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Anders Johansson

Publications and source records attributed to Anders Johansson.

48 records · Page 3Linked to original sources
arXiv2009

On the Controversy around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models

Daganzo's criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277-286 (1995)] and Aw and Rascle's proposal how to overcome them [A. Aw and M. Rascle, SIAM J. Appl. Math. 60, 916-938 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne's macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models.

physics.soc-ph↗
arXiv2008

Analytical and Numerical Investigation of Ant Behavior Under Crowded Conditions

Swarm intelligence is widely recognized as a powerful paradigm of self-organized optimization, with numerous examples of successful applications in distributed artificial intelligence. However, the role of physical interactions in the organization of traffic flows in ants under crowded conditions has only been studied very recently. The related results suggest new ways of congestion control and simple algorithms for optimal resource usage based on local interactions and, therefore, decentralized control concepts. Here, we present a mathematical analysis of such a concept for an experiment with two alternative ways with limited capacities between a food source and the nest of an ant colony. Moreover, we carry out microscopic computer simulations for generalized setups, in which ants have more alternatives or the alternative ways are of different lengths. In this way and by variation of interaction parameters, we can get a better idea, how powerful congestion control based on local repulsive interactions may be. Finally, we will discuss potential applications of this design principle to routing in traffic or data networks and machine usage in supply systems.

physics.soc-ph↗
arXiv2008

From Crowd Dynamics to Crowd Safety: A Video-Based Analysis

The study of crowd dynamics is interesting because of the various self-organization phenomena resulting from the interactions of many pedestrians, which may improve or obstruct their flow. Besides formation of lanes of uniform walking direction and oscillations at bottlenecks at moderate densities, it was recently discovered that stop-and-go waves [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)] and a phenomenon called "crowd turbulence" can occur at high pedestrian densities [D. Helbing et al., Phys. Rev. E 75, 046109 (2007)]. Although the behavior of pedestrian crowds under extreme conditions is decisive for the safety of crowds during the access to or egress from mass events as well as for situations of emergency evacuation, there is still a lack of empirical studies of extreme crowding. Therefore, this paper discusses how one may study high-density conditions based on suitable video data. This is illustrated at the example of pilgrim flows entering the previous Jamarat Bridge in Mina, 5 kilometers from the Holy Mosque in Makkah, Saudi-Arabia. Our results reveal previously unexpected pattern formation phenomena and show that the average individual speed does not go to zero even at local densities of 10 persons per square meter. Since the maximum density and flow are different from measurements in other countries, this has implications for the capacity assessment and dimensioning of facilities for mass events. When conditions become congested, the flow drops significantly, which can cause stop-and-go waves and a further increase of the density until critical crowd conditions are reached. Then, "crowd turbulence" sets in, which may trigger crowd disasters.

physics.soc-ph↗
arXiv2007

Crowd turbulence: the physics of crowd disasters

The panic stampede is a serious concern during mass events like soccer championship games. Despite huge numbers of security forces and crowd control measures, hundreds of lives are lost in crowd disasters each year. An analysis of video recordings of the annual pilgrimage in Makkah reveals how high-density crowds develop to turbulent dynamics and earthquake-like eruptions, which is impossible to control.

physics.soc-ph↗
arXiv2007

Modeling Crowd Turbulence by Many-Particle Simulations

A recent study [D. Helbing, A. Johansson and H. Z. Al-Abideen, {\it Phys. Rev. E} 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this new model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments are reproduced well, i.e. they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

physics.soc-ph↗
arXiv2007

Orthogonal latin rectangles

We use a greedy probabilistic method to prove that for every $ε> 0$, every $m\times n$ Latin rectangle on $n$ symbols has an orthogonal mate, where $m=(1-ε)n$. That is, we show the existence of a second Latin rectangle such that no pair of the $mn$ cells receives the same pair of symbols in the two rectangles.

math.CO↗
arXiv2007

The Dynamics of Crowd Disasters: An Empirical Study

Many observations in the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on January 12, 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and ``turbulent'' flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particularly, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

physics.soc-ph↗
arXiv2006

Square summability of variations and convergence of the transfer operator

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Brown and Dooley [2], under square summability of variations.

math.DS↗
arXiv2006

Analytical Approach to Continuous and Intermittent Bottleneck Flows

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.

physics.soc-ph↗
arXiv2005

Countable state shifts and uniqueness of g-measures

In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend the result in [11] that square summability of variations of g-functions ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where $g \geq 0$, relaxing the earlier requirement in [11] that inf g>0.

math.DS↗