Related papers: The Lagrangian coordinate system and what it means…
In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…
We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. Such results were previously only known in the convex case, of which the current work represents a significant improvement.…
Real-life, out-of-laboratory, measurements of pedestrian movements allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the wide heterogeneity that characterizes crowd flows over…
We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…
Different families of models first developed for fluid mechanics have been extended to road, pedestrian, or intracellular transport. These models allow to describe the systems at different scales and to account for different aspects of…
Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures that determine material…
Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs.…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
Crowd flow describes the elementary group behavior of crowds. Understanding the dynamics behind these movements can help to identify various abnormalities in crowds. However, developing a crowd model describing these flows is a challenging…
This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is…
We show how a recently published 2d model for traffic flow can be further improved. Besides other improvements and simplifications, we present not only a method to compute the necessary time step restrictions, but also a subcycling for the…
In this paper we devise a microscopic (agent-based) mathematical model for reproducing crowd behaviour in a specific scenario: a number of pedestrians, consisting of numerous social groups, flow along a corridor until a gate located at the…
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…
The formation and development of oscillations is an important traffic flow phenomenon. Recent studies found that along a vehicle platoon described in the Lagrangian specification, traffic oscillations grow in a concave way. Since stationary…
The Lagrangian complex-space singularities of the steady Eulerian flow with stream function $\sin x_1 \cos x_2$ are studied by numerical and analytical methods. The Lagrangian singular manifold is analytic. Its minimum distance from the…
Recently different formulations of the first-order Lighthill-Whitham-Richards (LWR) model have been identified in different coordinates and state variables. However, there exists no systematic method to convert higher-order continuum models…
In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers.Using an…
A numerical model and parallel software for 3D simulations of granular flows have been developed based on the Lagrangian particle (LP) method [R.Samulyak, X. Wang, H.-C. Chen, Lagrangian particle method for compressible fluid dynamics, J.…