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In this paper, the appearing probability of truck is introduced and an extended car-following model is presented to analyze the traffic flow based on the consideration of driver's characteristics, under honk environment. The stability condition of this proposed model is obtained through linear stability analysis. In order to study the evolution properties of traffic wave near the critical point, the mKdV equation is derived by the reductive perturbation method. The results show that the traffic flow will become more disorder for the larger appearing probability of truck. Besides, the appearance of leading truck affects not only the stability of traffic flow, but also the effect of other aspects on traffic flow, such as: driver's reaction and honk effect. The effects of them on traffic flow are closely correlated with the appearing probability of truck. Finally, the numerical simulations under the periodic boundary condition are carried out to verify the proposed model. And they are consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper presents the Finite Element formulation of the equations proposed by Tsiampousi et al. (2016) for coupled consolidation in unsaturated soils. Their coupling is discussed in relation to a conceptual model which divides soil behaviour into zones ranging from fully saturated to dry states. The numerical simulation of a laboratory experiment involving drainage of water from a vertical column of sand is used to validate the equations. Finally, the example of rainfall infiltration into a cut slope highlights how aspects of the conceptual model are reflected in the numerical analysis of boundary value problems involving unsaturated soils. [ABSTRACT FROM AUTHOR]

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L 2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we will extend the lattice Boltzmann model (LBM) to deal with the complex coupled nonlinear Schrödinger equations. A D1Q5 nonstandard complex lattice Boltzmann model (CLBM) with amending term for the coupled nonlinear Schrödinger equations (CNLSEs) is proposed. Complex equilibrium distribution functions and amending terms are selected, and the CNLSEs can be recovered by using the Chapman–Enskog multi-scale analysis and Taylor expansion technique. Some initial boundary value problems of the coupled system are simulated to verify the effectiveness and stability of our model. [ABSTRACT FROM AUTHOR]