Properties of pedestrians walking in line: Stepping behavior

In human crowds, interactions among individuals give rise to a variety of self-organized collective motions that help the group to effectively solve the problem of coordination. However, it is still not known exactly how humans adjust their behavior locally, nor what are the direct consequences on the emergent organization. One of the underlying mechanisms of adjusting individual motions is the stepping dynamics. In this paper, we present first quantitative analysis on the stepping behavior in a one-dimensional pedestrian flow studied under controlled laboratory conditions. We find that the step length is proportional to the velocity of the pedestrian, and is directly related to the space available in front of him, while the variations of the step duration are much smaller. This is in contrast with locomotion studies performed on isolated pedestrians and shows that the local density has a direct influence on the stepping characteristics. Furthermore, we study the phenomena of synchronization -walking in lockstep- and show its dependence on flow densities. We show that the synchronization of steps is particularly important at high densities, which has direct impact on the studies of optimizing pedestrians flow in congested situations. However, small synchronization and antisynchronization effects are found also at very low densities, for which no steric constraints exist between successive pedestrians, showing the natural tendency to synchronize according to perceived visual signals.Comment: 8 pages, 5 figure

Properties of pedestrians walking in line - Fundamental diagrams

We present experimental results obtained for a one-dimensional flow using high precision motion capture. The full pedestrians' trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between the instantaneous velocity and spatial headway (distance to the predecessor). While the latter was found to be linear in previous experiments, we show that it is rather a piecewise linear behavior which is found if larger density ranges are covered. Indeed, our data clearly exhibits three distinct regimes in the behavior of pedestrians that follow each other. The transitions between these regimes occur at spatial headways of about 1.1 and 3 m, respectively. This finding could be useful for future modeling.Comment: 9 figures, 3 table

Frozen shuffle update for an asymmetric exclusion process on a ring

We introduce a new rule of motion for a totally asymmetric exclusion process (TASEP) representing pedestrian traffic on a lattice. Its characteristic feature is that the positions of the pedestrians, modeled as hard-core particles, are updated in a fixed predefined order, determined by a phase attached to each of them. We investigate this model analytically and by Monte Carlo simulation on a one-dimensional lattice with periodic boundary conditions. At a critical value of the particle density a transition occurs from a phase with `free flow' to one with `jammed flow'. We are able to analytically predict the current-density diagram for the infinite system and to find the scaling function that describes the finite size rounding at the transition point.Comment: 16 page

Intersection of two TASEP traffic lanes with frozen shuffle update

Motivated by interest in pedestrian traffic we study two lanes (one-dimensional lattices) of length $L$ that intersect at a single site. Each lane is modeled by a TASEP (Totally Asymmetric Exclusion Process). The particles enter and leave lane $\sigma$ (where $\sigma=1,2$) with probabilities $\alpha_\sigma$ and $\beta_\sigma$, respectively. We employ the `frozen shuffle' update introduced in earlier work [C. Appert-Rolland et al, J. Stat. Mech. (2011) P07009], in which the particle positions are updated in a fixed random order. We find analytically that each lane may be in a `free flow' or in a `jammed' state. Hence the phase diagram in the domain $0\leq\alpha_1,\alpha_2\leq 1$ consists of four regions with boundaries depending on $\beta_1$ and $\beta_2$. The regions meet in a single point on the diagonal of the domain. Our analytical predictions for the phase boundaries as well as for the currents and densities in each phase are confirmed by Monte Carlo simulations.Comment: 7 figure

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].Comment: 4 pages, 3 eps figures, RevTex, minor changes to bring in line with published version. Mobility values added to Table

Observations of Toroidal Coupling for Low-N Alfven Modes in the Tca Tokamak

The antenna structure in the TCA tokamak is phased to excite preferentially Alfven waves with known toroidal and poloidal wave numbers. Surprisingly, the loading spectrum includes both discrete and continuum modes with poloidal wave numbers incompatible with the antenna phasing. These additional modes, which are important for our heating experiments, can be attributed to linear mode coupling induced by the toroidicity of the plasma column, when we take into account ion-cyclotron effects

The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the single-particle collision frequency and \tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.