Particle Trajectory Integrator in Guiding Center Phase Space

A trajectory integrator is developed based on a particle＇s guiding center Hamiltonian. It is verified by a series of benchmarks, which are in good accordance with theoretical prediction. This integrator can be used as the guiding center trajectory integrator of a particle-in-cell simulation platform, such as the newly developed VirtEx. It can also be used as a stand-alone tool to investigate particle dynamics in a given background field.

The Classification to Stationary Process of Tidal Motion Observed at the Time of Kuroshio’s Meandering

The tide level displays information about the state of the sea current and the tidal motion. The tide level of the southern coast of Japan Island is affected strongly by Kuroshio Current flowing in the western part of North Pacific Ocean. When Kuroshio takes the straight path and flow along the Japan Islands, the tide level increases, and it is calculated from two tide level data observed at Kushimoto and Uragami in the southern part of Kii Peninsula. In contrast, the tide level decreases at the time when Kuroshio leaves from the Japan Islands. In this paper, the hourly tidal data are analyzed using the Autocorrelation Function (ACF) and the Mutual Information (MI) and the phase trajectories at first. We classify the results into 5 types of tidal motion. Each categorized type is investigated and characterized precisely using the mean tide level and the unit root test (ADF test) next. The frequency of the type having unstable tidal motion increases when the Kuroshio Current is non-meandering or in a transition state or the tide level is high, and the type shows a non-stationary process. On the other hand, when the Kuroshio Current meanders, the tidal motion tends to take a periodical and stable state and the motion is a stationary process. Though it is not frequent, we also discover a type of stationary and irregular tidal motion.

Study of highly excited vibrational dynamics of HCP integrable system with dynamic potential methods

Highly excited vibrational dynamics of phosphaethyne(HCP)integrable system are investigated based on its dynamic potentials.Taking into consideration the 2:1 Fermi resonance between H–C–P bending vibrational mode and C–P stretching vibrational mode,it is found that the effects of H–C stretching vibrational mode on vibrational dynamic features of the HCP integrable system are significant and regularly vary with Polyad numbers(P number).The geometrical profiles of the dynamic potentials and the corresponding fixed points are sensitive to the variation of H–C stretching vibrational strength when P numbers are small,but are not sensitive when P numbers become larger and the corresponding threshold values become lower.The phase space trajectories of different energy levels in a designated dynamic potential(P=28)were studied and the results indicated that the dynamic potentials govern the various dynamic environments in which the vibrational states lie.Furthermore,action integrals of the energy levels contained in dynamic potential(P=28)were quantitatively analyzed and elucidated.It was determined that the dynamic environments could be identified by the numerical values of the action integrals of trajectories of phase space,which is equivalent with dynamic potentials.

Averaging Analysis of Self-Excited Motion of a Quasi-Axisymmetrical Gyrostat

The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.

Modified Tire-Slip-Angle Model for Chaotic Vehicle Steering Motion

The 5-DOF vehicle model employs the classical tire-slip-angle model to elicit the stability characteristics in vehicle handling during chaotic motion.However,the energy is not conserved,and the simulation results do not match actual behavior in that the vehicle should stop having lost balance.We have analyzed the limitations of the classical tire-slip-angle equation,and developed another model,which can be applied to all conditions.To ensure the correct use of the Pacejka’s magic formula for vehicle dynamics,we discuss the differences in tire axis systems between the ISO and adapted SAE(Pacejka),and propose a transformation method relating the two different tire axis systems.Finally,simulations are described that are performed in accordance with the established 5-DOF vehicle system dynamics model.The simulation results show that all states returned to the stable region after the vehicle had lost balance.The process involved energy dissipation,and approaches the response actually experienced.The limitations of the classical tire-slip-angle model are fully displayed and the effectiveness of the proposed slip angle model is demonstrated in unsteady vehicle states.

Chaotic characteristics and attractor evolution of friction noise during friction process

Friction experiments are conducted on a ring-on-disk tribometer, and friction noise produced during the friction process is extracted by a microphone. The phase trajectory and chaotic parameters of friction noise are obtained by phase-space reconstruction, and its attractor evolution is analyzed. The results indicate that the friction noise is chaotic because the largest Lyapunov exponent is positive. The phase trajectory of the friction noise follows a "convergence-stability-divergence" pattern during the friction process. The friction noise attractor begins forming in the running-in process, and the correlation dimension D increases gradually. In the stable process, the attractor remains steady, and D is stable. In the last step of the process, the attractor gradually disappears, and D decreases. The friction noise attractor is a chaotic attractor. Knowledge of the dynamic evolution of this attractor can help identify wear state changes from the running-in process to the steady and increasing friction processes.

Effects of pressure oscillation on aerodynamic characteristics in an aero-engine combustor

The effects of pressure oscillation on aerodynamic characteristics in an aero-engine combustor are investigated. A combustor test rig is designed to simulate the pressure drop characteristics of a practical annular combustor. The pressure drop characteristics are firstly measured under atmosphere condition with non-reacting flow(or cold flow), and the air mass flow proportion of each component(dome/liner) are obtained;these properties are base lines for comparison with combustion state. The combustion tests are then carried out under conditions of inlet temperature 340–450 K, fuel air ratio 0.010–0.028. The stability map and the oscillation frequencies are obtained in the tests, the results show that pressure oscillation amplitude increases with the increase of fuel air ratio. Phase trajectory reconstruction is applied to classify the pressure oscillation motion;there are three motions captured in the tests including: ‘‘disk", ‘‘ring" and ‘‘cluster". The pressure drops across the dome under strong pressure oscillation are distinctly divergent from the cold flow, and the changes of pressure drops are mainly affected by pressure oscillation amplitude, but is less influenced by pressure oscillation motion nor oscillation frequencies. Based on the mass flow conservation, the reduction of effective flow area of combustor under strong pressure oscillation is demonstrated. Liner wall temperatures are analyzed through Multiple Linear Regression(MLR)method to estimate the reduction of the air mass flow proportion of the liner cooling under strong pressure oscillation. Finally, the air mass flow proportions of each component under strong pressure oscillation are estimated, the results show that the pressure oscillation motion also has influence on air mass flow proportion.

Application Analysis of Multiple Neurons Connected with Fast Inhibitory Synapses

Almost all living organisms exhibit autonomic oscillatory activities,which are primarily generated by the rhythmic activities of their neural systems.Several nonlinear oscillator models have been proposed to elucidate these neural behaviors and subsequently applied to the domain of robot control.However,the oscillation patterns generated by these models are often unpredictable and need to be obtained through parameter search.This study introduces a mathematical model that can be used to analyze multiple neurons connected through fast inhibitory synapses.The characteristic of this oscillator is that its stationary point is stable,but the location of the stationary point changes with the system state.Only through reasonable topology and threshold parameter selection can the oscillation be sustained.This study analyzed the conditions for stable oscillation in two-neuron networks and three-neuron networks,and obtained the basic rules of the phase relationship of the oscillator network established by this model.In addition,this study also introduces synchronization mechanisms into the model to enable it to be synchronized with the sensing pulse.Finally,this study used these theories to establish a robot single leg joint angle generation system.The experimental results showed that the simulated robot could achieve synchronization with human motion,and had better control effects compared to traditional oscillators.