Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices We also discuss the physics of wind-blown sand and dune formation on Venus and Titan

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The physics of wind-blown sand and dust

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

/pdf/the-physics-of-wind-blown-sand-and-dust-4ggy9vm6xy.pdf

Granular materials display a variety of behaviors that are in many ways different from those of other substances. They cannot be easily classified as either solids or liquids. This has prompted the generation of analogies between the physics found in a simple sandpile and that found in complicated microscopic systems, such as flux motion in superconductors or spin glasses. Recently, the unusual behavior of granular systems has led to a number of new theories and to a new era of experimentation on granular systems.

https://science.sciencemag.org/content/sci/255/5051/1523.full.pdf

Physics of the Granular State

Traffic flow is a kind of many-body system of strongly interacting vehicles. Traffic jams are a typical signature of the complex behaviour of vehicular traffic. Various models are presented to understand the rich variety of physical phenomena exhibited by traffic. Analytical and numerical techniques are applied to study these models. Particularly, we present detailed results obtained mainly from the microscopic car-following models. A typical phenomenon is the dynamical jamming transition from the free traffic (FT) at low density to the congested traffic at high density. The jamming transition exhibits the phase diagram similar to a conventional gas-liquid phase transition: the FT and congested traffic correspond to the gas and liquid phases, respectively. The dynamical transition is described by the time-dependent Ginzburg-Landau equation for the phase transition. The jamming transition curve is given by the spinodal line. The metastability exists in the region between the spinodal and phase separation lines. The jams in the congested traffic reveal various density waves. Some of these density waves show typical nonlinear waves such as soliton, triangular shock and kink. The density waves are described by the nonlinear wave equations: the Korteweg-de-Vries (KdV) equation, the Burgers equation and the Modified KdV equation. Subjects like the traffic flow such as bus-route system and pedestrian flow are touched as well. The bus-route system with many buses exhibits the bunching transition where buses bunch together with proceeding ahead. Such dynamic models as the car-following model are proposed to investigate the bunching transition and bus delay. A recurrent bus exhibits the dynamical transition between the delay and schedule-time phases. The delay transition is described in terms of the nonlinear map. The pedestrian flow also reveals the jamming transition from the free flow at low density to the clogging at high density. Some models are presented to study the pedestrian flow. When the clogging occurs, the pedestrian flow shows the scaling behaviour.

http://iopscience.iop.org/article/10.1088/0034-4885/65/9/203/pdf

The physics of traffic jams

In the Brazil nut problem (BNP), hard spheres with larger diameters rise to the top. There are various explanations (percolation, reorganization, convection), but a broad understanding or control of this effect is by no means achieved. A theory is presented for the crossover from BNP to the reverse Brazil nut problem based on a competition between the percolation effect and the condensation of hard spheres. The crossover condition is determined, and theoretical predictions are compared to molecular dynamics simulations in two and three dimensions.

https://www2.msm.ctw.utwente.nl/sluding/PAPERS/PRL003423.pdf

Reverse Brazil nut problem: competition between percolation and condensation.

The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ``phantom'' traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg--de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.

Traffic jams, granular flow, and soliton selection

Current continuum models based on the theory of plasticity have failed to describe the observed gravitational flow patterns of granular particles in a confined geometry. We propose a random-walk model that correctly predicts the shape of the free surface of the granular media and the solid stream lines with and without obstacles. We present simulation results that qualitatively exhibit many of the unique features of granular flows. The simulation results are also compared with experimental data.

Random-walk approach to granular flows.

We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations.

Hydrodynamic description of granular convection.

We present a thermodynamic theory of weakly excited two-dimensional granular systems from the viewpoint of elementary excitations of spinless Fermions. We introduce a global temperature $T$ that is associated with the acceleration amplitude $\ensuremath{\gamma}$ in a vibrating bed. We show that the configurational statistics of weakly excited granular materials in a vibrating bed obey the Fermi statistics.

Daniel C. Hong

Papers

Reverse Brazil nut problem: competition between percolation and condensation.

Traffic jams, granular flow, and soliton selection

Random-walk approach to granular flows.

Hydrodynamic description of granular convection.

Thermodynamic Theory of Weakly Excited Granular Systems