Exact Entanglement Dynamics in Three Interacting Qubits

Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114（2015） 113002, Phys. Rev. Lett 120（2018） 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer,characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.

Synchronization Dynamics in a System of Multiple Interacting Populations of Phase Oscillators

We study the synchronization dynamics in a system of multiple interacting populations of phase oscillators. Using the dimensionality-reduction technique of Ott and Antonsen, we explore different types of synchronization dynamics when the incoherent state becomes unstable. We find that the inter-population coupling is crucial to the synchronization. When the intra-population interaction is repulsive, the local synchronization can still be maintained through the inter-population coupling. For attractive inter-population coupling, the local order parameters in different populations are of in-phase while the local synchronization are of anti-phase for repulsive inter-population coupling.

Influence of railway wheel tread damage on wheel-rail impact loads and the durability of wheelsets

Dynamic wheel-rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds.Based on laser scanning,the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle-track interaction to calibrate and verify a simulation model.The relation between the magnitude of the impact load and various operational parameters,such as vehicle speed,lateral position of wheel-rail contact,track stiffness and position of impact within a sleeper bay,is investigated.The calibrated model is later employed in simulations featuring other forms of tread damage;their effects on impact load and subsequent fatigue impact on bearings,wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed.The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear,and for general assessment of the severity of different types of railway wheel tread damage.

Structural Characteristics and Formation Dynamics: A Review of the Main Sedimentary Basins in the Continent of China

The formation and evolution of basins in the China continent are closely related to the collages of many blocks and orogenic belts. Based on a large amount of the geological, geophysical, petroleum exploration data and a large number of published research results, the basement constitutions and evolutions of tectonic-sedimentary of sedimentary basins, the main border fault belts and the orogenesis of their peripheries of the basins are analyzed. Especially, the main typical basins in the eight divisions in the continent of China are analyzed in detail, including the Tarim, Ordos, Sichuan, Songliao, Bohai Bay, Junggar, Qiadam and Qiangtang basins. The main five stages of superimposed evolutions processes of basins revealed, which accompanied with the tectonic processes of the Paleo-Asian Ocean, Tethyan and Western Pacific domains. They contained the formations of main Cratons （1850-800 Ma）, developments of marine basins （800-386 Ma）, developments of Marine- continental transition basins and super mantle plumes （386-252 Ma）, amalgamation of China Continent and developments of continental basins （252-205 Ma） and development of the foreland basins in the western and extensional faulted basin in the eastern of China （205~0 Ma）. Therefore, large scale marine sedimentary basins existed in the relatively stable continental blocks of the Proterozoic, developed during the Neoproterozoic to Paleozoic, with the property of the intracontinental cratons and peripheral foreland basins, the multistage superimposing and late reformations of basins. The continental basins developed on the weak or preexisting divisional basements, or the remnant and reformed marine basins in the Meso-Cenozoic, are mainly the continental margins, back-arc basins, retroarc foreland basins, intracontinental rifts and pull-apart basins. The styles and intensity deformation containing the faults, folds and the structural architecture of regional unconformities of the basins, responded to the openings, subductions, closures of oceans, the continent-continent collisions and reactivation of orogenies near the basins in different periods. The evolutions of the Tianshan-Mongol-Hinggan, Kunlun-Qilian-Qinling-Dabie-Sulu, Jiangshao-Shiwandashan, Helanshan-Longmengshan, Taihang-Wuling orogenic belts, the Tibet Plateau and the Altun and Tan- Lu Fault belts have importantly influenced on the tectonic-sedimentary developments, mineralization and hydrocarbon reservoir conditions of their adjacent basins in different times. The evolutions of basins also rely on the deep structures of lithosphere and the rheological properties of the mantle. The mosaic and mirroring geological structures of the deep lithosphere reflect the pre-existed divisions and hot mantle upwelling, constrain to the origins and transforms dynamics of the basins. The leading edges of the basin tectonic dynamics will focus on the basin and mountain coupling, reconstruction of the paleotectonic-paleogeography, establishing relationship between the structural deformations of shallow surface to the deep lithosphere or asthenosphere, as well as the restoring proto-basin and depicting residual basin of the Paleozoic basin, the effects of multiple stages of volcanism and paleo- earthquake events in China.

Ground substrates classification and adaptive walking through interaction dynamics for legged robots

Adaptive locomotion in different types of surfaces is of critical importance for legged robots.The knowledge of various ground substrates,especially some geological properties,plays an essential role in ensuring the legged robots'safety.In this paper,the interaction between the robots and the environments is investigated through interaction dynamics with the closed-loop system model,the compliant contact model,and the friction model,which unveil the influence of environment's geological characteristics for legged robots'locomotion.The proposed method to classify substrates is based on the interaction dynamics and the sensory-motor coordination.The foot contact forces,joint position errors,and joint motor currents,which reflect body dynamics,are measured as the sensing variables.We train and classify the features extracted from the raw data with a multilevel weighted k-Nearest Neighbor(kNN) algorithm.According to the interaction dynamics,the strategy of adaptive walking is developed by adjusting the touchdown angles and foot trajectories while lifting up and dropping down the foot.Experiments are conducted on five different substrates with quadruped robot FROG-I.The comparison with other classification methods and adaptive walking between different substrates demonstrate the effectiveness of our approach.

Interaction of cetyltrimethylammonium bromide with drug in aqueous/electrolyte solution:A combined conductometric and molecular dynamics method study

Interaction between beta-lactum antibiotic drug ciprofloxacin hydrochloride(CFH)and cationic surfactant cetyltrimethylammonium bromide(CTAB)was performed conductometrically in aqueous as well as in the occurrence of different salts(NaCl,KCl as well as NH_4Cl)over the temperature range of 298.15–323.15 K at the regular interval of 5 K.CFH drug has been suggested for the treatment of bacterial infections such as urinary tract infections and acute sinusitis.A clear critical micelle concentration(CMC)was obtained for pure CTAB as well as(CFH+CTAB)mixed systems.The decrease in CMC values of CTAB caused by the addition of CFH reveals the existence of the interaction between the components and therefore it is the indication of micelle formation at lower concentration of CTAB and their CMC values further decrease in attendance of salts.A nonlinear behavior in the CMC versus T plot was observed in all the cases.The ΔG_m^0 values are found to be negative in present study systems demonstrated the stability of the solution.The values of ΔH_m^0 and ΔS_m^0 reveal the existence of hydrophobic and electrostatic interactions between CFH and CTAB.The thermodynamic properties of transfer for the micellization were also evaluated and discussed in detail.Molecular dynamic simulation disclosed that environment of water and salts have impact on the hydrophobic interaction between CFH and CTAB.In water and salts,CTAB adopts spherical micelle in which charged hydrophilic groups are interacted with waters whereas hydrophobic tails form the core of the micelle.This hydrophobic core region is highly conserved and protected.In addition,micelle formation is more favorable in aqueous Na Cl solution than other solutions.

Population Interaction Dynamics Analysis of an Algae-Fish System

In this paper, before the implementation of ecological laboratory experiments, the population interaction dynamics of an algae-fish system were studied mathematically and numerically. The purpose of this study was to explore how filter-feeding fish population affects the growth dynamics of the algae population. Mathematically theoretical works have been pursuing the investigation of some key conditions for stability of the equilibrium and existence of Hopf bifurcation. Numerical simulation works have been parsing the discovery of the growth dynamics of the algae population in view of population interaction dynamics, which in turn could prove the feasibility of the theoretical derivation and reveal the relationship between filter-feeding fish abundance and algal biomass in fish-drift algae communiyua. Furthermore, it was successful to show that the filter-feeding fish population may be a crucial factor in controlling the proliferation of the algae population, which could also directly grasp the evolution of community dynamics. All these results were expected to be useful in the study of community dynamics and laboratory elimination experiment of the algae population.

Multi-scale calculation of settling speed of coarse particles by accelerated Stokesian dynamics without adjustable parameter

The calculation of settling speed of coarse particles is firstly addressed, with accelerated Stokesian dynamics without adjustable parameters, in which far field force acting on the particle instead of particle velocity is chosen as dependent variables to consider inter-particle hydrodynamic interactions. The sedimentation of a simple cubic array of spherical particles is simulated and compared to the results available to verify and validate the numerical code and computational scheme. The improved method keeps the same computational cost of the order O（NlogN） as usual accelerated Stokesian dynamics does. Then, more realistic random suspension sedimentation is investigated with the help of Mont Carlo method. The computational results agree well with experimental fitting. Finally, the sedimentation of finer cohesive particle, which is often observed in estuary environment, is presented as a further application in coastal engineering.

The dynamics of three coupled dipolar Bose Einstein condensates

The dynamics of the three coupled dipolar Bose–Einstein condensates containing N bosons is investigated within a mean-field semiclassical picture based on the coherent-state method. Varieties of periodic solutions （configured as vortex, single depleted well, and dimerlike states） are obtained analytically when the fixed points are identified on the N=constant. The system dynamics are studied via numeric integration of trimer motion equations, thus revealing macroscopic effects of population inversion and self-trapping with different initial states. In particular, the trajectory of the oscillations of the populations in each well shows how the dynamics of the condensates are effected by the presence of dipole–dipole interaction and gauge field.

Modal interactions in primary and subharmonic resonant dynamics of imperfect microplates with geometric nonlinearities

This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff＇s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct timeintegration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed.Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.

The Dynamics of Barotropic Vortex Merging

The merging of multiple vortices is a fundamental process of the dynamics of Earth＇s atmosphere and oceans. In this study, the interaction of like-signed vortices is analytically and numerically examined in a framework of two-dimensional inviscid barotropic flows. It is shown that barotropic vortex interaction turns out to be more intricate than simple merging scenarios often assumed in previous studies. Some particular configurations exist in which the vortex merging process is never complete despite strong interaction of like-signed vortices, regardless of the strengths or distances between the vortices.While the conditions for a complete vortex merging process introduced in this study appear to be too strict for most practical applications, this study suggests that careful criteria for vortex mergers should be properly defined when simulating the interaction of vortices, because the merging may not always result in a final enhanced circulation at the end of the interaction,as usually assumed in the literature.

An efficient method for train-track-substructure dynamic interaction analysis by implicit-explicit integration and multi-time-step solution

In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.

An Analysis of the Dynamic Behavior of Damaged Reinforced Concrete Bridges under Moving Vehicle Loads by Using the Moving Mesh Technique

This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete(RC)bridge structures commonly adopted in highway and railway networks.An effective three-dimensional FE-based numerical model is developed to analyze the bridge’s structural response under several damage scenarios,including the effects of moving vehicle loads.In particular,the longitudinal and transversal beams are modeled through solid finite elements,while horizontal slabs are made of shell elements.Damage phenomena are also incorporated in the numerical model according to a smeared approach consistent with Continuum Damage Mechanics(CDM).In such a context,the proposed method utilizes an advanced and efficient computational strategy for reproducing Vehicle-Bridge Interaction(VBI)effects based on a moving mesh technique consistent with the Arbitrary Lagrangian-Eulerian(ALE)formulation.The proposed model adopts a moving mesh interface for tracing the positions of the contact points between the vehicle’s wheels and the bridge slabs.Such modeling strategy avoids using extremely refined discretization for structural members,thus drastically reducing computational efforts.Vibrational analyses in terms of damage scenarios are presented to verify how the presence of damage affects the natural frequencies of the structural system.In addition,a comprehensive investigation regarding the response of the bridge under moving vehicles is developed,also providing results in terms of Dynamic Amplification Factor(DAFs)for typical design bridge variables.

Analysis of the Orbitation and Rotation of Celestial Bodies

We have developed a structure of dynamic knowledge for non-inertial systems, the so-called Theory of Dynamic Interactions (TDI) as a part of non-inertial dynamic knowledge, which incorporates a causal demonstration of phenomena accelerated by rotation, which would complement Classical Mechanics. We believe that the TDI mathematical model that we propose is of great conceptual importance. In addition, we think that it is not only necessary to understand the dynamics of rotating bodies, but also to understand the dynamics of the cosmos, with bodies that orbit and with constantly recurring movements, which make possible systems that have been in dynamic equilibrium for centuries and are not in a process of unlimited expansion. We even believe that this new dynamic theory allows us a better understanding of our universe, and the matter from which it is made.

Running safety analysis of a train on the Tsing Ma Bridge under turbulent winds

The dynamic responses of the Tsing Ma suspension bridge and the running behaviors of trains on the bridge under turbulent wind actions are analyzed by a three-dimensional wind-train-bridge interaction model. This model consists of a spatial finite element bridge model, a train model composed of eight 4-axle identical coaches of 27 degrees-of-freedom, and a turbulent wind model. The fluctuating wind forces, including the buffeting forces and the self-excited forces, act on the bridge only, since the train runs inside the bridge deck. The dynamic responses of the bridge are calculated and some results are compared with data measured from Typhoon York. The runnability of the train passing through the Tsing Ma suspension bridge at different speeds is researched under turbulent winds with different wind velocities. Then, the threshold curve of wind velocity for ensuring the running safety of the train in the bridge deck is proposed, from which the allowable train speed at different wind velocities can be determined. The numerical results show that rail traffic on the Tsing Ma suspension bridge should be closed as the mean wind velocity reaches 30 m/s.

A Train-Bridge Dynamic Interaction Analysis Method and Its Experimental Validation

The train-bridge dynamic interaction problem began with the development of railway technology, and requires an evaluation method for bridge design in order to ensure the safety and stability of the bridge and the running train. This problem is studied using theoretical analysis, numerical simulation, and experimental study. In the train-bridge dynamic interaction system proposed in this paper, the train vehicle model is established by the rigid-body dynamics method, the bridge model is established by the finite element method, and the wheel/rail vertical and lateral interaction are simulated by the corresponding assumption and the Kalker linear creep theory, respectively. Track irregularity, structure deformation, wind load, collision load, structural damage, foundation scouring, and earthquake action are regarded as the excitation for the system. The train-bridge dynamic interaction system is solved by inter-history iteration. A case study of the dynamic response of a CRH380BL high-speed train running through a standard-design bridge in China is discussed. The dynamic responses of the vehicle and of the bridge subsystems are obtained for speeds ranging from 200 km-b-1 to 400 km.h-1, and the vibration mechanism are analyzed.

Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

Elastic responses of underground circular arches considering dynamic soil-structure interaction:A theoretical analysis

Due to the wide applications of arches in underground protective structures, dynamic analysis of circular arches including soil-structure interactions is important. In this paper, an exact solution of the forced vibration of circular arches subjected to subsurface denotation forces is obtained. The dynamic soil-structure interaction is considered with the introduction of an interfacial damping between the structure element and the surrounding soil into the equa- tion of motion. By neglecting the influences of shear, rotary inertia and tangential forces and assuming the arch incompressible, the equations of motion of the buried arches were set up. Analytical solutions of the dynamic responses of the protective arches were deduced by means of modal super- position. Arches with different opening angles, acoustic impedances and rise-span ratios were analyzed to discuss their influences on an arch. The theoretical analysis suggests blast loads for elastic designs and predicts the potential failure modes for buried protective arches.

Dynamic interaction nursing intervention on functional rehabilitation and self-care ability of patients after aneurysm surgery

BACKGROUND Nursing practices based on the dynamic interaction model have been shown to be superior to generic nursing practices.However,whether this model is effective in patients recovering from intracranial aneurysm surgery is not well studied.AIM To investigate the effect of nursing based on a dynamic interaction model on functional rehabilitation of patients after aneurysm surgery.METHODS A total of 86 cases in our hospital with intracranial aneurysm from April 2019 to April 2021,were selected and divided into the study group and the control group,with 43 patients in each group.The control group received routine nursing,and the research group received nursing intervention based on a dynamic interaction model.The daily living ability(activities of daily living,ADL),cognitive function(Simple Intelligent Mental State Scale,MMSE),quality of life(Generic Quality of Life Inventory-74,GQOL-74),self-care ability(Exercise of Self-Care Agency scale),incidence of complications,and nursing satisfaction were recorded before and after intervention.RESULTS Before intervention,ADL(52.09±6.44),MMSE(18.03±4.11),and GQOL-74(53.68±4.34)scores in the study group were not significantly different from those in the control group(ADL:50.97±7.32,MMSE:17.59±3.82,GQOL-74:55.06±3.98)(P>0.05).After intervention,ADL(86.12±5.07),MMSE(26.64±2.66),and GQOL-74(83.13±5.67)scores in the study group were higher than those in the control group(ADL:79.81±6.35,MMSE:24.51±3.00,and GQOL-74:77.96±6.27)(P<0.05).Before intervention,self-concept(17.46±4.44),self-care skills(25.22±4.20),self-care knowledge(22.35±4.74),and self-care responsibility(15.06±3.29)scores in the study group was similar to those in the control group(self-concept:16.89±5.53,self-care skills:24.59±4.46,self-care knowledge:21.80±3.61,and self-care responsibility:14.83±3.11)(P>0.05).After the intervention,self-concept(26.01±3.18),self-care skills(37.68±6.05),self-care knowledge(45.56±5.83),and self-care responsibility(22.01±3.77)scores in the study group were higher than those in the control group(self-concept:22.97±3.46,self-care skills:33.02±5.65,selfcare skills knowledge:36.81±5.54,and self-care responsibility:17.97±3.56 points)(P<0.05).The incidence of complications in the study group(4.65%)was lower than that in the control group(18.60%)(P<0.05).Nursing satisfaction in the study group(95.35%)was higher than that in the control group(81.40%)(P<0.05).CONCLUSION Nursing intervention based on a dynamic interaction model can improve postoperative cognitive function,daily living ability,self-care ability,quality of life,and patient satisfaction,while reducing the risk of complications.

Seismic response of tall building considering soil-pile-structure interaction

The seismic behavior of tall buildings can he greatly affected by non-linear soil-pile interaction during strong earthquakes.In this study a 20-storey building is examined as a typical structure supported on a pile foundation for different conditions:(1) rigid base,i.e.no deformation in the foundation:(2) linear soil-pile system;and (3) nonlinear soil-pile system. The effects of pile foundation displacements on the behavior of tall building are investigated,and compared with the behavior of buildings supported on shallow foundation.With a model of non-reflective boundary between the near field and far field, Novak's method of soil-pile interaction is improved.The computation method for vibration of pile foundations and DYNAN computer program are introduced comprehensively.A series of dynamic experiments have been done on full-scale piles, including single pile and group,linear vibration and nonlinear vibration,to verify the validity of boundary zone model.