A Backward-Looking Optimal Current Lattice Model

An optimai current lattice model with backward-looking effect is proposed to describe the motion of traffic flow on a single lane highway. The behavior of the new model is investigated anaiytically and numerically. The stability, neutrai stability, and instability conditions of the uniform flow are obtained by the use of linear stability theory. The stability of the uniform flow is strengthened effectively by the introduction of the backward-looking effect. The numerical simulations are carried out to verify the validity of the new model. The outcomes of the simulation are corresponding to the linearly analyticai results. The analytical and numerical results show that the performance of the new model is better than that of the previous models.     

A Discrete Effect of the Thermal Lattice BGK Model

In this article, a discrete effect in the thermal Lattice BGK two-speed model is studied. These effects are due to the non-equilibrium state in the particle distribution function, and the non-equilibrium occurs near walls. The mechanism of the LBM counterpart of the thermal creep flow, which appears due to the temperature gradient of the boundary in rarefied gases, is clarified analytically and numerical calculations are performed for some cases. A technique for eliminating this effect is also shown.     

A Lattice Hydrodynamic Model for Traffic Flow Accounting for Driver Anticipation Effect of the Next-Nearest-Neighbor Site

In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation effect of next-nearest-neighbor site can enlarge the stable area of traffic flow. The space can be divided into three regions： stab/e, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation effect of the next-neaxest-neighbor site can stabilize tramc flow in our modified lattice model, which is consistent with the analytical results.     

A Lattice Hydrodynamic Model for Traffic Flow Accounting for Driver Anticipation Effect of the Next-Nearest-Neighbor Site

In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation effect of next-nearest-neighbor site can enlarge the stable area of traffic flow. The space can be divided into three regions: stable, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation effect of the next-nearest-neighbor site can stabilize traffic flow in our modified lattice model, which is consistent with the analytical 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-neighbor, 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.     

Lattice Model with Traveling Compactons

We introduce a purely anharmonic lattice model with specific double-well on-site potential, which admits traveling compacton-like solitary wave solutions by the inverse method with the help of Mathematica. By properly choosing the shape of the solitary wave solution of the system, we can calculate the parameters of the specific on-site potential. We also found that the localization of the compacton is related to the nonlinear coupling parameter Cnl and the potential parameter V0 of the on-site potential, and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential parameter V0. Numerical calculation results demonstrate that the narrow compacton is unstable while the wide compacton is stable when they move along the lattice chain.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.     

A New Lattice Model of Two-Lane Traffic Flow with the Consideration of the Honk Effect

In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries (KdV) equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coefficient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.     

Lattice Model with Traveling Compactons

We introduce a purely anharmonic lattice model with specific double-well on-site potential, which admits traveling compacton-like solitary wave solutions by the inverse method with the help of Mathematica. By properly choosing the shape of the solitary wave solution of the system, we can calculate the parameters of the specific on-site potential. We also found that the localization of the compacton is related to the nonlinear coupling parameter Cn1 and the potential parameter Vo of the on-site potential, and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential parameter Vo. Numerical calculation results demonstrate that the narrow compacton is unstable while the wide compacton is stable when they move along the lattice chain.     

A Lattice Model for Bidirectional Pedestrian Flow on Gradient Road

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes.This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries(mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg–Landan(TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.     

A Lattice Model for Bidirectional Pedestrian Flow on Gradient Road

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes. This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries (mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg—Landan (TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.     

Spin-Wave Excitations in Anisotropic Kondo Lattice Model

The spin-wave excitations in anisotropic Kondo lattice model are studied using the spin Green's function. Both the ferromagnetic and antiferromagnetic cases are considered. The equations to determine the spectrum of low-energy excitations are given. The anisotropy gaps are obtained, and the long-wavelength and strong-coupling limits are analyzed.     

A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.     

A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （2004） 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative （NND） scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, （i） Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; （ii） reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 (2004) 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model isvalidated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

A Lattice Hydrodynamic Model for Trafc Flow Accounting for Driver Anticipation Efect of the Next-Nearest-Neighbor Site

In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation efect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation efect of next-nearest-neighbor site can enlarge the stable area of trafc flow. The space can be divided into three regions: stable, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation efect of the next-nearest-neighbor site can stabilize trafc flow in our modified lattice model, which is consistent with the analytical results.     

Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation

In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.     

A Lattice Model for the Line Tension of a Sessile Drop

Within a semi-infinite three-dimensional lattice gas model describing the coexistence of two phases on a substrate, we study, by cluster expansion techniques, the free energy (line tension) associated with the contact line between the two phases and the substrate. We show that this line tension, is given at low temperature by a convergent series whose leading term is negative, and equals 0 at zero temperature.     

Highly Efficient Lattice Boltzmann Model for Compressible Fluids:Two-Dimensional Case

We present a highly efficient lattice Boltzmann model for simulatingcompressible flows. This model is based on the combination of an appropriatefinite difference scheme, a 16-discrete-velocity model [Kataoka andTsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion anddissipation terms. The dispersion term effectively reduces the oscillationat the discontinuity and enhances numerical precision. The dissipation termmakes the new model more easily meet with the von Neumann stabilitycondition. This model works for both high-speed and low-speed flows witharbitrary specific-heat-ratio. With the new model simulation results for thewell-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation ofstate or free-energy functional, the new model has the potential tostudythe complex procedure of shock wave reaction on porous materials.