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Mathematics Institute

Publications

Publications

  1. M.T. Wolfram, Semiconductor inverse dopant profiling from transient measurements , Journal of Computational Electronics, 6(4), 395-444, 2007
  2. M. Burger, R. Pinnau, M.T. Wolfram, On-off-state design of semiconductor doping profiles, Commun. Math. Sci., 6, 1021-1041, 2008
  3. P.A. Markowich, N. Matevosyan, J.F. Pietschmann, M.T. Wolfram, On a parabolic free boundary value problem modeling price formation , Math. Models Methods Appl. Sci., 11(19), 1929-1957, 2009
  4. B. Duering, P.A. Markowich, J.F. Pietschmann, M.T. Wolfram, Boltzmann and Fokker-Planck Equations modelling Opinion Formation in the Presence of Strong Leaders , Proc. Royal Soc. A., 465(2112), 3687-3708, 2009
  5. M. Burger, J.A. Carrillo, M.T. Wolfram, A mixed finite element method for nonlinear diffusion equations , KRM, 3(1), 59-83, 2010
  6. M.T. Wolfram, M. Buger, Z.S. Siwy, Mathematical modeling and simulation of nanopore blocking by precipitation ,J. Phys.: Condens. Matter, 22(45), 2010
  7. M. Burger, N. Matevosyan, M.T. Wolfram, A level set based shape optimization method for an elliptic obstacle problem, M3AS, 21(4), 616-649, 2011
  8. M. Di Francesco, P.A. Markowich, J.F. Pietschmann, M.T. Wolfram, On the Hughes' model of pedestrian flow: The one-dimensional case, JDE, 250(3), 1334-1362, 2011
  9. L.A. Caffarelli, P.A. Markowich, M.T. Wolfram, On a price formation free boundary value model by Lasry & Lions: The Neumann problem, C. R. Acad. Sci. Paris, 349, 841-844, 2011
  10. A. Lachapelle, M.T. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds, Trans. Res.: Part B: Methodological, 45(10), 1572-1589, 2011
  11. M. Burger, B. Schlake, M.T. Wolfram, Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries, Nonlinearity, 25, 961-990, 2012
  12. D. Brinkman, K. Fellner, P.A. Markowich, M.T. Wolfram, A drift-diffusion reaction model for excitonic photovoltaic bilayers: asymptotic analysis and a 2D HDG finite element scheme, M3AS., 23(5), 2013
  13. M. Burger, J. Haskovec, M.T. Wolfram, Individual based and mean-field modelling of direct aggregation, Physica D: Nonlinear Phenomena, 260, 145-158, 2013
  14. M. Burger, L. Cafferelli, P.A. Markowich, M.T. Wolfram, On a Boltzmann type price formation model, Proc. R. Soc. A, 469(2157), 20130126, 2013
  15. M. Burger, J.F. Pietschmann, M.T. Wolfram, Identification of non-linearities in transport-diffusion models modelling crowded motion, Inverse Problems and Imaging, 7(4), 1157-1182, 2013
  16. J.F. Pietschmann, M.T. Wolfram, M. Burger, C. Trautmann, G. Nguyen, M. Pevarnik, V. Bayer, Z. Siwy Rectification properties of conically shaped nanopores: consequences of miniaturization, Physical Chemistry Chemical Physics, 15, 16917-16926, 2013
  17. M. Burger, M. Di Francesco, P.A. Markowich, M.T. Wolfram, Mean field games with nonlinear mobilities in pedestrian dynamics, Discrete and Dynamical Systems - B, 19(5), 1311-1333, 2014
  18. M. Burger, L. Caffarelli, P.A. Markowich, M.T. Wolfram, On the asymptotic behavior of a Boltzmann-type price formation model, CMS, 12(7), 1353--1361, 2014
  19. D. Gomes, R.M. Velho, M.T. Wolfram, Socio economic applications of finite state mean field games, Phil. Trans. R. Soc. A, 372(2028), 20130405, 2014
  20. B. Duering, M.T. Wolfram, Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation, Proc Royal Soc A 471(2182), 2015
  21. J. Carrillo, S. Martin, M.T. Wolfram, A local version of the Hughes model for pedestrian flow, M3AS 26(4), 671-697, 2016 Arxiv
  22. M. Burger, S. Hittmeir, H. Ranetbauer, M.T. Wolfram, Lane formation by side-stepping, SIAM Math. Anal. 48(2), 981-1005, 2016 Arxiv
  23. M. Burger, A. Lorz, M.T. Wolfram, On a Boltzmann type model for knowledge growth, SIAM J. Appl. Math. 76(5), 1799-1818, 2016 Arxiv
  24. P.A. Markowich, J. Teichmann, M.T. Wolfram, Parabolic free boundary price formation models under market size fluctuations, SIAM MMS 14(4), 1211-1237, 2016 Arxiv
  25. E. Carlini, A. Festa, F. Silva, M.T. Wolfram, A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow, Dynamic Games and Applications 7, 2016 Arxiv 
  26. J. Carrillo, H. Ranetbauer, M.T. Wolfram, Numerical simulation of continuity equations by evolving diffeomorphisms, J Comput. Phys. 327, 186-202, 2016 Arxiv
  27. M. Burger, A. Lorz, M.T. Wolfram, Existence of balanced growth path solutions to a Boltzmann mean field game model for knowledge growth, KRM, 10(1), 117-140, 2016 Arxiv
  28. M. Bruna, M. Burger, H. Ranetbauer, M.T. Wolfram, Cross-diffusion systems with excluded-volume effects and asymptotic gradient flow structures, JNLS 27(2), 2017 Arxiv
  29. B. Matejczyk, M. Valisko, M.-T. Wolfram, J.-F. Pietschmann, D. Boda, Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo, J. Chem. Phys. 146, 2017 Arxiv
  30. S. Hittmeir, H. Ranetbauer, C. Schmeiser, M.T. Wolfram, Derivation and analysis of continuum models for crossing pedestrian traffic, M3AS 27, 2017 Arxiv
  31. A. Festa, A. Tosin, M.T. Wolfram, Kinetic description of collision avoidance in pedestrian dynamics by sidestepping, Kinet. Relat. Math. 11(3), 2018 Arxiv
  32. B. Matejczyk, J.-F. Pietschmann, G. Richardson, M.T. Wolfram, Asymptotic models for transport in large aspect ratio nanopores, EJAM 30(3) 2019 Arxiv
  33. B. Duering, M. Torregrossa, M.T. Wolfram, Boltzmann and Fokker-Planck Equations Modelling the Elo Rating System with Learning Effects, JNLS 29(3), 2019 Arxiv
  34. S. Gomes, A. Stuart and M.T. Wolfram, Parameter estimation for macroscopic pedestrian dynamics models from microscopic data, SIAM J. Appl. Math 79(4), 2019 Arxiv
  35. A. Stuart, M.T. Wolfram, Inverse optimal transport, SIAM J. Appl. Math 80(1), 2020 Arxiv
  36. M. Burger, J.F. Pietschmann, M.T. Wolfram, Data assimilation in price formation, Inverse Problems 36(6), 2020 Arxiv
  37. J. Carrillo, K. Hopf, M.T. Wolfram, Numerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosons, Kinet. Relat. Math. 13(3), 2020 Arxiv
  38. L. Alasio, H. Ranetbauer, M. Schmidtchen, M.T. Wolfram, Trend to equilibrium for systems with small cross diffusion, M2AN 54(5), 2020 Arxiv
  39. M. Fischer, G. Jankowiak, M.T. Wolfram, Micro- and macroscopic modeling of crowding and pushing in corridors, NHM 15(3), 2020 Arxiv
  40. C. Totzeck, M.T. Wolfram, Consensus-based global optimisation with personal best, Math. Biosci. Eng 17(5)., 2020 Arxiv
  41. J. Carrillo, D. Matthes, M.T. Wolfram, Lagrangian schemes for Wasserstein gradient flows, Handbook of Numerical Analysis 22, 2021 Arxiv
  42. M. Bruna, M. Burger, J.F. Pietschmann, and M.T. Wolfram, Active Crowds, Active Particles, Volume III, 2021 Arxiv
  43. M. Burger, J.-F. Pietschmann, H. Ranetbauer, C. Schmeiser, M.T. Wolfram, Mean field models for segregation dynamics, EJAM 33(1), 2022 Arxiv
  44. B. Duering, M. Fischer, M.T. Wolfram, An Elo-type rating model for players and teams of variable strength, Phil Trans R Soc A 380, 2022 Arxiv
  45. M. Barker, P. Degond, M.T. Wolfram, Comparing the best reply strategy and mean field games: the stationary case, EJAM 33(1), 2022 Arxiv
  46. A. Iuorio, G. Jankowiak, P. Szmolyan, and M.T. Wolfram, A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour, J Math Anal Appl 510(2), 2022 Arxiv
  47. O. R. A. Dunbar, A. Duncan, A.M. Stuart, and M.T. Wolfram, Ensemble Inference Methods for Models with Noisy and Expensive Liklihoods, SIADS 21(2), 2022 Arxiv
  48. D. Amadori, B. Andreianov, M. Di Francesco, S. Fagiolo, T. Girard, P. Goatin, P. Markowich, J.-F. Pietschmann, M.D. Rosini, G. Russo, G. Stivaletta and M.T. Wolfram, The mathematical theory of Hughes' model: a survery of results, Crowd Dynamics (4), Springer, 2023
  49. B. During, J. Evans and M.T. Wolfram, Steady States of an Elo-type Rating Model with Variable Strength, accepted at KRM, 2023 Arxiv
  50. A. Iuorio, G. Jankowiak, P. Szmolyan, M.T. Wolfram, Canards in a bottleneck, Physica D 451 2023 Arxiv
  51. S. Gomes, A. J. Nugent and M.T. Wolfram, On evolving network models and their influence on opinion formation, Physica D 456 2023 Arxiv
  52. M. Burger, L. Kanzler and M.T. Wolfram, Boltzmann mean-field game model for knowledge growth: limits to learning and general utilities, accepted for publication at Comm. Math. Sci, 2023 Arxiv

Conference proceedings

  1. M. Burger, M.T. Wolfram, Inverse dopant profiling for highly doped semiconductor devices,Proceedings of 5th MathMod, Vienna, 2006
  2. M.T. Wolfram, Opinion formation in a heterogenuous society, Proceedings of the Econophys V, India, 2010
  3. M. Buger, M. Di Francesco, P. Markowich, M.T. Wolfram, On a Mean Field Game Optimal Control Approach Modeling Fast Exit Scenarios in Human Crowds, 52nd IEEE Conference on Decision and Control, 3128--3133, 2013.
  4. D. Gomes, R.M. Vehlo, M.T. Wolfram, Dual two state mean field games, 53rd IEEE Conference on Decision and Control, 2014
  5. A. Festa, M.T. Wolfram, Collision avoidance in pedestrian dynamics, submitted, accepted at the 54th IEEE Conference on Decision and Control, 2015.
  6. C. Koutschan, H. Ranetbauer, G. Regensburger, M.T. Wolfram, Symbolic derivation of Mean-Field PDEs from Lattice Based Models, accepted at the SYNASC, 2015.

Submitted

  1. M. Bruna, M. Burger, H. Ranetbauer and M.T. Wolfram, Asymptotic gradient flow structures of a nonlinear Fokker-Planck equations, submitted, 2017 Arxiv
  2. L. M. Kreusser and M.T. Wolfram, On anisotropic equations for label propagation, submitted 2020 Arxiv
  3. A. Nungent, S. Gomes and M.T. Wolfram, Bridging the gap between agent based models and continuous opinion dynamics, 2023 Arxiv
  4. B. During, J. Franceschi, M.T. Wolfram and M. Zanella, Breaking consensus in kinetic opinion formation models on graphons, 2024 Arxiv
  5. A. Nungent, S. Gomes and M.T. Wolfram, Steering opinion dynamics through control of social networks, 2024 Arxiv