Research objectives

Crowded transport can be observed on various scales in life and social sciences. Examples include the motion of charged particles through ion channels, the flow of large pedestrian crowds or the collective behavior of animals like fish or bird. Crowding is generally caused by limitations of the physical domain or aggregation phenomena, hence multiscale effects appear naturally in this context. The common denominator of crowding processes is the fact that the size of the particles plays an important role in the transportation and should not be neglected in the mathematical modeling.

The research objectives of the New Frontiers group include general modeling approaches of crowded transport on different scales and their efficient numerical simulation. A main focus of the modeling is the systematic translation of finite size effects for different methods and scales as well as the consistent coupling of models in multiscale phenomena. Efficient numerical simulations are a further key issue of the project, since the transportation equations for crowded motion are in general highly nonlinear and require the development of flexible discretization techniques to capture the versatile behavior of the derived models in a reliable manner.

People

People

  • Adriano Festa , Post-doc
  • Bartlomiej Matejczyk , PhD student
  • Helene Ranetbauer, PhD student
  • Monika Wolfmayr , Post-doc
  • Marie-Therese Wolfram , PI

Publications

Publications

  • A. Festa, A. Tosin, M.T. Wolfram (2018) Kinetic description of collision avoidance in pedestrian dynamics bysidestepping. Kinetic and Related Models, Bd. NAN, S. NAN.
  • Hittmeir, Sabine; Ranetbauer, Helene; Schmeiser, Christian; Wolfram, Marie-Therese (2017) Derivation and analysis of continuum models for crossing pedestrian traffic. Math. Models Meth. Appl. Sci., Bd. 27 (7), S. 1301-1325.
  • M. Bruna, M. Burger, H. Ranetbauer, M.T. Wolfram (2017) Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures. Journal of Nonlinear Science, Bd. 27 (2), S. 1-33.
  • Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese (2017, online: 2016) BALANCED GROWTH PATH SOLUTIONS OF A BOLTZMANN MEAN FIELD GAME MODEL FOR KNOWLEDGE GROWTH. Kinet. Relat. Mod., Bd. 10 (1), S. 117-140.
  • Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese (2017, online: 2016) Existence of balanced growth path solutions to a Boltzmann mean field game model for knowledge growth. KRM, Bd. 10 (1), S. 117-140.
  • Carrillo, Jose A.; Ranetbauer, Helene; Wolfram, Marie-Therese (2016) Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms. J. Comput. Phys., Bd. 327, S. 186-202.
  • Bruna, Maria; Burger, Martin; Ranetbauer, Helene; Wolfram, Marie-Therese (2016) Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures. Journal of Nonlinear Science, Bd. 27 (2), S. 1-33.
  • Markowich, Peter; Teichmann, Josef; Wolfram, Marie-Therese (2016) Parabolic free boundary price formation models under market size fluctuations. SIAM MMS, Bd. 14 (4), S. 1211-1237.
  • E. Carlini, A. Festa, F.J. Silva, M-T. Wolfram (2016) Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow. Dyn. Games Appl., Bd. 1, S. 1-23.
  • Festa, Adriano (2016) RECONSTRUCTION OF INDEPENDENT SUB-DOMAINS FOR A CLASS OF HAMILTON-JACOBI EQUATIONS AND APPLICATION TO PARALLEL COMPUTING. ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., Bd. 50 (4), S. 1223-1240.
  • Festa, Adriano; Vinter, Richard B. (2016) Decomposition of Differential Games with Multiple Targets. J. Optim. Theory Appl., Bd. 169 (3), S. 848-875.
  • Burger, Martin; Lorz, Alexander; Wolfram, Marie-Therese (2016) ON A BOLTZMANN MEAN FIELD MODEL FOR KNOWLEDGE GROWTH. SIAM J. Appl. Math., Bd. 76 (5), S. 1799-1818.
  • Wolfmayr, Monika (online: 2016) A note on functional a posteriori estimates for elliptic optimal control problems. Numerical Methods for Partial Differential Equations, Bd. 33 (2), S. 403–424.
  • Carrillo, Jose A.; Martin, Stephan; Wolfram, Marie-Therese (2016) An improved version of the Hughes model for pedestrian flow. Math. Models Meth. Appl. Sci., Bd. 26 (4), S. 671-697.
  • Burger, Martin; Hittmeir, Sabine; Ranetbauer, Helene; Wolfram, Marie-Therese (2016) Lane formation by side-stepping. SIAM Journal on Mathematical Analysis (SIMA), Bd. 48 (2), S. 981-1005.
  • Langer, U.; Repin, S.; Wolfmayr, M. (2015) Functional a posteriori error estimates for parabolic time-periodic boundary value problems. Computational Methods in Applied Mathematics, Bd. 15 (3), S. 353-372.
  • Burger, Martin; Hittmeir, Sabine; Ranetbauer, Helene; Wolfram, Marie-Therese (2015) Lane formation by side-stepping. Bericht-Nr. 2015-48; RICAM: Linz.
  • Wolfmayr, M. (2015) Functional a posteriori estimates for elliptic optimal control problems. In: G. Zavarise, P. Cinnella and M. Campiti (Hrsg.), PAMM; Lecce: WILEY-VCH Verlag, S. 621-622.
  • Achleitner, Franz; Hittmeir, Sabine; Schmeiser, Christian (2014) On nonlinear conservation laws regularized by a Riesz-Feller operator. In: Ancona, Fabio; Bressan, Alberto; Marcati, Pierangelo; Marson, Andrea (Hrsg.), Hyperbolic Problems: Theory, Numerics, Applications, S. 241-248.
  • D. Gomes, R. Velho, M.T. Wolfram (2014) Socio economic applications of finite state mean field games. Proceedings of the Royal Society A, Bd. 372 (2028), S. NaN.
  • M. Burger, L. Caffarelli, P.A. Markowich, M.T. Wolfram (2014) On the asymptotic behaviour of a Boltzmann type price formation model. CMS, Bd. 12 (7), S. 1353-1361.
  • F. Achleitner, C.M. Cuesta, S. Hittmeir (2014) Travelling waves for a non-local Korteweg-de Vries-Burgers equation. Journal of Differential Equations, Bd. 257 (3), S. 720-758.
  • M. Burger, M. Di Francesco, P.A. Markowich and M.T. Wolfram (2014) Mean field games with nonlinear mobilities in pedestrian dynamics. Discete and Dynamical Systems-B, Bd. 19 (5), S. 1311-1333.
  • Jose A. Carrillo, Stephan Martin and Marie-Therese Wolfram A local version of the Hughes model for pedestrian flow. Mathematical Model and Methods in the Applied Sciences, Bd. 26 (4), S. 671-697.