RECORD
Lane formation by side-stepping
Analysis of PDEs · Submitted 30 Jul 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We discuss the existence of special stationary solutions, which correspond to the formation of directional lanes and prove existence of global in time bounded weak solutions.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. The pedestrian dynamics are driven by aversion and cohesion, i.e. the tendency to follow individuals from the own group and step aside in the case of contraflow. We start with a 2D lattice based approach, in which the transition rates reflect the described dynamics, and derive the corresponding PDE system by formally passing to the limit in the spatial and temporal discretization. We discuss the existence of special stationary solutions, which correspond to the formation of directional lanes and prove existence of global in time bounded weak solutions. The proof is based on an approximation argument and entropy inequalities. Furthermore we illustrate the behavior of the system with numerical simulations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. | contribution 0.76 | 0.76 | 0.03 | asserted 0.95 |
| s1 | The pedestrian dynamics are driven by aversion and cohesion, i.e. the tendency to follow individuals from the own group and step aside in the case of contraflow. | background 0.68 | 0.17 | 0.05 | asserted 1.00 |
| s2 | We start with a 2D lattice based approach, in which the transition rates reflect the described dynamics, and derive the corresponding PDE system by formally passing to the limit in the spatial and temporal discretization. | method 0.99 | 0.96 | 0.03 | asserted 1.00 |
| s3 | We discuss the existence of special stationary solutions, which correspond to the formation of directional lanes and prove existence of global in time bounded weak solutions. | result 0.92 | 0.95 | 0.57 | asserted 1.00 |
| s4 | The proof is based on an approximation argument and entropy inequalities. | method 1.00 | 0.89 | 0.04 | asserted 1.00 |
| s5 | Furthermore we illustrate the behavior of the system with numerical simulations. | method 0.63 | 0.95 | 0.05 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. The pedestrian dynamics are driven by aversion and cohesion, i.e. the tendency to follow individuals from the own group and step aside in the case of contraflow. We start with a 2D lattice based approach, in which the transition rates reflect the described dynamics, and derive the corresponding PDE system by formally passing to the limit in the spatial and temporal discretization. We discuss the existence of special stationary solutions, which correspond to the formation of directional lanes and prove existence of global in time bounded weak solutions. The proof is based on an approximation argument and entropy inequalities. Furthermore we illustrate the behavior of the system with numerical simulations.
Human review
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
-
Macroscopic models describing the individual interactions of these particles among themselves as well as their environment lead to complex systems of differential equations (cf. e.g. [ref] ).
Cross-diffusion systems with excluded volume effects and asymptotic gradient flows · Introduction · 0.95
What it cites · 2 sentences without a confident label
Uses the method or tool of 1 paper
-
The weak convergence of the terms in [ref] and [ref] can be shown with the help of a generalized Aubin-Lions Lemma (see Lemma 7 in [ref] ).
Analysis of degenerate cross-diffusion population models with volume filling · The limit $τ→0$ · 0.97
Compares with 2 papers
-
A major difference in the analysis of the system compared to related ones in the literature (cf. [ref] , [ref] , [ref] , [ref] ) is the fact that we have an anisotropic diffusion and no gradient flow structure, which requires a different entropy and a priori estimates.
Analysis of degenerate cross-diffusion population models with volume filling · Main result · 1.00
-
Note that we follow a different approach than Jüngel in [ref] , which has the advantage that the method is based on an $H^1$-regularization only and does not require the additional Bilaplace operator.
The boundedness-by-entropy principle for cross-diffusion systems · Introduction · 0.95
Cites as background 1 paper
-
Similar models have been proposed in the literature, for example in the context of ion transport, cf. [ref] or population dynamics, cf. [ref] .
Analysis of degenerate cross-diffusion population models with volume filling · Introduction · 0.86
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.