Multiscale modeling of granular flows with application to crowd dynamics
arXiv:1006.0694 · doi:10.1137/100797515
Abstract
In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting coupled model the two scales coexist and share information. This allows to perform numerical simulations in which the trajectories and the density of the particles affect each other. Crowd dynamics is the motivating application throughout the paper.
30 pages, 9 figures
References in corpus (3)
Cited by in corpus (57)
- Generalized Wasserstein distance and its application to transport equations with source
- Mean-Field Optimal Control
- Nonparametric inference of interaction laws in systems of agents from trajectory data
- Invisible control of self-organizing agents leaving unknown environments
- A hierarchy of heuristic-based models of crowd dynamics
- Mean-Field Sparse Optimal Control
- Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership
- Boltzmann type control of opinion consensus through leaders
- Vision-based macroscopic pedestrian models
- Modeling rationality to control self-organization of crowds: An environmental approach
- Handling obstacles in pedestrian simulations: models and optimization
- Emergent Structural Mechanisms for High-Density Collective Motion Inspired by Human Crowds
- A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line
- Differentiated cell behavior: a multiscale approach using measure theory
- Mathematical models and methods for crowd dynamics control
- Minimal-time mean field games
- Approximate and exact controllability of the continuity equation with a localized vector field
- How can macroscopic models reveal self-organization in traffic flow?
- Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls
- Super-hydrodynamic limit in interacting particle systems
- Leveraging Memory Effects and Gradient Information in Consensus-Based Optimization: On Global Convergence in Mean-Field Law
- Multiscale control of generic second order traffic models by driver-assist vehicles
- A generalized mean-field game model for the dynamics of pedestrians with limited predictive abilities
- Differential Equations Modeling Crowd Interactions
- The effect of perception anisotropy on particle systems describing pedestrian flows in corridors
- Mean-field limit of a hybrid system for multi-lane multi-class traffic
- Pedestrian models with congestion effects
- From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
- Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model
- Modeling micro-macro pedestrian counterflow in heterogeneous domains
- A local version of the Hughes model for pedestrian flow
- Conservation laws in the modeling of moving crowds
- An interface-free multi-scale multi-order model for traffic flow
- Can high-density human collective motion be forecasted by spatiotemporal fluctuations?
- Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
- Dynamic Pedestrian Traffic Assignment with Link Transmission Model for Bidirectional Sidewalk Networks
- Multilevel Modeling as a Methodology for the Simulation of Human Mobility
- Moving in a crowd: human perception as a multiscale process
- Particle based gPC methods for mean-field models of swarming with uncertainty
- Nonsmooth mean field games with state constraints
- Blended numerical schemes for the advection equation and conservation laws
- A Class of Non-Local Models for Pedestrian Traffic
- Control to flocking of the kinetic Cucker-Smale model
- Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
- Sparse Stabilization and Control of Alignment Models
- Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow
- The Mean Field Kinetic Equation for Interacting Particle Systems with Non-Lipschitz Force
- Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes
- Derivation and analysis of continuum models for crossing pedestrian traffic
- Hydrodynamic limit in a particle system with topological interactions
- A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks with application to traffic flow models
- From the Micro-scale to Collective Crowd Dynamics
- Preventing congestion in crowd dynamics caused by reversing flow
- Cyber-Physical Modeling and Control of Crowd of Pedestrians: A Review and New Framework
- Lane formation by side-stepping
- Modeling tagged pedestrian motion: a mean-field type game approach
- Crowds reaching targets by maximizing entropy: a Clausius-Duhem inequality approach