一个向心力问题的解法讨论

质点沿某一不固定的圆轨道运动时,其相对于地面的运动轨迹不是圆周,因而不能简单地应用向心力公式求解,通过对其实际运动轨迹的分析可知,如果作为圆周运动来处理,应使用质点相对于轨道的相对速度进行求解．     

椭圆摆的一种实现方法

对光滑水平面上具有圆弧形光滑面的物块和在圆弧上运动的质点构成的椭圆摆系统,利用非惯性系中质点沿圆轨道运动的特点,求出了椭圆摆的周期.     

用量子力学研究行星质心的圆轨道运动

用含时薛定谔方程导出了作为质点的行星沿圆形轨道运动的波函数．它是一个波包．它很窄小，扩散得极慢，沿圆运动的角速度公式与经典力学的公式相同．     

临界阻尼和过阻尼振动札记

本文讨论了在不同初始条件下临界阻尼和过阻尼振动的位移—时间关系和相轨道,给出了质点在不同情况下趋于平衡所需要的时间与初始条件的关系,指出了一些教材中在这个问题论述上的局限与不足.     

用激光演示李萨如图形的新方法

当一质点同时参与两个不同方向的振动时,质点的位移是这两个振动位移的矢量和.在一般情况下质点将在平面上作曲线运动,质点的轨道可有各种形状.轨道的形状由两个振动的周期、振幅和相位来决定.为了简单便于制作,仅对一质点如何受两个相互垂直的振动作了研究,对其运动轨迹如何用激光光束描绘作了实验.     

质点沿最速降线和首尾固定的两相连线段下落问题的研究

目前关于最速降线即圆滚线的由来原理的文章有不少,但多数是直接套用光学折射定律进行类比推理,缺少对方法原委的详细介绍和对运动细节的探讨,或者仅是局部的数值计算而缺乏物理内涵.至于与圆滚线存在关联的质点沿首尾固定的两相连直线段降落的时间这样更为基础的问题,却少有人撰文研究.本文首先推导出质点速降问题中的"折射定律",然后利用它推导出最速降线即圆滚线的方程.证明了质点沿圆滚线的速降运动等价于匀速滚动圆周上对应点的绝对运动.给出最速降运动方程和计算圆滚线具体参量及质点降落时间的方法,并举例说明.指出当降落终点处在圆滚线左右半拱时,圆滚线参量的计算公式有所区别.简单地论证了圆滚线是唯一的捷线.最后,通过求极值的方法,计算出首尾固定的两相连直线段的最速降折点位置,以及在纵、横坐标给定时的最速降折点位置.通过列表和作图,分析出降落时间随折点的变化规律.     

约束在光滑曲线上质点的摆动

本文给出约束在光滑曲线上质点的摆动为严格等时简谐摆的轨线Ｋ数条件，由此条件可以检查质点沿不同曲线摆动的等时性并给出周期。     

对地球中光滑直线轨道问题的延伸讨论

讨论了自由质点在地球内光滑直线轨道与圆弧轨道中的振动周期,并将质点在地球内光滑圆弧轨道最低点附近的运动与小角度单摆运动进行类比,得到了后者作小角度摆动的上限周期.     

用Adomian分解法求解非线性轨道微分方程

用Ａｄｏｍｉａｎ分解法求解了质点在有心作用下的非线性轨道微分方程，进而得到了质点在任意初始条件下的高精度逼近轨道以及特殊初始条件下的精确轨道。     

有心力场中圆形轨道稳定性非线性近似分析

利用微扰法研究质点在有心力作用下圆形轨道的稳定性问题.对比分析了一阶与二阶两种近似条件下质点运动轨道的微扰相图,给出了两种近似条件下圆形轨道稳定性的条件.     

On the penetration of etchant into tracks in polycarbonate

The time dependence of the uptake of NaOH/LiOH etchant in pristine polycarbonate (PC) and in PC irradiated with 3 GeV Pb ions has been examined. Different stages of etchant penetration can be distinguished. The overall surface-near etchant uptake along tracks is always higher than the the one of the nonirradiated pristine material. Furthermore, the directional dependence of the etchant penetration during the incubation time is studied. Though the shapes of the etchant distributions along the tracks are practically the same in all directions, they differ in their absolute magnitudes. This can be explained by the different cross-sectional track areas exposed at the surface, which enable different etchant penetration efficiencies. Therefore, tracks which run more or less parallel to the surface normal show less etchant uptake than those being strongly tilted.     

Damage morphology of Kr ion tracks in apatite: dependence on dE/dX

With the aim of characterizing damage along nuclear tracks in apatite, Durango fluoroapatite monocrystals were irradiated under a high fluence ⁸⁶Kr ion beam at the G.A.N.I.L. (Grand Accélérateur National d'Ions Lourds, Caen, France). The resulting irradiation damage was studied by associating CRBS spectrometry and chemical etching. By applying Poisson's law to the backscattering results, the nuclear track average effective radius R_e was calculated for different steps along the ion path. On the other hand, the chemical etching experiments allowed us to deduce three different damaging morphologies in correspondence to the R_e values. For the first time in apatite, it has been shown that a defect fragmentation produced along the ion paths may be detected by chemical etching. These results were also applied to fission tracks in order to quantify the damage rate and to describe the damage morphology evolution along fission fragment paths.     

A novel method for observation by unaided eyes of nitrogen ion tracks and angular distribution in a plasma focus device using 50 Hz–HV electrochemically-etched polycarbonate detectors

A novel ion detection method has been developed and studied in this paper for the first time to detect and observe tracks of nitrogen ions and their angular distribution by unaided eyes in the Amirkabir 4 kJ plasma focus device (PFD). The method is based on electrochemical etching (ECE) of nitrogen ion tracks in 1 mm thick large area polycarbonate (PC) detectors. The ECE method employed a specially designed and constructed large area ECE chamber by applying a 50 Hz–high voltage (HV) generator under optimized ECE conditions. The nitrogen ion tracks and angular distribution were efficiently (constructed for this study) amplified to a point observable by the unaided eyes. The beam profile and angular distribution of nitrogen ion tracks in the central axes of the beam and two- and three-dimensional iso-ion track density distributions showing micro-beam spots were determined. The distribution of ion track density along the central axes versus angular position shows double humps around a dip at the 0° angular positions. The method introduced in this paper proved to be quite efficient for ion beam profile and characteristic studies in PFDs with potential for ion detection studies and other relevant dosimetry applications.     

Spectral features of the water temperature and sound intensity variations measured on the shelf of the Sea of Japan

Results of a spectral analysis of the water temperature and sound intensity variations measured on stationary acoustic-hydrophysical tracks in the shelf zone of the Sea of Japan are presented. The measurements were carried out in different seasons with the use of equipment that included a vertical acoustic-hydrophysical measuring system, self-contained acoustic-hydrophysical radio buoys, and a self-contained electromagnetictype resonance (320 Hz) transmitter. Spectral features of temperature fluctuations caused by internal waves in a vertical water layer are studied, and their influence on the sound propagation is demonstrated on tracks of different lengths oriented along and across the shelf.     

Corrosion effects of nuclear tracks in polymers

Usually ion tracks are studies ex-situ, i.e. after removal of the ion-irradiated sample from the evacuated irradiation vessel. The exposure to ambient air leads to degradation effects which are frequently neglected and consequently have been studied rarely. They have never been explained consistently. In this work we compile and discuss them in the frame of today's general understanding of ion tracks in polymers. It appears that some pristine polymers such as polyethylene are covered by a surface layer which is badly permeable for gaseous contaminants. Ion irradiation leads to destruction of this protective layer so that oxygen and moisture from the ambient air can easily penetrate through the ion tracks, and eventually even into the surrounding pristine material. Moisture absorption along the tracks gives rise to some faint conductivity. Oxygen uptake adds new trapping centers to the existing ones along the tracks, so that on one hand an increased dopant uptake capability is recorded, and on the other hand oxygen-sensitive mobile dopants are immobilized along the ion tracks. Photooxidation processes contribute to the fading of the optical blackening of irradiated polymers.     

Formation of ion damage tracks

The formation of damage tracks in insulators from the passage of energetic (MeV/amu) ions indicates that the energy lost by an ion to electronic excitation is partially transferred to atomic motion. It is known that a track consists of localized regions of extended defects that are separated by lengths that exhibit only point defects. The utility of tracks for selective detection of various types of ions arises because of preferential chemical etching along the track as compared to etching the bulk material. In this letter we propose a new model to explain both the localized damage regions and the preferential etching of damage tracks. The formation of each region of extended defects is initiated by the Auger decay of a vacancy produced in an inner electronic shell of an atom of the insulator by the incident ion. This decay produces an intense source of ionization within a small volume around the decaying atom, which causes decomposition of the material in a manner similar to that observed in pulsed laser irradiation. The resulting chemical or crystalline modification of the material is the latent track, which because of its changed structure can be preferentially etched.     

Optical manipulation of microparticles using whispering-gallery modes in a silicon nitride microdisk resonator

We demonstrate optical manipulation of 1?μm sized polystyrene microparticles on silicon nitride microdisk resonator devices using whispering-gallery modes in an integrated optofluidic chip. We demonstrate multiple trapping tracks and extended trapping ranges within single wavelengths through exciting high-order modes. We observe various sets of trapping tracks and ranges through exciting various resonance modes. We switch particle traveling tracks by tuning the laser wavelength to various wavelengths. We also observe microparticles assembling along the trapping tracks.     

Doping of nuclear tracks with fullerene solution

Latent nuclear tracks in polymers can occasionally be doped with fullerene solution. A new technique - ‘Fullerene Tracer Profiling’, FTP - allows us to verify the success of the doping procedure by determining the fullerene depth distribution along the tracks. The basic principle of FTP is described, and first examples are given. Fullerene solution is found to penetrate into ion tracks in polyimide, but not into tracks in polypropylene, or into unirradiated polyimide or polypropylene foils.     

基于机载激光雷达点云的雪道坡度提取算法

滑雪场的雪道坡度信息不仅是雪场规划和建设所需的必要内容,也是滑雪运动员提高成绩、减少运动损伤的重要数据。传统的手动测量方式费时费力,且雪场的低温环境不利于测量人员长时间作业。为了解决滑雪场的雪道坡度计算问题,提出了一种基于激光雷达点云的雪道坡度自动提取算法。使用投影高程差滤波、聚类分割等算法对雪场点云进行预处理,获取雪道边缘特征数据。提出了一种自适应阈值的拟合算法,用于雪道中线的提取,该算法可根据点云数量信息及坐标信息,自动选择阈值拟合雪道中线,消除了实际应用中部分点云数据稀疏或缺失对中线拟合带来的不利影响。数据处理结果表明,该方法计算所得坡度值与多次手动测量平均值之间的相对误差为2.2%。这一方法对激光雷达在雪场目标上的应用、雪场测绘中雪道坡度计算等具有参考意义。     

Radial dose distribution from carbon ion incident on liquid water

We report calculations of the radial dose deposited along carbon-ion tracks in liquid water using different techniques depending on the energy range of secondary electrons. The models are developed in relation with the experimental data on electron penetration lengths. For electrons with energies higher than 45 eV, we use the Katz model. However, the main focus is on the low-energy electrons, which are largely responsible for DNA damage within 10 nm from the tracks. For these electrons, the dose calculation is based on their random walk behaviour. The results of this combined approach are compared to experimental measurements. Contributions to the deposited energy by electrons of different ranges of energy are discussed.