Convegno
Dagli individui alla collettività: folle e sciami
15-16 novembre 2012
Consiglio Nazionale delle Ricerche
Piazzale Aldo Moro 7, 00185 Roma
Aula Conferenze
Libretto degli abstract
Organizzazione:
Andrea Tosin
Istituto per le Applicazioni del Calcolo “M. Picone”
Consiglio Nazionale delle Ricerche
Patrocinio:
Gruppo di Attività SIMAI sui Sistemi Complessi
Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Bazzani
MODELING SELF-ORGANIZED PHENOMENA IN PEDESTRIAN
DYNAMICS
ARMANDO BAZZANI∗
Dipartimento di Fisica
Università di Bologna
Abstract
Pedestrian dynamics has been mainly simulated by using physical-like models
to study crowding effects for safety reasons. However despite of some successful
results, the Newtonian force models are still not fully consistent with experimental observations. In particular this is the case when one considers cognitive
aspects in individual behavior. Recently new cognitive inspired models have
been proposed where the pedestrian dynamics is related with cognitive processes due to local vision (e.g. collision avoidance dynamics) and cooperative versus
selfish behavior [1, 2]. The collective self-organized states of crowd dynamics
can be seen as emergent properties from decisional process at individual level.
We present a simple microscopic model for pedestrian dynamics that integrates
local vision effects and the existence of counteracting strategies in the individual
decision mechanisms. By using numerical simulations we discuss the emergence
of self-organized dynamical states and the transition from ordered cooperative
states to “panic states”. A statistical physics approach is also proposed.
Bibliografia
[1] A. Bazzani, B. Giorgini, F. Zanlungo, and S. Rambaldi. Cognitive Dynamics
in an Automata Gas. In R. Serra, M. Villani, and I. Poli, editors, Artificial
Life and Evolutionary Computation, pages 3–19, Singapore, 2009. World
Scientific. Proceedings of Wivace 2008.
[2] M. Moussaı̈d, D. Helbing, and G. Theraulaz. How simple rules determine pedestrian behavior and crowd disasters. Proc. Nat. Acad. Sci. USA,
108(17):6884–6888, 2011.
∗ Con
B. Giorgini, S. Rambaldi, Dipartimento di Fisica, Università di Bologna
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Bellomo
MODELING AND SIMULATION OF FREE BOUNDARY PROBLEMS
FOR CROWD DYNAMICS BY THE KINETIC THEORY FOR
ACTIVE PARTICLES
NICOLA BELLOMO
Dipartimento di Scienze Matematiche
Politecnico di Torino
Abstract
The contents of this lecture is presented in three parts. The first part presents
a modeling approach to crowd dynamics viewed as a large living system by methods of the mathematical kinetic theory for active particles [1], which includes
a detailed analysis of the complexity features of the system under consideration as well as development of multi-scale methods [2, 3]. The second part is
devoted to the development of splitting methods to simulate the overall dynamics focusing on depicting the evolution of the moving boundary of the domain
containing the crowd. The presentation is constantly focused on the modeling
complex large systems of individuals interacting in a non-linear manner, which,
as known, are difficult to model and understand at a global level. Specifically,
to describe the emerging collective behavior of the overall system, based only
on the knowledge of the dynamics of their individual elements. The third part
presents some perspective ideas and research hints towards the modeling and
simulation of animal swarms looking at the beautiful shapes of swarms [4].
Bibliografia
[1] N. Bellomo. Modeling complex living systems – A kinetic theory and stochastic game approach. Modeling and Simulation in Science, Engineering and
Technology. Birkhäuser, Boston, 2008.
[2] N. Bellomo and A. Bellouquid. On the modeling of crowd dynamics: Looking
at the beautiful shapes of swarms. Netw. Heterog. Media, 6(3):383–399, 2011.
[3] N. Bellomo and C. Dogbé. On the modelling of traffic and crowds. A survey
of models, speculations, and perspectives. SIAM Rev., 53(3):409–463, 2011.
[4] N. Bellomo and J. Soler. On the mathematical theory of the dynamics
of swarms viewed as complex systems. Math. Models Methods Appl. Sci.,
22(suppl. 1):1140006 (29 pages), 2012.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Bruno
PEDESTRIANS, GROUPS AND CROWDS: STRUCTURAL EFFECTS
ON FOOTBRIDGES
LUCA BRUNO∗
Dipartimento di Architettura e Design
Politecnico di Torino
Abstract
After the closure of the London Millennium Bridge in 2000 due to the so-called
Synchronous Lateral Excitation (SLE) phenomenon, an intense research activity related to footbridge dynamics under human-induced excitation has been
carried out (reviewed e.g. in [2, 5, 6]). The SLE is a crowd-structure interaction phenomenon, characterized by the following key features: self-excitation,
due to the synchronization between the pedestrians and the laterally moving
walking platform (lock-in); synchronization among the pedestrians themselves,
when walking is constrained by the surroundings pedestrians in dense crowd;
self-limitation of the structural response, when the pedestrians stop because of
excessive vibrations.
This contribution proposes an introduction to this engineering problem and
an overview on the modelling strategies and codified practices that have been
proposed in literature to deal with it. The earlier and most common approach
in engineering considers and models the pedestrians as a simple action applied
to the structure. The problem, therefore, reduces to the calculation of the structural response under the action of a suitable load model. According to this approach, several load models have been proposed (reviewed e.g. in [3]). Codified
design guidelines (e.g. [4]) handle collective phenomena by introducing different
design scenarios referred to single pedestrian and not well defined “groups” and
“crowd”. A different approach - inspired by crowd models mainly developed in
the fields of applied mathematics, physics and transportation engineering (e.g.
reviewed in [1]) - has been recently applied to this problem. It considers the
pedestrians as a dynamical system, which has its own governing rules and that
interacts with the structure system. This approach results in coupled models
characterized by non-linear, multi-physic and multi-scale features.
In particular, two issues of the problem are addressed in the contribution:
i. how to model the transition and the coexistence of individual and collective
phenomena (“pedestrian, group and crowd” in civil engineering literature) and
their effects on structures? ii. How to account for the inherent randomness of
the walking pedestrians (“intersubject” and “intrasubject variability” in civil
engineering literature) in a probability-based design of structures? The above
mentioned issues are still open and could benefit of the contribution of research
fields beside civil engineering (e.g. applied mathematics and physics) to evaluate
new modelling perspectives towards real world applications.
∗ Con
F. Venuti, Dipartimento di Architettura e Design, Politecnico di Torino
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Dagli individui alla collettività: folle e sciami
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Bibliografia
Bibliografia
[1] N. Bellomo and C. Dogbé. On the modelling of traffic and crowds. A survey
of models, speculations, and perspectives. SIAM Rev., 53(3):409–463, 2011.
[2] E. T. Ingólfsson, C. T. Georgakis, and J. Jönsson. Pedestrian-induced lateral
vibrations of footbridges: A literature review. Eng. Struct., 45:21–52, 2012.
[3] V. Racic, A. Pavic, and J. M. W. Brownjohn. Experimental identification
and analytical modelling of human walking forces: Literature review. J.
Sound Vib., 326(1):1–49, 2009.
[4] F. Sétra.
Assessment of vibrational behaviour of footbridges under
pedestrian loading. Technical report, 2006. Technical guide SETRA.
[5] F. Venuti and L. Bruno. Crowd-structure interaction in lively footbridges
under synchronous lateral excitation: A literature review. Phys. Life Rev.,
6(3):176–206, 2009.
[6] S. Živanović, A. Pavic, and P. Reynolds. Vibration serviceability of footbridges under human-induced excitation: a literature review. J. Sound Vib.,
279:1–74, 2005.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Colombo
INDIVIDUALS-POPULATION INTERACTIONS: MODELING AND
CONFINEMENT PROBLEMS
RINALDO M. COLOMBO
Dipartimento di Matematica
Università degli Studi di Brescia
Abstract
Various analytical frameworks are able to describe the interaction between agents and a moving population. First, within a PDE setting, this presentation describes a well posedness result. Then, a model based on differential inclusions is
presented. In this context, recently obtained positive and negative confinement
results are discussed.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Corbetta
INDIVIDUAL DYNAMICS AND COLLECTIVE PERCEPTION IN
BUILT ENVIRONMENTS
ALESSANDRO CORBETTA
Dipartimento di Ingegneria Strutturale, Edile e Geotecnica
Politecnico di Torino
Abstract
A mathematical model for the active motion of pedestrians in a crowd is proposed, hence a reasoned application is considered.
The pedestrian motion is phenomenologically approached reckoning the interactions that, in a crowd, exist between single individuals and the collectivity
around them. These interactions, indeed, are regarded as a reaction to perceptions one has of his surroundings. On this basis, a model formulated in terms
of a conservation law for the pedestrian mass is deduced. Particularly, the pedestrian mass is considered in the general sense of measures and its evolution
is determined by non-local interaction terms. The obtained model is further
read in a probabilistic sense, aiming at retrieving statistics about agents’ distribution. Affine statistical data are currently used in the engineering practice in
order to assess performances and serviceability of pedestrian facilities.
Finally, after outlining some of the ingredients necessary to apply the model in real situations (e.g. behavior at boundaries and inflow conditions), an
application is examined.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Di Carlo
DO WE HAVE ANYTHING TO LEARN FROM MOLECULAR
DYNAMICS?
ANTONIO DI CARLO
Dipartimento di Strutture
Università degli Studi “Roma Tre”
Abstract
The dynamics of large molecular systems, exactly like that of crowds and swarms,
is essentially driven by the mutual interactions between individual particles. In
this talk, I raise the question of which lessons we can learn from past experience
with Molecular Dynamics, and which methods hold better promise for application to more complex systems (more complex in a sense to be made precise). I
also attempt to give some partial answers, concentrating on the strategies to be
adopted for bridging the scale gap.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Freguglia
AN ATTEMPT TO DETERMINE A SAFE DRIVING INDEX
PAOLO FREGUGLIA
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica
Università degli Studi dell’Aquila
Abstract
The aim of our proposal is to explain some considerations in order to determine
a safe driving index with regard to a road and with regard to state of a driver.
In other words, we propose a measure which enables to establish when a road
can be covered with a sufficient safety. A driving index depends on a function
(driving function) F (t, x) consisting of an objective part f (t, x) [features of the
road and conditions of the journey] and a subjective part g(t, x) [state of heath
and decisions of driver] (t denotes the time and x the road course), that is:
F (t, x) = f (t, x) + g(t, x)
In its turn, f (t, x) and g(t, x) depend on other basic functions which on the
one hand describe the road width, the traffic density, the velocity of vehicles (in
the considered road) and the rainfall (bat also i.e. sun position on the horizon,
road typology [number of lanes, motorway ], dangerous curves, sharp curves,
etc.) and on the other hand the state of health (i.e. reaction time, etc.) and
the velocity of driver are considered. The safe driving indexes are particular
average values of F (t, x), that is, values belonging to a suitable intervals of t
and of x. But F (t, x) can be obtained also by means of a PDE or SDE which
expresses the following law: the variations during the time t and during the
course x of the road of F (t, x) depend on an assigned function pertinent to
state of driver (subjective part) and on another assigned function pertinent to
the state (possible harshness and windings) of the road (objective part). It is
possible to set this approach in the context of the information theory. Besides
an important general contribution can be obtained by the studies about the
mathematical models of traffic (the references about this topic are very large).
F (t, x) is established (as the safe driving indexes) a priori, but of course it is
necessary a posteriori a comparison with the accident data and a consequent
possible application of the DEA method. Our approach is consistent i.e. with
[1, 2, 3] but we would like give some new contribution.
Bibliografia
[1] E. Hermans, T. Brijs, G. Wets, and K. Vanhoof. Benchmarking road safety:
Lessons to learn from a data envelopment analysis. Accident Anal. Prev.,
41(1):174–182, 2009.
[2] E. Hermans, F. Van den Bossche, and G. Wets. Combining road safety
information in a performance index. Accident Anal. Prev., 40(4):1337–1344,
2008.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Bibliografia
[3] Y. Shen, E. Hermans, T. Brijs, G. Wets, and K. Vanhoof. Road safety
risk evaluation and target setting using data envelopment analysis and its
extensions. Accident Anal. Prev., 48:430–441, 2012.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Giardina
STATISTICAL MECHANICS MODELS FOR FLOCKS OF BIRDS
IRENE GIARDINA
Istituto Nazionale per la Fisica della Materia
Consiglio Nazionale delle Ricerche
Abstract
Collective animal behaviour has attracted enormous interest among physicists
in recent years. Self-organization of individuals into coordinated groups indeed
strongly reminds ordering phenomena in condensed matter systems. How much
can we push the analogy with physical systems? Can we describe animal aggregations in the same way we would do with a system of particles or spins?
Despite the intense work in theoretical studies and numerical modelling, the
scarce feedback with experimental data has restrained to give a clear answer to
these questions. In this talk I will show that, in some cases, this can actually
be done. Starting from field data of large flocks of starlings we indeed construct a maximum entropy model, which describes the statistics of individual
flight directions in the group. This model is of the same kind as models used
to describe ferromagnetic ordering and we can study and solve the statistical
mechanics associated to it. In this way, we prove that interactions between
individuals in a flock are local (a bird interacting with a finite number of neighbours) and topological (the number of interacting neighbours being independent
of group density). The model quantitatively predicts the propagation of order
throughout the flock, using no free parameters, even in very large aggregations.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Gosse
NUMERICAL STABILIZATION AND PATTERNS FOR WEAKLY
NONLINEAR KINETIC MODELS OF CHEMOTAXIS DYNAMICS
LAURENT GOSSE
Istituto per le Applicazioni del Calcolo “M. Picone”
Consiglio Nazionale delle Ricerche
Abstract
Well-balanced discretizations of scalar balance laws can be derived by lifting
the original equation at the level of a non-conservative (NC) 2 × 2 Temple class
system: the NC product renders locally the action of the source term by means
of a linearly degenerate field across which conservative variables jump according
to the steady-state equation. Such a reformulation allows to prove rigorously
improved L1 error estimates which don’t hold for more classical numerical schemes (joint result with Debora Amadori). Besides, this lifting can be applied
to linear kinetic equations in the discrete-ordinate approximation as soon as an
analytic expression of their steady-state solutions is available. Such expressions
were derived during the 60/70’s for several types of problems by following a seminal paper by Kenneth Case (the so-called “Caseology”). We shall explain how
these techniques can be used in order to derive interesting numerical schemes
in the context of two types of time-dependent chemotaxis models: one studied
by Hillen-Othmer, and another investigated by Bournaveas-Calvez.
Bibliografia
[1] D. Amadori and L. Gosse. Transient L1 error estimates for well-balanced
schemes on non-resonant scalar balance laws. Preprint, 2012.
[2] L. B. Barichello and C. E. Siewert. A discrete-ordinates solution for a nongrey model with complete frequency redistribution. J. Quant, Spectrosc. R.
A., 62(6):665–676, 1999.
[3] N. Bournaveas and V. Calvez. Critical mass phenomenon for a chemotaxis
kinetic model with spherically symmetric initial data. Ann. I. H. Poincaré
C, 26(5):1871–1895, 2009.
[4] K. M. Case. Elementary solutions of the transport equation and their
applications. Ann. Phys., 9(1):1–23, 1960.
[5] L. Gosse. Transient radiative transfer in the grey case: Well-balanced
and asymptotic-preserving schemes built on Case’s elementary solutions. J.
Quant, Spectrosc. R. A., 112(12):1995–2012, 2011.
[6] H. G. Othmer and T. Hillen. The diffusion limit of transport equations II:
Chemotaxis equations. SIAM J. Appl. Math., 62(4):1222–1250, 2002.
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Pareschi
MODELING SELF-ORGANIZED SYSTEMS INTERACTING WITH
FEW INDIVIDUALS: FROM MICROSCOPIC TO MACROSCOPIC
DYNAMICS
LORENZO PARESCHI∗
Dipartimento di Matematica
Università di Ferrara
Abstract
In nature self-organized systems as flock of birds, school of fishes or herd of sheep
have to deal with the presence of external agents such as predators or leaders
which modify their internal dynamic. Such situations take into account a large
number of individuals with their own social behavior which interact with a few
number of other individuals acting as external point source forces. In order
to describe this phenomena we consider the classical Cucker-Smale and the
D’Orsogna-Bertozzi et al. model for flocking and swarming dynamics, adding
the new feature of a predator/leader interaction. Starting from the microscopic
description we derive the kinetic model through a mean-field limit and finally
the macroscopic system through a suitable hydrodynamic limit.
∗ Con
G. Albi, Dipartimento di Matematica, Università di Ferrara
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Dagli individui alla collettività: folle e sciami
GA-MeMoMa-COMPLEX-SIMAI
Toscani
FLUID DYNAMIC MODELS OF FLOCKING
GIUSEPPE TOSCANI
Dipartimento di Matematica
Università di Pavia
Abstract
We introduce and discuss the possible dynamics of groups of indistinguishable
agents, which are interacting according to their relative positions, with the aim
of deriving hydrodynamic equations. These models are developed to mimic the
collective motion of groups of species such as bird flocks, fish schools, herds of
quadrupeds or bacteria colonies. Our starting model for these interactions is the
Povzner equation, which describes a dilute gas in which binary collisions of elastic spheres depend of their relative positions. Following the Cucker and Smale
model, we will consider binary interactions between agents that are dissipative
collisions in which the coefficient of restitution depends on their relative distance. Under the assumption of weak dissipation, it is shown that the Povzner
equation is modified through a correction in the form of a nonlinear friction type
operator. Using this correction we formally obtain from the Povzner equation in
a direct way a fluid dynamic description of a system of weakly interacting agents
interacting in a dissipative way, with a coefficient of restitution that depends on
their relative distance.
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