Sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays

In this letter, a distributed protocol for sampled-data synchronization of coupled harmonic oscillators with controller failure and communication delays is proposed, and a brief procedure of convergence analysis for such algorithm over undirected connected graphs is provided. Furthermore, a simple yet generic criterion is also presented to guarantee synchronized oscillatory motions in coupled harmonic oscillators. Subsequently, the simulation results are worked out to demonstrate the efficiency and feasibility of the theoretical results.

Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp（4,R） Lie Algebra

Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency

The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.

Finite Element Harmonic Solution of the Coupled Rotor-bearing System

Fluid-solid interaction problems have been studied q uite extensively in the past years. Rotor-bearing system is a typical example. Fluid field is changed under the exciting of rotor vibration. On the same ti me, a net force caused by fluid pressure exerts on rotor, which will change roto r vibration. So, the fluid-solid coupled analysis method must be used. Traditionally, numerical difference method was used to solve fluid problems. The coupled fluid-solid equation could not be set up based on the method. It is no t until finite element method was used in fluid dynamics area then can the coupl ed dynamics be researched. Recently many experimental, analytical and numerical studies have been used in the area . But in these investigations, it is a ssumed that the solid vibration could not be influenced by fluid. In the other w ords, the force exerted on solid from fluid was neglected in the papers. So, the models built were some kinds of semi-coupled model only. In this paper, the Galerkin finite-element method, two-dimension vibration equ ation of rigid body and Navier-Stokes equations are used to build a full-coupl ed fluid-solid model in rotor-bearing system. Some assumptions are taken: 1) In fluid equation, the nonlinear terms are relatively small and neglected. 2) The gravity takes no effect on this system. 3) The bearing and the rotor are long. Flow and leakage along the axis is neglec ted. 4) The fluid is a kind of Newtonian incondensable viscous fluid. 5) The rotor is considered to be a rigid body. Using the model established, we calculated all the examples given by paper , results show the error are less than 7%. So the full-coupled model is built c orrectly. Examples are given in the end of the paper. After analyzing the examples, we get some conclusions: 1) In rotor-bearing system, while being taken under two conditions that whether coupled method is taken or not, difference of pressure and vibration amplitude could reach 76% and 120%. Therefore coupled method must be taken to investigate fluid-solid system. 1) Amplitude of fluid pressure can be more or less influenced by rotor unbalance , gap, eccentricity and other factors. 2) By using coupling method, results show that the amplitudes of vibration and p ressure are greater than ignoring the method. It should be paid more attention t o.

New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator.

Conversion of out-of-phase to in-phase order in coupled laser arrays with second harmonics

A novel method for converting an array of out-of-phase lasers into one of in-phase lasers that can be tightly focused is presented.The method exploits second-harmonic generation and can be adapted for different laser arrays geometries.Experimental and calculated results,presented for negatively coupled lasers formed in a square,honeycomb,and triangular geometries are in good agreement.