Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

G Albi, N Bellomo, L Fermo, SY Ha, J Kim… - … Models and Methods …, 2019 - World Scientific
This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population

DA Messenger, GE Wheeler… - Journal of The Royal …, 2022 - royalsocietypublishing.org
Interacting particle system (IPS) models have proven to be highly successful for describing
the spatial movement of organisms. However, it is challenging to infer the interaction rules …

An improved version of the Hughes model for pedestrian flow

JA Carrillo, S Martin, MT Wolfram - Mathematical Models and …, 2016 - World Scientific
Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals
seek to minimize their travel time but try to avoid regions of high density. One of the basic …

Random feature models for learning interacting dynamical systems

Y Liu, SG McCalla, H Schaeffer - Proceedings of the …, 2023 - royalsocietypublishing.org
Particle dynamics and multi-agent systems provide accurate dynamical models for studying
and forecasting the behaviour of complex interacting systems. They often take the form of a …

An anisotropic interaction model with collision avoidance

C Totzeck - arxiv preprint arxiv:1912.04234, 2019 - arxiv.org
In this article an anisotropic interaction model avoiding collisions is proposed. Starting point
is a general isotropic interacting particle system, as used for swarming or follower-leader …

Self-organization on Riemannian manifolds

RC Fetecau, B Zhang - arxiv preprint arxiv:1802.06089, 2018 - arxiv.org
We consider an aggregation model that consists of an active transport equation for the
macroscopic population density, where the velocity has a nonlocal functional dependence …

[HTML][HTML] First-order aggregation models and zero inertia limits

RC Fetecau, W Sun - Journal of Differential Equations, 2015 - Elsevier
We consider a first-order aggregation model in both discrete and continuum formulations
and show rigorously how it can be obtained as zero inertia limits of second-order models. In …

An anisotropic interaction model for simulating fingerprints

B Düring, C Gottschlich, S Huckemann… - Journal of mathematical …, 2019 - Springer
Evidence suggests that both the interaction of so-called Merkel cells and the epidermal
stress distribution play an important role in the formation of fingerprint patterns during …

From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence

JHM Evers, IA Zisis, BJ van der Linden… - ZAMM‐Journal of …, 2018 - Wiley Online Library
In this paper, we derive from the principle of least action the equation of motion for a
continuous medium with regularized density field in the context of measures. The eventual …

From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

L Bruno, A Corbetta, A Tosin - Journal of Engineering Mathematics, 2016 - Springer
This paper proposes a crowd dynamic macroscopic model grounded on microscopic
phenomenological observations which are upscaled by means of a formal mathematical …