A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Energy shift and subharmonics induced by nonlinearity in a quantum dot system

The presence of anticrossings induced by coupling between two states causes curvature in energy levels, yielding a nonlinearity in the quantum system. When the system is driven back and forth along the bending energy levels, subharmonic transitions and energy shifts can be observed, which would cause a significant influence as the system is applied to quantum computing. In this paper, we study a longitudinally driven singlet-triplet(ST) system in a double quantum dot(DQD)system, and illustrate the consequences of nonlinearity by driving the system close to the anticrossings. We provide a straightforward theory to quantitatively describe the energy shift and subharmonics caused by nonlinearity, and find good agreement between our theoretical result and the numerical simulation. Our results reveal the existence of nonlinearity in the vicinity of anticrossings and provide a direct way of analytically assessing its impact, which can be applied to other quantum systems without excessive labor.

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

Explicit solutions to some nonlinear physical models by a two-step ansatz

Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.

Can We Obtain a Fractional Lorenz System from a Physical Problem？

A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2（∑cr2 〈∑cr1） at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of ∑ is found to delay the onset of it.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

ANALYTICAL SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS

The following partial differential equations are studied: generalized fifth-order KdV equation,water wave equation, Kupershmidt equation, couples KdV equation. The analytical solutions to these problems via using various ansatzes by introducing a second-order ordinary differential equation are found out.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.

Structure Identification of Nonlinearly Coupled Complex Networks with Non-Delayed and Delayed Coupling

Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.

An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.

INVERSION OF MOISTURE PROFILES BY A NONLINEAR ITERATIVE PHYSICAL RETRIEVAL

The Advanced TIROS-N Operational Vertical Sounder (ATOVS) measurements are used to generate the atmospheric parameters,such as temperature and moisture profiles,under both clear and cloudy situations.This paper describes briefly the nonlinear iterative physical retrieval method.By using this retrieval scheme,an experiment has been carried out to retrieve the moisture profiles from ATOVS measurements on the NOAA-16 satellite for July of 2002.ATOVS profile retrieval results are evaluated by root mean square (RMS) differences with respect to RAdiosonde OBservation (RAOB) profiles.The accuracy of the retrieval is about 15%-23% for the relative humidity profile in this study.

Evolution of a Thermo Vacuum State in a Single-Mode Amplitude Dissipative Channel

We investigate how an initial thermo vacuum state, in the context of thermo field dynamics, evolves in a single-mode amplitude dissipative channel, and find that in this process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic.

Interest-Driven Model for Human Dynamics

Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin of such heavy tails, however, it cannot explain all the temporal statistics of human behavior especially for the daily entertainments. We propose an interest-driven model, which can reproduce the power-law distribution of interevent time. The exponent can be analytically obtained and is in good accordance with the simulations. This model well explains the observed relationship between activities and power-law exponents, as reported recently for web-based behavior and the instant message communications.

Tracking Desired Trajectory in a Vibro-Impact System Using Backstepping Design

Based on the backstepping design of smooth systems, we developed a new control law to achieve chaos control for a vibro-impact system. In our control strategy, a novel and effective controller is designed such that the output of the vibro-impact system can track any desired trajectory in its domain. The single-degree-of-freedom vibro-impact system is taken as an example to show this control procedure. Numerical simulations are provided to verify the effectiveness of the proposed method.

Robustness of Complex Networks under Attack and Repair

To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to theunderstanding of robustness of complex networks with reparability.

Control of Fractal Erosion of Safe Basins in a Holmes-Duffing System via Delayed Position Feedback

A linear delayed position feedback control is applied to control the erosion of safe basins in a Holmes-Duffing system. The conditions of fractal erosion of the safe basin of the controlled system on the basis that the range of time delay leading to good control is obtained by the Melnikov method. It is found that the increasing time delay can reduce the basin erosion under a weak and positive feedback g^in. Then the evolutions of safe basins with time delay are presented in detail by the fourth Runge-Kutta and Monte-Carlo methods, which shows that the safe basin of the controlled Holmes Dulling system can be expanded, and its fractal can be reduced by the increasing time delay. These results suggest that delayed position feedbacks can be used as a good approach to control the erosion of safe basins.

Analysis of High Codimensional Bifurcation and Chaos for the Quad Bundle Conductor＇s Galloping

A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.

Cluster Model for Wave-Like Motions of a 2D Vertically Vibrated Granular System

The fact that trapezoid clusters exist in 2D vertically vibrated granular systems leads us to construct a cluster model, in which wave-like motions are explained as the result of cluster-plate and cluster-cluster collisions. By analyzing the collision of one cluster with the plate in detail, we deduce a basic equation from velocity relationship, which could be separated into two correlative equations： one relates wave-like motion with exciting acceleration, and we call it the excitation condition; the other relates wavelength with exciting frequency, viz., the dispersion relation. The theoretical results are in agreement with the experimental ones, which supports the idea of the cluster model. Moreover, from the cluster model, we also predict a possibility of abnormal dispersion relation of a 213 granular system.

Effects of Slip on Unsteady Mixed Convective Flow and Heat Transfer Past a Stretching Surface

Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.

Stochastic Resonance in a Time-Delayed Mono-Stable System with Multiplicative and Additive Noise

The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.