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Research Article

A micro-macro hybrid model with application for material and pedestrian flow

& | (Reviewing editor)
Article: 1476049 | Received 26 Jan 2018, Accepted 08 May 2018, Published online: 07 Jun 2018

References

  • Agarwal, P., & El-Sayed, A. A. (2018). Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation. Physica A: Statistical Mechanics and Its Applications, 500, 40–49. doi:10.1016/j.physa.2018.02.014
  • Aggarwal, A., Colombo, R. M., & Goatin, P. (2015). Nonlocal systems of conservation laws in several space dimensions. SIAM Journal Numerical Analysis, 53, 963–983. doi:10.1137/140975255
  • Bellomo, N., Piccoli, B., & Tosin, A. (2012). Modeling crowd dynamics from a complex system viewpoint. Mathematical Models Methods Applications Sciences, 22, 1230004–1230029. doi:10.1142/S0218202512300049
  • Carrillo, J. A., D’Orsogna, M. R., & Panferov, V. (2009). Double milling in self-propelled swarms from kinetic theory. Kinetic and Related Models, 2, 363–378. doi:10.3934/krm
  • Cleary, P., & Sawley, M. (2002). DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Applied Mathematical Modelling, 26, 89–111. doi:10.1016/S0307-904X(01)00050-6
  • Colombo, R. M., Garavello, M., & Lécureux-Mercier, M. (2012). A class of nonlocal models for pedestrian traffic. Mathematical Models Methods Applications Sciences, 22, 1150023. doi:10.1142/S0218202511500230
  • Colombo, R. M., & Lécureux-Mercier, M. (2012). Nonlocal crowd dynamics models for several populations. Acta Mathematica Scientia, 32, 177–196. doi:10.1016/S0252-9602(12)60011-3
  • Cristiani, E., Piccoli, B., & Tosin, A. (2011). Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Modelling and Simulation, 9, 155–182. doi:10.1137/100797515
  • Cristiani, E., Piccoli, B., & Tosin, A. (2014). Multiscale modeling of pedestrian dynamics, vol. 12 of MS&A. Modeling, Simulation and Applications. Cham: Springer.
  • Cundall, P. A., & Strack, O. D. L. (1979). A discrete numerical model for granular assemblies. Géotechnique, 29, 47–65. doi:10.1680/geot.1979.29.1.47
  • Degond, P., Ferreira, M. A., & Motsch, S. (2017). Damped Arrow-Hurwicz algorithm for sphere packing. Journal of Computational Physics, 332, 47–65. doi:10.1016/j.jcp.2016.11.047
  • Etikyala, R., Göttlich, S., Klar, A., & Tiwari, S. (2014). Particle methods for pedestrian flow models: From microscopic to nonlocal continuum models. Mathematical Models Methods Applications Sciences, 24, 2503–2523. doi:10.1142/S0218202514500274
  • Göttlich, S., Hoher, S., Schindler, P., Schleper, V., & Verl, A. (2014). Modeling, simulation and validation of material flow on conveyor belts. Applied Mathematical Modelling, 38, 3295–3313. doi:10.1016/j.apm.2013.11.039
  • Göttlich, S., Klar, A., & Tiwari, S. (2015). Complex material flow problems: A multi-scale model hierarchy and particle methods. Journal of Engineering Mathematics, 92, 15–29. doi:10.1007/s10665-014-9767-5
  • Göttlich, S., Knapp, S., & Schillen, P. (2017). A pedestrian flow model with stochastic velocities: Microscopic and macroscopic approaches. Retrieved from https://arxiv.org/pdf/1703.09134.pdf
  • Helbing, D., Farkas, I., & Vicsek, T. (2000). Simulating dynamical features of escape panic. Nature, 407, 487–490.
  • Herty, M., & Moutari, S. (2009). A macro-kinetic hybrid model for traffic flow on road networks. Computational Methods in Applied Mathematics, 9, 238–252. doi:10.2478/cmam-2009-0015
  • Moutari, S., & Rascle, M. (2007). A hybrid Lagrangian model based on the Aw-Rascle traffic flow model. SIAM Journal Applications Mathematical, 68, 413–436. doi:10.1137/060678415
  • Ruzhansky, M., Cho, Y., Agarwal, P., & Area, I. (2017). Advances in real and complex analysis with applications. Singapore: Trends in Mathematics, Springer.
  • Zhang, X., Agarwal, P., Liu, Z., Peng, H., You, F., & Zhu, Y. (2017). Existence and uniqueness of solutions for stochastic differential equations of fractional-order q>1 with finite delays. Advances in Difference Equation, 2017, 123. 18.