Elastic Collisions in Minkowski Momentum Space with Lorentz Transformations

We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity

The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Meissner Exclusion of Gravito-Magnetic Energy from a Momentum-Space Crystal

A primordial field theory of Quantum Gravity resolves a number of century-old paradoxes associated with general relativity and quantum mechanics. It allows re-interpretation of major experiments such as Michelson-Gale (1925) and Q-bounce (1999). I address herein an unexplained anomalous experiment by Martin Tajmar (2006), in terms of a gravitomagnetic-based Meissner effect.

Light beams with orbital angular momentum for free space optics

The light＇s orbital angular momentum （OAM） is a consequence of the spiral flow of the electromagnetic energy. In this paper, an analysis of light beams with OAM used for free space optics （FSO） is conducted. The basic description and conception of light＇s OAM are reviewed. Both encoding information into OAM states of single light beam and encoding information into spatial structure of the mixed optical vortex with OAM are discussed, and feasibility to improve the FSO＇s performance of security and obstruction of line of sight is examined.

The generators of Lorentz transformation in momentum space

In the momentum space, the angular momentum operator and the boost vector operator,i.e. the generators for the Lorentz transformation of a particle with arbitrary spin and nonzero mass are discussed. Some new expressions are obtained in terms of the orbital and spin parts.

Momentum-space crystal in narrow-line cooling of ^(87)Sr

The discovery of the momentum space crystal based on the alkaline-earth atom ^(88)Sr in narrow-line cooling has paved the way to explore this novel physical phenomenon in other cold atom systems. In this paper, a momentum space crystal based on the fermions ^(87)Sr in narrow-line cooling of transition^1S_0–~3P_1 is demonstrated. We theoretically analyze and compare the formation principle of the narrow-line with that of broad-line cooling, and achieve the momentum space crystal in experiment. Beyond that we present a series of numerical calculations of those important parameters which influence the distribution and size of the momentum space crystal. Correspondingly, we vary the values of these parameters in experiment to observe the momentum space crystal evolution and distribution. The experimental results are in conformity with the results of the theoretically numerical calculations. These results and analyses provide a detailed supplementary study on the formation and evolution of momentum space crystal. In addition, this work could also give a guideline on atomic manipulation by narrow-line cooling.

Conservation laws for energy and momentum in curved spaces

In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Moeller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.

Quasi-momentum theorem in Riemann-Cartan space

The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the non- holonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the Riemann- Cartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system~ the differential equations of motion in its Riemann-Cartan configuration space may be sim- pler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained prob- lems, which are difficult to be solved by the traditional analytical mechanics method. Three examples are given to illustrate the effectiveness of the method.

Energy-Momentum Density of Non-Diagonal Bianchi Type Space-Time in General Relativity and Teleparallel Gravity

We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstein, Landau-Lifshitz, Bergmann-Thomson and Møller prescriptions, using double index complexes in GR. Secondly, in the frame work of TG, we used the energy momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. We also study the spacial cases of non-diagonal Bianchi type space-time BII, BVIII and BIX. We obtained the same energy-momentum density components for Einstein and Bergmann-Thomson prescriptions for the above four mentioned space-times that we considered in our work. Also, we found that the energy density component in Møller prescription is zero for all Bianchi types space-times in GR. Furthermore, we show that if the metric components are functions of time t alone, then the total gravitational energy is identically zero.

Collisions in Classical Mechanics in Terms of Mass-Momentum “Vectors” with Galilean Transformations

We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

A new method of calculating the orbital angular momentum spectra of Laguerre-Gaussian beams in channels with atmospheric turbulence

Studying orbital angular momentum（OAM） spectra is important for analyzing crosstalk in free-space optical（FSO）communication systems. This work offers a new method of simplifying the expressions for the OAM spectra of Laguerre-Gaussian（LG） beams under both weak/medium and strong atmospheric turbulences. We propose fixing the radius to the extreme point of the intensity distribution, review the expression for the OAM spectrum under weak/medium turbulence,derive the OAM spectrum expression for an LG beam under strong turbulence, and simplify both of them to concise forms.Then, we investigate the accuracy of the simplified expressions through simulations. We find that the simplified expressions permit accurate calculation of the OAM spectrum for large transmitted OAM numbers under any type of turbulence. Finally,we use the simplified expressions to analytically address the broadening of the OAM spectrum caused by atmospheric turbulence. This work should contribute to the concise theoretical derivation of analytical expressions for OAM channel matrices for FSO-OAM communications and the analytical study of the laws governing OAM spectra.

基于AMASPGD算法的FSOC系统波前畸变校正及性能分析

为了抑制相干自由空间光通信系统中大气湍流引起光信号波前失真的不利影响,提出了一种基于聚合动量(AM)和自适应矩边界(AdaMod)优化器的增强型随机并行梯度下降(SPGD)算法。仿真结果表明,该优化算法可以显著提高收敛速度和鲁棒性,并有效降低波前畸变的峰谷值和均方根,从而更有效地抑制大气湍流对相干自由空间光通信(FSOC)系统混频效率和误码率的负面影响。

Riemannian Space-Time, de Donder Conditions and Gravitational Field in Flat Space-Time

Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.

一维超冷原子动量光晶格中的手征对称性破缺拓扑相

对称性在理解物质的拓扑态方面具有关键作用.过去人们认为手征对称性保证了一维晶格的量子化Zak相位及其对应的非平庸拓扑相.本文展现了在一维手征对称性破缺的情况下,晶格系统仍具有量子化Zak相位和非平庸拓扑相.具体而言,在超冷原子动量晶格系统中有效地模拟了一个链长为26、手征对称性破缺的Zigzag模型,其中相等的次近邻耦合强度能够在保留空间反演对称性的同时破坏手征对称性.通过测量原子的时间平均波包位移来获得系统的拓扑不变量,并得到了其对应的量子化的Zak相位.此外,还观测到系统随着最近邻耦合强度比例的变化会从非平庸拓扑相转变为平庸拓扑相.本文不仅为对称性及拓扑相的相关研究提供了一个完全可控的平台,还可以通过控制格点间耦合强度和原子间相互作用,探索例如Tasaki,Aharonov-Bohm caging模型中的平带拓扑以及引入相互作用研究的非线性拓扑现象.

基于类对比簇分配异构迁移学习的空间滚动轴承寿命阶段识别

针对变工况条件下因样本数据分布差异大、可训练用样本较少以及不同寿命阶段样本数量不均等造成的空间滚动轴承寿命阶段识别准确率较低的问题,提出一种无监督迁移学习方法--类对比簇分配异构迁移学习(CAHTL)。在CAHTL中,通过异构迁移学习将历史工况下少量有类标签样本和当前工况的无类标签样本(即待测样本)迁移到公共特征空间内,使得不同工况样本之间的分布差异最小化;利用源域聚类簇点构建目标域样本特征的正负样本实现两域样本的数量再分配,再对两域正负样本进行对比学习以使待测样本分类性更好;通过计算待测样本与聚类簇点的相似度完成待测样本分类,且该分类过程无需参数学习,因此可避免样本不均等情况下对于不同寿命阶段样本识别准确率差距过大和在少有类标签训练样本情况下网络出现过拟合的问题;利用随机梯度下降和动量更新对CAHTL参数进行不同步更新,以保持样本特征的一致性并提高CAHTL的收敛速度。CAHTL可利用空间滚动轴承历史工况下的少量、非均等的已知寿命阶段的训练样本对当前工况的待测样本进行较高精度的寿命阶段识别。空间滚动轴承寿命阶段识别实例验证了该方法的有效性。

Dynamics and nonlinear control of space electromagnetic docking

Space electromagnetic docking technology, free of propellant and plume contamination, offers continuous, reversible and synchronous controllability, which is widely applied in the future routine on-orbit servicing missions. Due to the inherent nonlinearities, couplings and uncertainties of an electromagnetic force model, the dynamics and control problems of them are difficult. A new modeling approach for relative motion dynamics with intersatellite force is proposed. To resolve these control problems better, a novel nonlinear control method for soft space electro-magnetic docking is proposed, which combines merits of artificial potential function method, Lyapunov theory and extended state observer. In addition, the angular momentum management problem of space electromagnetic docking and approaches of handling it by exploiting the Earth＇s magnetic torque are investigated. Finally, nonlinear simulation results demonstrate the feasibility of the dynamic model and the novel nonlinear control method.

Look at Neutrino Oscillations in Space-Like Continuum

Based on the special theory of relativity in space-like continuum, the pre-sent author points that if there exist tachyons in nature, they should be neutral point-like particles with lepton appearance, which are very much like our early understanding about neutrinos before. The author also points that an alternative explanation for neutrino oscillations may be the conversion between mass-less neutrinos with different flavors expressed in different “lowest limited momentum” during their flight journey, which originates from that the argument in the squared sine function of the probability of neutrino oscillation may be less than zero, which is mathematical foresight and may not be ignored.

Power and Cross-Spectra for the Turbulent Atmospheric Motion and Transports in the Domain of Wave Number Frequency Space: Theoretical Aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.