2011, 6(3): i-iii. doi: 10.3934/nhm.2011.6.3i



Department of Mathematics, University of Brescia, Via Branze, 38, 25133 Brescia


Department of Mathematical Sciences & Center for Computational and Integrative Biology, Rutgers University, Camden, NJ

Published  August 2011

The research about crowd dynamics has undergone a dramatic development in the recent years. This fast advancement made it rather difficult for researchers in applied mathematics to keep contacts with the variety of analytical and numerical techniques recently introduced, as well as with the new problems being considered. Indeed, Crowd Dynamics is of interest to disciplines ranging from pure mathematical analysis to operation research, from numerical analysis to computer graphics, from model theory to statistics. The variety of MSC classifications labeling the papers of this special issue testifies the broadness of the subjects covered hereafter and, hence, also of this whole field.
   This special issue of Networks and Heterogeneous Media aims at bridging several different research directions of interest to applied mathematicians. Each of the present papers describes key problems of particular interest for the authors, points at the related most relevant techniques and includes the corresponding main results. The common spirit is to share, also with non specialists of the very same field, achieved results in their full depth.
Citation: Rinaldo M. Colombo, Benedetto Piccoli. Preface. Networks & Heterogeneous Media, 2011, 6 (3) : i-iii. doi: 10.3934/nhm.2011.6.3i

Nicola Bellomo, Abdelghani Bellouquid. On the modeling of crowd dynamics: Looking at the beautiful shapes of swarms. Networks & Heterogeneous Media, 2011, 6 (3) : 383-399. doi: 10.3934/nhm.2011.6.383


Veronika Schleper. A hybrid model for traffic flow and crowd dynamics with random individual properties. Mathematical Biosciences & Engineering, 2015, 12 (2) : 393-413. doi: 10.3934/mbe.2015.12.393


Philippe Pécol, Pierre Argoul, Stefano Dal Pont, Silvano Erlicher. The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 547-565. doi: 10.3934/dcdss.2013.6.547


Bertrand Maury, Aude Roudneff-Chupin, Filippo Santambrogio, Juliette Venel. Handling congestion in crowd motion modeling. Networks & Heterogeneous Media, 2011, 6 (3) : 485-519. doi: 10.3934/nhm.2011.6.485


Lambertus A. Peletier. Modeling drug-protein dynamics. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 191-207. doi: 10.3934/dcdss.2012.5.191


Rinaldo M. Colombo, Andrea Corli. Dynamic parameters identification in traffic flow modeling. Conference Publications, 2005, 2005 (Special) : 190-199. doi: 10.3934/proc.2005.2005.190


Tong Li, Kun Zhao. On a quasilinear hyperbolic system in blood flow modeling. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 333-344. doi: 10.3934/dcdsb.2011.16.333


Andreas Schadschneider, Armin Seyfried. Empirical results for pedestrian dynamics and their implications for modeling. Networks & Heterogeneous Media, 2011, 6 (3) : 545-560. doi: 10.3934/nhm.2011.6.545


Steady Mushayabasa, Drew Posny, Jin Wang. Modeling the intrinsic dynamics of foot-and-mouth disease. Mathematical Biosciences & Engineering, 2016, 13 (2) : 425-442. doi: 10.3934/mbe.2015010


Darja Kalajdzievska, Michael Yi Li. Modeling the effects of carriers on transmission dynamics of infectious diseases. Mathematical Biosciences & Engineering, 2011, 8 (3) : 711-722. doi: 10.3934/mbe.2011.8.711


Dominik Wodarz. Computational modeling approaches to studying the dynamics of oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 939-957. doi: 10.3934/mbe.2013.10.939


Adélia Sequeira, Rafael F. Santos, Tomáš Bodnár. Blood coagulation dynamics: mathematical modeling and stability results. Mathematical Biosciences & Engineering, 2011, 8 (2) : 425-443. doi: 10.3934/mbe.2011.8.425


Pierre Degond, Gadi Fibich, Benedetto Piccoli, Eitan Tadmor. Special issue on modeling and control in social dynamics. Networks & Heterogeneous Media, 2015, 10 (3) : i-ii. doi: 10.3934/nhm.2015.10.3i


Marina Dolfin, Mirosław Lachowicz. Modeling opinion dynamics: How the network enhances consensus. Networks & Heterogeneous Media, 2015, 10 (4) : 877-896. doi: 10.3934/nhm.2015.10.877


Lan Zou, Jing Chen, Shigui Ruan. Modeling and analyzing the transmission dynamics of visceral leishmaniasis. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1585-1604. doi: 10.3934/mbe.2017082


Christophe Chalons, Paola Goatin, Nicolas Seguin. General constrained conservation laws. Application to pedestrian flow modeling. Networks & Heterogeneous Media, 2013, 8 (2) : 433-463. doi: 10.3934/nhm.2013.8.433


Stanisław Migórski. A note on optimal control problem for a hemivariational inequality modeling fluid flow. Conference Publications, 2013, 2013 (special) : 545-554. doi: 10.3934/proc.2013.2013.545


Changli Yuan, Mojdeh Delshad, Mary F. Wheeler. Modeling multiphase non-Newtonian polymer flow in IPARS parallel framework. Networks & Heterogeneous Media, 2010, 5 (3) : 583-602. doi: 10.3934/nhm.2010.5.583


Alexandre M. Bayen, Hélène Frankowska, Jean-Patrick Lebacque, Benedetto Piccoli, H. Michael Zhang. Special issue on Mathematics of Traffic Flow Modeling, Estimation and Control. Networks & Heterogeneous Media, 2013, 8 (3) : i-ii. doi: 10.3934/nhm.2013.8.3i


Fanghua Lin, Chun Liu. Partial regularity of the dynamic system modeling the flow of liquid crystals. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 1-22. doi: 10.3934/dcds.1996.2.1

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