Velocity statistics of the Nagel-Schreckenberg model

Bain, Nicolas; Emig, Thorsten; Ulm, Franz‐Josef; Schreckenberg, Michael

doi:10.1103/physreve.93.022305

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…In other words, the cells cannot efficiently transit the confined geometry of the ADM when the motion is overly disordered. As a result, the net outflow from the ADM decreases relative to the inflow creating a condition that resembles automobile traffic congestion (Bain et al, 2016). These simulations thus suggest that overly disordered cell motion slows trunk elongation.…”

Section: Resultsmentioning

confidence: 99%

Patterned Disordered Cell Motion Ensures Vertebral Column Symmetry

et al. 2017

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Summary The biomechanics of posterior embryonic growth must be dynamically regulated to ensure bilateral symmetry of the spinal column. Throughout vertebrate trunk elongation, motile mesodermal progenitors undergo an order to disorder transition via EMT and sort symmetrically into the left and right paraxial mesoderm. We combine theoretical modeling of cell migration in a tailbud-like geometry with experimental data analysis to assess the importance of ordered and disordered cell motion. We find that increasing order in cell motion causes a phase transition from symmetric to asymmetric body elongation. In silico and in vivo, overly ordered cell motion converts normal anisotropic fluxes into stable vortices near the posterior tailbud, contributing to asymmetric cell sorting. Thus, disorder is a physical mechanism that ensures the bilateral symmetry of the spinal column. These physical properties of the tissue connect across scales such that patterned disorder at the cellular level leads to the emergence of organism-level order.

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Section: Resultsmentioning

confidence: 99%

Patterned Disordered Cell Motion Ensures Vertebral Column Symmetry

et al. 2017

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“…,N}) outside moved with velocities v i v max −1, the maximum of the flow, classically defined as should appear at ρ f . Due to a more complex velocity distribution [12] with nonzero probabilities for velocities between 1 and v max − 2, the free density ρ f is not the same as the critical density ρ c defined as the point where the maximum flow is reached (see Fig. 5).…”

Section: Free Density With Jamsmentioning

confidence: 99%

“…The continuous transition is, however, very interesting, especially considering the probability distribution functions presented in Ref. [12] as they show an almost zero probability for any velocities except for v max or v max − 1 in the free-flow regime. Therefore, we argue that stopped vehicles are at least a good indicator for existing jams, although not being a genuine order parameter for a finite number v max of velocity levels.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the aforementioned velocity statistics presented in Ref. [12] indicate that deceleration and acceleration around jams can be neglected for total densities inside the free-flow regime of the model. To approximate P in (ρ f ), we consider up to d = v max cells upstream of a jam; see Fig.…”

Section: Free Density With Jamsmentioning

confidence: 99%

“…[12] took a closer look at the velocity statistics in the NaSch-CA and presented a possibly noncontinuous transition in the probability to find a stopped vehicle. However, improved simulations performed for the present work show that the impression of a noncontinuity turns out to be a finite-size effect, and the aforementioned argument in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow

et al. 2017

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We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P (v = 0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P (v ∈ {0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.

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