Picture of Jan-Frederik Pietschmann

Welcome



Welcome to my Homepage. I am currently a Post-Doc researcher at the Arbeitsgruppe Numerische Mathematik und Wissenschaftliches at TU Darmstadt, Germany.


Research Interests

My current research interest are inverse Problems of non-linear PDEs, parameter identification problems, socio-economic PDE models (especially crowd motion), finite element methods, long time behaviour of non-linear Fokker-Planck equatations

Submitted preprints

[1] H. Egger, J.-F. Pietschmann, M. Schlottbom, Identification of Chemotaxis Models with Volume Filling. submitted. 2014. (Arxiv)
[2] H. Egger, J.-F. Pietschmann, M. Schlottbom, Identification of nonlinear heat conduction laws. submitted. 2014. (Arxiv)

Publications in Journals

[1] G. Trevor, K. Decker, T. Plett, M. Pevarnik, J.-F. Pietschmann, I. Vlassiouk, A. Aksimentiev, Z. Siwy. Rectification of Ion Current in Nanopores Depends on the Type of Monovalent Cations Experiments and Modeling, Journal of Physical Chemistry Part C, 118(18):9809–9819, 2014. (published version)
[2] H. Egger, J.-F. Pietschmann, M. Schlottbom, Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales, inverse problems 30(2):025004, 2014, (Arxiv, published version)
[3] H. Egger, J.-F. Pietschmann, M. Schlottbom, Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem, inverse problems 30(3):035009, 2014, (Arxiv, published version)
[4] J.-F. Pietschmann, M.-T. Wolfram, M. Burger, C. Trautmann, V. Bayer, G. Nguyen, M. Pevarnik, Z. Siwy, Rectification properties of conically shaped nanopores: consequences of miniaturization, Phys. Chem. Chem. Phys., 15:16917-16926, 2013 (Arxiv, published version)
[5] M. Burger, J.-F. Pietschmann, M.-T. Wolfram, Identification of non-linearities in transport-diffusion models of crowded motion, Inverse Problems and Imaging 7(4) 2013, (preprint, published version),
[6] L.A. Caffarelli, P.A. Markowich, J.-F. Pietschmann, On a price formation free boundary model by Lasry & Lions, C. R. Acad. Sci. Paris, Ser. I, Volume 349, Issues 11-12, 2011(preprint, published version)
[7] M. Burger, P.A. Markowich, J.F. Pietschmann, Continuous Limit of a Crowd Motion and Herding Model: Analysis and Numerical Simulations,Kinetic and Related Modells, Volume 4, Issue 4, 2011, (preprint, published version)
[8] M. Di Francesco, P.A. Markowich, J.F. Pietschmann, M.T. Wolfram, On the Hughes' model of pedestrian flow: The one-dimensional case, J. Diff. Eq. Volume 250, Issue 3, 1 pp. 1334-1362, 2011 (preprint, published version)
[9] M. Burger, M. Di Francesco, J.-F. Pietschmann and B. Schlake, Nonlinear Cross-Diffusion with Size Exclusion, 2010, SIAM J. Math. Anal. Volume 42, Issue 6, pp. 2842-2871, 2010 (preprint, published version)
[10] B. Düring, 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), p. 3687-3708, 2009, (preprint, published version)
[11] P.A. Markowich, N. Matevosyan, J.-F. Pietschmann, M.-T. Wolfram, On a parabolic free boundary equation modeling price formation, Math. Models Methods Appl. Sci., 11(19), 1929-1957, 2009, (preprint, published version)

Conference Proceedings and Book Chapters

[1] B. Schlake, J.-F. Pietschmann Lane Formation in a Microscopic Model and the corresponding Partial Differential Equation, 1st IEEE Workshop on Modeling, Simulation and Visual Analysis of Large Crowds, Barcelona (preprint)
[2] J.-F. Pietschmann The connection between microscopic and macroscopic models for pedestrian movement with applications to lane formation. To appear in: Modeling, Simulation, and Visual Analysis of Large Crowds, Springer Verlag.

Misc

[1] J.-F. Pietschmann On Some Partial Differential Equation Models in Socio-Economic Contexts - Analysis and Numerical Simulations, Ph.D. thesis, University of Cambridge, 2011, pdf


Projects

"Neue mathematische Modelle und Methoden für ein besseres Verständnis von synthetischen Nanoporen", DAAD PPP mit Prof. Z. Siwy, UC Irvine, 2013-2014

"Forward and Inverse Problems in Non-Linear Drift-Diffusion", DFG Einzelförderung, 10/2012-3/2015

"Post-Doc Stipendium" Daimler und Benz Stiftung, 2/2013-6/2016

Teaching

SS 2014 Lecture: Computational Inverse Problems, with M. Schlottbom. TU Darmstadt
28.6-1.7. 2012 Mini-course: "Inverse Problems for Partial Differential Equations", Weissensee Summercamp

part1,part2,part3

WS 2011/2012 Lecture: "Inverse und schlecht gestellte Probleme", together with Dr. F. Wübbeling.
MT 2009 Supervision, Lecture Partial Differential Equations (Univ. Cambridge)
MT 2008 Supervision and Preparation of Example Sheets, Lecture Partial Differential Equations (Univ. Cambridge)


Selected Stays and Talks

3/2014 Invited participant: Isaac Newton Institute, Free Boundary Problems, Newton Institute, Cambridge
6/2013 Applied Inverse Problems Conference, Dejon, South Korea
4/2013 Inverse Problems and Applications, Linköping, Sweden
12/2011 Seminar in Applied Mathematics, KTH, Stockholm
12/2011 Inverse Problems in Science and Engineering, Newton Institute, Cambridge, talk
09/2011 Chemnitz Symposium on Inverse Problems, TU Chemnitz, talk
3/2011 Workshop on Numerical Methods for Optimal Control and Inverse Problems, TU München
9/2009 Mathematical Models in Life and Social Sciences, Alba Adriatica (Italy), talk
7/2009 Workshop on 'Kinetic and Mean-field models in the Socio-Economic Sciences' @ ICMS (Edinburgh), talk
6/2008 Workshop on 'Kinetic and Macroscopic Models for Cars, Supply Chains, and Pedestrian Flows' @ WPI (Vienna)
3/2008-6/2008 Core participant of the 'Optimal Transport' longterm programm @ IPAM (Los Angeles)

Short CV

since 10/0212 Post-Doc, TU Darmstadt
02/0212-8/2012 Post-Doc, Center for Industrial and Applied Mathematics, KTH, Stockholm
10/0211-01/2012 Post-Doc, Institute for Computational and Applied Mathematics, University of Münster
10/2008-11/0211 PhD Student in Cambridge, Thesis: On Some Partial Differential Equation Models in Socio-Economic Contexts - Analysis and Numerical Simulations
10/2008 Master in Mathematics (Mathediplom), Title: Long-time Behaviour of nonlinear Fokker-Planck equations, Supervisor: Prof. Martin Burger, thesis
6/2008 Master in Physics (Physikdiplom), Title: Development of a Novel Readout System for Small Animal Positron Emmision Tomography, Supervisor: Prof. Johannes Wessels, thesis
2002 A-levels (Abitur)

If you have any questions or comments, please contact me.