PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL

The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques,but also discusses prediction techniques of chaotic time series and its applications based on chaotic data noise reduction.In the paper,we first decompose the phase space of chaotic time series to range space and null noise space.Secondly we restructure original chaotic time series in range space.Lastly on the basis of the above,we establish order of the nonlinear model and make use of the nonlinear model to predict some research.The result indicates that the nonlinear model has very strong ability of approximation function,and Chaos predict method has certain tutorial significance to the practical problems.     

The Mechanical Properties of the Slurry and the Resistance Force of a Sphere Moving With Uniform Velocity in the Slurry

It is commonly considered that the mechanical properties of the slurryare different from that of ordinary Newtonian fluid,and can be describedby that of Bingham fluid.Hence its shearing stress should be described bythe formula of the shearing stress of Bingham fluid.But the author holdsthe contrary opinion and firmly believes that the slurry is a highly viscousfluid with very long relaxation time such as those of asphalt,glass,etc.In this article,we have discussed the mechanical properties of the slurryand the reslstance of a sphere moving with uniform veloclty in the slurry.In the process of discussion.we use Stokes solution of the vlscous fluidpassing around a sphere.When the sphere is in equilibrium under theaction of gravitational force,the force of buoyancy and the resistance,we get the velocity of sedimentation.When the velocity of sedimentationis equal to zero,we get the relation between the yield stress of Binghamfluid and the diameter of the particles which will not sink.The theoreticalresults     

Global analysis of Ivlev＇s type predator-prey dynamic systems

Consider a class of Ivlev＇s type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.     

Effects of relaxation time on start-up time for starting flow of Maxwell fluid in a pipe

Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.     

Electric potential and energy band in ZnO nanofiber tuned by local mechanical loading

Recent success in strain engineering has triggered tremendous interest in its study and potential applications in nanodevice design. In this paper, we establish a coupled piezoelectric/semiconducting model for a wurtzite structure ZnO nanofiber under the local mechanical loading. The energy band structure tuned by the local mechanical loading and local length is calculated via an eight-band k·p method, which includes the coupling of valance and conduction bands. Poisson's effect on the distribution of electric potential inversely depends on the local mechanical loading. Numerical results reveal that both the applied local mechanical loading and the local length exhibit obvious tuning effects on the electric potential and energy band. The band gap at band edges varies linearly with the applied loading. Changing the local length shifts the energy band which is far away from the band edges. This study will be useful in the electronic and optical enhancement of semiconductor devices.     

Instantaneous spectrum estimation of earthquake ground motions based on unscented Kalman filter method

Representing earthquake ground motion as time varying ARMA model,the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model.In this paper,unscented Kalman filter is applied to es- timate the time varying coefficients.The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman fil- ter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter,and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions nd to identify the systems with nonlinearity or abruptness.Moreover,the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former studies has great effect on the estima- tion precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.     

Adaptive thermo-fluid moving boundary computations for interfacial dynamics

In this study,we present adaptive moving boundary computation technique with parallel implementation on a distributed memory multi-processor system for large scale thermo-fluid and interfacial flow computations.The solver utilizes Eulerian-Lagrangian method to track moving(Lagrangian) interfaces explicitly on the stationary(Eulerian) Cartesian grid where the flow fields are computed.We address the domain decomposition strategies of Eulerian-Lagrangian method by illustrating its intricate complexity of the computation involved on two different spaces interactively and consequently,and then propose a trade-off approach aiming for parallel scalability.Spatial domain decomposition is adopted for both Eulerian and Lagrangian domain due to easy load balancing and data locality for minimum communication between processors.In addition,parallel cell-based unstructured adaptive mesh refinement(AMR) technique is implemented for the flexible local refinement and even-distributed computational workload among processors.Selected cases are presented to highlight the computational capabilities,including Faraday type interfacial waves with capillary and gravitational forcing,flows around varied geometric configurations and induced by boundary conditions and/or body forces,and thermo-fluid dynamics with phase change.With the aid of the present techniques,large scale challenging moving boundary problems can be effectively addressed.     

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell–Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.     

Nonlocal thermo-elastic constitutive relation of fibre-reinforced composites

The effective properties of composite materials have been predicted by various micromechanical schemes.For composite materials of constituents which are described by the classical governing equations of the local form,the conventional micromechanical schemes usually give effective properties of the local form.However,it is recognized that under general loading conditions,spatiotemporal nonlocal constitutive equations may better depict the macroscopic behavior of these materials.In this paper,we derive the thermo-elastic dynamic effective governing equations of a fibre-reinforced composite in a coupled spatiotemporal integral form.These coupled equations reduce to the spatial nonlocal peridynamic formulation when the microstructural inertial effects are neglected.For static deformation and steady-state heat conduction,we show that the integral formulation is superior at capturing the variations of the average displacement and temperature in regions of high gradients than the conventional micromechanical schemes.The approach can be applied to analogous multi-field coupled problems of composites.     

A direct proof of uniqueness of square-root of a positive semi-definite tensor

Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.     

Investigation into improving the efficiency and accuracy of CFD/DEM simulations

The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.     

Second-order effect of an elastic circular shaft during torsion

In this paper we deal with the second-order effect of an elastic circular shaft duringtorsion.The analysis is based on the method of co-moving coordinates and the strain-rotation decomposition theorem in continuum mechanics.By using asymptotic expansionmethods,we comfirm that the effect of axial elongation and distortion of plane cross-section exists in an elastic circular shaft during large torsion and give the expressions ofthe axial force and the torque.     

Multi-resonator coupled metamaterials for broadband vibration suppression

In this study,multi-resonator coupled metamaterials(MRCMs)with local resonators are proposed to obtain the multiple and wide band gaps.Kinetic models of the MRCMs are established,and the boundary conditions of the unit cell are obtained with Bloch's theorem.The effects of structural parameters,including the mass of the resonator and the spring stiffness,on the distributions of the band gaps are studied.Furthermore,the frequency domain responses and the time domain responses are calculated for analyzing the structural vibration characteristics and the effects of damping on structural vibration.The results show that the frequency domain response can accurately express the distributions of the band gaps of the MRCMs,and we can increase the number and the width of the band gaps by using the MRCMs for the superior vibration suppression capability.     

Improved non-singular local boundary integral equation method

When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM),singularities in the local boundary integrals need to be treated specially. In the current paper,local integral equations are adopted for the nodes inside the domain trod moving least square approximation (MLSA) for the nodes on the global boundary,thus singularities will not occur in the new al- gorithm.At the same time,approximation errors of boundary integrals are reduced significantly.As applications and numerical tests,Laplace equation and Helmholtz equa- tion problems are considered and excellent numerical results are obtained.Furthermore, when solving the Hehnholtz problems,the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions.Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.     

Global analysis of Ivlev's type predator-prey dynamic systems

Consider a class of Ivlev's type predator-prey dynamic systems with prey and predator both having linear density restricts. By using the qualitative methods of ODE, the global stability of positive equilibrium and existence and uniqueness of non-small amplitude stable limit cycle are obtained. Especially under certain conditions, it shows that existence and uniqueness of non-small amplitude stable limit cycle is equivalent to the local un-stability of positive equilibrium and the local stability of positive equilibrium implies its global stability. That is to say, the global dynamic of the system is entirely determined by the local stability of the positive equilibrium.     

A multifractal model for linking Lagrangian and Eulerian velocity structure functions

A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.     

CALCULATION FOR CYLINDRICAL SHELL UNDER LOCAL VERTICAL LOADINGS

In this paper,we use the method of mixed-type series to derive the analytical solutionsof cylindrical shell,which is simply supported along the transverse edges and subjected tothe local vertical loads,and give the analytical expressions of the solutions for this kind ofshell under five types of local vertical loading.A numerical example for a cylindrical shellroof,which is simply supported along the transverse edges and is free along the longitudinaledges.is given in this paper and from the calculated results it may be seen that theconvergence of the solutions is considerably satisfactory.Using the solutions of this paper,we can deal with some practical problems of underground structure.     

VECTOR ANALYSIS OF SPATIAL MECHANISMS PART 1 CONFIGURATION ANALYSIS OF SPATIAL MECHANISMS BY THE METHOD OF VECTOR DECOMPOSITION

In this series of four papers we present pure vectorial methods in establishing the configuration,kinematics and dyna-mics of some of the four-link spatial mechanisms.In Part1,the method of vector decomposition is used to establish the configurations of the R-G-G-R and H-R-G-R mechanisms,respec-tively.     

WHY CAN THE MAJOR PLANETS HAVE THEIR SATELLITES MOVING IN DIRECT AND RETROGRADE ORBITS AS WELL?

Now we use the Jacobian integral of circular restricted three-body problem toestablish a testing function of the stability of satellites.This method of criterion may beapplied to the stability problem of satellites when the six elements of the instantaneous orbitof the satellite with respect to its parent planet are known.By means of an electronic computer,we can find the stable region of a satellite with aquasi-circular orbit.The boundary surface of this region is a nearly oblate ellipsoid.Thevolume of this enclosed space is much smaller than that of binding by Hill surface and thatof“sphere of action”.As the expressions of relative kinetic energy of a satellite with respect to its parentplanet have the same form for the direct as well as the retrograde orbits,they can coexist inthe same region at the same time.     

Fixed point theorems of local contraction mappings on menger spaces

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.