What Projective Angle Makes the Arc-Length of the Trajectory in a Resistive Media Maximum? A Reverse Engineering Approach

We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically Mathematica [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.

Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load

An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.

IMPROVEMENTS ON THE ARC-LENGTH-TYPE METHOD

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.

Research on the arc length and droplet transition control strategy for the full digital pulse MIG welding power supply

Arc length stability and droplet transition consistency are key factors for the pulse metal inert gas （MIG） welding quality. A new control strategy is proposed based on pulse current waveform adjustment to stabilize the welding process. After sufficient analysis of the droplet transition process, key current waveform parameters are refined that can affect the welding quality greatly. In order to achieve the optimal nonlinear control of parameters, the fuzzy controller is designed successfully with two inputs and three outputs in field programmable gate array （ FPGA ）, which occupies fewer resources than PID controller and has higher control performance. Experimental results show that the arc length can be adjusted fast in full range of welding current, the welding process is stable, the droplet transition has good consistency, and the welding quality is perfect.

AN IMPROVED ARC-LENGTH METHOD AND APPLICATION IN THE POST-BUCKLING ANALYSIS FOR COMPOSITE STRUCTURES

Based on the conventional arc-length method, an improved arc-length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc-length. An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and shells structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.

Effect of La on arc erosion behaviors and oxidation resistance of Cu alloys

Cu with and without La addition was prepared and the effect of a trace amount of La on the arc erosion behaviors and oxidation resistance of Cu alloys was investigated. The results indicate that CuLa alloy exhibits superior oxidation resistance and arc erosion resistance. The contact resistance and temperature rise were obviously improved. The oxidation resistance of CuLa alloy mainly is due to the interface wrapping of La2O3 particles and CuLa alloy phase on Cu atoms. Thermodynamic calculation indicated that La2O3 could form preferentially in the CuLa alloy, which was beneficial for the protection of the Cu substrate. According to kinetics analysis, the activation energy of CuLa alloy was higher than that of pure Cu, indicating the better oxidation resistance of CuLa alloys.

Realizing precision pulse TIG welding with arc length control and visual image sensing based weld detection

Methods of arc length control and visual image based weld detection for precision pulse TIG welding were investigated. With a particular all hardware circuit, arc voltage during peak current stage is sampled and integrated to indicate arc length, deviation of arc length and adjusting parameters are calculated and output to drive a step motor directly. According to the features of welding image grabbed with CCD camera, a special algorithm was developed to detect the central line of weld fast and accurately. Then an application system were established, whose static arc length error is ±0.1 mm with 20 A average current and 1 mm given arc length, static detection precision of weld is 0.01 mm , processing time of each image is less than 120 ms . Precision pulse TIG welding of some given thin stainless steel components with complicated curved surface was successfully realized.

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.

C^2 CONTINUOUS NEARLY ARC-LENGTH PARAMETERIZED CURVE

An efficient method for C2 nearly arc-length parameterized curve is presented.An idea of approximation for the arc-length function of parametric curve which interpolates CAD data points is discussed.The parameterization is implemented by using parameter transformation.Finally,two numerical examples are given.

Volt-ampere characteristics of a nitrogen DC plasma arc with anode melting

The characteristics of a nitrogen arc using a graphite cathode and a melting anode in a pilot-scale plasma furnace are investigated. The voltage is examined as a function of current and apparent plasma length. The voltage increases non-linearly with the increase of apparent plasma length, with the current fixed. The experimental data so obtained are compared with the predictions of the Bowman model for the electric arc, and with numerical simulations as well. The level of agreement between the experimental data at the melting anode and the numerical predictions confirms the suitability of the proposed the Bowman model. These characteristics are relevant to the engineering design and evaluation of a DC plasma furnace and reactor for the treatment of hazardous fly ash waste.

Numerical Simulation for Shaping Feature of Molten Pool in Twin-Arc Submerged Arc Welding

The notion of ratio of width to length is proposed to describe the shaping feature of molten pool of twin-Arc submerged arc welding accurately, and analyze the law of molten pool variation and weld formation. The temperature field finite element numerical simulation model of twin arc movement is established. The loading form of twin-arc with double ellipsoid heat source is discussed. The molten pool temperature field of twin-arc submerged arc welding is calculated and analyzed under different process parameters. The law of molten pool characteristics influenced by the welding speed, current and voltage of twin-arc submerged arc welding parameters is analyzed. The relation between shaping feature of molten pool and weld formation is discussed according to the ratio of width to length. The results manifested that the width to length ratio of weld pool decreases with the improvement of welding speed, which result in gene- ration of weld defects. The width to length ratio of weld pool is increased by adjusting the proportion of the current, voltage and the distance of the two arcs, which avoids the generation of weld defects.

Study on Key Issues of the One-step Inverse Method

Even though the inverse method is less accurate than that of the incremental one,it has great potential in the conceptual design stage for its less calculation load and quick speed. However,it faces a number of unsolved problems,which limit its application. The first question is how to find a suitable initial solution while the other one is how to deal with the numerical problems caused by the vertical walls. In this paper,new methods have been proposed to solve above two questions. The methods have also been coded and applied to two parts to test its feasibility.

Optimal Rational Parameterization of Quadratic Curves Based on the Geographic Information of Both Ends

In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeedsat both endsareequal. Comparing withotherliteratures, the methodofthis paper has advantage in efficiency andiseasy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. Large numbers ofexperimental data show that our method hasbeen given withmore self-adaptability and accuracy than that ofotherliteratures, and if the parametricspeedat any end reaches its maximum or minimum value, the parameterization is optimal; otherwise itis close tooptimal rational parameterization.

基于Profibus的真空自耗电弧炉控制系统

通过对真空自耗电弧炉工艺及控制过程的分析,基于Profibus开发了一套真空自耗电弧炉控制系统;介绍了控制系统软硬件设计方案,提出了电弧炉控制中的关键点和难点,系统分析了真空自耗电弧炉控制原理和各个参数之间的关系以及对控制的影响,提出了一些有助于应对熔炼过程中各种特殊情况的局部策略,如熔速转电流控制、熔滴短路控制、解耦控制等;结合设计中出现的问题,对电弧炉控制中的关键问题—熔速率控制和弧长控制提出了进一步的解决方法。

Nongrashof机构连杆曲线的等弧长创成法

根据Nongrashof机构的原动件角位移及其微分系数的变化关系 ,利用原动件的角位移在端点附近 ,其微分系数的值急剧增大的特征 ,对连杆曲线上点的坐标进行变换 ,提出了输出输入角相互切换的基准和算法 ,以较少的计算量实现了连杆曲线上输出点的等间隔分布 。

软件Mathematica10.2在曲线绘制和弧长计算上的应用

Mathematica10.2新功能的图形离散化命令Discretize Region和弧长计算命令Arclength使曲线绘制和弧长计算上更加简洁,本文结合该软件其他命令,通过实例说明和分析该软件在曲线绘制和弧长计算上的应用。

均布载荷下Arc型与S型悬臂梁的临界长度

研究了悬臂梁、Arc型梁以及S型梁随着一无量纲参数的变化而逐渐演化的过程,求得了悬臂梁与基底接触形成Arc型梁以及S型梁的条件,并且通过最小势能原理,采用两种方法推导出了S型梁的临界悬空长度,通过叠加原理,求得了形成Arc型梁时基底的支持力.给出了随着无量纲参数的变化各种梁的挠曲线.这些分析对于工程设计,以及微机电系统、生物的毛细黏附等有一定的参考价值.

On Discordance Tests for the Wrapped Cau-chy Distribution

Circular data as any other types of data are subjected to contamination with some unexpected observations which are known outliers. In this paper, four tests of discordancy for circular data based on M, C, D, and A statistics are extended to the wrapped Cauchy distribution to detect possible outliers. The cut-off points and the power of performances are investigated via extensive simulation study. Results show that tests perform better as the concentration of the samples is increased. Two real circular data sets are analysed for illustration.

A simple method to extract glacier length based on Digital Elevation Model and glacier boundaries for simple basin type glacier

Glacier length is a key morphological element that has many glaciological applications; however, it is often difficult to determine, especially for glaciers that cover larger spatial areas or those that exhibit frequent temporal change. In this paper, we describe a new Arc GIS-based method that can derive glacier flow lines for determining glacier length based on digital elevation model and glacier outlines. This method involves(1) extraction of the highest and lowest points on a glacier,(2) calculation of 10-m contour lines on the glacier from 10 m to 100 m height, and(3) connection of the midpoints of each contour line with the highest and the lowest points in order to create a flow line, which is subsequently smoothed. In order to assess the reliability of this method, we tested the algorithm's results against flow lines calculated using field measurements, analysing data from the Chinese Glacier Inventory, and manual interpretation. These data showed that the new automated method is effective in deriving glacier flow lines when contour lines are relatively large; in particular, when they are between 70 m and 100 m. Nonetheless, a key limitation of the algorithm is the requirement to automatically delete repeated and closed curves in the pre-treatment processes. In addition to calculating glacier flow lines for derivation of glacier length, this method also can be used to effectively determine glacier terminus change.

An Analysis and Computation of Optimum Earth Geographical Coverage for Global Satellite Communications

This paper presents simple mathematical mobility models for configuration of Global interconnectivity with LEO satellite systems. The aim of this paper is to investigate on the performance measures of the satellite mobility models regarding optimum Global coverage arc length depending on the satellite locations relative to the four zones (quadrants) of the earth surface. A typical body of the satellite was positioned at a modified height of 780 Km from the earth surface and revolving round the earth in a circle of radius, 7160 Km was carefully studied and analytically parameterized enabling the generation of realistic instantaneous coverage arc lengths data. We compared the minimum required instantaneous arc lengths for the three mobility models that should cover the geographical coverage areas of the earth. The impact of the satellite movements relative to the earth locations was that the instantaneous coverage arc lengths were exponentially varying with time and continuously distributed within the four zones of the earth surface to provide continuous coverage around one polar orbit plane and assuming operations can continue down to an elevation angle of zero degree. The advantage of the derived mobility models is achieving almost 100% global coverage as a result of the dynamic behavior of the satellite playing an important role of providing instantaneous coverage arc lengths. This procedure also allows comparisons among different degrees of built-up zones of the earth surface as well as extra-polation to the different locations on the earth surface.