Speed limit effect during lane change in a two-lane lattice model under V2X environment

Speed limit measures are ubiquitous due to the complexity of the road environment,which can be supplied with the help of vehicle to everything(V2X)communication technology.Therefore,the influence of speed limit on traffic system will be investigated to construct a two-lane lattice model accounting for the speed limit effect during the lane change process under V2X environment.Accordingly,the stability condition and the mKdV equation are closely associated with the speed limit effect through theory analysis.Moreover,the evolution of density and hysteresis loop is simulated to demonstrate the positive role of the speed limit effect on traffic stability in the cases of strong reaction intensity and high limited speed.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Dark Matter and Dark Energy from Lattice Model of Universe

The article considers a conceptual universe model as a periodic lattice (network) with nodes defined by the wave function in a background-independent Hamiltonian based on their relations and interactions. This model gives rise to energy bands, similar to those in semiconductor solid-state models. In this context, valence band holes are described as dark matter particles with a heavy effective mass. The conducting band, with a spontaneously symmetry-breaking energy profile, contains particles with several times lighter effective mass, which can represent luminous matter. Some possible analogies with solid-state physics, such as the comparison between dark and luminous matter, are discussed. Additionally, tiny dark energy, as intrinsic lattice Casimir energy, is calculated for a lattice with a large number of lattice nodes.

Nonlinear Waves in Two-Dimensional (2D) Square Lattice Frenkel-Kontorova (FK) System

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.

Coarse-graining Calcium Dynamics on Stochastic Reaction-diffusion Lattice Model

We develop a coarse grained （CG） approach for efficiently simulating calcium dynamics in the endoplasmic reticulum membrane based on a fine stochastic lattice gas model. By grouping neighboring microscopic sites together into CG cells and deriving CG reaction rates using local mean field approximation, we perform CG kinetic Monte Carlo （kMC） simulations and find the results of CG-kMC simulations are in excellent agreement with that of the microscopic ones. Strikingly, there is an appropriate range of coarse proportion rn, corresponding to the minimal deviation of the phase transition point compared to the microscopic one. For fixed m, the critical point increases monotonously as the system size increases, especially, there exists scaling law between the deviations of the phase transition point and the system size. Moreover, the CG approach provides significantly faster Monte Carlo simulations which are easy to implement and are directly related to the microscopics, so that one can study the system size effects at the cost of reasonable computational time.

Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [ Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multirelaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling.

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani＇s model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink -antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.

A LATTICE BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GAS

A new lattice Boltzmann model for compressible perfect gas is proposed. The numerical example shows that it can be used to simulate shock wave and contact discontinuity. The results are comparable with those obtained by traditional methods. The ratio of specific heats gamma may be chosen according to the requirement of problems.

Lattice models of traffic flow considering drivers' delay in response

This paper proposes two lattice traffic models by taking into account the drivers＇ delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink-antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers＇ delay in sensing headway plays an important role in jamming transition.

A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect

We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world. Applying the linear stability theory, we obtain the linear stability condition of the model. Through nonlinear analysis, we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi^anticipation effect is considered.

Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect

By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic （AELH） model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries （KdV） equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered.

Simulation of rheological behavior of asphalt mixture with lattice model

A three-dimensional(3D) lattice model for predicting the rheological behavior of asphalt mixtures was presented.In this model asphalt mixtures were described as a two-phase composite material consisting of asphalt sand and coarse aggregates distributed randomly.Asphalt sand was regarded as a viscoelastic material and aggregates as an elastic material.The rheological response of asphalt mixture subjected to different constant stresses was simulated.The calibrated overall creep strain shows a good approximation to experimental results.

A Solvable Decorated Ising Lattice Model

A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-nelghbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2= -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.

Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion

We propose a boundary scheme for addressing multi-mechanism flow in a porous medium in slip and early transition flow regimes, which is frequently encountered in shale gas reservoirs. Micro-gaseous flow in organic-rich shale involves a complex flow mechanism. A self-developed boundary scheme that combines the non-equilibrium extrapolation scheme and the combined diffusive reflection and bounce-back scheme(half-way DBB) to embed the Langmuir slip boundary into the single-relaxation-time lattice Boltzmann method(SRT-LBM) enables us to describe this process, namely, the coupling effect of micro-gaseous flow and surface diffusion in organic-rich nanoscale pores. The present LBM model comes with the careful consideration of the local Knudsen number, local pressure gradient, viscosity correction model, and regularization procedure to account for the rarefied gas flows in irregular pores. Its validity and accuracy are verified by several benchmarking cases, and the calculated results by this boundary scheme accord well with our analytical solutions.This boundary scheme shows a higher accuracy than the existing studies. Additionally, a subiteration strategy is presented to tackle the coupled micro-gaseous flow and surface diffusion, which necessitates the iteration process matching of these two mechanisms. The multi-mechanism flow in the self-developed irregular pores is also numerically investigated and analyzed over a wide range of parameters. The results indicate that the present model can effectively capture the coupling effect of micro-gaseous flow and surface diffusion in a tree-like porous medium.

A traffic flow lattice model considering relative current influence and its numerical simulation

Based on Xue＇s lattice model, an extended lattice model is proposed by considering the relative current information about next-nearest-neighbour sites ahead. The linear stability condition of the presented model is obtained by employing the linear stability theory. The density wave is investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries （mKdV） equation. The simulation results are in good agreement with the analytical results, showing that the stability of traffic flow can be enhanced when the relative current of next-nearest-neighbour sites ahead is considered.

INTRINSIC INSTABILITY OF THE LATTICE BGK MODEL

Based on the stability analysis with no linearization and expansion, it is argued that instability in the lattice BGK model is originated from the linear relaxation hypothesis of collision in the model. The hypothesis stands up only when the deviation from the local equilibrium is weak. In this case the computation is absolutely stable for real fluids. But for flows of high Reynolds number, this hypothesis is violated and then instability takes place physically. By performing a transformation a quantified stability criteria is put forward without those approximation. From the criteria a sufficient condition for stability can be obtained and serve as an estimation of the limited Reynolds number as high as possible.

Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

The search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor.A long list of complex phenomena underlies the physics of this problem.In the past decades,the lattice Boltzmann method has emerged as a promising tool to address such complexities.In this regard,we have applied a 121-velocity multiphase lattice Boltzmann model to an asymmetric cluster of bubbles in an acoustic field.A problem as a benchmark is studied to check the consistency and applicability of the model.The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics,as well as the screening effect on an acoustic multibubble medium.It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.

Modified surface tension model for free surface flow with single-phase lattice Boltzmann method

A single-phase lattice Boltzmann model with modified surface tension is developed in this paper to solve the problem of high-density-ratio free surface flow.The computational efficiency and accuracy are both enhanced.The restriction to the relaxation factor （which needs to be smaller than 1） is circumvented by the new surface tension algebra,due to its rational physical nature compared with the treatment of Xing,Buther and Yang in their paper （Comp.Mater.Sci.,2007,39（2）：282-290）.The proposed stable surface tension scheme is applied to simulate the free deformation of a square droplet with surface tension effect and the process of a droplet impinging on a liquid film.The numerical solution for free deformation of a droplet agrees well with thermodynamic principles,and also achieves high accuracy in comparison with Xing,et al.＇s model.Three typical impinging modes are successfully obtained with the new scheme,and another particular mode found by Wang and Chen is also successfully simulated.The evolutions of liquid crown agree well with the power law related to time.

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403（2）. A convincing finite-size scaling analysis of the model yields ν=0.9995（21）, β/ν=0.12400（17）, γ/v=1.75223（22）, γ^1/ν=1.7555（22）, α/ν=0.00077（420） （scaling） and α/ν=0.0010（42） （hyperscaling）. The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase（MCMP） pseudopotential lattice Boltzmann（LB） model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000：1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young＇s equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie＇s law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.