Related papers: Analyzing Stop-and-Go Waves by Experiment and Mode…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
Pedestrians adjust both speed and stride length when they navigate difficult situations such as tight corners or dense crowds. They try to avoid collisions and to preserve their personal space. State-of-the-art pedestrian motion models…
Experiments with pedestrians could depend strongly on initial conditions. Comparisons of the results of such experiments require to distinguish carefully between transient state and steady state. In this work, a feasible algorithm -…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
Real-world potential of stop-and-go wave smoothing at scale remains largely unquantified. Smoothing freeway traffic waves requires creating a gap so the wave can dissipate, but the gap suggested is often too large and impractical. We…
Since the beginning of the century, capturing trajectories of pedestrian streams precisely from video recordings has been possible. To enable measurements at high density, the heads of the pedestrians are marked and tracked, thus providing…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
Classical second order models of pedestrian dynamics, like the social-force model, suffer from various unrealistic behaviors in the dynamics, e.g. backward motion, oscillations and overlapping of pedestrians. These effects are not related…
A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
This paper offers a comprehensive examination of single-file experiments within the field of pedestrian dynamics, providing a review from both theoretical and analytical perspectives. It begins by tracing the historical context of…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…
A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…
In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…
We study the Korteweg--de Vries equation on a metric star graph and investigate existence of solitary waves on the metric graph in terms of the coefficients of the equation on each edge, the coupling condition at the central vertex of the…
Extensive research in pedestrian dynamics has primarily focused on crowded conditions and associated phenomena, such as lane formation, evacuation, etc. Several force-based models have been developed to predict the behavior in these…
Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The…
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like…
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…