TWO-DIMENSIONAL CELLULAR AUTOMATON TRAFFIC MODELWITH RANDOMLY SWITCHING TRAFFIC LIGHTS

I.IntroductionWiththedevelopmentofsocietyandeconomyinmetropolises,thecontradictionbet\"eentheincreaseoftrat'ficflowandtheexistingconditionoftrafticftlcilitiesbecolllesmorealldmore'serious,resultinginaprincipalI'actorofconstrainingthedevelopmentofmetropolititneconomy.Therefore,inrecentdecadesthetrat'l'ictlowproblemhasdrawntheattelltiollofInanyspecialistsinvariousfieldsincludingphysics,mechanicsalldmathelllatics.Alargenumberoftraftic1llodelshavebeenpropes.Inthispaper,thecellularautomaton(CA)tr…     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

A fully anisotropic hierarchical hybrid cellular automaton algorithm to simulate bone remodeling

Computational models of the bone remodeling process have been utilized to further our understanding of the adaptation of bone architecture to changes in its mechanical environment. The hierarchical hybrid cellular automata (HHCA) algorithm is a multi-scale approach for the simulation of the adaptation of bone. Currently, this remodeling algorithm utilizes the apparent material properties of the trabecular architecture. The objective of this work is to increase the fidelity of the HHCA algorithm by incorporating the local anisotropic properties of these structures. Preliminary analyses display improved efficiency and a more consistent material distribution when incorporating anisotropic properties into the HHCA methodology.     

A dynamic cellular vertex model of growing epithelial tissues

Intercellular interactions play a significant role in a wide range of biological functions and processes at both the cellular and tissue scales, for example, embryogenesis, organogenesis, and cancer invasion. In this paper, a dynamic cellular vertex model is presented to study the morphome-chanics of a growing epithelial monolayer. The regulating role of stresses in soft tissue growth is revealed. It is found that the cells originating from the same parent cell in the monolayer can orchestrate into clustering patterns as the tis-sue grows. Collective cell migration exhibits a feature of spatial correlation across multiple cells. Dynamic intercel-lular interactions can engender a variety of distinct tissue behaviors in a social context. Uniform cell proliferation may render high and heterogeneous residual compressive stresses, while stress-regulated proliferation can effectively release the stresses, reducing the stress heterogeneity in the tissue. The results highlight the critical role of mechanical factors in the growth and morphogenesis of epithelial tissues and help understand the development and invasion of epithelial tumors.     

A mesoscopic approach on stability and phase transition between different traffic flow states

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong resemblance to the phase transition in thermodynamics. In this work, we explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein. By using a mesoscopic approach, one entitles the catastrophe model the same physical content as in the Landau's theory, and uncovers its close connections to the instability of the equation of motion and to the transition between different traffic states. In addition to the one-dimensional configuration space, we generalize our discussions to the higher-dimensional case, where the observed temporal oscillation in traffic flow data is attributed to the curl of a vector field. We exhibit that our model can reproduce the main features of the observed fundamental diagram including the inverse-λ shape and the wide scattering of congested traffic data. When properly parameterized, the main feature of the data can be reproduced reasonably well either in terms of the oscillating congested traffic or in terms of the synchronized flow.     

A plasticity model for pressure-dependent anisotropic cellular solids

The initial and subsequent yield surfaces for an anisotropic and pressure-dependent 2D stochastic cellular material, which represents solid foams, are investigated under biaxial loading using finite element analysis. Scalar measures of stress and strain, namely characteristic stress and characteristic strain, are used to describe the constitutive response of cellular material along various stress paths. The coupling between loading path and strain hardening is then investigated in characteristic stress–strain domain. The nature of the flow rule that best describes the plastic flow of cellular solid is also investigated. An incremental plasticity framework is proposed to describe the pressure-dependent plastic flow of 2D stochastic cellular solids. The proposed plasticity framework adopts the anisotropic and pressure-dependent yield function recently introduced by Alkhader and Vural [Alkhader M., Vural M., 2009a. An energy-based anisotropic yield criterion for cellular solids and validation by biaxial FE simulations. J. Mech. Phys. Solids 57(5), 871–890]. It has been shown that the proposed yield function can be simply calibrated using elastic constants and flow stresses under uniaixal loading. Comparison of stress fields predicted by continuum plasticity model to the ones obtained from FE analysis shows good agreement for the range of loading paths and strains investigated.     

Simulation of free boarding process using a cellular automaton model for passenger dynamics

Budget airlines adopt free boarding strategy when conducting passengers to board the airplanes. In such a boarding strategy, passengers are not offered any preassigned seats, and they choose their favorite seats freely once they are inside the airplane. A simulation framework based on cellular automaton is developed to mimic the dynamics of passenger flow in the free boarding process. In the model, each seat in the cabin is assigned a positive value to characterize how desirable it appears to the overall passengers. A logit-based discrete choice principle is applied to formulate the seat choice behaviors of passengers. The influence of the sensitivity parameters on the mean boarding time is discussed to identify the different classes of behavior exhibited by the model. The numerical results illustrate that the new model can qualitatively reproduce some dynamic properties of the free boarding process. Besides, two grouped strategies in a manner of freestyle are proposed, and quantitative comparisons are made with those involve assigned seats.     

Continuum modeling for two-lane traffic flow

In this paper, we study the continuum modeling of traffic dynamics for two-lane freeways. A new dynamics model is proposed, which contains the speed gradient-based momentum equations derived from a car-following theory suited to two-lane traffic flow. The conditions for securing the linear stability of the new model are presented. Numerical tests are carried out and some nonequilibrium phenomena are observed, such as small disturbance instability, stop-and-go waves, local clusters and phase transition. The project supported by the National Natural Science Foundation of China (70521001) The English text was polished by Yunming Chen.     

Lane changing analysis for two-lane traffic flow

In this paper, the two-lane traffic are studied by using the lane-changing rules in the car-following models. The simulation show that the frequent lane changing occurs when the lateral distance in car following activities is considered and it gives rise to oscillating waves. In contrast, if the lateral distance is not considered (or considered occasionally), the lane changing appears infrequently and soliton waves occurs. This implies that the stabilization mechanism no longer functions when the lane changing is permitted. Since the oscillating and soliton waves correspond to the unstable and metastable flow regimes, respectively, our study verifies that a phase transition may occur as a result of the lane changing. The project supported by the National Natural Science Foundation of China (70521001, 10404025, 10532060), the National Basic Research Program of China (2006CB705503) and the Research Grants Council of the Hong Kong Special Administrative Region (HKU7031/02E, HKU7187/05E). The English text was polished by Boyi Wang.     

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅａｕｔｈｏｒｓｐｒｅｓｅｎｔｅｄａｎｅｗｄｙｎａｍｉｃｓｍｏｄｅｌｆｏｒｔｒａｆｆｉｃｆｌｏｗ[1].Ｔｈｅｍｏｄｅｌｃｏｍｐｒｉｓｅｓａｃｏｎｔｉｎｕｕｍｅｑｕａｔｉｏｎａｎｄａｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎ ｋ/ ｔ+ (ｋｕ) / ｘ=0 ,( 1 ) ｕ ｔ+ｕ ｕ ｘ=ｕｅ(ｋ) -ｕＴ +ａ ｕ ｘ,( 2 )ｗｈｅｒｅｋｉｓｔｒａｆｆｉｃｄｅｎｓｉｔｙ ;ｕｉｓｍｅａｎｓｐｅｅｄ ;ｘ ,ｔａｒｅｓｐａｃｅａｎｄｔｉｍｅｃｏｏｒｄｉｎａｔｅｓｒｅｓｐｅｃｔｉｖｅｌｙ .Ｔｉｓｒｅｌ…     

WAVE INTERACTIONS IN SULICIU MODEL FOR DYNAMIC PHASE TRANSITIONS

Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis.For any given initial data with two pieces of constant states,the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states,the solution may be constructed from the Riemann solutions,with each two adjacent states connected by elementary waves.A new Riemann problem forms when these two waves collide.Through the exploration of these Riemann problems,the outcome of wave interactions may be classified in a suitable parametric space.     

Limit thermodynamic model for compositional gas–liquid systems moving in a porous medium

It is shown that a multicomponent two-phase system moving through a porous medium may be described by a limit model in which the thermodynamic subsystem is totally separated from the hydrodynamics. The limit corresponds to a contrast phase mobility and a fast pressure relaxation process. The obtained limit thermodynamic model includes several differential thermodynamic equations and describes the equilibrium in an open system. The model is validated by comparing with the full compositional flow simulations. A numerical solution to the limit thermodynamic model is constructed. An application to the gas-condensate systems is compared to the full compositional model.     

Global weak solutions to a phase-field model for motion of grain boundaries

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces. The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain. The existence proof is valid in the one-dimensional case.     

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.     

Investigation of the adaptive features of a real-time nonlinear freeway traffic state estimator

This paper reports on real-data testing results for a real-time nonlinear freeway traffic state estimator with particular focus on its adaptive features. The pursued general approach to the real-time adaptive estimation of the complete traffic state in freeway stretches is based on stochastic nonlinear macroscopic traffic flow modeling and extended Kalman filtering that are outlined in the paper. One major innovative aspect of the estimator is the on-line estimation of important model parameters (free speed, critical density, and capacity) simultaneously with the estimation of traffic flow variables (flows, mean speeds, and densities), which leads to three significant advantages of the traffic state estimator: (1) avoidance of off-line model calibration; (2) automatic adaptation to changing external conditions (e.g. weather and light conditions); (3) enabling of incident alarms. The purpose of the reported real-data testing is, first, to demonstrate advantage (1) by investigating some basic properties of the estimator and, second, to explore some adaptive capabilities of the estimator that enable the other two advantages. The achieved testing results are quite satisfactory and promising for subsequent work.     

A one-dimensional model for incoherent phase changes

We present here a simplified version of the model of incoherent solid-solid transitions with mass diffusion developed by Gurtin and Cermelli in [3]. An incoherent phase change is always associated with some kind of defect production at the interface: we consider here a one-dimensional continuum, so that the resulting equations allow study to be made of the influence of volume (vacancy) production on the evolution of the system.

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Sommario In questo lavoro viene presentato un adattamento del modello di transizione di fase incoerente sviluppato da Gurtin e Cermelli in [3]. Una transizione incoerente è sempre associata alla produzione di un qualche tipo di difetto all'interfaccia: consideriamo qui un modello semplificato di continuo unidimensionale, in modo da poter studiare l'effetto dei difetti di volume (lacune) sull'evoluzione del sistema.

     

明渠气二相流的双流体模型

从解决平均二相流基本方程的封闭问题出发,分析了水利工程中气水二相流的特点,介绍了据此提出的可用于水利工程稀疏气泡流计算的双流体模型,并对明渠气水二相流进行了算例验证。     

基于相变松弛法则的水下爆炸空化模型研究

水下爆炸过程中存在着大量的空化现象,空化的产生、演化及其溃灭过程对于水下冲击波传播、爆炸气泡运动以及水下结构物冲击损伤都会产生重要影响。本文基于多相可压缩流体理论模型,考虑空化发生过程中汽-液两相流体亚平衡状态下两相之间发生的热力学-化学平衡机制,分析汽-液两相介质之间的质量和热量交换,从而实现对相变过程的自动捕捉。该系统的控制方程采用分步法处理,首先利用二阶MUSCL-Hancock格式和HLLC黎曼求解器来求解齐次双曲型方程,再采用牛顿迭代法求解相变方程。数值测试结果表明,本文的计算模型对于空化相变过程具有较好的捕捉能力。最后将该模型应用到水下近水面爆炸空化的数值模拟当中,研究发现空泡的溃灭压力峰值约为冲击波压力峰值的15%,有效作用时间是冲击波载荷有效作用时间的2倍以上。本文的空化相变模型能够为水下爆炸空化现象的机理研究提供重要支撑。     

A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material简

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.