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1.
This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space.The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided.The conformal factor expression is deduced from conformal invariance and Lie symmetry.The relationship between the conformal invariance and the Lie symmetry is discussed,and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced.The conserved quantities of the system are given.An example is given to illustrate the application of the result.  相似文献   

2.
彭俊  邬云文  李小娟 《中国物理 B》2012,21(6):60302-060302
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.  相似文献   

3.
武相军  卢宏涛 《中国物理 B》2010,19(7):70511-070511
Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper.Based on the stability theory of the fractional-order system,the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods.The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks.Neither a symmetric nor irreducible coupling configuration matrix is required.In addition,no constraint is imposed on the inner-coupling matrix.Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme.Numeric evidence shows that both the feedback strength k and the fractional order α can be chosen appropriately to adjust the synchronization effect effectively.  相似文献   

4.
李凡  王春妮  马军 《中国物理 B》2013,(10):146-153
Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.  相似文献   

5.
邓雅瀚  莫中凯  陆宏谦 《中国物理 B》2022,31(2):20503-020503
We investigate the dynamic event-triggered state estimation for uncertain complex networks with hybrid delays suffering from both deception attacks and denial-of-service attacks.Firstly,the effects of time-varying delays and finitedistributed delays are considered during data transmission between nodes.Secondly,a dynamic event-triggered scheme(ETS)is introduced to reduce the frequency of data transmission between sensors and estimators.Thirdly,by considering the discussed plant,dynamic ETS,state estimator,and hybrid attacks into a unified framework,this framework is transferred into a novel dynamical model.Furthermore,with the help of Lyapunov stability theory and linear matrix inequality techniques,sufficient condition to ensure that the system is exponentially stable and satisfies H∞performance constraints is obtained,and the design algorithm for estimator gains is given.Finally,two numerical examples verify the effectiveness of the proposed method.  相似文献   

6.
We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths(IHBs) or two common heat baths(CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steadystate with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation(RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime,the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures.We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong(weak) coupling regime, the heat current increases(decreases) with coupling strength increasing when the temperature of one bath is lower(higher) than the other, and the energy detuning leads to a positive(negative) effect when the temperature is low(high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.  相似文献   

7.
刘兆冰  张化光  孙秋野 《中国物理 B》2010,19(9):90506-090506
This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.  相似文献   

8.
A time domain finite volume method(TDFVM)based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structural-acoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structural-acoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structural-acoustic coupling problems in the heterogeneous fluid.  相似文献   

9.
夏丽莉  蔡建乐 《中国物理 B》2010,19(4):40302-040302
Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied.The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided.The conformal factor expression is deduced from conformal invariance and Lie symmetry.The relationship between the conformal invariance and the Lie symmetry is discussed,and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal oneparameter transformation group is deduced.The conserved quantities of the system are given.An example is given to illustrate the application of the result.  相似文献   

10.
The influences of σ* and Φ mesons,temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star(PNS) are examined in the framework of relativistic mean field theory for the baryon octet {n,p,Λ,Σ+,Σ0,Σ+,Ξ-,Ξ0} system.It is found that,compared with that without considering σ* and Φ mesons,the moment of inertia decreases.It is also found that the higher the temperature,the larger the incompressibility and symmetry energy coeficient,and the larger the moment of inertia of a PNS.The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ* and Φ mesons.  相似文献   

11.
ABSTRACT

This study investigated the effects of coupled thermo-hydro- mechanical dynamics on an isotropic, uniform, fully saturated, and poroelastic half-space subgrade whose surface is subjected to either mechanical force or thermal load. In this paper, our formulation is deduced in the context of two theories of generalized thermoelasticity: the Lord-Shulman theory and the Green-Lindsay theory. We then deduce the general relationships among non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution using Normal Mode Analysis (NMA) and depict them graphically. NMA is a method using weighted residuals to derive analytical solutions and can thus solve partial differential equations more quickly compared to other methods. This study continues our work of applying NMA to derive theoretical results in the multi-field coupling of soil. Following the analysis, the theoretical results are illustrated with a numerical example and a Maple program is developed. Furthermore, the differences between the coupled thermo-hydro-mechanical dynamic model (THMD) and the thermo-elastic dynamic model (TED) are presented. This proposed derivation method can be widely applied in the geotechnical engineering field, especially with regard to the mechanical and thermal behaviors of commercial buildings, high-speed railways, and highway energy foundations.  相似文献   

12.
The thermally induced vibrations of simply supported circular plates are investigated analytically. The solution is composed of two parts; the first is obtained by neglecting the inertia term and the second represents the vibrating component which oscillates about the first, due to the effect of the inertia. One of the reasons for separating the solution in two parts is to obtain the complete solution expediently. But when this is represented in non-dimensional form, the quasi-static part has the particular desirable feature that it is independent of the strength of the thermal shock and thus will give an index for the displacement due to the temperature moment if (and only if) the inertia force has a small effect. The basic equation is governed by only one non-dimensional parameter B which contains the density, the thermal diffusivity of the material and the radius of the plate in its numerator, and the flexural rigidity and thickness of the plate in its denominator, all to various powers. B represents the strength of the thermal shock. As B increases the non-dimensional amplitude of the vibration becomes large and the natural frequency decreases.  相似文献   

13.
This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novel synchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method.  相似文献   

14.
The dynamic stability of a spinning unconstrained beam subjected to a pulsating follower forceP0 +P1cos Ωt is analyzed. A concentrated mass is located at an arbitrary location on the beam, and the stability of the beam is studied with the mass at various locations. The beam is analyzed using the Timoshenko-type shear deformation theory with the rotary inertia. Hamilton's principle is used to derive the equations of motion, and the spinning speed of the beam with various non-dimensional parameters subjected to a pulsating follower force is investigated. The finite element method is applied to analyze the spinning beam model, and the method of multiple scales is used to investigate the dynamic stability characteristics. A pulsating follower force is applied, and then the stability regions are changed with the transitions of the stability area in many regions. The results show that the concentrated mass increases the dynamic stability of the spinning unconstrained beam subjected to a thrust. As the spinning speed of the beam is increased, the instability regions are reduced, but various slight instability regions are additionally developed.  相似文献   

15.
We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.  相似文献   

16.
In order for an electromagnetic transducer to operate well as either a mechanical shunt damper or as a vibration energy harvester, it must have good electromechanical coupling. A simple two-port analysis is used to derive a non-dimensional measure of electromechanical coupling, which must be large compared with unity for efficient operation in both of these applications. The two-port parameters for an inertial electromagnetic transducer are derived, from which this non-dimensional coupling parameter can be evaluated. The largest value that this parameter takes is approximately equal to the square of the magnetic flux density times the length of wire in the field, divided by the mechanical damping times the electrical resistance. This parameter is found to be only of the order of one for voice coil devices that weigh approximately 1 kg, and so such devices are generally not efficient, within the definition used here, in either of these applications. The non-dimensional coupling parameter is found to scale in approximate proportion to the device's characteristic length, however, and so although miniaturised devices are less efficient, greater efficiency can be obtained with large devices, such as those used to control civil engineering structures.  相似文献   

17.
A model which enables dynamic analysis of flexibly coupled misaligned shafts is presented. The model is setup to account for both angular and parallel misalignment in the presence of mass unbalance and incorporates a coupling having angular, torsional and axial flexibility. Among the important features is the ability to simulate both nonlinear bearing stiffness and coupling angular-stiffness anisotropy. The equations of motion are derived for the linear system, extended to include nonlinear bearing effects and subsequently transformed into non-dimensional form for general application. A series of numerical analyses are performed and the influence of important system parameters assessed thereby providing insight to the resulting static and dynamic forces and motions. Angular and parallel misalignments are shown to produce fundamentally different system response. It is found that the static preload induced by both types of misalignment can play a key role in producing complex vibration resulting from it's interaction with rotating-element anisotropy and bearing nonlinear properties. Bearing static forces are altered and rotating elements are subjected to alternating forces which could affect fatigue life. Bearing forces can be further modified by the application of transmitted torque. The potential for great variability in system response is shown to exist due to the participation of numerous influential variables.  相似文献   

18.
The mammalian visual cortex maps retinal position (retinotopy) and orientation preference (OP) across its surface. Simultaneous measurements in vivo suggest that positive correlation exists between the location of dislocations in these two maps, contradicting the predictions of classical dimension reduction models. Model symmetries exert a significant influence on pattern development. However, classical models for cortical map formation have inappropriate symmetry properties. By applying equivariant bifurcation theory we derive symmetry induced, model independent coupling of the OP and retinotopic maps and show that this coupling replicates observations.  相似文献   

19.
A three-degrees of freedom semi-definite torsional system representing an automotive driveline is studied in presence of a torque converter clutch that manifests itself as a dry friction path. An analytical procedure based on the linear system theory is proposed first to establish the stick-to-slip boundaries. Smoothened and discontinuous Coulomb friction formulations are then applied to the nonlinear system, and the differential governing equations are numerically solved given harmonic torque excitation and a mean load. Time domain histories illustrating dry friction-induced stick–slip motions are predicted for different saturation torques and system parameters. Approximate analytical solutions based on distinct states are also developed and successfully compared with numerical studies. Analysis shows that the conditioning factor associated with the smoothened friction model (hyperbolic tangent) must be carefully selected. Then nonlinear frequency responses are constructed from cyclic time histories and the stick–slip boundaries predictions (as yielded by the linear system theory) are confirmed. In particular, the effect of secondary inertia is analytically and numerically investigated. Results show that the secondary inertia has a significant influence on the dynamic response. A quasi-discontinuous oscillation is found with the conventional bi-linear friction model in which the secondary inertia is ignored. Finally, our methods are successfully compared with two benchmark analytical and experimental studies, as available in the literature on two-degrees of freedom translational systems.  相似文献   

20.
Involving the intrinsic power transmission torque/speed coupling characteristics of prime-movers, a rotating elastic connection disk subjected to periodically fluctuating transmitted torque and rotational speed generated by the fluctuation of external loads is investigated. Using Galerkin's method, the rotating elastic connection disk is modeled as a parametrically excited gyroscopic system. The effects of the torque/speed coupling, transmitted torque fluctuation amplitude and frequency, and constant parts of the transmitted torque and the rotational speed on the system dynamic stability are explored for the disk modes possessing different nodal diameters. The rotational speed, transmitted torque and their fluctuations can all result in system instability of the elastic connection disk. The instability can be suppressed or avoided by operating at small amplitude and low frequency of the transmitted torque fluctuation, and by operating in the weakly coupled torque/speed regime of the prime-movers. Low rotational speed avoids the instability in the case of a small transmitted torque, but medium rotational speed operation is valuable to suppress the instability induced by a large transmitted torque and its fluctuation. Instability parameter regions for the positive and negative torque/speed coupling coefficient are roughly similar in shape, but there are some differences in the value of the instability coefficient.  相似文献   

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