Influence of the type of light polarization on photoinduced processes

We investigate the influence of the type of light polarization (linear or circular) on the efficiency of non-linear optical processes in photoanisotropic materials. A theoretical model of photoprocesses in materials in which optical non-linearity is related to absorbing centres with intrinsic linear anisotropy is constructed. Theoretical calculations show that the photostationary concentration of the photoproducts (and the mean values of the non-linear changes in optical constants) in these materials is higher if the exciting light is circularly polarized. Experimental results on non-linear processes in samples of fluorescein incorporated in orthoboric acid and in azodye/polymer layers are in good agreement with the theory. This revised version was published online in November 2006 with corrections to the Cover Date.     

具有非线性阻尼涨落的线性谐振子的随机共振

较之于线性噪声, 非线性噪声更广泛地存在于实际系统中, 但其研究远不能满足实际情况的需要. 针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声, 本文考虑了周期信号与之共同作用下的线性谐振子, 关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响. 利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式, 并分析了稳态响应振幅的共振行为, 且以数值仿真验证了理论分析的有效性. 研究发现: 系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系, 特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度; 而且, 非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为; 同时, 二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象; 而在这些现象和性质中, 非线性噪声项的非线性性质对共振行为起着关键的作用. 显然, 以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声, 可以有助于提高微弱周期信号检测的灵敏度和实现对周期信号的频率估计.     

Identification of the dynamic characteristics of a structure with coulomb friction

The effect of coulomb friction on the Kennedy and Pancu vector plot of a single degree-of-freedom system is analyzed by using the method of harmonic balance. It is shown that the resulting diagram no longer conforms to a locus of a circle in the resonant region, which restricts the usual methods of analysis. A technique, based upon the in-phase and quadrature power dissipated when exciting a normal mode, is presented which allows the magnitude of the non-linear friction force and the hysteretic damping constant to be evaluated. The technique is also applied to systems having several degrees-of-freedom and it shows that it is possible to identify the characteristics of a single non-linear coulomb device situated within a structure, but in the case of more than one device, the technique has some restrictions. The theoretical results are compared with experimental data from a structure containing a non-linear coulomb device.     

Experimental and Numerical Study of Structural Identification Using Non-Linear Resonant Decay Method

One of the practical approaches in identifying structures is the non-linear resonant decay method which identifies a non-linear dynamic system utilizing a model based on linear modal space containing the underlying linear system and a small number of extra terms that exhibit the non-linear effects. In this paper, the method is illustrated in a simulated system and an experimental structure. The main objective of the non-linear resonant decay method is to identify the non-linear dynamic systems based on the use of a multi-shaker excitation using appropriated excitation which is obtained from the force appropriation approach. The experimental application of the method is indicated to provide suitable estimates of modal parameters for the identification of non-linear models of structures.     

Seismic response of bridge piers on elasto-plastic Winkler foundation allowed to uplift

When the bridge piers with shallow foundation are subject to intensive earthquake excitations, uplift of foundations will occur and the foundation soil will partly become plastic. It is very difficult to use an accurate method to simulate the uplifting and yielding of supporting soil. An improved Winkler foundation model, which could be used to consider the uplift and yield, was employed in the analysis. The 1940 El Centro earthquake record is inputted to a rigid pier with shallow foundation so that the non-linear history response is obtained. From the non-linear analysis, it is concluded that the non-linear effect is very remarkable when uplifting and yielding of supporting soil are considered. Compared with the linear analysis, the stiffness of bridge pier-soil system degrades in each cycle after considering uplifting and yielding. It is shown that the non-linear analysis can get larger rotational angles and smaller bending moments compared with the linear analysis.     

Dynamical behaviour of non-linear quantum ion acoustic wave in weakly magnetized electron–positron–ion plasma

In order to investigate the propagation characteristics of linear and non-linear ion acoustic waves (IAWs) in electron–positron–ion quantum plasma in the presence of external weak magnetic field, we have used a quantum hydrodynamic model, and degenerate statistics for the electrons and positrons are taken into account. It is found that the linear dispersion relation of the IAW was modified by the externally applied magnetic field. By using the reductive perturbation technique, a gyration-modified Korteweg-de Vries equation is derived for finite amplitude non-linear IAWs. Time-dependent numerical simulation shows the formation of an oscillating tail in front of the ion acoustic solitons in the presence of a weak magnetic field. It is also seen that the amplitude and width of solitons and oscillating tails are affected by the relevant plasma parameters such as quantum diffraction, positron concentration, and magnetic field. We have performed our analysis by extending it to account for approximate soliton solution by asymptotic perturbation technique and non-linear analysis via a dynamical system approach. The analytical results show the distortion of the shape of the localized soliton with time, and the non-linear analysis confirms the generation of oscillating tails.     

Dynamics of linear discrete systems connected to local, essentially non-linear attachments

The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.     

DYNAMIC MODELLING AND VIBRATION ANALYSIS OF A FLEXIBLE CABLE-STAYED BEAM STRUCTURE

In this paper, the non-linear vibration of a cable-stayed beam with time-varying length and tension in the cable is investigated. A set of non-linear, time-varying differential equations describing this coupling system is derived by Hamilton's principle and the finite element method. According to the results of numerical simulation, the tension of the cable is related to the cable length, which in turn is a function of the longitudinal and transverse displacements of the cable. Furthermore, it is shown that the tension and length of the cable can be considerably different by using linear and non-linear models.     

Multi-photon fluorescence microscopy--the response of plant cells to high intensity illumination

Multi-photon fluorescence microscopy has been cited for its advantage in increased depth penetration due to low linear absorption and scattering coefficient of biological specimen in the near infrared (NIR) range. Because of the need of high peak power for efficiently exciting two-photon fluorescence, the relationship between cell damage and peak power has become an interesting and much debated topic in the applications of multi-photon fluorescence microscopy. It is conceivable that at high illumination intensity, non-linear photochemical processes have impacts on cell physiology and viability in ways much different from low illumination in the linear domain. In this article, we discuss some of the issues in two-photon fluorescence microscopy, including the degree of transparency of the specimen, a comparison of single- and two-photon excited fluorescence spectra, and the cell damage under high intensity illumination, using plant cells as a model.     

A theoretical study of the effect of an inhomogeneous medium upon a transmitter which exploits the non-linear properties of acoustic propagation

A theoretical study is made of the effect of a random medium upon the difference frequency wave produced by non-linear interaction. The difference-frequency mean square fluctuation level is shown to depend upon a series of coherence functions. An application of the theory to a simple but reasonably practical model establishes that the non-linear system in a random medium behaves virtually identically to a linear system operating in the same environment and at the same frequency in a number of practical cases. A simple method of experimentally verifying this result is suggested.     

Propagation of Chirped Non-Linear Pulses in a Lossy Highly Birefringent Single-Mode Optical Fibre

A new model of the non-linear propagation of optical solitons with initial linear frequency chirp through lossy highly birefringent fibres, allowing the improvement of the practical results concerning the distortionless signal transmission in ultra-high-speed communications, is presented within the framework of a system of coupled non-linear Schrödinger (CNLS) equations. This model demonstrates the existence of bound chirped solitons in a lossy single-mode highly briefringent fibre.     

LIMIT CYCLE FLUTTER OF AIRFOILS IN STEADY AND UNSTEADY FLOWS

The limit cycle flutter of a two-dimensional wing with non-linear pitching stiffness is investigated. For modelling the aerodynamic forces of the wing steady linear and non-linear models as well as an unsteady model were used. The flutter speed was calculated using the harmonic balance method and by predicting Hopf bifurcation. Analytical solutions based on the centre manifold theory and normal forms were obtained as were results given by the harmonic balance method. The analytical solutions were compared with those obtained by numerical integration. The results show that the harmonic balance method can forecast flutter speed with a good accuracy while analytical solutions based on centre manifold theorem are accurate only in a small neighbourhood of the bifurcation point. The oscillation of the airfoil after flutter for two different models, linear and non-linear pitching stiffness were compared with each other and the flutter speeds for two linear steady and an unsteady aerodynamic model calculated. The obtained results show that flutter analysis based on the linear steady model is conservative only for the ratios of plunge frequency to pitch frequency lower than 1.     

Some New Features of Linear Theory for Describing Non-linear Diffusion

The non-linear flux equation, the non-linear Fokker-Planck equation (or Smoluchowski equation), and the non-linear Langiven equation are the basicequations for describing particle diffusion in non-ideal system subjected totime-dependent external fields. Nevertheless, the exact solution of thoseequations is still a challenge because of their inherent complexity of thenon-linear mathematics. Li et al. found that, based on the defined apparentvariables, the non-linear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or local equilibrium assumption. In this paper, some new features of the theory were found: (i) The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; (ii) The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planck equation, can be derived more consistently from the microscopic molecular statistical theory; (iii) In the theory, thenon-linear Langiven equation also bears a linear form; (iv) For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor.     

Equivalent linear models for non-linear non-autonomous systems

Equivalence between a class of non-linear non-autonomous systems of second order and a linear model of lower order is established through a differential transformation relation. It is shown that this equivalence can be established only under a certain constraint on the non-linear functional parameters of the given system. The equivalence automatically leads to the first integral which then can be analyzed further to obtain the response of the system. The feasibility of obtaining closed form solutions through such analysis is illustrated by considering certain sub-classes of systems. Further, the practical value of the technique is demonstrated through an example.     

Transient response of a hydraulic engine mount

Linear and non-linear transient responses of a typical hydraulic engine mount are analytically and experimentally studied in this paper. First, a lumped parameter linear model is used to approximate the typical step response and to suggest parameters that must be experimentally determined. Various configurations as related to inertia track and decoupler are analyzed. Two bench experiments are constructed for the identification of non-linear compliances and resistances. One of the main non-linear characteristics, however, comes from the decoupler mechanism. To accurately predict the time events of the decoupler opening and closing, an equivalent viscous damper model is employed along with a multi-staged switching mechanism. Additionally, non-linear behavior arising due to the vacuum formation in the top chamber is studied by defining a bi-linear asymmetric stiffness curve. New transient experiments are conducted on an elastomer test system, and measured transmitted force and top chamber pressure signals are analyzed. Results of the proposed simulation model match well with measured responses when step up, step down and triangular waveforms are applied. Areas for future research are identified.     

Limit cycle oscillation of missile control fin with structural non-linearity

Non-linear aeroelastic characteristics of a deployable missile control fin with structural non-linearity are investigated. A deployable missile control fin is modelled as a two-dimensional typical section model. Doublet-point method is used for the calculation of supersonic unsteady aerodynamic forces, and aerodynamic forces are approximated by using the minimum-state approximation. For non-linear flutter analysis structural non-linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and non-linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the non-linear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary. The non-linear flutter characteristics and the non-linear aeroelastic responses are investigated.     

OPTIMAL VIBRATION ESTIMATION OF A NON-LINEAR FLEXIBLE BEAM MOUNTED ON A ROTATING COMPLIANT HUB

To eliminate the need for sensor placement on rotating flexible beams such as turbine blades, helicopter rotors and like applications, a new approach has been developed based on the linear quadratic estimator (LQE) technique for estimating the vibration of any point on the span of a rotating flexible beam mounted on a compliant hub (plant) in the presence of process and measurements noise. A non-linear model of the plant is utilized in this study to mimic the actual plant behavior. The corresponding plant dynamics of the LQE are in the form of a reduced order linear model constructed from the eigenvalues and eigenfuctions of a finite element dynamic model of the plant formulated in the state space. A virtual hub deflection (that mimics the actual measurement of the vertical hub deflection needed by the estimation process) is generated by the non-linear model of the plant. The LQE reconstructs the states of the plant, including transverse deflection of the beam at any point, from the measurements of the vertical deflection of the hub, assuming that it is the most accessible state for measurement. Estimated beam tip deflection obtained by the proposed technique is then compared to the tip deflection generated by the non-linear model and the results show good agreement.     

Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force

We have proposed a mechanism of interaction between two non-linear dissipative oscillators, leading to exact and robust anti-phase and in-phase synchronization. The system we have analyzed is a model for the Huygens’s two pendulum clocks system, as well as a model for synchronization mediated by an elastic media. Here, we extend these results to arrays, finite or infinite, of conservative pendula coupled by linear elastic forces. We show that, for two interacting pendula, this mechanism leads always to synchronized anti-phase small amplitude oscillations, and it is robust upon variation of the parameters. For three or more interacting pendula, this mechanism leads always to ergodic non-synchronized oscillations. In the continuum limit, the pattern of synchronization is described by a quasi-periodic longitudinal wave.     

A CFD assisted control system design with applications to NO x control in a FGR furnace

In this paper, a novel technique to design control systems for industrial processes with non-linear distributed parameters is proposed. The technique utilizes computational fluid dynamics (CFD) simulation to extract the most essential characteristics from the non-linear industrial process, and then represent them as a set of linear dynamic models around a specific operating point. Based on the linear dynamic representation, a closed-loop feedback linear control system can be designed to maintain the desired performance for the system around the chosen operating point. To illustrate such a design process, an industrial reheating furnace with flue gas recirculation (FGR) is selected herein. The method involves the numerical solution of the partial differential equations describing the fluid flow, heat transfer and combustion process in the furnace. The resulting dynamic relations between the furnace inputs and outputs can then be represented in terms of a multi-input and multi-output transfer function matrix. The objective of the control system is then to maintain the optimally selected furnace operating conditions and compensate for any deviations caused by disturbances to minimize the nitric oxides (NO _x ) emission through feedback mechanisms. The performance of the closed-loop controlled furnace is evaluated not only in the linear domain, but also with the detailed full-scale non-linear CFD model. The results have shown that the proposed method is viable and the designed control system can indeed minimize the deviation of the furnace from the desired operating conditions and hence to prevent any excessive NO _x formation in the combustion process.     

Structure of phenomenological lagrangians for broken supersymmetry

We consider the explicit connection between linear representations of supersymmetry and the non-linear realizations associated with the generic effective lagrangians of the Volkov-Akulov type. We specify and illustrate a systematic approach for deriving the appropriate phenomenological lagrangian by transforming a pedagogical linear model, in which supersymmetry is broken at the tree level, into its corresponding non-linear lagrangian, in close analogy to the linear σ model of pion dynamics. We discuss the significance and some properties of such phenomenological lagrangians.