Motion Law of a Sphere in Bingham Fluid with Thixotropy

The thixotropy properties and the motion law of a sphere in the Bingham fluid have been studied. Through observation of the settling motion of a single sphere in the Bingham fluid on the X-ray screen, it has been discovered that the mud in estuaries and along sea bay, and the hyperconcentrated flow all behave as the Bingham fl fluid with thixotropy properties as the large sediment concentration. Through derivation, the theoretical relationship between the yield stress and non-settling maximum sphere supported by the stress for the Bingham fluid has been developed, the equations for calculating the increasing yield stress and the non-settling maximum sphere diameter with the duration at rest of the slurry have been obtained. In consideration of the effect of thixotropy on fluid motion, the Navier-Stokes equation group for the Bingham thixotropy fluid has been developed. Through further study of the flow boundary condition of settling motion of ii single sphere in the Bingham thixotropy fluid, and the solving of the Navier-Stokes equation group, under the small Reynolds number, the theoretical equation of the drag force of the Bingham thixotropy fluid flowing around a sphere has been deduced. The theoretical relationship between drag coefficient and Reynolds number has been derived. By use of the experimental data of rheological test of various slurries measured with viscometer and those of single sphere motion observed on the X-ray screeen, the above equations have been verified. The equations are in good agreement with the experimental data for various slurries.

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

Generation methodology of isolines of earthquake ground motion

Due to limited financial resources and challenging geographical conditions, the number of seismic observation networks in China is still very small and they are not widely distributed. Therefore, the available earthquake records obtained after an earthquake have been limited. In this paper, auto-generation methods to obtain strong motion isolines under different conditions are proposed. To verify the accuracy of these methods, some examples, including application to the 2008 Wenchuan earthquake, are given.

The Arc-Sine Laws for the Skew Brownian Motion and Their Interpretation

We consider the skew Brownian motion as a solution of some stochastic differential equation. We prove for the skew Brownian motion the analogues of the arc-sine laws for Wiener process. Unlike of existing results, we are forced to consider a stochastic differential equation with discontinuous diffusion coefficient. Possible interpretations of obtained results are suggested.

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.

Motion machines of second kind

The second law of thermodynamics, i.e. the law stating that the entropy in isolated macroscopic system can never decrease, is tightly connected to the work of the device called perpetual motion machine of second kind. Often this law is also defined as the inability to construct such a device. In the current paper we give complete, independent and consistent definitions of static, stationary and changing physical field. Based on that for the first time we give summarising, correct and complete definitions of natural resource machine and perpetual motion machine of second kind as well as motion machine of second kind in the set of tardyons and luxons. We present a principal structure of a motion machine of second kind using which we show that the Clausius statement and its equivalent statements in the thermodynamics can be violated for a practically big interval-time even under equilibrium fluctuations.

Erratum to “The Faraday Isolator, Detailed Balance and the Second Law” [Journal of Applied Mathematics and Physics, Vol. 5, No. 4, April 2017 PP. 889-899]

A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguishable. This result is a consequence of the H-theorem which assumes homogeneity and indistinguishability of particles. However, when a thermal feedback path is added, in which heat carriers have physical properties different from the photons in the isolator, then a heterogeneous system is formed not covered by the H-theorem, and the second law is violated.

Some Limit Results for Transient Subsequence of Brownian Motion on Line

Let {W(t), 0≤t<∞} be a standard, one dimensional Brownian motion, and {t n, n≥1} be a sequence of positive constans with t n+1 ≥C 2t n (C>1). We obtain that liminf n→∞ inf k≥n|W(t k)|t n 1logn =1e a.s.and the set of the limit points of inf k≥n|W(t k)|t n 1logn is 1e, 1 almost surely.

Effect of the time-weakening friction law during the nucleation process

Based on dynamic rupture simulations on a planar fault in a homogeneous half-space, we investigated the nucleation processes using the time-weakening friction law. Both the characteristic time and the rupture speed in the nucleation asperity play an important role in determining rupture behaviors on a fault plane following the time-weakening friction law, with which rupture starts from a single point in the nucleation asperity and propagates at a given speed toward the boundary of the nucleation area. Rupture with a small characteristic time or a large rupture speed in the nucleation asperity propagates earlier from the hypocenter. Rupture following the slipweakening friction law requires a smaller radius of nucleation patch to have similar rupture front contours of the time-weakening friction law. Even if the rupture velocity in the nucleation patch of the time-weakening friction law increases to infinity, the peak slip rate in the nucleation asperity is smaller than that of the slip-weakening law. The peak ground velocity distributions of ruptures following the two friction laws are also compared.

Influence of Oscillation Frequency of a Sieve on the Screening Process for a Conical Sieve with Oscillatory Circular Motion

Removal of foreign bodies from seed mixtures, or their calibration for use as planting material, as well as fraction classification of granular materials requires screening surfaces with vibratory motion. This paper presents some aspects on the working process of a sieve, made of perforated sheet and having an outer conical surface with oscillatory circular motion （alternative） on the horizontal. Results are presented for some experimental researches on the movement of material on the sieve, for various kinematical parameters of the sieve （amplitude and oscillation frequency）. A conical sieve, suspended at the upper and lower in three points, was tested for screening of rapeseeds in order to estimate the influence of oscillation frequency on the screening process. Curves were drawn for separation intensity on the sieve generating line, and by regression analysis with normal distribution law were determined the equation coefficients and the correlation with experimental data. Movement of material on the sieve and its working process, in general, was appreciated by means of the peak position of distribution curve depending on the oscillation frequency of the sieve, considering that the normal distribution law correlates very well the data obtained by experiments.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

New Interpretation of Newton’s Law of Universal Gravitation

Elliptical motions of orbital bodies are treated here using Fourier series, Fortescue sequence components and Clarke’s instantaneous space vectors, quantities largely employed on electrical power systems analyses. Using this methodology, which evidences the analogy between orbital systems and autonomous second-order electrical systems, a new theory is presented in this article, in which it is demonstrated that Newton’s gravitational fields can also be treated as a composition of Hook’s elastic type fields, using the superposition principle. In fact, there is an identity between the equations of both laws. Furthermore, an energy analysis is conducted, and new concepts of power are introduced, which can help a better understanding of the physical mechanism of these quantities on both mechanical and electrical systems. The author believes that, as a practical consequence, elastic type gravitational fields can be artificially produced with modern engineering technologies, leading to possible satellites navigation techniques, with less dependency of external sources of energy and, even, new forms of energy sources for general purposes. This reinterpretation of orbital mechanics may also be complementary to conventional study, with implications for other theories such as relativistic, quantum, string theory and others.

The Natural Law of Transition of a Charged Particle into a Compound State under the Action of an Electroscalar Field

This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.

旋转对置活塞发动机运动学特性研究

高功率密度发动机是未来内燃机的发展趋势.旋转对置活塞发动机结构简单,做功频率是传统往复式活塞发动机的两倍,可以显著提高发动机的理论功率密度,是小型无人机、混合动力系统的理想动力源.文中通过建立数学模型,探究了旋转对置活塞发动机的结构参数对活塞运动规律、气缸容积变化规律和压缩比的影响,分析了相邻活塞运动碰撞的边界条件.研究结果表明,活塞线速度对椭圆齿轮节曲线偏心率的变化最为敏感,当线速度大于平均值时,线速度与偏心率成正比,线速度小于平均值时则成反比;偏心率的增大可以减小气缸的余隙容积,且使下止点对应的气缸容积增大,进而调节发动机的压缩比;活塞端面夹角增大可以减小气缸的余隙容积;偏心率和活塞端面夹角在±10%的范围内变化时,压缩比相应的变化范围分别为5.62~12.04和5.01~23.45,当偏心率过大时将导致相邻活塞发生碰撞.

基于345-修正梯形运动规律的4-RR(SS)_(2)并联机器人运动轨迹规划

研究了一种新型四自由度高速并联机器人运动轨迹规划方法。该机器人采用单动平台结构以减轻末端平台质量,提升机器人加减速性能。建立机器人机构运动学逆解模型,通过融合345多项式和梯形运动规律的优点,构造一种可兼顾运动时长和运动平稳性的345-修正梯形运动规律。在此基础上,通过插补叠加轨迹过渡传统门形轨迹的直角部分,并统筹考虑总运动时长最短以及角加速度峰值最小为目标完成插补叠加时机的优选,最后在样机上开展运动频次试验。试验结果显示,采用优化后的运动规律和轨迹样机运动频次可提升至218次/min,工作效率较传统Adept门形轨迹提高55.7%。

Discrete element simulation of the grain mixing law in brown rice germination device

The discrete element method(DEM)was used in this study to numerically simulate the mixing process and motion law of particles in brown rice germination device.And the reliability of simulation experiments was verified through physical experiments.In the discrete element simulation experiment,there were three mixing stages in the mixing process of the particles.The particle motion conditions at different rotational speeds were rolling,cascading,cataracting and centrifuging.The lower the filling degree,the higher the particle mixing efficiency.The radial trajectory of the particles was approximated as an elliptical helix that continuously shrank towards the axis.The research results indicated that under the same speed and filling conditions,the motion of brown rice particles in both the simulated and physical test environments is rolling and the drop height is the same.

高速柔性容差机构抑振研究及其最优驱动设计

智能建造中需要引入钢筋自动捆扎设备,以提高捆扎效率及质量,降低工人劳动强度,为人机协作提供新的应用场景。针对现阶段钢筋自动捆扎设备视觉定位精度不高的技术瓶颈问题,引入容差机构,利用容差机构欠驱动的特性弥补视觉定位误差。但欠驱动中的弹性构件在运动平台高速运行时会因惯性力导致系统振动,影响捆扎精度并限制工作效率。针对这一问题,运用最优化动态控制理论,确定了控制运动规律和关键的系统结构设计参数,旨在减少非稳定过渡时间、能量消耗和稳态误差。对研究结果进行了数字仿真与实验验证,结果显示:与传统驱动方法相比,经最优控制设计的驱动方式在非稳定过渡时间和稳态误差方面具有明显的综合优势。

Brown运动增量的小时间Chung重对数律

在本文中,我们研究了Brown运动增量的小时间参数泛函极限问题,得到了Brown运动增量的小时间Chung泛函重对数律.证明中的主要工具是Brown运动的大偏差和小偏差.

基于弧面分度凸轮机构的舰炮弹鼓运动规律研究

某舰炮弹鼓为实现间歇步进运动,采用了余弦加速度运动规律的弧面分度凸轮机构,由于在运动始末处加速度发生突变,运动停止时会产生振动和柔性冲击,导致弹鼓运动平稳性较差,不利于弹鼓与扬弹机交接弹药。基于弧面分度凸轮机构基本运动规律中速度和加速度相对较小、且连续无突变的改进正弦加速度运动规律,对跃度曲线进行优化,建立数学模型,利用Matlab求解相关系数,得到跃度连续的改进正弦加速度运动规律。通过改进前后凸轮机构运动曲线对比分析,说明改进运动规律的有效性,为提高弹鼓运动平稳性提出一种解决途径。

储气库压缩机宽工况气阀优选及运动规律仿真

以某储气库压缩机为研究对象,分析气阀结构及阀片材料性能,根据工况参数开展气阀的运动状态模拟,设计出阀片运动规律仿真可视化图形用户输入界面,实时显示计算结果及阀片运动模拟曲线,降低研究开发的成本,为储气库气阀可靠性设计提供参考。