Narrow Results

The development of real time traffic flow models for urban road networks is of paramount importance for the purposes of optimizing and control of traffic flow. Motivated by the modeling of road networks in last decade, this paper proposes a different and simplified approach, known as section approach to model road networks in the framework of macroscopic traffic flow models. For evaluation of the traffic states on a single road, an anisotropic continuum GK-model developed by [Gupta and Katiyar, J. Phys. A38, 4069 (2005)] is used as a single-section model. This model is applied to a two-section single lane road with points of entry and exits. In place of modeling the effect of off- and on-ramps in the continuity equation, a set of special boundary condition is taken into account to treat the points of entry and exit. A four-section road network comprised of two one-lane roads is also modeled using this methodology. The performances of the section approaches are investigated and obtained results are demonstrated over simulated data for different boundary conditions.

In this paper, we present an extended car-following model with consideration of the gravitational force. A new macroscopic model taking into account the slope effects is developed using the relationship between the microscopic and macroscopic variables. The proposed model is applied to reflect the effect of the slope on uniform flow, traffic waves and small perturbation. The simulation results demonstrate that both the angle and the length of the slope have important impacts on traffic flow. The effect of the slope becomes more significant with the increase of the slope angle.

In this paper, a macroscopic traffic flow model for three-lane highways is proposed. The model is an extension of the speed gradient model by taking into account the lane changing. The new source and sink terms of lane change rate are added into the continuity equations and the speed dynamic equations to describe the lane-changing behavior. The result of the steady state analysis shows that our model can describe the lane usage inversion phenomenon. The numerical results demonstrate that the present model effectively reproduces several traffic phenomena observed in real traffic such as shock and rarefaction waves, stop-and-go waves and local clusters.

Based on tremendous real data, a macroscopic model is established, which can depict the process of volatile organic compound (namely, VOC) emissions. Different from previous work, a complete set of sources is taken into account rather than only an isolated source. These data have been processed to support the sample set in order to prove the validity of the theoretical analyses. Besides, the relationship between the industrial production and VOC emissions of industrial source is discussed and depicted. Furthermore, the relationship between the electronic industrial production and VOC emissions is emphasized and calculated. VOC emissions per unit production is investigated. Additionally, the relationship between the number of sample points in the sample set and VOC emissions is illustrated. Then, the control strategy of VOC emissions is proposed by calculating the optimal solutions of each sample set. It is found that the lower the slope of optimal solutions, the lower the average VOC emissions, the better the VOC emissions control effect.

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle $𝜃$ of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

The relapse of tumor is a crucial problem in hormonal therapy of prostate cancer. The so-called androgen-independent cells are considered to be responsible for such a recurrence. These cells are not sensitive to androgen suppression but rather apt to proliferate even in an androgen-poor environment. Bruchovsky et al. in their experimental and clinical studies suggested that intermittent androgen suppression may delay or prevent the relapse when compared with continuous androgen suppression. This paper proposes a model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression. Qualitative analysis shows that the tumor relapse cannot be avoided under continuous androgen suppression for typical parameter values. Numerical simulation supports the above-mentioned experimental and clinical suggestion, and implies an optimal medication scheme of intermittent androgen suppression therapy.

Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a “social crowd”. This paper introduces a novel approach by explicitly incorporating an “activity” variable into the modeling framework, which represents the evolving psychological states of pedestrians and is linked to crowd dynamics. To demonstrate the role of activity, we model pedestrian egress when this variable captures stress and awareness of contagion. In addition, to highlight the importance of dynamic changes in activity, we examine a scenario in which an unexpected incident necessitates alternative exits. These case studies demonstrate that activity plays a pivotal role in shaping crowd behavior. The proposed modeling approach thus opens avenues for more realistic macroscopic crowd descriptions with practical implications for crowd management.

Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In return, relative positions modulate phase synchronization between interacting particles. In the present model, there is no force reciprocity: when a particle attracts another one, the latter repels the former. This results in a pursuit behavior. In this paper, we derive a hydrodynamic model of this swarmalator system and show that it has explicit doubly periodic traveling wave solutions in two space dimensions. These special solutions enjoy non-trivial topology quantified by the index of the phase vector along a period in either dimension. Stability of these solutions is studied by investigating the conditions for hyperbolicity of the model. Numerical solutions of both the particle and hydrodynamic models are shown. They confirm the consistency of the hydrodynamic model with the particle one for small times or large phase noise but also reveal the emergence of intriguing patterns in the case of small phase noise.