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15 August 2019, Volume 36 Issue 4 Previous Issue    Next Issue

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Research on the Buckling Behavior of Thermoelectric Films on Infinite Elastic Substrates ZHANG Chen-xi, DING Sheng-hu 2019, 36 (4):  367-375.  doi: 10.3969/j.issn.1005-3085.2019.04.001 Abstract ( 212 )   PDF (236KB) ( 451 )   Save In this paper, the buckling behavior of thermoelectric thin film bonded to elastic substrates is studied. Combining the interface shear stress with the axial stress of the thin film, the calculation model of the thermoelectric thin film is established and the problem is transformed into a singular integral equation by using boundary conditions. The singular integral equation is separated by using Chebyshev polynomials, and the normalized stress intensity factors are obtained. The effects of film stress and interfacial stress intensity factors are determined by the film thickness and the stiffness ratio of substrate to film. The influence of the film length and the thickness ratio on film stress and interface stress intensity factors is discussed. The result shows that the stiffness ratio between the film and the substrate has a significant effect on the stress level of the film. Related Articles | Metrics

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An Event-triggered Control Scheme Subject to Deception Attacks and Unknown Inputs TAN Rui-mei 2019, 36 (4):  376-388.  doi: 10.3969/j.issn.1005-3085.2019.04.002 Abstract ( 129 )   PDF (643KB) ( 338 )   Save In this paper, an event-triggered controller is designed for a class of stochastic systems subject to external attacks and unknown inputs. Concretely an event-triggered control strategy and its corresponding event-triggered transmission mechanism are presented based on a class of stochastic systems subject to external attacks and unknown inputs in the wireless transmission. Moreover, the transmission scheme on data of sensor is designed to determine when the transmission data can be sent. The controller gains that is designed derived by using the stochastic stability exponentially boundedness theory under the desired event-triggered condition. In addition, the corresponding event-triggered transmission strategy is derived in terms of an approximate quadratic performance index which gives a good balance among the control performance, the communication rates and the battery life of the node. A numerical example is given to verify the validity of the theoretical results in the simulation. The simulation results show that the estimator and event-triggered transmission strategy designed in this paper can balance the estimated accuracy and the number of transmissions well, which is of great significance for the energy saving of sensors. Related Articles | Metrics

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Wind Stability Finite Point Method for Soil Solute Transport Equations QIN Xin-qiang, SU Li-jun, WANG Xing, LI Yong-zhen, WANG Yue-ling 2019, 36 (4):  389-405.  doi: 10.3969/j.issn.1005-3085.2019.04.003 Abstract ( 138 )   PDF (443KB) ( 275 )   Save A finite point method for windward stability of soil solute transport equation is proposed. This method adopts an adaptive windward format to make its support field lean to the windward side, so it can obtain upstream information and avoid numerical oscillation when convection is dominant. The convergence, the order of convergence and the stability of the numerical solution of the new algorithm are analyzed in detail under the action of different distribution points, different time steps and different influence factors through the numerical calculation of the one-dimensional and two-dimensional soil solute transport equation. Numerical results show that the proposed method can effectively improve the computational accuracy and eliminate the numerical oscillation in the boundary region and gradient variations large region. Related Articles | Metrics

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Stability of an Eco-epidemiological Model with Stage Structure and Saturation Incidence WANG Ling-shu, ZHANG Ya-nan, SU Huan 2019, 36 (4):  406-418.  doi: 10.3969/j.issn.1005-3085.2019.04.004 Abstract ( 152 )   PDF (179KB) ( 241 )   Save In this paper, an eco-epidemiological predator-prey model with saturation incidence and stage structure for the prey is investigated. A time delay describing the latent period of the disease in this model is discussed. By analyzing the characteristic equations, the local stability of the boundary equilibria and the positive equilibrium is established, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using Lyapunov functions and the LaSalle's invariance principle, the global stability of the boundary equilibria and the positive equilibrium is addressed, respectively. Therefore, the sufficient conditions are given for the disease extinction and permanence of the model. Related Articles | Metrics

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A Finite Element Variational Multiscale Method Based on Crank-Nicolson Scheme for the Unsteady Navier-Stokes Equations XUE Ju-feng, SHANG Yue-qiang 2019, 36 (4):  419-430.  doi: 10.3969/j.issn.1005-3085.2019.04.005 Abstract ( 241 )   PDF (195KB) ( 615 )   Save The incompressible viscous flows are fluid movements that do not change in density. They are used to describe many important physical phenomena such as weather, ocean currents, flow around airfoil, and blood flow within the arteries. The Navier-Stokes equations are the basic equations for incompressible viscous flows. Therefore, the numerical method for solving Navier-Stokes equations has been paid more and more attention in recent decades. In this paper, we mainly study a two-level fully discrete finite element variational multiscale method  based on Crank-Nicolson scheme for the unsteady Navier-Stokes equations. The method is carried out in two steps. A stabilized nonlinear Navier-Stokes system is solved on a coarse grid at the first step, and the second step is that a stabilized linear problem is solved on a fine grid to correct the coarse grid solution. Error estimate of the velocity which is derived via the two-level finite element variational multiscale method is of second-order in time. Numerical experiments show that the method of this paper can save a lot of computation time compared with the finite element variational method which uses a one-level grid directly on the fine grid in the case of coarse grid matching. Related Articles | Metrics

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A New Moving Mesh Method for Solving the Two-dimensional Navier-Stokes Equation DUAN Xian-bao, CAO Qin-qin, TAN Hong-xia 2019, 36 (4):  431-438.  doi: 10.3969/j.issn.1005-3085.2019.04.006 Abstract ( 461 )   PDF (405KB) ( 439 )   Save In order to reduce the computational cost of solving partial differential equation (PDE), whose solution has strong singularity or drastic change in a small local area, a moving mesh method based on equation solution is proposed and applied to solve the two-dimensional incompressible Navier-Stokes equations. Different from the most existing moving mesh methods, the moving distance of the nodes is obtained by solving a variable-coefficient diffusion equation, which avoids regional mapping and does not need to smooth the monitoring function, so the algorithm is easier to program and implement. Numerical examples show that the proposed algorithm can refine the mesh in the position where the gradient of the solution changed drastically, which can save a lot of computation time on the premise of improving the resolution of the numerical solution. Due to the typicality of the Navier-Stokes equations, the proposed algorithm can be generalized to solve many similar partial differential equations numerically. Related Articles | Metrics

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Qualitative Analysis of a Class of Predator-prey Model with Fear Effect WANG Rong, YANG Wen-bin, LI Yan-ling 2019, 36 (4):  439-450.  doi: 10.3969/j.issn.1005-3085.2019.04.007 Abstract ( 163 )   PDF (169KB) ( 270 )   Save The nature of the reaction-diffusion system solution contains abundant information, which is of great significance to the study of population ecological phenomena. In this paper, the existence of positive solutions to the steady-state system of a predator-prey model with fear effect is studied. Firstly, some priori estimates of positive constant steady-state solution are obtained using the maximum principle, which lay the foundation for the subsequent research. Secondly, the sufficient condition of the unique existence for the equilibrium solution is given, and the stability of positive constant steady-state solution is discussed using the stability theory of linear operators. Finally, on the basis of the degree theory, the existence of non-constant steady-state solution is given. Related Articles | Metrics

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Global Analysis for an Epidemic Model with the Beverton-Holt Birth Function and Stage Structure WANG Yu-ping, LIN Xiao-lin, LI Jian-quan 2019, 36 (4):  451-460.  doi: 10.3969/j.issn.1005-3085.2019.04.008 Abstract ( 191 )   PDF (170KB) ( 227 )   Save Based on the facts that some diseases spread only among adults, and that the growth of adult individuals is density-dependent an adult epidemic model with stage structure is proposed in this paper, where it is assumed that individuals in the population consist of juveniles and adults, that the birth function of juveniles is of the Beverton-Holt type. The global stability of the model is completely investigated by constructing the appropriate Lyapunov functions and qualitative analysis, and the basic reproduction numbers of the population growth and the disease transmission, determining the dynamics of the model, is found. The obtained results suggest that, when the basic reproduction number of the population growth is not greater than unity, the population eventually dies out; when the basic reproduction number of the population growth is greater than unity, and the number of the disease transmission is less than or equal to unity, the population persists and the disease dies out; when the basic reproduction number of the disease transmission is greater than unity, the disease persists and becomes endemic as the population survives. Related Articles | Metrics

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RS-BART: a Novel Technique to Boost the Prediction Ability of Bayesian Additive Regression Trees WANG Guan-wei, ZHANG Chun-xia, YIN Qing-yan 2019, 36 (4):  461-477.  doi: 10.3969/j.issn.1005-3085.2019.04.009 Abstract ( 485 )   PDF (192KB) ( 392 )   Save In supervised learning tasks, it is crucial for any algorithm to make accurate predictions on future data. As a Bayesian version of the gradient boosting algorithm, Bayesian additive regression trees (BART) have great potential to achieve high prediction accuracy. As far as we know, however, BART has not received as much attention as random forests and boosting. Thus, a comprehensive overview of BART is first presented to facilitate its understanding. Considering that BART may suffer from over-fitting in high-dimensional situations, one novel technique called RS-BART is developed to enhance its performance. Through first sorting all the variables with their relative importance, some low- or medium-dimensional BART models are trained with important variables. The predictions produced by these BART models are then integrated into the final result. By conducting experiments with some simulated and real data, RS-BART is demonstrated to perform better than or competitively with some state-of-the-art techniques including random forests, boosting and BART. Thus, RS-BART can be deemed as a competitive tool to solve real prediction tasks, especially high-dimensional but sparse ones. Related Articles | Metrics

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Construction of Framelet Packets on ${\mathbb{Z}}$ and Algorithm Implementation LU Da-yong, YI Hua 2019, 36 (4):  478-488.  doi: 10.3969/j.issn.1005-3085.2019.04.010 Abstract ( 164 )   PDF (199KB) ( 325 )   Save In order to facilitate the use of wavelets, the study on frame wavelets (also called framelets) and framelet packets in digital setting has been addressed in recent years. An approach to construct a class of $J$-stage framelet packets for $\ell^2(\mathbb{Z})$ is given by Lu and Yi. However, the detailed results on how to use them are missing. To further improve the theoretical system of $J$-stage framelet packets for $\ell^2(Z)$, by following the work of Lu and Yi, the fast decomposition and reconstruction algorithms are given in this paper, with which one can establish the relationship of coefficients between different stages. For the convenience of using, the detailed data of framelet packets for $\ell^2(Z)$ when the number $n$ of mother framelet ranges from $1$ to $4$ are constructed. Finally, a numerical experiment is given to illustrate the perfect reconstruction of framelet packets. Related Articles | Metrics