Synchronization of Chaotic Storage-Ring Free-Electron Laser by Bi-Directional Coupling Scheme with the Coupling Strength Varied Periodically

We analyse the chaotic dynamics of storage-ring free-electron lasers and report a bi-directional coupled scheme with the coupling strength varied periodically to synchronize two chaotic storage-ring free-electron lasers. The period is the same as the period of system＇s external modulation. ,The possibility of synchronization is proven according to the Lyapunov stability theory. The results of numerical simulation are obtained. Both the numerical simulation and theoretic analysis show that two storage-ring free-electron lasers can be controlled in the synchronization in a short time with this method.     

A Possible Generalized Form of Jarzynski Equality

The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.     

Stochastic period-doubling bifurcation in biharmonic driven Dulling system with random parameter

Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations.     

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment.Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla.Particularly,via preparing the state of the system to the highest excited state with hight fidelity,the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously.We explain these results using the definition of state fidelity.Furthermore,we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control.Therefore,our results may be of importance in the context of quantum information technologies.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Numerical Investigation for the Properties of Nonintegrable Quantum SYstems Eigenspace in the Line of Quantum—Classical Correspondence

The properties of the eigenspace of nonintegrable quantum systems are explored in detail in the light of the viewpoint of quantum-classical completely correspondence proposed recently by Xu et al.The changes of the topological structure in the state space of autonomous quantum system due to the nonlinear resonance are displayed numerically with the uncertainty measure of a special initial state ρα（λ） and the transformation matrix U(λ δλ-λ-δλ）,The statistical behavior of the subspace occupied by the state in eigenspace of quantum nonintegrable system is discussed carefully with the help of a special renormalization method.The results show that the randomness of effective Hamilonian matrix,the transition matrix and the nearest level spacings in this region can be described by random matrix theory.And the extent of agreement of our calculation with the prediction of GOE is in correspondence to the extent of the classical torus violation.     

Influence of Multi-Photon Process on Entanglement of Interacting System of the Qubit and Thermal Field

We study the system of a single qubit couples to a single mode thermal field according to a multi-photon Jaynes-Cummings-type interaction with phase decoherence. Both the time evolving entanglement and the stationary state entanglement are calculated by adopting the log-negativity as a measure. It is found that the multi-photonprocess can enhance the stationary state entanglement of this system and can enlarge the range of the parameter Δ/g and the mean photon number of initial thermal field in which the stationary state is distillable.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Study on random and coherence states using a family of CML models

A family of coupled map lattice (CML) models has been developed to simulate the interaction of convection, diffusion and dispersion in both weakly and strongly coupled cases. With variation of parameters, the models can simulate those systems of convection dominating, diffusion dominating, and dispersion dominating states. Not only coherent and turbulent properties as well as their interrelations, but also the transitional state between any modes with local coupling and global coupling are analysed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and thus can be conveniently used to analyse an initiative and driven coupled system. Results of numerical simulation also lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. Finally, the duality of wave and particle characters of turbulence is illustrated in the numerical simulation.     

Dynamics of entropic uncertainty for three types of three-level atomic systems under the random telegraph noise

We study the dynamics of the entropic uncertainty for three types of three-level atomic systems coupled to an environment modeled by random matrices. The results show that the entropic uncertainty in the Ξ-type atomic system is lower than that in the V-type atomic system which is exactly the same as that in the Λ-type atomic system. In addition, the effect of relative coupling strength on entropic uncertainty is opposite in Markov region and non-Markov region, and the influence of a common environment and independent environments in Markov region and non-Markov region is also opposite. One can reduce the entropic uncertainty by decreasing relative coupling strength or placing the system in two separate environments in the Markov case. In the non-Markov case, the entropic uncertainty can be reduced by increasing the relative coupling strength or by placing the system in a common environment.     

Coexisting Condensates of Weakly Interacting Bose Gas in a Harmonic Trap

We study particles in a vortex state driven to a core state with lower energy and zero angular momentum by the trap potential asymmetries. We find that at T=0 when the role of the thermal gas can be ignored, there will be coexisting condensates. We also calculate the fluctuation of the number difference and argue that in certa/n range of the parameters the state of the whole system is the macroscopic quantum serf-trapping in the Josephson tunnelling regime.     

The effects of a static magnetic field on the microwave absorption of hydrogen plasma in carbon nanotubes： a numerical study

We theoretically investigate the microwave absorption properties of hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes under an external static magnetic field in the frequency range 0.3 GHz to 30 GHz, using the Maxwell equations in conjunction with a general expression for the effective complex permittivity of magnetized plasma known as the Appleton-Hartree formula. The effects of the external static magnetic field intensity and the incident microwave propagation direction on the microwave absorption of hydrogen plasma in CNTs are studied in detail. The numerical results indicate that the microwave absorption properties of hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes can be obviously improved when the exter- nal static magnetic field is applied to the material. It is found that the specified frequency microwave can be strongly absorbed by the hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes over a wide range of incidence angles by adjusting the external magnetic field intensity and the parameters of the hydrogen plasma.     

Open-loop frequency response for a chaotic masking system

In this paper, a new numerical simulation approach is proposed for the study of open-loop frequency response of a chaotic masking system. Using Chua's circuit and the Lorenz system as illustrative examples, we have shown that one can employ chaos synchronization to separate the feedback network from a chaotic masking system, and then use numerical simulation to obtain the open-loop synchronization response, the phase response, and the amplitude response of a chaotic masking system. Based on the analysis of the frequency response, we have also proved that changing the amplitude of the exciting (input) signal within normal working domain does not influence the frequency response of the chaotic masking system. The new numerical simulation method developed in this paper can be extended to consider the open-loop frequency response of other systems described by differential or difference equations.     

Direct numerical simulation methods of hypersonic flat-plate boundary layer in thermally perfect gas

High-temperature effects alter the physical and transport properties of air such as vibrational excitation in a thermally perfect gas,and this factor should be considered in order to compute the flow field correctly.Herein,for the thermally perfect gas,a simple method of direct numerical simulation on flat-plat boundary layer is put forward,using the equivalent specific heat ratio instead of constant specific heat ratio in the N-S equations and flux splitting form of a calorically perfect gas.The results calculated by the new method are consistent with that by solving the N-S equations of a thermally perfect gas directly.The mean flow has the similarity,and consistent to the corresponding Blasius solution,which confirms that satisfactory results can be obtained basing on the Blasius solution as the mean flow directly in stability analysis.The amplitude growth curve of small disturbance is introduced at the inlet by using direct numerical simulation,which is consistent with that obtained by linear stability theory.It verified that the equation established and the simulation method is correct.     

Heat Conductivity of One-Dimensional Carbon Chain in an External Potential

The heat transport m a one-dimensional （ID） carbon nanowire （CNW） lying in an external potential with different amplitudes and periods is studied by the non-equilibrium molecular dynamics method. It is found that the thermal conductivity of CNW is always anomalous, increasing with the CNW length and obeying the power law k- N, in which a decreases with the increasing external potential amplitude. The thermal conductivity could be enhanced by the external potential with rather larger amplitudes, which means that an applied external potential could be an efficient tool to improve the heat conductivity of a real 1D material In addition, the effect of different periods of the external potential is studied, finding the external potential with an incommensurate period leads to the smaller a value.     

Scaling Behaviour and Memory in Heart Rate of Healthy Human

We investigate a set of complex heart rate time series from healthy human in different behaviour states with the detrended fluctuation analysis and diffusion entropy （DE） method. It is proposed that the scaling properties are influenced by behaviour states. The memory detected by DE exhibits an approximately same pattern after a detrending procedure. Both of them demonstrate the long-range strong correlations in heart rate. These findings may be helpful to understand the underlying dynamical evolution process in the heart rate control system, as well as to model the cardiac dynamic process.     

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Ф is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Ф changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the soiral turbulence.     

Effects of phase fluctuation in an open four-level inversionless lasing system

A steady analytical solution of an open four-level inversionless lasing system with a driving field having the phase fluctuation has been given, and the effects of the finite width due to the phase fluctuation on the gain, dispersion, and population difference have been analyzed by using the numerical simulation from the steady analytical solution. It is found that: with the linewidth increasing, the gain decreases and the absolute value of population difference between levels coupled by the probe field increases, but the variation of the linewidth cannot change the properties of the inversionless lasing and refractive index increase of the system; when the linewidth does not equal to zero, the system can still get a high refractive index with zero absorption, and these conclusions have very obvious difference from those obtained in other inversionless lasing systems.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.     

Unpredictability of Iteration Destination in an Integrate-and-Fire Circuit

Based on our previous study that discovered a new mechanism of the riddled-like basin appearance in piecewise continuous and noninvertible links of two conservative mappings, and the mechanism being the mixing of different attraction basins on a fat-fractal set, which was addressed as the forbidden region net [Phys. Rev. E 72 （2005） 025201（R）], we show numerically that the riddled-like attraction basins and the new mechanism appear in an integrate-and-fire circuit that can be described by piecewise continuous and noninvertible links of two dissipative mappings. This leads to the fact that vast increase of the precision of the initial condition results in practically no improvement in predictability of the iteration destination. Predictability is usually characterized by examining how error probability in the prediction, f（ε）, scales with the precision ε under the initial condition. Typically, f（ε） - ε^α with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, a should be zero, which is in good agreement with the numerical simulation results.