A continuum theory for the flow of pedestrians

By Roger L. Hughes. 2002

1,098 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Ocean Engineering, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/d167eb654abd485d9de28a6c004797c958a44e5c

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In Control and Systems Engineering

In Ocean Engineering

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Citations in the corpus

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives (2011, background): “The generalization is immediate as both equations can be written in two space dimensions (see Hughes [123], [124]) as   ∂tρ+∇x · (ρ ξ) = 0 ,”
A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC (2011, background): “We note that the constructions in [22, 23] and [14] fit in the present setting.”
An efficient discontinuous Galerkin method on triangular meshes for a pedestrian flow model (2008, background): “A systematic framework for the dynamic macroscopic modeling of pedestrian flow problems was given in [1], but the user equilibrium concept was not explicitly considered.”
A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE (2010, background): “Crowd motion; Gradient Flow; Wasserstein distance; Continuity equation.”
Simulation of pedestrian crowds in normal and evacuation situations (2002, background): “He conjectured that pedestrian crowds behave similar to gases or fluids ([35–38], see also [39,40]).”
Human mobility: Models and applications (2017, neutral): “Possible choices are a linear relation, f (ρ) = ρ − ρmax, keeping ρ < ρmax or a non linear one, f (ρ) = (ρ− ρmax)(2), among others [221, 222, 223].”
Modeling crowd evacuation of a building based on seven methodological approaches (2009, background): “In order to understand the mechanics of pedestrian crowd motion in especially large crowds, Hughes [50] derived the equations of motion governing the two-dimensional flow of pedestrians.”
Abnormal crowd behavior detection using social force model (2009, background): “individual and group behaviors in crowded scenes [17][18].”
Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow (2011, background): “Some of these models are local in ρ (see [4,11,17,18,20,21]); other models use not only the local density ρ(t, x) but the entire distribution of ρ, typically they depend on the convolution product ρ(t) ∗ η (see [6–9,14,23]) which represents the spatial average of the density.”
Crowded Scene Analysis: A Survey (2015, methodology): “For the continuum-based approach, the crowd is treated as a physical ﬂuid with particles, thus a lot of analytical methods from statistical mechanics and thermodynamics are introduced [43], [44].”
Pedestrian flows and non‐classical shocks (2005, methodology): “The study of models for pedestrian flows is receiving an increasing attention in the specialized literature, see [12, 13, 14, 15, 16, 23, 24].”
Evacuation Dynamics: Empirical Results, Modeling and Applications (2008, background): “Therefore it is not surprising that, very much like for vehicular dynamics, the earliest models of pedestrian dynamics took inspiration from hydrodynamics or gas-kinetic theory [51, 62, 69, 70].”
Simulation of pedestrian flows by optimal control and differential games (2003, background): “Pedestrian co-operation plays a very important role in pedestrian flows (see References [4–6]).”
Continuum crowds (2006, methodology): “A full derivation can be found in [Hughes 2002], and in a subsequent application to a medieval battle analysis [Clements and Hughes 2004].”
Control of the Continuity Equation with a Non Local Flow (2009, methodology): “A model for pedestrian flow Macroscopic models for pedestrian movements are based on the continuity equation, see [12,14,16,19], possibly together with a second equation, as in [17].”
Core Challenges of Social Robot Navigation: A Survey (2021, methodology): “The continuum model [108, 113] describes the pedestrian flow dynamics through the use of the continuum theory.”