The He–McKellar–Wilkens effect for spin-1 particles on non-commutative space

By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.

Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space

The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.

Minimal Length Quantum Mechanics of Dirac Particles in Noncommutative Space

We study the two-dimensional harmonic oscillator in commutative and noncommutative space within the framework of minimal length quantum mechanics for spin-l^2 particles. The energy spectra and the eigenfunction are obtained in both cases. Special cases are also deduced.

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.

Noncommutative Phase Space and the Two Dimensional Quantum Dipole in Background Electric and Magnetic Fields

The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.

Research on a toolpath generation method of NC milling based on space-filling curve

Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.

Two-Dimensional Linear Dependencies on the Coordinate Time-Dependent Interaction in Relativistic Non-Commutative Phase Space

In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.

螺旋锥齿轮空间曲面NC加工插补误差分析

基于空间曲面共轭原理 ,建立螺旋锥齿轮的齿面矢量方程 .由空间坐标系的变换 ,确定出刀具相对工件的位置和姿态 ,实现刀具与工件的相对运动 .在综合考虑齿面形状、刀具形状及机床结构等因素的基础上 ,分析了五坐标螺旋锥齿轮齿面NC过程插补误差 ,建立考虑齿面NC插补误差的螺旋锥齿轮数控加工方法 ,计算结果与加工实验结果基本一致 .

结合子孔径NCS算法和运动补偿的机载UWB SAR实时处理

低频机载UWB SAR实现高分辨成像需要大积累角和长孔径,实时成像面临大数据量和大运算量的挑战;此外,较长的孔径时间内载机运动比较复杂,增加了实时运动补偿的难度。本文讨论了机载UWB SAR实时成像的子孔径NCS算法,分析了其降低数据量和提高成像精度的改进措施;然后讨论了基于运动测量数据的实时运动补偿方案,利用实时PRI调整补偿前向运动误差,并在实时成像流程中嵌入视线运动误差补偿环节。在上述分析的基础上,提出了结合子孔径NCS算法和运动补偿的机载UWB SAR实时处理流程。最后,给出了实际飞行实验中机载UWB SAR的实时处理结果,证明本文所提流程可以满足机载UWB SAR处理实时性以及处理精度的要求。

一体化舱体狭小空间孔的数控加工

某型号一体化加工航天器产品安装孔位于舱体内部,且上部存在特征干涉,常规加工方式无法实现该部位的加工。针对此问题,通过分析直角铣头的结构特点,研究华中数控系统刀尖点补偿算法,实现机床控制器与直角铣头刀尖点的双向补偿;结合龙门五轴机床结构及坐标系变换特点,开展基于NX的后处理开发,完成基于直角铣头坐标系补偿的后处理文件开发,在原后处理不改变的情况下,以事件形式实现直角铣头补偿程序的自动输出,成功解决了超薄舱体内部狭小部位安装孔加工,提高了华中数控系统龙门五轴机床的适用性。

CNC系统加工复杂空间曲线的编程处理

采用等间隔直线逼近的方法,用Autolisp语言编程实现复杂空间曲线的自动绘制,并利用DXF文件将图形信息传输到MasterCAM软件中,生成CNC系统可以识别的NC代码。该方法为CNC系统中任意空间曲线的加工提供了一种有效方法。

三坐标NC加工几何验证算法的研究与实现

基于实体造型 ,综合现有NC几何验证方法的优点 ,研究与实现了一种新的Z&N验证算法。利用Z高度法效率高的优点 ,判断采样点是否超差 ;利用矢量分割法检测结果可靠性高的优点 ,求解沿着设计曲面的法矢方向以及采样点到刀具扫略体的距离 (切削误差 )。

Dirac equation with a magnetic field in 3D non-commutative phase space

For a spin-l/2 particle moving in a background magnetic field in noncommutative phase space, the Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the motion of the charged particle along the magnetic field has the effect of increasing the magnetic field. In the classical limit, matrix elements of the velocity operator related to the probability give a clear physical picture. Along an effective magnetic field, the mechanical momentum is conserved and the motion perpendicular to the effective magnetic field follows a round orbit. If using the velocity operator defined by the coordinate operators, the motion becomes complicated.

Non-commutative phase space and its space-time symmetry

First a description of 2＋1 dimensional non-commutative（NC） phase space is presented,and then we find that in this formulation the generalized Bopp＇s shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space.

Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space

We explore the non-commutative(NC)effects on the energy spectrum of a two-dimensional hydrogen atom.We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces.By considering the Rashba interaction,we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space.We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling.Finally,we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.

Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential

The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.

色彩性格分析下的社区养老室内空间营建策略

空间界面元素色彩的选择和搭配对于老年人的情绪、感受和行为具有一定的影响,而空间色彩品质与色彩性格的变化是密不可分的。为了进一步提高社区养老室内空间的舒适性和适宜性,通过对社区养老室内空间中外向型性格、内向型性格及中性性格色彩功效进行分析,并从老年人生理、心理和行为研究出发,探索色彩性格设计与老年人空间感受之间的关联性,剖析不同功能空间对色彩性格的真实需求。利用NCS自然色彩体系对空间背景色、点缀色、家具色及陈设品的色彩配置进行对比分析,总结出外向型、内向型及中性三种性格色彩在空间中的营建策略及配色参考范围,以期通过科学、合理、精细化的色彩性格设计来实现社区养老室内空间品质的全面提升。

翡翠数控雕刻加工效率与质量研究——以加工坐式弥勒佛为例

数控玉石雕刻技术能够降低玉石雕刻行业人力成本,提高生产效率,完成产业升级。本文选取坐式弥勒佛为例,运用JDPaint5.50设置不同参数,加工了13件质地近似的翡翠,测试了平头刀开轮廓、锥形球头刀粗刀工序和细刀工序中的加工效果、刀具损耗程度和耗时之间的关系。结果显示:速率一致时,使用平头刀开轮廓的耗时与加工深度正相关,耗时(s)为142.27×加工深度(mm)。加工翡翠粗刀工序采用0.6 mm锥形球头刀时,安全的最大路径间距为0.08 mm,速率为25%。粗刀和细刀工序的耗时与路径间距及速率均有关系,耗时减少的幅度随着路径间距和速率的增加都越来越少。翡翠数控雕刻的表面质量主要与细刀工序的锥形球头刀刀头直径和路径间距有关,与速率大小无关。若粗刀工序路径间距较大,应通过增加粗刀工序加工余量让细刀工序去除刀路痕迹。

Spin-1/2 relativistic particle in a magnetic field in NC phase space

This work provides an accurate study of the spin-l/2 relativistic particle in a magnetic field in NC phase space. By detailed calculation we find that the Dirac equation of the relativistic particle in a magnetic field in noncommutative space has similar behaviour to what happens in the Landau problem in commutative space even if an exact map does not exist. By solving the Dirac equation in NC phase space, we not only obtain the energy level of the spin-1/2 relativistic particle in a magnetic field in NC phase space but also explicitly offer some additional terms related to the momentum-momentum non-commutativity.

三轴数控侧铣空间刀具半径补偿算法

通过深入分析三轴数控侧铣加工的特点,利用几何平面投影原理,采用平面轮廓刀具半径补偿算法推导的类似方法,建立三轴数控侧铣加工的空间刀具半径补偿算法。将三轴数控侧铣加工的空间刀具半径补偿归纳为三种转接过渡类型处理,通过加工平面的投影相交求出空间两相邻程序段的过渡转接点坐标分量x、y,然后通过逆投影计算转接点的第三分量z,从而推导出各类型转接点的坐标计算公式。基于UG平台编写了三轴数控侧铣刀具补偿仿真软件,模拟和铣削加工实例结果表明所建立的三轴数控侧铣加工空间刀具半径补偿算法正确有效。基于该算法的空间刀具半径补偿G指令将可避免由于刀具磨损和刀具更换导致的三轴侧铣数控代码重生成。