液体表面张力测定( 拉脱法)的误差分析与修正

拉脱法是测量液体表面张力最常见的一种方法, 此方法具有现象直观, 实验原理易被学生接受, 仪器简 单等优点. 但在大学物理实验教学中忽略金属丝框所受的浮力和水膜所受的重力对测量公式进行了简化, 给测定结 果带来了误差. 从误差分析的角度对拉脱法测定液体表面张力系数公式进行了分析与修正, 得出了相关结论     

由相对不确定度研究气体比热容比的测量仪器选择

该实验利用测量气体比热容比的经典装置,证明小球装置中做简谐振动,并依据周期推导气体比热容比理论公式,分析了测定气体比热容比的误差来源采用计算机实时测量技术获得气体在任意时刻的压强,利用比热容比的相对不确定度确定了测量仪器,从而利用精确的测量量求得气体比热容比值,利用确定的仪器测量,最终实验相对百分误差控制在0.5％.     

基于智能手机的振动现象研究及应用

本文利用智能手机内置传感器与Phyphox软件,探究了简谐振动的周期公式和耦合双自由度振动的规律,测量了多自由度振动系统(人行天桥)的固有频率.实验结果表明,用手机和Phyphox得出的简谐振动周期公式与理论公式非常接近.对双自由度系统,验证了简正模思想在分析耦合振动系统是可行的.对于桥梁这样复杂的多自由度振动系统,运用手机就可以很方便地测量其固有频率.     

不等精度测量中的最可信赖值及误差的理论研究

本文应用数学理论推导出不等精度测量中的最可信赖值及误差 ,使测量中使用公式在理论上得以证明     

用实验验证简谐振动周期公式

高一物理现行课本简谐振动的周期一节,对简谐振动周期公式,只给出了结果没有推导过程,学生学过之后印象不深,如果教师在讲授时用实验验证一下,可以收到事半功倍的效果. 多数学校都有如图1所示的演示弹簧振子.如果用弹簧振子验证公式,则公式中的m表示振子锤的质量,k表示弹簧的倔强系数.     

合成孔径激光成像雷达中非线性啁啾补偿算法的误差分析

可调谐激光器产生的非线性啁啾相位误差会降低合成孔径激光成像雷达(SAIL)的距离向分辨率。已有的补偿算法中使用的相移公式存在估算误差,外差脉冲补偿方法也存在补偿误差。由理论推导得到适合于实际有限数据的相移公式,对理想相移公式产生估算误差的物理原因进行了分析。建立了条带扫描模式下星载SAIL的计算机仿真模型,并对两个相移公式的估算误差、整体补偿和逐一扫描滤波补偿两种方法的补偿误差进行了模拟。仿真结果验证了理论推导结论。最后,给出了减少SAIL非线性啁啾补偿算法中估算误差和补偿误差的方法。     

菲涅耳衍射公式误差相位的讨论

根据波动光学的理论,对菲涅耳近场衍射公式误差相位的影响进行了分析。以单缝衍射为例,讨论了误差相位与计算精度的联系。结合菲涅耳线波带片焦面光强分布的计算,对比了菲涅耳衍射公式与基尔霍夫衍射公式的计算结果,说明在不满足误差相位近似条件下使用菲涅耳衍射公式带来的影响。最后对影响波带片焦面光强分布的几个因素进行了讨论。     

轨迹成型法精密磨削加工机床的精度分析

为了保证用轨迹成型法加工光学零件的面形精度,对精密磨削机床影响工件面形误差的因素进行了理论分析。推导出机床调整机构可消除误差的公式。并以误差公式计算出的误差值来调整机床的微调机构,可达到减少面形误差,进而保证面形精度的目的。     

投影栅相位法轮廓测量的非线性误差分析

分析了投影栅相位法三维轮廓测量系统的非线性误差。建立了几何光学模型,从理论上推导出被测点的相对高度与像点坐标的关系,研究了系统结构参数改变引起的高度误差的变化。详细阐述了像点坐标误差和系统非线性误差对系统精度的影响,并给出了高度误差补偿方法。据此提出修正的非线性高度拟合公式,实验结果证明新拟合公式的优越性。     

代数误差公式的适用条件

在实验数据的处理中。估算问接测得量的误差时。经常引用加减运算、乘除运算的代数误差公式。但是。代数误差公式并不是普遍适用的。本证明。代数误差公式适用的充分条件是取误差的各量相互独立。     

紫外-可见吸收光谱法测定配合显色反应的焓变

本文提出一种测定显色反应焓变的简单实验方法,推导出吸光度与温度的关系式,用Tween-80介质中的硫氰酸钴（Ⅱ)配合物显色反应验证了关系式的线性关系,得到相关系数r为0．9957,ΔH＝－44．7kJ.moL^-1,同Vant Hoff方程得到的结果基本一致。     

重力场中的气温公式

热学教材中大都讨论了等温气压公式，但实际上大气并不等温．本文通过对温度场的描述，导出了重力场中的温度梯度公式，并利用该公式推出了重力场中的气温公式，描绘了地球周围低高处大气温度随高度变化的近似曲线。     

Some useful upper bounds for the selection of optimal profiles

In enhanced oil recovery by chemical flooding within tertiary oil recovery, it is often necessary to choose optimal viscous profiles of the injected displacing fluids that reduce growth rates of hydrodynamic instabilities the most thereby substantially reducing the well-known fingering problem and improving oil recovery. Within the three-layer Hele–Shaw model, we show in this paper that selection of the optimal monotonic viscous profile of the middle-layer fluid based on well known theoretical upper bound formula [P. Daripa, G. Pasa, A simple derivation of an upper bound in the presence of a viscosity gradient in three-layer Hele–Shaw flows, Journal of Statistical Mechanics (2006) 11. http://dx.doi.org/10.1088/1742-5468/2006/01/P01014] agrees very well with that based on the computation of maximum growth rate of instabilities from solving the linearized stability problem. Thus, this paper proposes a very simple, fast method for selection of the optimal monotonic viscous profiles of the displacing fluids in multi-layer flows.     

一维多通道正常金属结构的透射几率

本文考虑一个严格一维的正常金属多分支结构,指出把Büttiker等人处理两分支结构的方法加以改进。即可解决这种多分支结构问题。我们给出了多分支结构的透射系数公式,作为一个简单的例子,求出了一个对称三分支结构的具体结果,并表明在这种结构中存在透射几率的共振现象。 关键词：     

类Li离子电偶极跃迁的碰撞强度

用半径经典方法计算类Ｌｉ离子电偶极跃迁的碰撞强度。用碰撞参数为ｂ的双曲线轨道描述入射电子的运动，用时间有关的微扰理论方法描述靶态的跃迁几率，通过对碰撞参数的积分求出电子碰撞激发截面。碰撞强度可表示成与振子强度成线性关系的简单公式。计算了若干个类Ｌｉ离子２ｓ－２ｐ１／２、２ｐ３／２的碰撞强度。结果表明，除在阈能附近以外，大部分数据与用较精确的相对论扭曲波的计算结果符合得很好。所用方法简单，而且可以进行快速计算，有很大的实用价值和参考价值     

高能反应末态强子产率的普适质量关系

最近实验上发现高能粒子反应末态强子多重数与其质量之间满足简单普适经验公式.计算了e⁺e^－湮没与pp(p)反应过程的直生介子与重子多重数,与经验公式中的参数完全一致.对经验公式中与反应能量有关的参数给出合理解释,并讨论了质量普适关系的原因.     

Numerical errors of diffraction computing using plane wave spectrum decomposition

In the paper the numerical determination of diffraction patterns using plane wave spectrum decomposition (PWS) is investigated. The simple formula for sampling selection for error-free numerical computation is proposed and its applicability is discussed. The usage of this formula presents practical difficulty for some diffraction problems due to required large memory load. A new multi-Fourier transform PWS (MPWS) method is elaborated which overcomes memory requirement of the PWS method. The performances of the PWS and MPWS methods are verified through extensive numerical simulations.     

自由电子激光器中的电子阻尼运动

建立了有阻尼项的摆方程,在小信号情况下,对方程进行了迭代求解.由解得的结果得到了增益函数的表达式.特别对弱阻尼和过阻尼情况进行了计算,分别得到了相应的增益函数简化公式.对阻尼项的来源和物理意义进行了详细的讨论. 关键词：     

Determination of the best carrier frequency based on the system and environmental parameters in underwater acoustic systems

One of the most challenging features of underwater acoustic (UWA) channel in comparison with its terrestrial radio frequency counterpart is highly frequency-dependent path loss. Thus, utilizing efficient carrier frequencies in UWA systems can considerably reduce the path loss. In this context, this paper presents an approximate formula for determining the best carrier frequency based on both the system and environmental parameters. To achieve this goal, this research first addresses a simple algorithm including general steps for tuning the parameters of Francois and Garrison (FG) formula in the frequency range of 10 to 100 kHz based on the appropriate experimental data which can be acquired from any interest region. Second, for a more accurate modeling of path loss, this paper considers the loss due to the reflections of sound from both the rough surface and bottom of the sea by employing the ray theory. Third, this study presents a general algorithm for modification of the power spectral density (PSD) of ambient noise based on Wenz formula in the frequency range of 10 to 100 kHz and the required experimental measurements which can be simply collected from any interest channel. Moreover, it is mathematically demonstrated that the ambient noise in the frequency range of 10 to 100 kHz, can be generally approximated with a strict sense stationary (SSS) colored normal stochastic process which is ergodic not only in mean and covariance but also in distribution. Finally, an approximate formula for the best carrier frequency is derived by maximizing the sound to noise intensity ratio (SNR). To verify the validity of simplifications and approximations utilized in this study and to assess the performance of our proposed algorithms and formulas, experimental results obtained in the Strait of Hormuz (SoH) are compared with the original, simplified, and modified models under different scenarios.     

Zur Bestimmung des D2O-Gehaltes in schwerem Wasser nach der Schwimmer-Methode

For the evaluation of float measurements all individual steps of the calculations are comprised under the expression of “precise float formula”. From this simplified approximations can be deduced. Their errors are estimated under little restraining conditions. The rather simple “difference formula” in the range of high D₂O-concentration together with a density scale for pure D₂O gained by interpolation suffice for most practical purposes. This is proved by numerical comparing with the precise formula.