conditions for branch crack are presented. It is found from the computed results that the interaction for T-stress among branches is complicated.