MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Oscillatory instability of Rayleigh-Marangoni-Bénard convection in two-layer liquid systems

The oscillatory behaviour of the Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) regarding two combinations of two-layer fluid systems has been investigated theoretically and numerically. For the two-layer system of Silicone oil (10cSt) over Fluorinert (FC70), both linear instability analysis and 2D numerical simulation show that the instability of the system depends strongly on the depth ratio Hr = H1/H2 of the two-layer liquid. The oscillatory regime at the onset of R-M-B convection enlarges with reducing Γ = Ra/Ma values. In the two-layer system of Silicone oil (2cSt) over water, it loses its stability and onsets to steady convection at first, then the steady convection bifurcates to oscillatory convection with increasing Rayleigh number Ra. This behaviour was found through numerical simulation above the onset of steady convection in the case of r = 2.9, ε=(Ra-Ruc)/Rac = 1.0, and Hr = 0.5. Our findings are different from the previous study of the Rayleigh-Benard instability and show the strong effects of the thermocapillary force at the interface on the time-dependent oscillations at or after the onset of convection. We propose a secondary oscillatory instability mechanism to explain the experimental observation of Degen et al. [Phys. Rev. E, 57 (1998), 6647-6659].

Thermovibrational Instability Of Rayleigh-Marangoni-Benard Convection In Two-Layer Fluid Systems

The thermovibrational instability of Rayleigh-Marangoni-Benard convection in a two-layer system under the high-frequency vibration has been investigated by linear instability analysis in the present paper. General equations for the description of the convective flow and within this framework, the generalized Boussinesq approximation are formulated. These equations are dealt with using the averaging method. The theoretical analysis results show that the high-frequency thermovibrations can change the Marangoni-Benard convection instabilities as well as the oscillatory gaps of the Rayleigh-Marangoni-Benard convection in two-layer liquid systems. It is found that vertical high-frequency vibrations can delay convective instability of this system, and damp the convective flow down. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

The evolution of cooperation in asymmetric systems

Explaining "Tragedy of the Commons" of evolution of cooperation remains one of the greatest problems for both biology and social science. Asymmetrical interaction, which is one of the most important characteristics of cooperative system, has not been sufficiently considered in the existing models of the evolution of cooperation. Considering the inequality in the number and payoff between the cooperative actors and recipients in cooperation systems, discriminative density-dependent interference competition will occur in limited dispersal systems. Our model and simulation show that the local but not the global stability of a cooperative interaction can be maintained if the utilization of common resource remains unsaturated, which can be achieved by density-dependent restraint or competition among the cooperative actors. More intense density dependent interference competition among the cooperative actors and the ready availability of the common resource, with a higher intrinsic contribution ratio of a cooperative actor to the recipient, will increase the probability of cooperation. The cooperation between the recipient and the cooperative actors can be transformed into conflict and, it oscillates chaotically with variations of the affecting factors under different environmental or ecological conditions. The higher initial relatedness (i.e. similar to kin or reciprocity relatedness), which is equivalent to intrinsic contribution ratio of a cooperative actor to the recipient, can be selected for by penalizing less cooperative or cheating actors but rewarding cooperative individuals in asymmetric systems. The initial relatedness is a pivot but not the aim of evolution of cooperation. This explains well the direct conflict observed in almost all cooperative systems.

Weak measurement of qubit oscillations with strong response detectors: Violation of the fundamental bound imposed on linear detectors

Qubit measurement by mesoscopic charge detectors has received great interest in the community of mesoscopic transport and solid-state quantum computation, and some controversial issues still remain unresolved. In this work, we revisit the continuous weak measurement of a solid-state qubit by single electron transistors (SETs) in nonlinear-response regime. For two SET models typically used in the literature, we find that the signal-to-noise ratio can violate the universal upper bound "4," which is imposed quantum mechanically on linear-response detectors. This different result can be understood by means of the cross correlation of the detector currents by viewing the two junctions of the single SET as two detectors. Possible limitation of the potential-scattering approach to this result is also discussed.

Processing network models of energy/environment systems

Processing networks are a variant of the standard linear programming network model which are especially useful for optimizing industrial energy/environment systems. Modelling advantages include an intuitive diagrammatic representation and the ability to incorporate all forms of energy and pollutants in a single integrated linear network model. Added advantages include increased speed of solution and algorithms supporting formulation. The paper explores their use in modelling the energy and pollution control systems in large industrial plants. The pollution control options in an ethylene production plant are analyzed as an example. PROFLOW, a computer tool for the formulation, analysis, and solution of processing network models, is introduced.

CHARACTERISTICS OF THE MAGNETIC DEPOPULATION OF SUBBANDS IN VERY NARROW SYSTEMS

We present a model for electrons confined in narrow conducting channels by a parabolic well under moderate to high magnetic fields which takes into account a cutoff in the filling of the subbands. Such a cutoff gives rise to energy-separated subbands and a two-dimensional (2D) like subband depopulation, resulting in a relation between sublevel index n and inverse magnetic field B-1 such that in the high-field regime it changes over to the well-known 2D form as expected, and in the moderate field regime it shows pronounced deviation from linearity. This agrees well with the experimental results. The linear region of the n-B-1 experimental plot is believed to arise from the two dimensionality of the system. Calculations show that no resolvable 1D sublevel exists in the 0.5-mu-m-wide wire at very small magnetic fields (including zero field), which agrees qualitatively with the experimental results found in other wires that the Hall resistance, R(H), approaches its classical value B/n(e)e in this region and R(H) = 0 at B = 0, where n(e) is the electron concentration. In this model the linear and nonlinear regions in the experimental n-B-1 plot are used to extract the characteristic frequency omega-0, and the effective 2D electron concentration N(e)2D, respectively.

Comparison of aggregation behaviors between branched and linear block polyethers: MesoDyn simulation study

The comparison of aggregation behaviors between the branched block polyether T1107 (polyether A) and linear polyether (EO)(60)(PO)(40)(EO)(60) (polyether B) in aqueous solution are investigated by the MesoDyn simulation. Polyether A forms micelles at lower concentration and has a smaller aggregation number than B. Both the polyethers show the time-dependent micellar growth behaviors. The spherical micelles appear and then change to rod-like micelles with time evolution in the 10 vol% solution of polyether A. The micellar cluster appears and changes to pseudo-spherical micelles with time evolution in the 20 vol% solution of polyether A. However, the spherical micelles appear and change to micellar cluster with time evolution in the 20 vol% polyether B solution. The shear can induce the micellar transition of both block polyethers. When the shear rate is 1x10(5) s(-1), the shear can induce the sphere-to-rod transition of both polyethers at the concentration of 10 and 20 vol%. When the shear rate is lower than 1x10(5) s(-1), the huge micelles and micellar clusters can be formed in the 10 and 20 vol% polyether A systems under the shear, while the huge micelles are formed and then disaggregated with the time evolution in the 20 vol% polyether B system.