Conformation of aromatic rings in isolable atropisomers of 2-arylindoline derivatives and kinetic evidences for π-π interaction

The equilibrium constants [K=anti/syn] of a pair of atropisomers due to restricted rotation about Csp³-Csp² bond for [2-(2-hydroxynaphthalen-1-yl)-3,3-dimethylindolin-1-yl](4-substituted phenyl)methanone were determined in some solvents. The presence of the effective π-π interaction was demonstrated by the correlation between the equilibrium constants (K) and the substituent effect of the phenyl groups (σ_p), suggesting that the ‘neutral-type’ interaction is operative.     

Optimal velocity difference model for a car-following theory

In this Letter, we present a new optimal velocity difference model for a car-following theory based on the full velocity difference model. The linear stability condition of the new model is obtained by using the linear stability theory. The unrealistically high deceleration does not appear in OVDM. Numerical simulation of traffic dynamics shows that the new model can avoid the disadvantage of negative velocity occurred at small sensitivity coefficient λ in full velocity difference model by adjusting the coefficient of the optimal velocity difference, which shows that collision can disappear in the improved model.     

Time-dependent Ginzburg-Landau equation in a car-following model considering the driver’s physical delay

In this paper, an extended car-following model considering the delay of the driver’s response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver’s physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. By applying the reductive perturbation method, we get the time-dependent Ginzburg-Landau (TDGL) equation from the car-following model to describe the transition and critical phenomenon in traffic flow. We show the connection between the TDGL equation and the mKdV equation describing the traffic jam.     

Impact of the honk effect on the stability of traffic flow

In this paper, we propose an extended car-following model which takes into account the honk effect. The analytical and numerical results show that the honk effect improves the stability of traffic flow. The dependence of the stability on the properties of the honk effect is investigated in this paper.     

Effect of looking backward on traffic flow in an extended multiple car-following model

In this paper, a new car-following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow. And the neutral stability condition of this model can be obtained by using the linear stability theory. Numerical simulation shows that the proposed model is theoretically an improvement over previous ones.     

On dividend strategies with non-exponential discounting

In this paper, we study the dividend maximization problem with a non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to Markov strategies. This is a time inconsistent control problem. The equilibrium HJB-equation is given and the verification theorem is proven for a general discount function. Considering a mixture of exponential discount functions and a pseudo-exponential discount function, we get equilibrium dividend strategies and the corresponding equilibrium value functions by solving the equilibrium HJB-equations.     

Analysis of a modified two-lane lattice model by considering the density difference effect

In this paper, a modified lattice hydrodynamic model of traffic flow is proposed by considering the density difference between leading and following lattice for two-lane system. The effect of density difference on the stability of traffic flow is examined through linear stability analysis and shown that the density difference term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, the Burgers equation and mKdV equation near the critical point are derived through nonlinear analysis. To verify the theoretical findings, numerical simulation is conducted which confirms that traffic jam can be suppressed efficiently by considering the density difference effect in the modified lattice model for two-lane traffic.     

An extended multi-anticipative delay model of traffic flow

An extended multi-anticipative delay model is proposed by introducing multiple velocity differences and incorporating the reaction-time delay of drivers. The stability condition of the new model is obtained by applying the linear stability theory, and the modified Korteweg–de Vries (mKdV) equation is derived by the use of the nonlinear analysis method. The analytical and numerical results show that both the reaction-time delay of drivers and the information of multiple velocity differences have an important influence on the stability of the model, and that the stabilization of traffic flow is enhanced by appending the velocity difference information of multiple vehicles ahead or by decreasing the delay time.