Relativistic Center-of-Mass Vector and Electric Polarizability of a Charged PionMeson

Comparing the relativistic and nonrelativistic frame works, we study the effect of the relativistic center-of-mass vector on the electric polarizability of a compound system.

Correction of Relativistic Center-of-Mass Vector on Electric Polarizability of Pion Meson

We estimate the correction of relativistic center-of-mass vector on electric polarizability of an equal-mass quark-antiquark system numerically. Effect on the system confined by different interactive potentials is analysed. A great improvement for the electric polarizability of pion meson is obtained.

Measurements of the center-of-mass energies at BESⅢ via the di-muon process

From 2011 to 2014, the BESIII experiment collected about 5 fb^-1 data at center-of-mass energies around 4 GeV for the studies of the charmonium-like and higher excited charmonium states. By analyzing the di-muon process e＋e- →yma/Fsμ^＋μ^-, the center-of-mass energies of the data samples are measured with a precision of 0.8 MeV. The center-of-mass energy is found to be stable for most of the time during data taking.

A stability locomotion-control strategy for quadruped robots with center-of-mass dynamic planning

Locomotion stability is essential for controlling quadruped robots and adapting them to unstructured terrain.We propose a control strategy with center-of-mass(CoM)dynamic planning for the stable locomotion of these robots.The motion trajectories of the swing legs are synchronized with the CoM of the robot.To implement the synchronous control scheme,we adjusted the swing legs to form a support triangle.The strategy is applicable to both static walk gait and dynamic trot gait.In the motion control processes of the robot legs,the distribution of the ground reaction forces is optimized to minimize joint torque and locomotion energy consumption.We also used an improved joint-torque controller with varied controller coefficients in the stance and swing phases.The simulation and experimental results demonstrate that the robot can complete omnidirectional locomotion in both walk and trot gaits.At a given locomotion speed,the stability margins for the robot during walking and trotting were 27.25%and 37.25%higher,respectively,than in the scheme without CoM planning.The control strategy with energy consumption optimization(ECO)reduced the energy consumption of the robot in walk and trot gaits by 11.25%and 13.83%,respectively,from those of the control scheme without ECO.

Optimal Center-of-Mass Pivot Effect of Spinal Motion in Feline Galloping

In this paper,we studied the acceleration behavior of a quadruped animal during a galloping motion.Because the development of many quadruped robotic systems has been focused on dynamic movements,it is obvious that guidance from the dynamic behavior of quadruped animals is needed for robotics engineers.To fulfill this demand,this paper deals with analysis of the galloping motions of a domestic cat,which is well known for its excellent acceleration performance among four-legged animals.Based on the planar motion capture environment,the movement data of a galloping feline was acquired and the dynamic motions were estimated using a spring-mass system.In particular,the effects of the position and angle of the center-of-mass of the cat,angular displacement of the spine,and angular velocity of the spine were analyzed and are discussed below.Through this process,it was possible to understand the dynamic movement characteristics of the cat,and to understand the relationships between,and the influences of,these parameters.From this analysis,we provide significant data applicable to the design of joint movements in quadruped robot systems.

Measurements of the center-of-mass energies of e^(+)e^(-)collisions at BESIII

During the 2016-17 and 2018-19 running periods,the BESIII experiment collected 7.5 fb of e^(+)e^(-)collision data at center-of-mass energies ranging from 4.13 to 4.44 GeV.These data samples are primarily used for the study of excited charmonium and charmoniumlike states.By analyzing the di-muon process e^(+)e^(-)→(γISR=FSR)μ^(+)μ^(-),we measure the center-of-mass energies of the data samples with a precision of 0.6 MeV.Through a run-by-run study,we find that the center-of-mass energies were stable throughout most of the data-collection period.

Center-of-mass correction and rotational correction in covariant density functional theory

Center-of-mass（c.m.） correction and rotational correction in even-even Ge isotopes are systematically investigated within the triaxially deformed relativistic Hartree-Bogoliubov model using the PC-PK1 force. The shell effect and deformation effect on the microscopic c.m. correction and rotational correction are discussed, and the importance of both corrections on reproducing the binding energy is demonstrated.

Online monitoring of the center-of-mass energy from real data at BESⅢ

Background Data Quality Monitoring system(DQM)was developed to monitor data quality at BESⅢexperiment in real time.The stable center-of-mass energy(E_(cms))is essential for the data taking.Online monitoring the E_(cms)can help find the beam energy shift in time.Purpose The purpose is to monitor the E_(cms)in DQM system in real time.Methods The E_(cms)is measured using Bhabha scattering process in DQM system,due to its large cross section and low background level.The E_(cms)is calculated from the invariant mass of e^(+)e^(-),and the correction value from radiation effect and momentum calibration.Result The E_(cms)calculated with DQM system shows a good consistency with that from offline reconstruction within error.The results are validated with data taken in 2013.The overall systematic uncertainty includes 0.39 MeV/c^(2) from signal extraction and 2.54 MeV/c^(2) from calibration and radiation correction.Conclusions The E_(cms)calculated from Bhabha scattering process is now available on DQM system in real time,which can be used as references for researchers to operate BESⅢexperiment.

Measurement of integrated luminosity and center-of-mass energy of data taken by BESⅢ at s^(1/2)=2.125 GeV

To study the nature of the state Y（2175）,a dedicated data set of e ＋ e-collision data was collected at the center-of-mass energy of 2.125 GeV with the BESⅢ detector at the BEPCⅡ collider.By analyzing large-angle Bhabha scattering events,the integrated luminosity of this data set is determined to be 108.49±0.02±0.85 pb-1,where the first uncertainty is statistical and the second one is systematic.In addition,the center-of-mass energy of the data set is determined with radiative dimuon events to be 2126.55±0.03±0.85 MeV,where the first uncertainty is statistical and the second one is systematic.

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.

Emission spectrum of a harmonically trapped Λ-type three-level atom

We theoretically investigate the emission spectrum for a A-type three-level atom trapped in the node of a standing wave. We show that the atomic center-of-mass motion not only directly affects the peak number, peak position, and peak height in the atomic emission spectrum, but also influences the effects of the cavity field and the atomic initial state on atomic emission spectrum.

Vibratile Coherence and Squeezing in Two Trapped Ions

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummingsmodel. For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal stateis prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass modeare discussed, particularly, a 'weak' coherent state and a 'weak' squeezed vacuum state are obtained. Collapse andrevival are also observed in this type of initial condition.

Rotating Bardeen black hole surrounded by perfect fluid dark matter as a particle accelerator

We study the event horizon of a rotating Bardeen black hole surrounded by perfect fluid dark matter and the black hole as a particle accelerator.The black hole is represented by four parameters:mass M,rotation parameter a,dark matter parameterαand magnetic charge g.It is interesting that when we determine the values of magnetic charge g and dark matter parametersαwe can get a critical rotation parameter aEand then we get a contour plane withΔ=0 taking three parameters as coordinates.We also derive the effective potential of the particle and the center-of-mass(CM)energy of the two particles outside the black hole by using the motion equations of the particle in the equatorial plane of the black hole.We find that the CM energy depends not only on the rotation parameter a,but also on the parameters g andα.We discuss the CM energy for two particles colliding at the black hole horizon in the extreme and non-extreme cases,respectively.It is found that the CM energy can become arbitrarily high when the angular momentum of one of the two particles is the critical angular momentum under the background of extreme black holes and there is no such result for non-extreme black holes,because the particles do not reach the black hole horizon when the angular momentum of the particles is critical angular momentum.Therefore,we prove that the rotating Bardeen black hole surrounded by perfect fluid dark matter can be used as a particle accelerator.

Acceleration of particles in Einstein-Maxwell-dilaton black holes

It has recently been pointed out that, under certain conditions, the energy of particles accelerated by black holes in the center-of-mass frame can become arbitrarily high. In this paper, we study the collision of two particles in the case of four-dimensional charged nonrotating, extremal charged rotating and near-extremal charged rotating Kaluza-Klein black holes as well as the naked singularity case in Einstein-Maxwell-dilaton theory. We find that the center-of-mass energy for a pair of colliding particles is unlimited at the horizon of charged nonrotating Kaluza-Klein black holes, extremal charged rotating Kaluza-Klein black holes and in the naked singularity case.

Luminosities and energies of e^(+)e^(−) collision data taken between √s=4.61 GeV and 4.95 GeV at BESⅢ

From December 2019 to June 2021,the BESⅢ experiment collected approximately 5.85 fb^(−1) of data at center-of-mass energies between 4.61 and 4.95 GeV.This is the highest collision energy BEPCⅡ has reached to date.The accumulated e^(+)e^(−) annihilation data samples are useful for studying charmonium(-like)states and charmed-hadron decays.By adopting a novel method of analyzing the production of A_(c)^(+)A_(c)^(-) pairs in e^(+)e^(−) annihilation,the center-of-mass energies are measured with a precision of 0.6 MeV.Integrated luminosities are measured with a precision of better than 1% by analyzing the events of large-angle Bhabha scattering.These measurements provide important inputs to analyses based on these data samples.