THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY

This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method.

Suppression of Noises in Open-Loop-Closed-Loop Coupled Systems

Suppression of noises is studied for the open-loop-closed-loop （OPCL） coupling systems between the driver and response systems. In OPCL coupling systems, the error signal of noise is found to be suppressed and shows bounds. The error signal can be decreased exponentially by enlarging the absolute value of the eigenvalues＇ real part of the Hurwitz matrix. A method is provided to reduce the error signal sufficiently and achieve complete synchronization （US） effectively for the OPCL coupling systems under noises. Based on this method, three numerical examples are reported in this paper,

Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller

In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new nonautonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.

The Setting of Boundary Conditions for Boundary Value Problems of Hyperbolic-elliptic Coupled Systems

This paper is devoted to the study of the proper setting of the boundary conditions for the boundary value problems of the hyperbolic-elliptic coupled systems of first order. The wellposedness of the corresponding boundary value problems is also established. The Lopatinski conditions for the boundary value problems of the elliptic systems is then extended to the case for hyperbolic-elliptic coupled systems. The result in this paper can be applied to the Euler system in fluid dynamics, especially to give wellposed boundary value problems describing subsonic flow.

Statistical energy analysis of similarly coupled systems

Based on the principle of Statistical Energy Analysis (SEA) for non-conservatively coupled dynamical systems under non-correlative or correlative excitations, energy relationship between two similar SEA systems is established in the paper. The energy relationship is verified theoretically and experimentally from two similar SEA systems i.e., the structure of a coupled panel-beam and that of a coupled panel-sideframe, in the cases of conservative coupling and non-conservative coupling respectively. As an application of the method, relationship between noise power radiated from two similar cutting systems is studied. Results show that there are good agreements between the theory and the experiments, and the method is valuable to analysis of dyuamical problems associated with a complicated system from that with a simple one.

Principle of statistical energy analysis for non-conservatively coupled systems

Traditional Statistical Energy Analysis (SEA) theory can not deal with dynamic problems concerned with non-conservatively coupled systems. In this paper, based on the theory of power flow between them and energy distribution in non-conservatively coupled osillators, equations of power balance and those for calculation of each concerned power flow and other power items are derived to develop SEA theory for non-conscrvativcly coupled systems. Results show that conservative coupling is only a special case of non-conservative coupling situations, effect of coupling damping on power flow and energy distribution in non-conservatively coupled systems arc not negligible unless coupling damping is much smaller compared with internal one. As an application of the theory, energy problems of non-conservatively coupled plates are studied theoretically and experimentally.

The Coupled Operational Systems:A Linear Optimisation Review

The purpose of this review is to summarise the existing literature on the operational systems as to explain the current state of understanding on the coupled operational systems.The review only considers the linear optimisation of the operational systems.Traditionally,the operational systems are classified as decoupled,tightly coupled,and loosely coupled.Lately,the coupled operational systems were classified as systems of time-sensitive and time-insensitive operational cycle,systems employing one mix and different mixes of factors of production,and systems of single-linear,single-linear-fractional,and multi-linear objective.These new classifications extend the knowledge about the linear optimisation of the coupled operational systems and reveal new objective-improving models and new state-of-the-art methodologies never discussed before.Business areas affected by these extensions include product assembly lines,cooperative farming,gas/oil reservoir development,maintenance service throughout multiple facilities,construction via different locations,flights traffic control in aviation,game reserves,and tramp shipping in maritime cargo transport.

Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems

This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.

An iterative algorithm for analysis of coupled structural-acoustic systems subject to random excitations

This paper analyzes the random response of structural-acoustic coupled systems. Most existing works on coupled structural-acoustic analysis are limited to systems under deterministic excitations due to high computational cost required by a random response analysis. To reduce the computational burden involved in the coupled random analysis, an iterative procedure based on the Pseudo excitation method has been developed. It is found that this algorithm has an overwhelming advantage in computing efficiency over traditional methods, as demonstrated by some numerical examples given in this paper.

Vibrational resonance in globally coupled bistable systems under the noise background

Effects of system size,coupling strength,and noise on vibrational resonance(VR)of globally coupled bistable systems are investigated.The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values.The increase in system size induces and enhances the VR,while the increase in noise intensity suppresses and eventually eliminates the VR.Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions.This research has potential applications to the weak signal detection process in stochastic multi-body systems.

Tangent response in coupled dynamical systems

We construct new unidirectional coupling schemes for autonomous and nonautonomous drive systems, respectively. Each of these schemes makes the state of the response system asymptotically approach the first-order derivative of the state of the driver. From the point of view of geometry, the first-order derivative of the state of the driver can be viewed as a tangent vector of the trajectory of the driver, so the proposed schemes are named tangent response schemes. Numerical simulations of the Lorenz system and the forced Duffing oscillator verify the validity of the tangent response schemes. We further point out that the tangent response can be interpreted as a special kind of generalised synchronisation, thereby explaining why the response system can exhibit rich geometrical structures in its state space.

ON NONLINEAR COUPLED REACTION-DIFFUSION SYSTEMS

In this paper, the problem of initial boundary value for nonlinear coupled reaction-diffusion systems arising in biochemistry, engineering and combustion_theory is considered.

Periodic electron oscillation in coupled two-dimensional lattices

We study the time evolution of electron wavepacket in the coupled two-dimensional(2D)lattices with mirror symmetry,utilizing the tight-binding Hamiltonian framework.We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions.The frequency of this oscillation is determined by the strength of the interlayer hopping.Additionally,we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorderW,with the decay time being inversely proportional to the square ofW and the frequency change being proportional to the square of W,which is similar to the case in the coupled 1D disordered lattices.Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal,independent of lattice geometry,as demonstrated in AA-stacked bilayer and tri-layer graphene systems.Unlike the Bloch oscillation driven by electric fields,the periodic oscillation induced by interlayer coupling does not require the application of an electric field,has an ultrafast periodicity much shorter than the electron decoherence time in real materials,and can be tuned by adjusting the interlayer coupling.Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

In this paper, by applying Lagrange, multiplier method and high order Lagrange multiplier method [1], we systematically derive coupled potential energy principle.coupled complementary energy principle,and generalized coupled potential energy principles and generalized coupled complementary energy principles with two and three kinds of variables in photoelasticity.

A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.

Synchronizing Complex Networks by an Adaptive Adjustment Mechanism

We propose an adaptive adjustment mechanism for synchronizing complex networks, in particular for sociological or/and biological systems. We do not take it for granted that a dynamical system is put on isolated nodes and they are coupled with each other by one （or more） variable（s）, as employed in most previous models. As a replacement, we suppose that each node may have any finite number of possible states, and their evolutions with time are determined by their nearest-neighbouring （or even second-nearest-neighbouring, etc） nodes in an adaptive adjustment mechanism. It is found that synchronization can be achieved for almost all connected networks and that the scale-free property can evidently improve the synchronizing speed.

Periodic oscillation of quantum diffusion in coupled one-dimensional systems

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper(AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of underdamped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength.Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.

Boundary Control of Coupled Non-Constant Parameter Systems of Time Fractional PDEs with Different-Type Boundary Conditions

This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations(PDEs)with non-constant(space-dependent)coefficients and different-type boundary conditions(BCs).The BCs could be heterogeneous-type or mixed-type.Specifically,this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for mixed-type.The main contribution is to extend PDE backstepping to the boundary control problem of time fractional PDEs with space-dependent parameters and different-type BCs.With the backstepping transformation and the fractional Lyapunov method,the Mittag-Leffler stability of the closed-loop system is obtained.A numerical scheme is proposed to simulate the fractional case when kernel equations have not an explicit solution.

Dissolution Precipitation Wave Structure of Hydrothermal Ore Zoning

Hydrothermal ore zoning is a transport-reaction problem in which infiltration is the principal Prcness of transport and dissolution/Precipitation is the Principal process of chemical reactions.Neglecting diffusion and ion exchange/adsorption would not affect the basic attributes of hydrothermal ore zoning. Hydrothermal ore zoning belongs essentially to infiltration metasomatic zoning, it results from the formation and propagation of dissolution/precipitation waves through Permeable media. The authors apply the theory of coupled infiltration and dissolution/precipitation reactions in Physicochemical hydrodynamics to studying the structural characteristics of dissolution/precipitation waves, and apply furthermore the coherence principle in dynamic theory of multicomponent coupled systems to revealing the dynamic mechanisms of their formation. The results of investigation verify and develop . C. 's theory of infiltration metasomatic zoning,on the one hand, raising it from the qualitative, equilibrium thermodynamic basis to the quantitative dynamic level;on the other hand, and more importantly, applying theories of Physicochemical hydrodynamics and dynamics of multicomponent coupled systems to bringing to light the dynamic mechanisms of formation of the structure of hydrothermal ore zoning, and advancing a theory of hydrothermal ore zoning, putting forward new ideas on the nature of the problem of hydrothermal ore zoning, the essence of hydrothermal ore zoning and the structural characteristics and mechanisms of formation of hydrothermal ore zoning.

The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model

This work illustrates the application of the 1st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.