Crowds reaching targets by maximizing entropy: a Clausius-Duhem inequality approach
| Autor: | Evers, J.H.M., Muntean, A., Ven, van de, A.A.F., Le Gorrec, Y. |
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| Přispěvatelé: | Center for Analysis, Scientific Computing & Appl., Applied Analysis |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Particle system
Continuous modelling media_common.quotation_subject Mathematical analysis Second law of thermodynamics Clausius–Duhem inequality Dissipation 91Cxx 35Qxx Mathematics - Analysis of PDEs Continuity equation Time derivative FOS: Mathematics Statistical physics Entropy (arrow of time) Analysis of PDEs (math.AP) Mathematics media_common |
| Zdroj: | 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE 2013, Paris, France, September 25-27, 2013), 263-268 STARTPAGE=263;ENDPAGE=268;TITLE=1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE 2013, Paris, France, September 25-27, 2013) |
| Popis: | In this paper we make a connection between the study of crowd dynamics and concepts from thermodynamics. The basic component of our continuous model is the continuity equation for the density of people, which we complete by prescribing the velocity eld. This velocity eld includes a nonlocal term modelling interactions between individuals. To provide support for our modelling assumptions we wish to prove an inequality that resembles the Second Law of Thermodynamics. To this end we dene an entropy-like functional and show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case we support the claim that the corrector term is small by performing simulations for the corresponding particle system. In fact, this term is suciently small for the entropy still to increase. Moreover, we can show that the entropy converges in time towards a limit value. Keywords: Traffic Control and Network Congestion; Stability Theory; Computational Methods |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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