Related papers: Probabilistic dynamics of small groups in crowd fl…
Currently, the safety of people has become a very important problem in different places including subway station, universities, colleges, airport, shopping mall and square, city squares. Therefore, considering intelligence event detection…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
In a recent paper a set of differential equations was proposed to describe a social process, where pairs of partners emerge in a community. The choice was performed on a basis of attractive resources and of random initial preferences. An…
Modeling the dynamics of people walking is a problem of long-standing interest in computer vision. Many previous works involving pedestrian trajectory prediction define a particular set of individual actions to implicitly model group…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
An ongoing challenge in the mathematical modeling of biological aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid,…
A drop bouncing on a vertically-vibrated surface may self-propel forward by standing waves and travels along a fluid interface. This system called walking drop forms a non-quantum wave-particle association at the macroscopic scale. The…
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…
The mathematical modeling of crowds is complicated by the fact that crowds possess the behavioral ability to develop and adapt moving strategies in response to the context. For example, in emergency situations, people tend to alter their…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Walking is a fundamental activity of our daily life not only for moving to other places but also for interacting with surrounding environment. While walking on the streets, pedestrians can be aware of attractions like shopping windows. They…
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…
Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors,…
Collective human movement is a hallmark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and…
We study the influence of selfish vs. polite behaviours on the dynamics of a pedestrian evacuation through a narrow exit. To this end, experiments involving about 80 participants with distinct prescribed behaviours are performed;…
Understanding pedestrian dynamics is critical for mitigating crowd-related risks and improving public safety. In this work, we propose a data-driven mesoscopic modeling framework that combines the kinetic theory of active particles with…
Environments such as shopping malls, airports, or hospital emergency departments often experience crowding, with many people simultaneously requesting service. Crowding is highly noisy, with sudden overcrowding "spikes". Past research has…
We consider the problem of categorizing and describing the dynamic properties and behaviours of crowds over time. Previous work has tended to focus on a relatively static "typology"-based approach, which does not account for the fact that…
We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…