396 research outputs found
Multiscale modeling of granular flows with application to crowd dynamics
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.Comment: 30 pages, 9 figure
Multiscale modeling of granular flows with application to crowd dynamics
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.Comment: 30 pages, 9 figure
From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
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 tested by considering the pedestrian traffic along footbridges, of
interest for Structural and Transportation Engineering. The genuinely
macroscopic quantitative description of the crowd flow directly matches the
engineering need of bulk results. However, three issues beyond the sole
modelling are of primary importance: the pedestrian inflow conditions, the
numerical approximation of the equations for non trivial footbridge geometries,
and the calibration of the free parameters of the model on the basis of in situ
measurements currently available. These issues are discussed and a solution
strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201
How can macroscopic models reveal self-organization in traffic flow?
In this paper we propose a new modeling technique for vehicular traffic flow,
designed for capturing at a macroscopic level some effects, due to the
microscopic granularity of the flow of cars, which would be lost with a purely
continuous approach. The starting point is a multiscale method for pedestrian
modeling, recently introduced in Cristiani et al., Multiscale Model. Simul.,
2011, in which measure-theoretic tools are used to manage the microscopic and
the macroscopic scales under a unique framework. In the resulting coupled model
the two scales coexist and share information, in the sense that the same system
is simultaneously described from both a discrete (microscopic) and a continuous
(macroscopic) perspective. This way it is possible to perform numerical
simulations in which the single trajectories and the average density of the
moving agents affect each other. Such a method is here revisited in order to
deal with multi-population traffic flow on networks. For illustrative purposes,
we focus on the simple case of the intersection of two roads. By exploiting one
of the main features of the multiscale method, namely its
dimension-independence, we treat one-dimensional roads and two-dimensional
junctions in a natural way, without referring to classical network theory.
Furthermore, thanks to the coupling between the microscopic and the macroscopic
scales, we model the continuous flow of cars without losing the right amount of
granularity, which characterizes the real physical system and triggers
self-organization effects, such as, for example, the oscillatory patterns
visible at jammed uncontrolled crossroads.Comment: 7 pages, 7 figure
Mean-Field Sparse Optimal Control
We introduce the rigorous limit process connecting finite dimensional sparse
optimal control problems with ODE constraints, modeling parsimonious
interventions on the dynamics of a moving population divided into leaders and
followers, to an infinite dimensional optimal control problem with a constraint
given by a system of ODE for the leaders coupled with a PDE of Vlasov-type,
governing the dynamics of the probability distribution of the followers. In the
classical mean-field theory one studies the behavior of a large number of small
individuals freely interacting with each other, by simplifying the effect of
all the other individuals on any given individual by a single averaged effect.
In this paper we address instead the situation where the leaders are actually
influenced also by an external policy maker, and we propagate its effect for
the number of followers going to infinity. The technical derivation of the
sparse mean-field optimal control is realized by the simultaneous development
of the mean-field limit of the equations governing the followers dynamics
together with the -limit of the finite dimensional sparse optimal
control problems.Comment: arXiv admin note: text overlap with arXiv:1306.591
Modeling, Evaluation, and Scale on Artificial Pedestrians: A Literature Review
Modeling pedestrian dynamics and their implementation in a computer are challenging and important issues in the knowledge areas of transportation and computer simulation. The aim of this article is to provide a bibliographic outlook so that the reader may have quick access to the most relevant works related to this problem. We have used three main axes to organize the article's contents: pedestrian models, validation techniques, and multiscale approaches. The backbone of this work is the classification of existing pedestrian models; we have organized the works in the literature under five categories, according to the techniques used for implementing the operational level in each pedestrian model. Then the main existing validation methods, oriented to evaluate the behavioral quality of the simulation systems, are reviewed. Furthermore, we review the key issues that arise when facing multiscale pedestrian modeling, where we first focus on the behavioral scale (combinations of micro and macro pedestrian models) and second on the scale size (from individuals to crowds). The article begins by introducing the main characteristics of walking dynamics and its analysis tools and concludes with a discussion about the contributions that different knowledge fields can make in the near future to this exciting area
Macroscopic modeling and simulations of room evacuation
We analyze numerically two macroscopic models of crowd dynamics: the
classical Hughes model and the second order model being an extension to
pedestrian motion of the Payne-Whitham vehicular traffic model. The desired
direction of motion is determined by solving an eikonal equation with density
dependent running cost, which results in minimization of the travel time and
avoidance of congested areas. We apply a mixed finite volume-finite element
method to solve the problems and present error analysis for the eikonal solver,
gradient computation and the second order model yielding a first order
convergence. We show that Hughes' model is incapable of reproducing complex
crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally,
using the second order model, we study numerically the evacuation of
pedestrians from a room through a narrow exit.Comment: 22 page
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