Entanglement Dynamics of Two Qubits Coupled Independently to Cavities in the Ultrastrong Coupling Regime:Analytical Results

Dynamics of quantum entanglement of two qubits in two identical quantum Rabi models is studied analytically in the framework of corrections to the rotating-wave approximations. A closed-form expression for the entanglement dynamics initiated from the well-known Bell states is derived, which is very close to the numerical exact results up to the ultrastrong coupling regime. It is found that the vanishing entanglement can be purely induced by the counter-rotating terms, and can be enhanced with the atom-cavity coupling.

Coupled Dynamics and Integrated Control for Position and Attitude Motions of Spacecraft:A Survey

Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety of study results in last over two decades,fully incorporating control requirements and actuator characteristics of space missions.This paper presents a novel and comprehensive survey to the coupled position and attitude motions of spacecraft from the perspective of dynamics and control.To this end,a systematic analysis is firstly conducted in details to show the position and attitude mutual couplings of spacecraft.Particularly,in terms of the time discrepancy between spacecraft position and attitude motions,space missions can be categorized into two types:space proximity operation and space orbital maneuver.Based on this classification,the studies on the coupled dynamic modeling and the integrated control design for position and attitude motions of spacecraft are sequentially summarized and analyzed.On the one hand,various coupled position and dynamic formulations of spacecraft based on various mathematical tools are reviewed and compared from five aspects,including mission applicability,modeling simplicity,physical clearance,information matching and expansibility.On the other hand,the development of the integrated position and attitude control of spacecraft is analyzed for two space missions,and especially,five distinctive development trends are captured for space operation missions.Finally,insightful prospects on future development of the integrated position and attitude control technology of spacecraft are proposed,pointing out current primary technical issues and possible feasible solutions.

Vibration control of pedestrian-bridge vertical dynamic coupling interaction based on biodynamic model

The human-induced vertical vibration serviceability of low-frequency and lightweight footbridges is studied based on the moving mass-spring-damper（MMSD） biodynamic model, and the mass damper（TMD） with different optimal model parameters being used to control the vertical vibration.First, the MMSD biodynamic model is employed to simulate the pedestrians, and the time-varying control equations of the vertical dynamic coupling system of the pedestrian-bridgeTMD are established with the consideration of pedestrianbridge dynamic interaction; and the equations are solved by using the Runge-Kutta-Felhberg integral method with variable step size. Secondly, the footbridge dynamic response is calculated under the model of pedestrian-structure dynamic interaction and the model of moving load when the pedestrian pace frequency is consistent with the natural frequency of footbridge. Finally, a comparative study and analysis are made on the control effects of the vertical dynamic coupling system in different optimal models of the TMD. The calculation results show that the pedestrian-bridge dynamic interaction cannot be ignored when the vertical human-induced vibration serviceability of low-frequency and light-weight footbridge is evaluated. The TMD can effectively reduce the vibration under the resonance of pedestrian-bridge, and TMD parameters are recommended for the determination by the Warburton optimization model.

Experimental study and numerical simulation of the impact of under-sleeper pads on the dynamic and static mechanical behavior of heavy-haul railway ballast track

Laying the under-sleeper pad(USP)is one of the effective measures commonly used to delay ballast degradation and reduce maintenance workload.To explore the impact of application of the USP on the dynamic and static mechanical behavior of the ballast track in the heavy-haul railway system,numerical simulation models of the ballast bed with USP and without USP are presented in this paper by using the discrete element method(DEM)-multi-flexible body dynamic(MFBD)coupling analysis method.The ballast bed support stiffness test and dynamic displacement tests were carried out on the actual operation of a heavy-haul railway line to verify the validity of the models.The results show that using the USP results in a 43.01%reduction in the ballast bed support stiffness and achieves a more uniform distribution of track loads on the sleepers.It effectively reduces the load borne by the sleeper directly under the wheel load,with a 7.89%reduction in the pressure on the sleeper.Furthermore,the laying of the USP changes the lateral resistance sharing ratio of the ballast bed,significantly reducing the stress level of the ballast bed under train loads,with an average stress reduction of 42.19 kPa.It also reduces the plastic displacement of ballast particles and lowers the peak value of rotational angular velocity by about 50%to 70%,which is conducive to slowing down ballast bed settlement deformation and reducing maintenance costs.In summary,laying the USP has a potential value in enhancing the stability and extending the lifespan of the ballast bed in heavy-haul railway systems.

Uncertainty quantification of mechanism motion based on coupled mechanism—motor dynamic model for ammunition delivery system

In this paper,a dynamic modeling method of motor driven electromechanical system is presented,and the uncertainty quantification of mechanism motion is investigated based on this method.The main contribution is to propose a novel mechanism-motor coupling dynamic modeling method,in which the relationship between mechanism motion and motor rotation is established according to the geometric coordination of the system.The advantages of this include establishing intuitive coupling between the mechanism and motor,facilitating the discussion for the influence of both mechanical and electrical parameters on the mechanism,and enabling dynamic simulation with controller to take the randomness of the electric load into account.Dynamic simulation considering feedback control of ammunition delivery system is carried out,and the feasibility of the model is verified experimentally.Based on probability density evolution theory,we comprehensively discuss the effects of system parameters on mechanism motion from the perspective of uncertainty quantization.Our work can not only provide guidance for engineering design of ammunition delivery mechanism,but also provide theoretical support for modeling and uncertainty quantification research of mechatronics system.

Dynamic mechanical characteristics of deep Jinping marble in complex stress environments

To reveal the dynamic mechanical characteristics of deep rocks,a series of impact tests under triaxial static stress states corresponding to depths of 300-2400 m were conducted.The results showed that both the strain rates and the stress environments in depth significantly affect the mechanical characteristics of rocks.The sensitivity of strain rate to the dynamic strength and deformation modulus shows a negative correlation with depth,indicating that producing penetrative cracks in deep environments is more difficult when damage occurs.The dynamic strength shows a tendency to decrease and then increase slightly,but decreases sharply finally.Transmissivity demonstrates a similar trend as that of strength,whereas reflectivity indicates the opposite trend.Furthermore,two critical depths with high dynamically induced hazard possibilities based on the China Jinping Underground Laboratory(CJPL)were proposed for deep engineering.The first critical depth is 600-900 m,beyond which the sensitivity of rock dynamic characteristics to the strain rate and restraint of circumferential stress decrease,causing instability of surrounding rocks under axial stress condition.The second one lies at 1500-1800 m,where the wave impedance and dynamic strength of deep surrounding rocks drop sharply,and the dissipation energy presents a negative value.It suggests that the dynamic instability of deep surrounding rocks can be divided into dynamic load dominant and dynamic load induced types,depending on the second critical depth.

The dynamic coupling model and its application of urbanization and eco-environment in Hexi Corridor

This paper, taking Hexi Corridor as an example, analyzes the altemating intimidation and the dynamic evolving relation between urbanization and eco-environment in arid area of West China. We argue that the harmonious development system of the urbanization and eco-environment would go through four phases： rudimentary symbiotic phase, harmonious developmental phase, utmost increasing phase and spiral type rising phase. Throughout the four phases, the elements of the system would influence each other, coerce each other, and complete the spiral type rising process from low-grade symbiosis to high-grade harmony together. The study on Hexi Corridor shows that the urbanization level in Hexi Corridor has increased gradually from 1985 to 2003 accompanied with the fluctuations of eco-environment state. The response of eco-environment to urbanization has been evident, but lagged behind the urbanization course. At present, the harmonious development system in Hexi Corridor was in its harmonious developmental phase. However, the coupling degree has increased quickly and approached 90 yet, which is signaling that the system is about to enter the utmost increasing phase, and the ecological crisis will enter the latent period. We have found that the coupling degree can well reflect the interactive coercing and dynamic evolving situation between urbanization and eco-environment in Hexi Corridor. From the temporal change of the coupling degree, it can be concluded that urbanization sometimes needs to pay a certain cost for the damage of the eco-environment in its initial stages, but as the urbanization continues, the state of the eco-environment would be meliorated.

Continuum and Discrete Element Coupling Approach to Analyzing Seismic Responses of a Slope Covered by Deposits

Numerical analyses of earthquake effects on the deformation, stability, and load transfer of a slope covered by deposits are traditionally based on the assumption that the slope is a continuum. It would be problematic, however, to extend these approaches to the simulation of the slide, collapse and disintegration of the deposits under seismic loading. Contrary to this, a discrete element method （DEM） provides a means to consider large displacement and rotation of the non-continuum. To take the advantages of both methods of continuum and non- continuum analyses, seismic responses of a slope covered by deposits are studied by coupling a twodimensional （a-D） finite difference method and a 2-D DEM, with the bedrock being modelled by the finite difference grids and the deposits being represented by disks. A smooth transition across the boundaries of the continuous/discontinuous domains is obtained by imposing the compatibility condition and equilibrium condition along their interfaces. In the course of computation, the same time-step value is chosen for both continuous and discontinuous domains. The free-field boundaries are adopted for lateral grids of bedrock domain to eliminate the radiation damping effect. When the static equilibrium under gravity load is obtained, dynamic calculation begins under excitation of the seismic wave input from the continuum model bottom. In this way, responses to the earthquake of a slope covered by deposits are analyzed dynamically. Combined with field monitoring data, deformation and stability of the slope are discussed. The effects of the relevant parameters of spectrum characteristic, duration, andpeak acceleration of seismic waves are further investigated and explained from the simulations.

Experiment Study of Dynamics Response for Wind Turbine System of Floating Foundation

The floating foundation is designed to support a 1.5 MW wind turbine in 30 m water depth. With consideration of the viscous damping of foundation and heave plates, the amplitude-frequency response characteristics of the foundation are studied. By taking into account the elastic effect of blades and tower, the classic quasi-steady blade-element/momentum（BEM） theory is used to calculate the aerodynamic elastic loads. A coupled dynamic model of the turbine-foundationmooring lines is established to calculate the motion response of floating foundation under Kaimal wind spectrum and regular wave by using the FAST codes. The model experiment is carried out to test damping characteristics and natural motion behaviors of the wind turbine system. The dynamics response is tested by considering only waves and the joint action of wind and waves. It is shown that the wind turbine system can avoid resonances under the action of wind and waves. In addition, the heave motion of the floating foundation is induced by waves and the surge motion is induced by wind. The action of wind and waves is of significance for pitch.

Roll System and Stock's Multi-parameter Coupling Dynamic Modeling Based on the Shape Control of Steel Strip

The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.

Nonlinear Coupled Dynamics Analysis of A Truss Spar Platform

Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code ＇COUPLE＇. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooting and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooting/riser system in predicting the mooting line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.

Dynamics of Large-Truncated Mooring Systems Coupled with A Catenary Moored Semi-Submersible

With the floating structures pushing their activities to the ultra-deep water, model tests have presented a challenge due to the limitation of the existing wave basins. Therefore, the concept of truncated mooring system is implemented to replace the full depth mooring system in the model tests, which aims to have the same dynamic responses as the full depth system. The truncated mooring system plays such a significant role that extra attention should be paid to the mooring systems with large truncation factor. Three different types of large truncation factor mooring system are being employed in the simulations, including the homogenously truncated mooring system, non-homogenously truncated mooring system and simplified truncated mooring system. A catenary moored semi-submersible operating at 1000 m water depth is presented. In addition, truncated mooring systems are proposed at the truncated water depth of 200 m. In order to explore the applicability of these truncated mooring systems, numerical simulations of the platform’s surge free decay interacting with three different styles of truncated mooring systems are studied in calm water. Furthermore, the mooring-induced damping of the truncated mooring systems is simulated in the regular wave. Finally, the platform motion responses and mooring line dynamics are simulated in irregular wave. All these simulations are implemented by employing full time domain coupled dynamic analysis, and the results are compared with those of the full depth simulations in the same cases. The results show that the mooring-induced damping plays a significant role in platform motion responses, and all truncated mooring systems are suitable for model tests with appropriate truncated mooring line diameters. However, a large diameter is needed for simplified truncated mooring lines. The suggestions are given to the selection of truncated mooring system for different situations as well as to the truncated mooring design criteria.

Dynamics of Ore-Forming Processesof the Stratabound Skarn Copper Depositsof Tongling, Anhui Province

The skarn and ore bodies of the stratabound skarn copper deposits of Tongling, Anhui Province, are both controlled by definite stratigraphic horizons, and they are concordant with the strata. They occur as layers and layer-like bodies in permeable carbonate rocks of the Middle-Upper Carboniferous Huanglong and Chuanshan Formations which are underlain by impermeable shale or siliceous rocks of the Upper Devonian Wutong Formation. The authors study the dynamics of ore-forming processes of the ore deposits with the dynamic model of coupled transport and reaction, and the following results are obtained: The salinity gradient and flow rate of the ore-forming fluids can both promote the mixing and reaction of juvenile water and formation water, and the permeable strata are favourable sites for the intense transport-reaction of mixing and the formation of deposits. (2) As isothermal transport-reaction took place along the bedding of strata, the moving transport-reaction front formed at the contact between the ore-forming fluids and the rocks advanced slowly along the permeable strata, and then stratiform skarn and ore bodies concordant with the strata were formed. (3) The gradient transport-reaction taking place across the isotherms in the cross-bedding direction caused the mineralogical composition to alter gradually from magnesian skarn to sulphide ore bodies.

Nonlinear coupled dynamics of liquid-filled spherical container in microgravity

Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid flee surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange＇s method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.

Characteristic analysis of mechanical thermal coupling model for bearing rotor system of high-speed train

Based on Newton’s second law and the thermal network method,a mechanical thermal coupling model of the bearing rotor system of high-speed trains is established to study the interaction between the bearing vibration and temperature.The influence of lubrication on the vibration and temperature characteristics of the system is considered in the model,and the real-time relationship between them is built up by using the transient temperature field model.After considering the lubrication,the bearing outer ring vibration acceleration and node temperature considering grease are lower,which shows the necessity of adding the lubrication model.The corresponding experiments for characteristics of vibration and temperature of the model are respectively conducted.In the envelope spectrum obtained from the simulation signal and the experimental signal,the frequency values corresponding to the peaks are close to the theoretical calculation results,and the error is very small.In the three stages of the temperature characteristic experiment,the node temperature change of the simulation model is consistent with the experiment.The good agreement between simulation and experiments proves the effectiveness of the model.By studying the influence of the bearing angular and fault size on the system node temperature,as well as the change law of bearing lubrication characteristics and temperature,it is found that the worse the working condition is,the higher the temperature is.When the ambient temperature is low,the viscosity of grease increases,and the oil film becomes thicker,which increases the sliding probability of the rolling element,thus affecting the normal operation of the bearing,which explains the phenomenon of frequent bearing faults of high-speed trains in the low-temperature area of Northeast China.Further analysis shows that faults often occur in the early stage of train operation in the low-temperature environment.

The integration of nitrogen dynamics into a land surface model. Part 1: model description and site-scale validation

Nitrogen cycling has profound effects on carbon uptake in the terrestrial ecosystem and the response of the biosphere to climate changes.However,nutrient cycling is not taken into account in most land surface models for climate change.In this study,a nitrogen model,based on nitrogen transformation processes and nitrogen fluxes exchange between the atmosphere and terrestrial ecosystem,was incorporated into the Atmosphere–Vegetation Interaction Model(AVIM)to simulate the carbon cycle under nitrogen limitation.This new model,AVIM-CN,was evaluated against site-scale eddy covariance–based measurements of an alpine meadow located at Damxung station from the FLUXNET 2015 dataset.Results showed that the annual mean gross primary production simulated by AVIM-CN(0.7073 gC m^-2 d^-1)was in better agreement with the corresponding flux data(0.5407 gC m^-2 d^-1)than the original AVIM(1.1403 gC m^-2 d^-1)at Damxung station.Similarly,ecosystem respiration was also down-regulated,from 1.7695 gC m^-2 d^-1 to 1.0572 gC m^-2 d^-1,after the nitrogen processes were introduced,and the latter was closer to the observed vales(0.8034 gC m^-2 d^-1).Overall,the new results were more consistent with the daily time series of carbon and energy fluxes of observations compared to the former version without nitrogen dynamics.A model that does not incorporate the limitation effects of nitrogen nutrient availability will probably overestimate carbon fluxes by about 40%.

Evaluating the dynamical coupling between spatiotemporally chaotic signals via an information theory approach

An information-theoretic measure is introduced for evaluating the dynamical coupling of spatiotemporally chaotic signals produced by extended systems. The measure of the one-way coupled map lattices and the one-dimensional, homogeneous, diffusively coupled map lattices is computed with the symbolic analysis method. The numerical results show that the information measure is applicable to determining the dynamical coupling between two directly coupled or indirectly coupled chaotic signals.

Improved Dynamics Model of Locomotive Traction Motor with Elasticity of Rotor Shaft and Supporting Bearings

The locomotive traction motor is described as a rotor-bearing system coupling the kinetic equations of the traction shaft and its support bearings with the determination of their elastic deformations in this study.Under the effect of excitations induced by the dynamic rotor eccentric distance and time-varying mesh stiffness,the elastic structure deformations of the shaft and support bearings are formulated in the vibration environment of the locomotive.In addition,the nonlinear contact forces between the components of the rolling bearing,the lubricating oil film,and radial clearance are comprehensively considered in this study.The results indicate that the elastic deformations of the shaft and bearings can change the dynamic responses of the traction motor and its support bearings.There are large differences between the ranges of the rotor motion calculated by the rigid and the flexible traction motor models when the intensified wheel-rail interaction is considered.With the increase of the rotor eccentricity,the results underscore the role of the elasticity of traction shaft and support bearings in dynamic researches of the traction motor.The critical value of the initial eccentric distance for the rub-impact phenomenon decreases from 1.23 mm to 1.15 mm considering the flexible effect of the shaft and bearings.This dynamics model of the traction motor can provide more accurate and reasonable simulation results for correlational dynamic researches.

Synchronization of networks with time-varying couplings

In this paper, we present a review of our recent works on complete synchro-nization analyses of networks of the coupled dynamical systems with time-varying cou-plings. The main approach is composed of algebraic graph theory and dynamic system method. More precisely, the Hajnal diameter of matrix sequence plays a key role in in-vestigating synchronization dynamics and the joint graph across time periods possessing spanning tree is a doorsill for time-varying topologies to reach synchronization. These techniques with proper modification count for diverse models of networks of the cou-pled systems, including discrete-time and continuous-time models, linear and nonlinear models, deterministic and stochastic time-variations. Alternatively, transverse stability analysis of general time-varying dynamic systems can be employed for synchronization study as a special case and proved to be equivalent to Hajnal diameter.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.