Convegno

Dagli individui alla collettivita: folle e sciami

15-16 novembre 2012

Consiglio Nazionale delle RicerchePiazzale Aldo Moro 7, 00185 Roma

Aula Conferenze

Libretto degli abstract

Organizzazione: Andrea TosinIstituto per le Applicazioni del Calcolo “M. Picone”Consiglio Nazionale delle Ricerche

Patrocinio: Gruppo di Attivita SIMAI sui Sistemi Complessi

Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Bazzani

MODELING SELF-ORGANIZED PHENOMENA IN PEDESTRIANDYNAMICS

ARMANDO BAZZANI∗

Dipartimento di FisicaUniversita di Bologna

Abstract

Pedestrian dynamics has been mainly simulated by using physical-like modelsto study crowding effects for safety reasons. However despite of some successfulresults, the Newtonian force models are still not fully consistent with experi-mental observations. In particular this is the case when one considers cognitiveaspects in individual behavior. Recently new cognitive inspired models havebeen proposed where the pedestrian dynamics is related with cognitive proces-ses due to local vision (e.g. collision avoidance dynamics) and cooperative versusselfish behavior [1, 2]. The collective self-organized states of crowd dynamicscan be seen as emergent properties from decisional process at individual level.We present a simple microscopic model for pedestrian dynamics that integrateslocal vision effects and the existence of counteracting strategies in the individualdecision mechanisms. By using numerical simulations we discuss the emergenceof self-organized dynamical states and the transition from ordered cooperativestates to “panic states”. A statistical physics approach is also proposed.

Bibliografia

[1] A. Bazzani, B. Giorgini, F. Zanlungo, and S. Rambaldi. Cognitive Dynamicsin an Automata Gas. In R. Serra, M. Villani, and I. Poli, editors, ArtificialLife and Evolutionary Computation, pages 3–19, Singapore, 2009. WorldScientific. Proceedings of Wivace 2008.

[2] M. Moussaıd, D. Helbing, and G. Theraulaz. How simple rules determi-ne pedestrian behavior and crowd disasters. Proc. Nat. Acad. Sci. USA,108(17):6884–6888, 2011.

∗Con B. Giorgini, S. Rambaldi, Dipartimento di Fisica, Universita di Bologna

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Bellomo

MODELING AND SIMULATION OF FREE BOUNDARY PROBLEMSFOR CROWD DYNAMICS BY THE KINETIC THEORY FOR

ACTIVE PARTICLES

NICOLA BELLOMO

Dipartimento di Scienze MatematichePolitecnico di Torino

Abstract

The contents of this lecture is presented in three parts. The first part presentsa modeling approach to crowd dynamics viewed as a large living system by me-thods of the mathematical kinetic theory for active particles [1], which includesa detailed analysis of the complexity features of the system under considera-tion as well as development of multi-scale methods [2, 3]. The second part isdevoted to the development of splitting methods to simulate the overall dyna-mics focusing on depicting the evolution of the moving boundary of the domaincontaining the crowd. The presentation is constantly focused on the modelingcomplex 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 onlyon the knowledge of the dynamics of their individual elements. The third partpresents some perspective ideas and research hints towards the modeling andsimulation of animal swarms looking at the beautiful shapes of swarms [4].

Bibliografia

[1] N. Bellomo. Modeling complex living systems – A kinetic theory and stocha-stic game approach. Modeling and Simulation in Science, Engineering andTechnology. Birkhauser, Boston, 2008.

[2] N. Bellomo and A. Bellouquid. On the modeling of crowd dynamics: Lookingat the beautiful shapes of swarms. Netw. Heterog. Media, 6(3):383–399, 2011.

[3] N. Bellomo and C. Dogbe. On the modelling of traffic and crowds. A surveyof models, speculations, and perspectives. SIAM Rev., 53(3):409–463, 2011.

[4] N. Bellomo and J. Soler. On the mathematical theory of the dynamicsof swarms viewed as complex systems. Math. Models Methods Appl. Sci.,22(suppl. 1):1140006 (29 pages), 2012.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Bruno

PEDESTRIANS, GROUPS AND CROWDS: STRUCTURAL EFFECTSON FOOTBRIDGES

LUCA BRUNO∗

Dipartimento di Architettura e DesignPolitecnico di Torino

Abstract

After the closure of the London Millennium Bridge in 2000 due to the so-calledSynchronous Lateral Excitation (SLE) phenomenon, an intense research acti-vity related to footbridge dynamics under human-induced excitation has beencarried out (reviewed e.g. in [2, 5, 6]). The SLE is a crowd-structure interac-tion phenomenon, characterized by the following key features: self-excitation,due to the synchronization between the pedestrians and the laterally movingwalking 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 ofexcessive vibrations.

This contribution proposes an introduction to this engineering problem andan overview on the modelling strategies and codified practices that have beenproposed in literature to deal with it. The earlier and most common approachin engineering considers and models the pedestrians as a simple action appliedto the structure. The problem, therefore, reduces to the calculation of the struc-tural response under the action of a suitable load model. According to this ap-proach, several load models have been proposed (reviewed e.g. in [3]). Codifieddesign guidelines (e.g. [4]) handle collective phenomena by introducing differentdesign scenarios referred to single pedestrian and not well defined “groups” and“crowd”. A different approach - inspired by crowd models mainly developed inthe fields of applied mathematics, physics and transportation engineering (e.g.reviewed in [1]) - has been recently applied to this problem. It considers thepedestrians as a dynamical system, which has its own governing rules and thatinteracts with the structure system. This approach results in coupled modelscharacterized 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 collectivephenomena (“pedestrian, group and crowd” in civil engineering literature) andtheir effects on structures? ii. How to account for the inherent randomness ofthe walking pedestrians (“intersubject” and “intrasubject variability” in civilengineering literature) in a probability-based design of structures? The abovementioned issues are still open and could benefit of the contribution of researchfields beside civil engineering (e.g. applied mathematics and physics) to evaluatenew modelling perspectives towards real world applications.

∗Con F. Venuti, Dipartimento di Architettura e Design, Politecnico di Torino

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Bibliografia

Bibliografia

[1] N. Bellomo and C. Dogbe. On the modelling of traffic and crowds. A surveyof models, speculations, and perspectives. SIAM Rev., 53(3):409–463, 2011.

[2] E. T. Ingolfsson, C. T. Georgakis, and J. Jonsson. Pedestrian-induced lateralvibrations of footbridges: A literature review. Eng. Struct., 45:21–52, 2012.

[3] V. Racic, A. Pavic, and J. M. W. Brownjohn. Experimental identificationand analytical modelling of human walking forces: Literature review. J.Sound Vib., 326(1):1–49, 2009.

[4] F. Setra. Assessment of vibrational behaviour of footbridges underpedestrian loading. Technical report, 2006. Technical guide SETRA.

[5] F. Venuti and L. Bruno. Crowd-structure interaction in lively footbridgesunder synchronous lateral excitation: A literature review. Phys. Life Rev.,6(3):176–206, 2009.

[6] S. Zivanovic, A. Pavic, and P. Reynolds. Vibration serviceability of foot-bridges under human-induced excitation: a literature review. J. Sound Vib.,279:1–74, 2005.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Colombo

INDIVIDUALS-POPULATION INTERACTIONS: MODELING ANDCONFINEMENT PROBLEMS

RINALDO M. COLOMBO

Dipartimento di MatematicaUniversita degli Studi di Brescia

Abstract

Various analytical frameworks are able to describe the interaction between agen-ts and a moving population. First, within a PDE setting, this presentation de-scribes a well posedness result. Then, a model based on differential inclusions ispresented. In this context, recently obtained positive and negative confinementresults are discussed.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Corbetta

INDIVIDUAL DYNAMICS AND COLLECTIVE PERCEPTION INBUILT ENVIRONMENTS

ALESSANDRO CORBETTA

Dipartimento di Ingegneria Strutturale, Edile e GeotecnicaPolitecnico di Torino

Abstract

A mathematical model for the active motion of pedestrians in a crowd is pro-posed, hence a reasoned application is considered.

The pedestrian motion is phenomenologically approached reckoning the in-teractions that, in a crowd, exist between single individuals and the collectivityaround them. These interactions, indeed, are regarded as a reaction to percep-tions one has of his surroundings. On this basis, a model formulated in termsof a conservation law for the pedestrian mass is deduced. Particularly, the pe-destrian mass is considered in the general sense of measures and its evolutionis determined by non-local interaction terms. The obtained model is furtherread in a probabilistic sense, aiming at retrieving statistics about agents’ distri-bution. Affine statistical data are currently used in the engineering practice inorder to assess performances and serviceability of pedestrian facilities.

Finally, after outlining some of the ingredients necessary to apply the mo-del in real situations (e.g. behavior at boundaries and inflow conditions), anapplication is examined.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Di Carlo

DO WE HAVE ANYTHING TO LEARN FROM MOLECULARDYNAMICS?

ANTONIO DI CARLO

Dipartimento di StruttureUniversita 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. Inthis talk, I raise the question of which lessons we can learn from past experiencewith Molecular Dynamics, and which methods hold better promise for applica-tion to more complex systems (more complex in a sense to be made precise). Ialso attempt to give some partial answers, concentrating on the strategies to beadopted for bridging the scale gap.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Freguglia

AN ATTEMPT TO DETERMINE A SAFE DRIVING INDEX

PAOLO FREGUGLIA

Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversita degli Studi dell’Aquila

Abstract

The aim of our proposal is to explain some considerations in order to determinea 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 roadcan 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 theroad and conditions of the journey] and a subjective part g(t, x) [state of heathand 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 theone hand describe the road width, the traffic density, the velocity of vehicles (inthe 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.) andthe velocity of driver are considered. The safe driving indexes are particularaverage values of F (t, x), that is, values belonging to a suitable intervals of tand of x. But F (t, x) can be obtained also by means of a PDE or SDE whichexpresses the following law: the variations during the time t and during thecourse x of the road of F (t, x) depend on an assigned function pertinent tostate of driver (subjective part) and on another assigned function pertinent tothe state (possible harshness and windings) of the road (objective part). It ispossible to set this approach in the context of the information theory. Besidesan important general contribution can be obtained by the studies about themathematical 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 isnecessary a posteriori a comparison with the accident data and a consequentpossible 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 safetyinformation in a performance index. Accident Anal. Prev., 40(4):1337–1344,2008.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Bibliografia

[3] Y. Shen, E. Hermans, T. Brijs, G. Wets, and K. Vanhoof. Road safetyrisk evaluation and target setting using data envelopment analysis and itsextensions. Accident Anal. Prev., 48:430–441, 2012.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Giardina

STATISTICAL MECHANICS MODELS FOR FLOCKS OF BIRDS

IRENE GIARDINA

Istituto Nazionale per la Fisica della MateriaConsiglio Nazionale delle Ricerche

Abstract

Collective animal behaviour has attracted enormous interest among physicistsin recent years. Self-organization of individuals into coordinated groups indeedstrongly reminds ordering phenomena in condensed matter systems. How muchcan we push the analogy with physical systems? Can we describe animal ag-gregations in the same way we would do with a system of particles or spins?Despite the intense work in theoretical studies and numerical modelling, thescarce feedback with experimental data has restrained to give a clear answer tothese questions. In this talk I will show that, in some cases, this can actuallybe done. Starting from field data of large flocks of starlings we indeed con-struct a maximum entropy model, which describes the statistics of individualflight directions in the group. This model is of the same kind as models usedto describe ferromagnetic ordering and we can study and solve the statisticalmechanics associated to it. In this way, we prove that interactions betweenindividuals in a flock are local (a bird interacting with a finite number of neigh-bours) and topological (the number of interacting neighbours being independentof group density). The model quantitatively predicts the propagation of orderthroughout the flock, using no free parameters, even in very large aggregations.

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Gosse

NUMERICAL STABILIZATION AND PATTERNS FOR WEAKLYNONLINEAR 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 liftingthe original equation at the level of a non-conservative (NC) 2× 2 Temple classsystem: the NC product renders locally the action of the source term by meansof a linearly degenerate field across which conservative variables jump accordingto the steady-state equation. Such a reformulation allows to prove rigorouslyimproved L1 error estimates which don’t hold for more classical numerical sche-mes (joint result with Debora Amadori). Besides, this lifting can be appliedto linear kinetic equations in the discrete-ordinate approximation as soon as ananalytic expression of their steady-state solutions is available. Such expressionswere derived during the 60/70’s for several types of problems by following a se-minal paper by Kenneth Case (the so-called “Caseology”). We shall explain howthese techniques can be used in order to derive interesting numerical schemesin the context of two types of time-dependent chemotaxis models: one studiedby Hillen-Othmer, and another investigated by Bournaveas-Calvez.

Bibliografia

[1] D. Amadori and L. Gosse. Transient L1 error estimates for well-balancedschemes on non-resonant scalar balance laws. Preprint, 2012.

[2] L. B. Barichello and C. E. Siewert. A discrete-ordinates solution for a non-grey 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 chemotaxiskinetic model with spherically symmetric initial data. Ann. I. H. PoincareC, 26(5):1871–1895, 2009.

[4] K. M. Case. Elementary solutions of the transport equation and theirapplications. Ann. Phys., 9(1):1–23, 1960.

[5] L. Gosse. Transient radiative transfer in the grey case: Well-balancedand 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 collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Pareschi

MODELING SELF-ORGANIZED SYSTEMS INTERACTING WITHFEW INDIVIDUALS: FROM MICROSCOPIC TO MACROSCOPIC

DYNAMICS

LORENZO PARESCHI∗

Dipartimento di MatematicaUniversita di Ferrara

Abstract

In nature self-organized systems as flock of birds, school of fishes or herd of sheephave to deal with the presence of external agents such as predators or leaderswhich modify their internal dynamic. Such situations take into account a largenumber of individuals with their own social behavior which interact with a fewnumber of other individuals acting as external point source forces. In orderto describe this phenomena we consider the classical Cucker-Smale and theD’Orsogna-Bertozzi et al. model for flocking and swarming dynamics, addingthe new feature of a predator/leader interaction. Starting from the microscopicdescription we derive the kinetic model through a mean-field limit and finallythe macroscopic system through a suitable hydrodynamic limit.

∗Con G. Albi, Dipartimento di Matematica, Universita di Ferrara

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Dagli individui alla collettivita: folle e sciamiGA-MeMoMa-COMPLEX-SIMAI Toscani

FLUID DYNAMIC MODELS OF FLOCKING

GIUSEPPE TOSCANI

Dipartimento di MatematicaUniversita di Pavia

Abstract

We introduce and discuss the possible dynamics of groups of indistinguishableagents, which are interacting according to their relative positions, with the aimof deriving hydrodynamic equations. These models are developed to mimic thecollective motion of groups of species such as bird flocks, fish schools, herds ofquadrupeds or bacteria colonies. Our starting model for these interactions is thePovzner equation, which describes a dilute gas in which binary collisions of ela-stic spheres depend of their relative positions. Following the Cucker and Smalemodel, we will consider binary interactions between agents that are dissipativecollisions in which the coefficient of restitution depends on their relative di-stance. Under the assumption of weak dissipation, it is shown that the Povznerequation is modified through a correction in the form of a nonlinear friction typeoperator. Using this correction we formally obtain from the Povzner equation ina direct way a fluid dynamic description of a system of weakly interacting agentsinteracting in a dissipative way, with a coefficient of restitution that depends ontheir relative distance.

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