Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is diff...Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is different from other quantum nonlocalities.Here,we consider the strategy in which two atoms compose a two-qubit X state,and the two atoms are owned by Alice and Bob,respectively.The atom of Alice suffers from a reservoir,and the atom of Bob couples with a bit flip channel.The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation.The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits.The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime.In the weak coupling regime,the EPR steering monotonously decreases as t increases when coupling auxiliary qubits.The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob(or from Bob to Alice) can be more effectively revealed.Notably,the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.展开更多
Various strategies have been proposed to harness and protect space-like quantum correlations in different models under decoherence.However,little attention has been given to temporal-like correlations,such as quantum ...Various strategies have been proposed to harness and protect space-like quantum correlations in different models under decoherence.However,little attention has been given to temporal-like correlations,such as quantum temporal steering(TS),in this context.In this work,we investigate TS in a frequency-modulated two-level system coupled to a zero-temperature reservoir in both the weak and strong coupling regimes.We analyze the impact of various frequency-modulated parameters on the behavior of TS and non-Markovian.The results demonstrate that appropriate frequency-modulated parameters can enhance the TS of the two-level system,regardless of whether the system is experiencing Markovian or non-Markovian dynamics.Furthermore,a suitable ratio between modulation strength and frequency(i.e.,all zeroes of the 0th Bessel function J_(0)(δ/?))can significantly enhance TS in the strong coupling regime.These findings indicate that efficient and effective manipulation of quantum TS can be achieved through a frequency-modulated approach.展开更多
Duo to fluctuations in atmospheric turbulence and yaw control strategies,wind turbines are often in a yaw state.To predict the far wake velocity field of wind turbines quickly and accurately,a wake velocity model was ...Duo to fluctuations in atmospheric turbulence and yaw control strategies,wind turbines are often in a yaw state.To predict the far wake velocity field of wind turbines quickly and accurately,a wake velocity model was derived based on the method of momentum conservation considering the wake steering of the wind turbine under yaw conditions.To consider the shear effect of the vertical incoming wind direction,a two-dimensional Gaussian distribution function was introduced to model the velocity loss at different axial positions in the far wake region based on the assumption of nonlinear wake expansion.This work also developed a“prediction-correction”method to solve the wake velocity field,and the accuracy of the model results was verified in wake experiments on the Garrad Hassan wind turbine.Moreover,a 33-kW two-blade horizontal axis wind turbine was simulated using this method,and the results were compared with the classical wake model under the same parameters and the computational fluid dynamics(CFD)simulation results.The results show that the nonlinear wake model well reflected the influence of incoming flow shear and yaw wake steering in the wake velocity field.Finally,computation of the wake flow for the Horns Rev offshore wind farm with 80 wind turbines showed an error within 8%compared to the experimental values.The established wake model is less computationally intensive than other methods,has a faster calculation speed,and can be used for engineering calculations of the wake velocity in the far wakefield of wind turbines.展开更多
In wireless communication networks,mobile users in overlapping areas may experience severe interference,therefore,designing effective Interference Management(IM)methods is crucial to improving network performance.Howe...In wireless communication networks,mobile users in overlapping areas may experience severe interference,therefore,designing effective Interference Management(IM)methods is crucial to improving network performance.However,when managing multiple disturbances from the same source,it may not be feasible to use existing IM methods such as Interference Alignment(IA)and Interference Steering(IS)exclusively.It is because with IA,the aligned interference becomes indistinguishable at its desired Receiver(Rx)under the cost constraint of Degrees-of-Freedom(DoF),while with IS,more transmit power will be consumed in the direct and repeated application of IS to each interference.To remedy these deficiencies,Interference Alignment Steering(IAS)is proposed by incorporating IA and IS and exploiting their advantages in IM.With IAS,the interfering Transmitter(Tx)first aligns one interference incurred by the transmission of one data stream to a one-dimensional subspace orthogonal to the desired transmission at the interfered Rx,and then the remaining interferences are treated as a whole and steered to the same subspace as the aligned interference.Moreover,two improved versions of IAS,i.e.,IAS with Full Adjustment at the Interfering Tx(IAS-FAIT)and Interference Steering and Alignment(ISA),are presented.The former considers the influence of IA on the interfering user-pair's performance.The orthogonality between the desired signals at the interfered Rx can be maintained by adjusting the spatial characteristics of all interferences and the aligned interference components,thus ensuring the Spectral Efficiency(SE)of the interfering communication pairs.Under ISA,the power cost for IS at the interfered Tx is minimized,hence improving SE performance of the interfered communication-pairs.Since the proposed methods are realized at the interfering and interfered Txs cooperatively,the expenses of IM are shared by both communication-pairs.Our in-depth simulation results show that joint use of IA and IS can effectively manage multiple disturbances from the same source and improve the system's SE.展开更多
An improved RRT∗algorithm,referred to as the AGP-RRT∗algorithm,is proposed to address the problems of poor directionality,long generated paths,and slow convergence speed in multi-axis robotic arm path planning.First,a...An improved RRT∗algorithm,referred to as the AGP-RRT∗algorithm,is proposed to address the problems of poor directionality,long generated paths,and slow convergence speed in multi-axis robotic arm path planning.First,an adaptive biased probabilistic sampling strategy is adopted to dynamically adjust the target deviation threshold and optimize the selection of random sampling points and the direction of generating new nodes in order to reduce the search space and improve the search efficiency.Second,a gravitationally adjustable step size strategy is used to guide the search process and dynamically adjust the step-size to accelerate the search speed of the algorithm.Finally,the planning path is processed by pruning,removing redundant points and path smoothing fitting using cubic B-spline curves to improve the flexibility of the robotic arm.Through the six-axis robotic arm path planning simulation experiments on the MATLAB platform,the results show that the AGP-RRT∗algorithm reduces 87.34%in terms of the average running time and 40.39%in terms of the average path cost;Meanwhile,under two sets of complex environments A and B,the average running time of the AGP-RRT∗algorithm is shortened by 94.56%vs.95.37%,and the average path cost is reduced by 55.28%vs.47.82%,which proves the effectiveness of the AGP-RRT∗algorithm in improving the efficiency of multi-axis robotic arm path planning.展开更多
We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dyna...We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.展开更多
In order to improve the elbow passing performance and different diameter adaptability of pipeline robot,a supported crawler pipeline robot is designed,which adopts screw nut mechanism and hinge four-bar mechanism to a...In order to improve the elbow passing performance and different diameter adaptability of pipeline robot,a supported crawler pipeline robot is designed,which adopts screw nut mechanism and hinge four-bar mechanism to adapt to the complex environment such as variable diameter pipeline and elbow.The steering characteristics passing through the elbow are studied,the kinematic of pipeline robot bending steering is established,the geometric constraint(GC)and steering constraint(SC)in the elbow are analyzed,and the steering experiment is conducted.The results show that the robot can pass through the elbow by the SC model.The SC model can reduce the motor current and energy consumption when the robot passes through the elbow.展开更多
A quantum steering ellipsoid(QSE)is a visual characterization for bipartite qubit systems,and it is also a novel avenue for describing and detecting quantum correlations.Herein,by using a QSE,we visualize and witness ...A quantum steering ellipsoid(QSE)is a visual characterization for bipartite qubit systems,and it is also a novel avenue for describing and detecting quantum correlations.Herein,by using a QSE,we visualize and witness the first-order coherence(FOC),Bell nonlocality(BN)and purity under non-inertial frames.Also,the collective influences of the depolarizing channel and the non-coherence-generating channel(NCGC)on the FOC,BN and purity are investigated in the QSE formalism.The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system,the lengths of the QSE semiaxis visualize the BN,and the QSE's shape and position dominate the purity of the system.One can capture the FOC,BN and purity via the shape and position of the QSE in the non-inertial frame.The depolarizing channel(the NCGC)gives rise to the shrinking and degradation(the periodical oscillation)of the QSE.One can use these traits to visually characterize and detect the FOC,BN and purity under the influence of external noise.Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC.The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.展开更多
We propose a scheme for establishing the stationary one-way quantum steering in a three-level Λ-type atomic ensemble. In our system, the cavity modes are generated from two atomic dipole-allowed transitions, which ar...We propose a scheme for establishing the stationary one-way quantum steering in a three-level Λ-type atomic ensemble. In our system, the cavity modes are generated from two atomic dipole-allowed transitions, which are in turn driven by two external classical fields. The atomic ensemble can act as an engineered reservoir to put two cavity modes into a squeezed state by two Bogoliubov dissipation pathways. When the damping rates of the two cavity modes are different,the steady-state one-way quantum steering of the intracavity and output fields is presented by adjusting the normalized detuning. The physical mechanism is analyzed based on a dressed state representation and Bogoliubov mode transformation.The achieved optical one-way quantum steering scheme has potential applications in quantum secret information sharing protocols.展开更多
We aim to explore all possible scenarios of(1→2)(where one wing is untrusted and the others two wings are trusted)and(2→1)(where two wings are untrusted,and one wing is trusted)genuine tripartite Einstein-Podolsky-R...We aim to explore all possible scenarios of(1→2)(where one wing is untrusted and the others two wings are trusted)and(2→1)(where two wings are untrusted,and one wing is trusted)genuine tripartite Einstein-Podolsky-Rosen(EPR)steering.The generalized Greenberger-Horne-Zeilinger(GHZ)state is shared between three spatially separated parties,Alice,Bob and Charlie.In both(1→2)and(2→1),we discuss the untrusted party and trusted party performing a sequence of unsharp measurements,respectively.For each scenario,we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality.The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters.Moreover,both the sharpness parameters range and the state parameters range in the scenario of(1→2)steering are larger than those in the scenario of(2→1)steering.展开更多
Orbital Angular Momentum(OAM)is an intrinsic feature of electromagnetic waves which has recently found many applications in several areas in radio and optics.In this paper,we use OAM wave characteristics to present a ...Orbital Angular Momentum(OAM)is an intrinsic feature of electromagnetic waves which has recently found many applications in several areas in radio and optics.In this paper,we use OAM wave characteristics to present a simple method for beam steering over both elevation and azimuth planes.The design overcomes some limitations of traditional steering methods,such as limited dynamic range of steering,the design complexity,bulky size of the steering structure,the limited bandwidth of operation,and low gain.Based on OAM wave characteristics,the proposed steering method avoids design complexities by adopting a simple method for generating the OAM-carrying waves.The waves are generated by an array of Planar Circular Dipole(PCD)elements.These elements are designed to cover a wide bandwidth range between 3 and 30 GHz.The transmitting array shows an enhanced gain value from 8.5 dBi to almost 11.5 dBi at the broadside angle.Besides the enhanced PCD-based OAM generation,the novelty of the design lies in a new method of beam steering.Beam steering is then performed by controlling the electrical feeding of the PCD elements;the beam azimuthal location is managed by turning off some of the PCD elements,while the elevation is determined by changing the gradient phase of excitation for the turned-on PCD elements.Detailed analysis of the steering method is carried out by finding the mathematical model of the system and the generated waves.The performance has been verified through numerical simulators.展开更多
To resolve the response delay and overshoot problems of intelligent vehicles facing emergency lane-changing due to proportional-integral-differential(PID)parameter variation,an active steering control method based on ...To resolve the response delay and overshoot problems of intelligent vehicles facing emergency lane-changing due to proportional-integral-differential(PID)parameter variation,an active steering control method based on Convolutional Neural Network and PID(CNNPID)algorithm is constructed.First,a steering control model based on normal distribution probability function,steady constant radius steering,and instantaneous lane-change-based active for straight and curved roads is established.Second,based on the active steering control model,a three-dimensional constraint-based fifth-order polynomial equation lane-change path is designed to address the stability problem with supersaturation and sideslip due to emergency lane changing.In addition,a hierarchical CNNPID Controller is constructed which includes two layers to avoid collisions facing emergency lane changing,namely,the lane change path tracking PID control layer and the CNN control performance optimization layer.The scaled conjugate gradient backpropagation-based forward propagation control law is designed to optimize the PID control performance based on input parameters,and the elastic backpropagation-based module is adopted for weight correction.Finally,comparison studies and simulation/real vehicle test results are presented to demonstrate the effectiveness,significance,and advantages of the proposed controller.展开更多
Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls ...Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.展开更多
A 1-bit electronically controlled metasurface reflectarray is presented to achieve beam steering with multiple polarization manipulations. A metsurface unit cell loaded by two PIN diodes is designed. By switching the ...A 1-bit electronically controlled metasurface reflectarray is presented to achieve beam steering with multiple polarization manipulations. A metsurface unit cell loaded by two PIN diodes is designed. By switching the two PIN diodes between ON and OFF states, the isotropic and anisotropic reflections can be flexibly achieved. For either the isotropic reflection or the anisotropic reflection, the two operation states achieve the reflection coefficients with approximately equal magnitude and 180°out of phase, thus giving rise to the isotropic/anisotropic 1-bit metasurface unit cells. With the 1-bit unit cells, a 12-by-12 metasurface reflectarray is optimally designed and fabricated. Under either y-or x-polarized incident wave illumination, the reflectarray can achieve the co-polarized and cross-polarized beam scanning, respectively, with the peak gains of 20.08 d Bi and 17.26 d Bi within the scan range of about ±50°. With the right-handed circular polarization(RHCP) excitation, the left-handed circular polarization(LHCP) radiation with the peak gain of 16.98 d Bic can be achieved within the scan range of ±50°. Good agreement between the experimental results and the simulation results are observed for 2D beam steering and polarization manipulation capabilities.展开更多
Integrated photonic devices are essential for on-chip optical communication,optical-electronic systems,and quantum information sciences.To develop a high-fidelity interface between photonics in various frequency domai...Integrated photonic devices are essential for on-chip optical communication,optical-electronic systems,and quantum information sciences.To develop a high-fidelity interface between photonics in various frequency domains without disturbing their quantum properties,nonlinear frequency conversion,typically steered with the quadratic(χ2)process,should be considered.Furthermore,another degree of freedom in steering the spatial modes during theχ2 process,with unprecedent mode intensity is proposed here by modulating the lithium niobate(LN)waveguide-based inter-mode quasi-phasematching conditions with both temperature and wavelength parameters.Under high incident light intensities(25 and 27.8 dBm for the pump and the signal lights,respectively),mode conversion at the sum-frequency wavelength with sufficient high output power(−7–8 dBm)among the TM01,TM10,and TM00 modes is realized automatically with characterized broad temperature(ΔT≥8°C)and wavelength windows(Δλ≥1 nm),avoiding the previous efforts in carefully preparing the signal or pump modes.The results prove that high-intensity spatial modes can be prepared at arbitrary transparent wavelength of theχ2 media toward on-chip integration,which facilitates the development of chip-based communication and quantum information systems because spatial correlations can be applied to generate hyperentangled states and provide additional robustness in quantum error correction with the extended Hilbert space.展开更多
The dynanaic model of a novel electric power steering(EPS) system integrated with active front steer- ing function and the three-freedom steering model are built. Based on these models, the concepts and the quanti- ...The dynanaic model of a novel electric power steering(EPS) system integrated with active front steer- ing function and the three-freedom steering model are built. Based on these models, the concepts and the quanti- tative expressions of road feel, sensitivity, and operation stability of the steering are introduced. Then, according to constrained optimization features of multi-variable function, a genetic algorithm is designed. Making the road feel of the steering as optimization objective, and operation stability and sensitivity of the steering as constraints, the system parameters are optimized by the genetic and the coordinate rotation algorithms. Simulation results show that the optimization of the novel EPS system by the genetic algorithm can effectively improve the road feel, thus providing a theoretical basis for the design and optimization of the novel EPS system.展开更多
The existing research of steering efficiency mainly focuses on the mechanism efficiency of steering system, aiming at designing and optimizing the mechanism of steering system. In the development of assist steering sy...The existing research of steering efficiency mainly focuses on the mechanism efficiency of steering system, aiming at designing and optimizing the mechanism of steering system. In the development of assist steering system especially the evaluation of its comfort, the steering efficiency of driver physiological output usually are not considered, because this physiological output is difficult to measure or to estimate, and the objective evaluation of steering comfort therefore cannot be conducted with movement efficiency perspective. In order to take a further step to the objective evaluation of steering comfort, an estimating method for the steering efficiency of the driver was developed based on the research of the relationship between the steering force and muscle activity. First, the steering forces in the steering wheel plane and the electromyography (EMG) signals of the primary muscles were measured. These primary muscles are the muscles in shoulder and upper ann which mainly produced the steering torque, and their functions in steering maneuver were identified previously. Next, based on the multiple regressions of the steering force and EMG signals, both the effective steering force and the total force capacity of driver in steering maneuver were calculated. Finally, the steering efficiency of driver was estimated by means of the estimated effective force and the total force capacity, which represented the information of driver physiological output of the primary muscles. This research develops a novel estimating method for driver steering efficiency of driver physiological output, including the estimation of both steering force and the force capacity of primary muscles with EMG signals, and will benefit to evaluate the steering comfort with an objective perspective.展开更多
The evaluation method on steering is based on qualitative manner in existence, which causes the result inaccurate and fuzziness. It reduces the efficiency of process execution. So the method by quantitative manner for...The evaluation method on steering is based on qualitative manner in existence, which causes the result inaccurate and fuzziness. It reduces the efficiency of process execution. So the method by quantitative manner for the shape-shifting robot in different configurations is proposed. Comparing to traditional evaluation method, the most important aspects which can influence the steering abilities of the robot in different configurations are researched in detail, including the energy, angular velocity, time and space. In order to improve the robustness of system, the ideal and slippage conditions are all considered by mathematical model. Comparing to the traditional weighting confirming method, the extent of robot steering method is proposed by the combination of subjective and objective weighting method. The subjective weighting method can show more preferences of the experts and is based on five-grade scale. The objective weighting method is based on information entropy to determine the factors. By the sensors fixed on the robot, the contract force between track grouser and ground, the intrinsic motion characteristics of robot are obtained and the experiment is done to prove the algorithm which is proposed as the robot in different common configurations. Through the method proposed in the article, fuzziness and inaccurate of the evaluation method has been solved, so the operators can choose the most suitable configuration of the robot to fulfil the different tasks more quickly and simply.展开更多
The existing research of steering comfort mainly focuses on the subjective evaluation,aiming at designing and optimizing the steering system.In the development of steering system,especially the evaluation of steering ...The existing research of steering comfort mainly focuses on the subjective evaluation,aiming at designing and optimizing the steering system.In the development of steering system,especially the evaluation of steering comfort,the objective evaluation methods considered the kinematic characteristics of driver steering maneuver are not proposed,which means that the objective evaluation of steering cannot be conducted with the evaluation of kinematic characteristics of driver in steering maneuver.In order to propose the objective evaluation methods of steering comfort,the evaluation of steering movement quality of driver is developed on the basis of the study of the kinematic characteristics of steering maneuver.First,the steering motion trajectories of the driver in both comfortable and certain extreme uncomfortable operation conditions are detected using the Vicon motion capture system.The operation conditions are under the restrictions of the vertical height and horizontal distance between steering wheel center and the H-point of driver,and the steering resisting torque else.Next,the movement quality evaluation of driver steering maneuver is assessed using twelve kinds of evaluation indices based on the kinematic analyses of the steering motion trajectories to propose an objective evaluation method.Finally,an integrated discomfort index of steering maneuver is proposed on the basis of the regression analysis of subjective evaluation rating and the movement quality evaluation indices,including the Jerk,Discomfort and Joint Torque indices.The test results show that the proposed integrated discomfort index gives a good fitting with the subjective evaluation of discomfort,which means it can be used to evaluate or predict the discomfort level of steering maneuver.This paper proposes an objective evaluation method of steering comfort based on the movement quality evaluation of driver steering maneuver.展开更多
Needle insertion is a common surgical procedure used in diagnosis and treatment.The needle steering technologies make continuous developments in theoretical and practical aspects along with the in-depth research on ne...Needle insertion is a common surgical procedure used in diagnosis and treatment.The needle steering technologies make continuous developments in theoretical and practical aspects along with the in-depth research on needle insertion.It is necessary to summarize and analyze the existing results to promote the future development of theories and applications of needle insertion.Thus,a survey of the state of the art of research is presented on algorithms of needle steering techniques,the surgical robots and devices.Based on the analysis of the needle insertion procedure,the concept of needle steering is defined as a kinematics problem,which is to place the needle at the target and avoid the obstacles.The needle steering techniques,including the artificial potential field method and the nonholonomic model,are introduced to control the needles for improving the accuracy.Based on the quasi-static thinking,the virtual spring model and the cantilever-beam model are developed to calculate the amount of needle deflection and generate the needle path.The phantoms instead of the real tissue are used to verify the models mentioned in most of the experimentations.For the desired needle trajectories,the image-guided robotic devices and some novel needles are presented to achieve the needle steering.Finally,the challenges are provided involving the controllability of the long flexible needle and the properties of soft tissue.The results and investigations can be used for further study on the precision and accuracy of needle insertion.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12175001)the Key Project of Natural Science Research of West Anhui University(Grant No.WXZR202311)+7 种基金the Natural Science Research Key Project of Education Department of Anhui Province of China(Grant Nos.KJ2021A0943,2022AH051681,and 2023AH052648)the Open Fund of Anhui Undergrowth Crop Intelligent Equipment Engineering Research Center(Grant No.AUCIEERC-2022-01)Anhui Undergrowth Crop Intelligent Equipment Engineering Research Center(Grant No.2022AH010091)the University Synergy Innovation Program of Anhui Province(Grant No.GXXT-2021-026)the Anhui Provincial Natural Science Foundation(Grant Nos.2108085MA18 and 2008085MA20)Key Project of Program for Excellent Young Talents of Anhui Universities(Grant No.gxyq ZD2019042)the open project of the Key Laboratory of Functional Materials and Devices for Informatics of Anhui Higher Education Institutes(Grant No.FMDI202106)the research start-up funding project of High Level Talent of West Anhui University(Grant No.WGKQ2021048)。
文摘Einstein–Podolsky–Rosen(EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world.The directivity(or asymmetry) is a fascinating trait of EPR steering,and it is different from other quantum nonlocalities.Here,we consider the strategy in which two atoms compose a two-qubit X state,and the two atoms are owned by Alice and Bob,respectively.The atom of Alice suffers from a reservoir,and the atom of Bob couples with a bit flip channel.The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation.The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits.The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime.In the weak coupling regime,the EPR steering monotonously decreases as t increases when coupling auxiliary qubits.The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob(or from Bob to Alice) can be more effectively revealed.Notably,the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.
基金Project supported by the National Natural Science Foundation of China(Grant No.62375140)。
文摘Various strategies have been proposed to harness and protect space-like quantum correlations in different models under decoherence.However,little attention has been given to temporal-like correlations,such as quantum temporal steering(TS),in this context.In this work,we investigate TS in a frequency-modulated two-level system coupled to a zero-temperature reservoir in both the weak and strong coupling regimes.We analyze the impact of various frequency-modulated parameters on the behavior of TS and non-Markovian.The results demonstrate that appropriate frequency-modulated parameters can enhance the TS of the two-level system,regardless of whether the system is experiencing Markovian or non-Markovian dynamics.Furthermore,a suitable ratio between modulation strength and frequency(i.e.,all zeroes of the 0th Bessel function J_(0)(δ/?))can significantly enhance TS in the strong coupling regime.These findings indicate that efficient and effective manipulation of quantum TS can be achieved through a frequency-modulated approach.
基金Supported by the Key R&D Program of Shandong Province,China(No.2023ZLYS01)the National Key R&D Program of China(No.2022YFC3104200)+2 种基金the National Natural Science Foundation of China(No.12302301)the China Postdoctoral Science Foundation(No.2023M742229)the Zhejiang Provincial Natural Science Foundation(ZJNSF)(No.LQ22F030002)。
文摘Duo to fluctuations in atmospheric turbulence and yaw control strategies,wind turbines are often in a yaw state.To predict the far wake velocity field of wind turbines quickly and accurately,a wake velocity model was derived based on the method of momentum conservation considering the wake steering of the wind turbine under yaw conditions.To consider the shear effect of the vertical incoming wind direction,a two-dimensional Gaussian distribution function was introduced to model the velocity loss at different axial positions in the far wake region based on the assumption of nonlinear wake expansion.This work also developed a“prediction-correction”method to solve the wake velocity field,and the accuracy of the model results was verified in wake experiments on the Garrad Hassan wind turbine.Moreover,a 33-kW two-blade horizontal axis wind turbine was simulated using this method,and the results were compared with the classical wake model under the same parameters and the computational fluid dynamics(CFD)simulation results.The results show that the nonlinear wake model well reflected the influence of incoming flow shear and yaw wake steering in the wake velocity field.Finally,computation of the wake flow for the Horns Rev offshore wind farm with 80 wind turbines showed an error within 8%compared to the experimental values.The established wake model is less computationally intensive than other methods,has a faster calculation speed,and can be used for engineering calculations of the wake velocity in the far wakefield of wind turbines.
基金supported in part by NSF of Shaanxi Province under Grant 2021JM-143the Fundamental Research Funds for the Central Universities under Grant JB211502+5 种基金the Project of Key Laboratory of Science&Technology on Communication Network under Grant 6142104200412the National Natural Science Foundation of China under Grant 62072351the Academy of Finland under Grant 308087,Grant 335262 and Grant 345072the Shaanxi Innovation Team Project under Grant 2018TD-007the 111 Project under Grant B16037,JSPS KAKENHI Grant Number JP20K14742the Project of Cyber Security Establishment with Inter University Cooperation.
文摘In wireless communication networks,mobile users in overlapping areas may experience severe interference,therefore,designing effective Interference Management(IM)methods is crucial to improving network performance.However,when managing multiple disturbances from the same source,it may not be feasible to use existing IM methods such as Interference Alignment(IA)and Interference Steering(IS)exclusively.It is because with IA,the aligned interference becomes indistinguishable at its desired Receiver(Rx)under the cost constraint of Degrees-of-Freedom(DoF),while with IS,more transmit power will be consumed in the direct and repeated application of IS to each interference.To remedy these deficiencies,Interference Alignment Steering(IAS)is proposed by incorporating IA and IS and exploiting their advantages in IM.With IAS,the interfering Transmitter(Tx)first aligns one interference incurred by the transmission of one data stream to a one-dimensional subspace orthogonal to the desired transmission at the interfered Rx,and then the remaining interferences are treated as a whole and steered to the same subspace as the aligned interference.Moreover,two improved versions of IAS,i.e.,IAS with Full Adjustment at the Interfering Tx(IAS-FAIT)and Interference Steering and Alignment(ISA),are presented.The former considers the influence of IA on the interfering user-pair's performance.The orthogonality between the desired signals at the interfered Rx can be maintained by adjusting the spatial characteristics of all interferences and the aligned interference components,thus ensuring the Spectral Efficiency(SE)of the interfering communication pairs.Under ISA,the power cost for IS at the interfered Tx is minimized,hence improving SE performance of the interfered communication-pairs.Since the proposed methods are realized at the interfering and interfered Txs cooperatively,the expenses of IM are shared by both communication-pairs.Our in-depth simulation results show that joint use of IA and IS can effectively manage multiple disturbances from the same source and improve the system's SE.
基金supported by Foundation of key Laboratory of AI and Information Processing of Education Department of Guangxi(No.2022GXZDSY002)(Hechi University),Foundation of Guangxi Key Laboratory of Automobile Components and Vehicle Technology(Nos.2022GKLACVTKF04,2023GKLACVTZZ06)。
文摘An improved RRT∗algorithm,referred to as the AGP-RRT∗algorithm,is proposed to address the problems of poor directionality,long generated paths,and slow convergence speed in multi-axis robotic arm path planning.First,an adaptive biased probabilistic sampling strategy is adopted to dynamically adjust the target deviation threshold and optimize the selection of random sampling points and the direction of generating new nodes in order to reduce the search space and improve the search efficiency.Second,a gravitationally adjustable step size strategy is used to guide the search process and dynamically adjust the step-size to accelerate the search speed of the algorithm.Finally,the planning path is processed by pruning,removing redundant points and path smoothing fitting using cubic B-spline curves to improve the flexibility of the robotic arm.Through the six-axis robotic arm path planning simulation experiments on the MATLAB platform,the results show that the AGP-RRT∗algorithm reduces 87.34%in terms of the average running time and 40.39%in terms of the average path cost;Meanwhile,under two sets of complex environments A and B,the average running time of the AGP-RRT∗algorithm is shortened by 94.56%vs.95.37%,and the average path cost is reduced by 55.28%vs.47.82%,which proves the effectiveness of the AGP-RRT∗algorithm in improving the efficiency of multi-axis robotic arm path planning.
文摘We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.
基金Supported by the National Natural Science Foundation of China(No.51775323).
文摘In order to improve the elbow passing performance and different diameter adaptability of pipeline robot,a supported crawler pipeline robot is designed,which adopts screw nut mechanism and hinge four-bar mechanism to adapt to the complex environment such as variable diameter pipeline and elbow.The steering characteristics passing through the elbow are studied,the kinematic of pipeline robot bending steering is established,the geometric constraint(GC)and steering constraint(SC)in the elbow are analyzed,and the steering experiment is conducted.The results show that the robot can pass through the elbow by the SC model.The SC model can reduce the motor current and energy consumption when the robot passes through the elbow.
基金Project supported by the National Natural Science Foundation of China(Grant No.12175001)the Natural Science Research Key Project of the Education Department of Anhui Province of China(Grant No.KJ2021A0943)+3 种基金the Research Start-up Funding Project of High Level Talent of West Anhui University(Grant No.WGKQ2021048)an Open Project of the Key Laboratory of Functional Materials and Devices for Informatics of Anhui Higher Education Institutes(Grant No.FMDI202106)the University Synergy Innovation Program of Anhui Province(Grant No.GXXT-2021-026)the Anhui Provincial Natural Science Foundation(Grant Nos.2108085MA18 and 2008085MA20)。
文摘A quantum steering ellipsoid(QSE)is a visual characterization for bipartite qubit systems,and it is also a novel avenue for describing and detecting quantum correlations.Herein,by using a QSE,we visualize and witness the first-order coherence(FOC),Bell nonlocality(BN)and purity under non-inertial frames.Also,the collective influences of the depolarizing channel and the non-coherence-generating channel(NCGC)on the FOC,BN and purity are investigated in the QSE formalism.The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system,the lengths of the QSE semiaxis visualize the BN,and the QSE's shape and position dominate the purity of the system.One can capture the FOC,BN and purity via the shape and position of the QSE in the non-inertial frame.The depolarizing channel(the NCGC)gives rise to the shrinking and degradation(the periodical oscillation)of the QSE.One can use these traits to visually characterize and detect the FOC,BN and purity under the influence of external noise.Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC.The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.
基金Project supported by Wuhan Donghu University Youth Foundation of Natural science (Grant No. 2022dhzk009)。
文摘We propose a scheme for establishing the stationary one-way quantum steering in a three-level Λ-type atomic ensemble. In our system, the cavity modes are generated from two atomic dipole-allowed transitions, which are in turn driven by two external classical fields. The atomic ensemble can act as an engineered reservoir to put two cavity modes into a squeezed state by two Bogoliubov dissipation pathways. When the damping rates of the two cavity modes are different,the steady-state one-way quantum steering of the intracavity and output fields is presented by adjusting the normalized detuning. The physical mechanism is analyzed based on a dressed state representation and Bogoliubov mode transformation.The achieved optical one-way quantum steering scheme has potential applications in quantum secret information sharing protocols.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62171056 and 61973021)Henan Key Laboratory of Network Cryptography Technology(Grant No.LNCT2022-A03)。
文摘We aim to explore all possible scenarios of(1→2)(where one wing is untrusted and the others two wings are trusted)and(2→1)(where two wings are untrusted,and one wing is trusted)genuine tripartite Einstein-Podolsky-Rosen(EPR)steering.The generalized Greenberger-Horne-Zeilinger(GHZ)state is shared between three spatially separated parties,Alice,Bob and Charlie.In both(1→2)and(2→1),we discuss the untrusted party and trusted party performing a sequence of unsharp measurements,respectively.For each scenario,we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality.The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters.Moreover,both the sharpness parameters range and the state parameters range in the scenario of(1→2)steering are larger than those in the scenario of(2→1)steering.
文摘Orbital Angular Momentum(OAM)is an intrinsic feature of electromagnetic waves which has recently found many applications in several areas in radio and optics.In this paper,we use OAM wave characteristics to present a simple method for beam steering over both elevation and azimuth planes.The design overcomes some limitations of traditional steering methods,such as limited dynamic range of steering,the design complexity,bulky size of the steering structure,the limited bandwidth of operation,and low gain.Based on OAM wave characteristics,the proposed steering method avoids design complexities by adopting a simple method for generating the OAM-carrying waves.The waves are generated by an array of Planar Circular Dipole(PCD)elements.These elements are designed to cover a wide bandwidth range between 3 and 30 GHz.The transmitting array shows an enhanced gain value from 8.5 dBi to almost 11.5 dBi at the broadside angle.Besides the enhanced PCD-based OAM generation,the novelty of the design lies in a new method of beam steering.Beam steering is then performed by controlling the electrical feeding of the PCD elements;the beam azimuthal location is managed by turning off some of the PCD elements,while the elevation is determined by changing the gradient phase of excitation for the turned-on PCD elements.Detailed analysis of the steering method is carried out by finding the mathematical model of the system and the generated waves.The performance has been verified through numerical simulators.
基金Supported by National Key R&D Program of China(Grant No.2018YFB1600500)Jiangsu Provincial Postgraduate Research&Practice Innovation Program of(Grant No.KYCX22_3673).
文摘To resolve the response delay and overshoot problems of intelligent vehicles facing emergency lane-changing due to proportional-integral-differential(PID)parameter variation,an active steering control method based on Convolutional Neural Network and PID(CNNPID)algorithm is constructed.First,a steering control model based on normal distribution probability function,steady constant radius steering,and instantaneous lane-change-based active for straight and curved roads is established.Second,based on the active steering control model,a three-dimensional constraint-based fifth-order polynomial equation lane-change path is designed to address the stability problem with supersaturation and sideslip due to emergency lane changing.In addition,a hierarchical CNNPID Controller is constructed which includes two layers to avoid collisions facing emergency lane changing,namely,the lane change path tracking PID control layer and the CNN control performance optimization layer.The scaled conjugate gradient backpropagation-based forward propagation control law is designed to optimize the PID control performance based on input parameters,and the elastic backpropagation-based module is adopted for weight correction.Finally,comparison studies and simulation/real vehicle test results are presented to demonstrate the effectiveness,significance,and advantages of the proposed controller.
基金supported by the National Natural Science Foundation of China (61973153)。
文摘Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.
基金Project supported by the National Key Research and Development Program of China (Grant No.2021YFA1401001)the National Natural Science Foundation of China (Grant No.62371355)。
文摘A 1-bit electronically controlled metasurface reflectarray is presented to achieve beam steering with multiple polarization manipulations. A metsurface unit cell loaded by two PIN diodes is designed. By switching the two PIN diodes between ON and OFF states, the isotropic and anisotropic reflections can be flexibly achieved. For either the isotropic reflection or the anisotropic reflection, the two operation states achieve the reflection coefficients with approximately equal magnitude and 180°out of phase, thus giving rise to the isotropic/anisotropic 1-bit metasurface unit cells. With the 1-bit unit cells, a 12-by-12 metasurface reflectarray is optimally designed and fabricated. Under either y-or x-polarized incident wave illumination, the reflectarray can achieve the co-polarized and cross-polarized beam scanning, respectively, with the peak gains of 20.08 d Bi and 17.26 d Bi within the scan range of about ±50°. With the right-handed circular polarization(RHCP) excitation, the left-handed circular polarization(LHCP) radiation with the peak gain of 16.98 d Bic can be achieved within the scan range of ±50°. Good agreement between the experimental results and the simulation results are observed for 2D beam steering and polarization manipulation capabilities.
基金financial supports from National Key Research and Development Program of China(2021YFB3602500)Self-deployment Project of Fujian Science&Technology Innovation Laboratory for Optoelectronic Information of China(2021ZZ101)National Natural Science Foundation of China(Grant Nos.62275247 and 61905246).
文摘Integrated photonic devices are essential for on-chip optical communication,optical-electronic systems,and quantum information sciences.To develop a high-fidelity interface between photonics in various frequency domains without disturbing their quantum properties,nonlinear frequency conversion,typically steered with the quadratic(χ2)process,should be considered.Furthermore,another degree of freedom in steering the spatial modes during theχ2 process,with unprecedent mode intensity is proposed here by modulating the lithium niobate(LN)waveguide-based inter-mode quasi-phasematching conditions with both temperature and wavelength parameters.Under high incident light intensities(25 and 27.8 dBm for the pump and the signal lights,respectively),mode conversion at the sum-frequency wavelength with sufficient high output power(−7–8 dBm)among the TM01,TM10,and TM00 modes is realized automatically with characterized broad temperature(ΔT≥8°C)and wavelength windows(Δλ≥1 nm),avoiding the previous efforts in carefully preparing the signal or pump modes.The results prove that high-intensity spatial modes can be prepared at arbitrary transparent wavelength of theχ2 media toward on-chip integration,which facilitates the development of chip-based communication and quantum information systems because spatial correlations can be applied to generate hyperentangled states and provide additional robustness in quantum error correction with the extended Hilbert space.
基金Supported by the National Natural Science Foundation of China(51005115)the Risiting Scholar Foundation of the State Key Lab of Mechanical Transmission in Chongqing University(SKLMT-KFKT-201105)theScience Fund of State Key Laboratory of Automotive Satefy and Energy in Tsinghua University(KF11202)~~
文摘The dynanaic model of a novel electric power steering(EPS) system integrated with active front steer- ing function and the three-freedom steering model are built. Based on these models, the concepts and the quanti- tative expressions of road feel, sensitivity, and operation stability of the steering are introduced. Then, according to constrained optimization features of multi-variable function, a genetic algorithm is designed. Making the road feel of the steering as optimization objective, and operation stability and sensitivity of the steering as constraints, the system parameters are optimized by the genetic and the coordinate rotation algorithms. Simulation results show that the optimization of the novel EPS system by the genetic algorithm can effectively improve the road feel, thus providing a theoretical basis for the design and optimization of the novel EPS system.
基金Supported by National Natural Science Foundation of China(Grant No.51005133)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA11A244)Special Financial Grant of National Science Foundation for Post-doctoral Scientists of China(Grant No.201104098)
文摘The existing research of steering efficiency mainly focuses on the mechanism efficiency of steering system, aiming at designing and optimizing the mechanism of steering system. In the development of assist steering system especially the evaluation of its comfort, the steering efficiency of driver physiological output usually are not considered, because this physiological output is difficult to measure or to estimate, and the objective evaluation of steering comfort therefore cannot be conducted with movement efficiency perspective. In order to take a further step to the objective evaluation of steering comfort, an estimating method for the steering efficiency of the driver was developed based on the research of the relationship between the steering force and muscle activity. First, the steering forces in the steering wheel plane and the electromyography (EMG) signals of the primary muscles were measured. These primary muscles are the muscles in shoulder and upper ann which mainly produced the steering torque, and their functions in steering maneuver were identified previously. Next, based on the multiple regressions of the steering force and EMG signals, both the effective steering force and the total force capacity of driver in steering maneuver were calculated. Finally, the steering efficiency of driver was estimated by means of the estimated effective force and the total force capacity, which represented the information of driver physiological output of the primary muscles. This research develops a novel estimating method for driver steering efficiency of driver physiological output, including the estimation of both steering force and the force capacity of primary muscles with EMG signals, and will benefit to evaluate the steering comfort with an objective perspective.
基金Supported by National Key Technology R&D Program of China(Grant No.2014BAK12B01)
文摘The evaluation method on steering is based on qualitative manner in existence, which causes the result inaccurate and fuzziness. It reduces the efficiency of process execution. So the method by quantitative manner for the shape-shifting robot in different configurations is proposed. Comparing to traditional evaluation method, the most important aspects which can influence the steering abilities of the robot in different configurations are researched in detail, including the energy, angular velocity, time and space. In order to improve the robustness of system, the ideal and slippage conditions are all considered by mathematical model. Comparing to the traditional weighting confirming method, the extent of robot steering method is proposed by the combination of subjective and objective weighting method. The subjective weighting method can show more preferences of the experts and is based on five-grade scale. The objective weighting method is based on information entropy to determine the factors. By the sensors fixed on the robot, the contract force between track grouser and ground, the intrinsic motion characteristics of robot are obtained and the experiment is done to prove the algorithm which is proposed as the robot in different common configurations. Through the method proposed in the article, fuzziness and inaccurate of the evaluation method has been solved, so the operators can choose the most suitable configuration of the robot to fulfil the different tasks more quickly and simply.
基金Supported by National Natural Science Foundation of China(Grant Nos.51005133,51375009)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA11A244)
文摘The existing research of steering comfort mainly focuses on the subjective evaluation,aiming at designing and optimizing the steering system.In the development of steering system,especially the evaluation of steering comfort,the objective evaluation methods considered the kinematic characteristics of driver steering maneuver are not proposed,which means that the objective evaluation of steering cannot be conducted with the evaluation of kinematic characteristics of driver in steering maneuver.In order to propose the objective evaluation methods of steering comfort,the evaluation of steering movement quality of driver is developed on the basis of the study of the kinematic characteristics of steering maneuver.First,the steering motion trajectories of the driver in both comfortable and certain extreme uncomfortable operation conditions are detected using the Vicon motion capture system.The operation conditions are under the restrictions of the vertical height and horizontal distance between steering wheel center and the H-point of driver,and the steering resisting torque else.Next,the movement quality evaluation of driver steering maneuver is assessed using twelve kinds of evaluation indices based on the kinematic analyses of the steering motion trajectories to propose an objective evaluation method.Finally,an integrated discomfort index of steering maneuver is proposed on the basis of the regression analysis of subjective evaluation rating and the movement quality evaluation indices,including the Jerk,Discomfort and Joint Torque indices.The test results show that the proposed integrated discomfort index gives a good fitting with the subjective evaluation of discomfort,which means it can be used to evaluate or predict the discomfort level of steering maneuver.This paper proposes an objective evaluation method of steering comfort based on the movement quality evaluation of driver steering maneuver.
基金supported by National Natural Science Foundation of China (Grant Nos. 51165040,50775119)Visiting Scholar Foundation of Key Lab in University of China (Grant No. GZKF-201020)
文摘Needle insertion is a common surgical procedure used in diagnosis and treatment.The needle steering technologies make continuous developments in theoretical and practical aspects along with the in-depth research on needle insertion.It is necessary to summarize and analyze the existing results to promote the future development of theories and applications of needle insertion.Thus,a survey of the state of the art of research is presented on algorithms of needle steering techniques,the surgical robots and devices.Based on the analysis of the needle insertion procedure,the concept of needle steering is defined as a kinematics problem,which is to place the needle at the target and avoid the obstacles.The needle steering techniques,including the artificial potential field method and the nonholonomic model,are introduced to control the needles for improving the accuracy.Based on the quasi-static thinking,the virtual spring model and the cantilever-beam model are developed to calculate the amount of needle deflection and generate the needle path.The phantoms instead of the real tissue are used to verify the models mentioned in most of the experimentations.For the desired needle trajectories,the image-guided robotic devices and some novel needles are presented to achieve the needle steering.Finally,the challenges are provided involving the controllability of the long flexible needle and the properties of soft tissue.The results and investigations can be used for further study on the precision and accuracy of needle insertion.