Daniel Karrasch
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Dr. Daniel Karrasch Technische Universität München Zentrum Mathematik Boltzmannstr. 3 D-85748 Garching bei München |
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ma.tum.deNews
- October 2019: Our paper "Barriers to the Transport of Diffusive Scalars in Compressible Flows", jointly written with George Haller
and Florian Kogelbauer, was accepted for publication in SIADS.
- September 2019: I was invited to join "The Julia Language team Contributors", as a member of the @JuliaLang github organization. Long live open-source software!
- July 2019: I entered the TOP100 of contributors to Julia . Long live open-source software!
- July 2019: We have submitted our manuscript Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains (joint with N. Schilling) for publication.
- June 2019: Suggestion from the teaching evaluation of "Numerik gewöhnlicher Differentialgleichungen", that I have nothing to do with! :-D
- June 2019:
- February 2019: We resubmitted our revised manuscript of "A geometric heat-flow theory of Lagrangian coherent structures".
- January 2019: As part of his Bachelor thesis, my student Philipp Rohrmüller has successfully implemented the MEBDF2 solver in OrdinaryDiffEq.jl . Congrats Philipp! And long live OSS!
- January 2019: We have submitted our manuscript Barriers to the Transport of Diffusive Scalars in Compressible Flows (joint with G. Haller and F. Kogelbauer) for publication.
- September 2018: Due to (very) small contributions to Julia , I now have Contributor status there. Long live open-source software!
- September 2018: Our group's Julia package CoherentStructures.jl for computing (Lagrangian) coherent structures has been released!
- August 2018: Our paper "Material barriers to diffusive and stochastic transport", jointly written with George Haller and Florian Kogelbauer, was published online by PNAS .
- July 2018: I got promoted to "Collaborator" in LinearMaps.jl , a Julia package for defining and working with linear maps as defined by their action on vectors. Check it out!
- June 2018: I gave a talk in the Mathematical Physics and Dynamical Systems Seminar at the Friedrich-Schiller-Universität in Jena, Germany.
- Feb 2018: Our paper, jointly written with my former B.Sc. student Florian, was published online by SIADS .
- Jan 2018: Alvaro de Diego has joined the group as a Ph.D. student. Welcome Alvaro!
Short CV
| since 2015 | Postdoctoral Fellow, TU München (with O. Junge) | |
| 2012-2015 | Postdoctoral Fellow, ETH Zürich (with G. Haller ) | |
| 09/2012 | Ph.D. in Mathematics, Technische Universität Dresden (with S. Siegmund ) | |
| 08/2009 | Diploma in Mathematics, Technische Universität Dresden | |
| 2006-2007 | Student's year abroad, Moscow State University |
Research interests
- Applied mathematics
- Nonautonomous dynamical systems
- Applied analysis, differential geometry and topology
- Fluid dynamics and coherent structures
- Scientific computing and programming in Julia
- Numerical linear algebra, lazy implementation, block matrix algebra
Research projects
- Member of the SFB Transregio 109 Discretization in Geometry and Dynamics
- Co-PI in a project within DFG - Priority Programme 1881 Turbulent Superstructures (joint with O. Junge)
Upcoming and recent activities
- May 2019: SIAM Conference on Applications of Dynamical Systems , Snowbird, Utah, USA
- February 2019: 5th Applied Mathematics Münster Symposium on Transport, Mixing and Fluids , Münster, Germany
- October 2018: International Conference on Discretization in Geometry and Dynamics, Hotel Döllnsee-Schorfheide, Germany
- September 2018: Annual meeting of the Priority Programme on Turbulent Superstructures, Lüneburg, Germany
- September 2018: Co-organizer of a minisymposium on Dynamical Systems Methods in Fluid Mechanics at Dynamics Days Europe , Loughborough, UK.
- June 2018: Talk in the Dynamical Systems and Mathematical Physics Seminar, Friedrich-Schiller-University, Jena, Germany
- March 2018: Co-organizer of Young Investigators Workshop of the SFB/TR109, Erfurt, Germany
- March 2018: Invited participant of the workshop on Mathematical Aspects of Physical Oceanography , Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria
- January 2018: talk in the Oberseminar Dynamics, TU Munich, Germany
- December 2017: Annual meeting of the Priority Programme on Turbulent Superstructures, Göttingen, Germany
- October 2017: Plenary speaker at the Fall school of the Priority Programme on Turbulent Superstructures, Bad Hersfeld, Germany
- July 2017: Speaker at Euromech Colloquium on Turbulent Superstructures in Closed and Open Flows , Erfurt, Germany
- May 2017: Co-organizer of minisymposium and speaker at SIAM Conference on Applications of Dynamical Systems , Snowbird, Utah, USA. See the talks of our minisymposium, including mine, here .
- March 2017: Speaker at Joint Annual Meeting of GAMM , Ilmenau@Weimar, Germany: my PDF slides (8MB)
- January 2017: Invited speaker at the Workshop on Transport in Unsteady Flows , Banff International Research Station, Canada. See my talk here .
- May 2016: Speaker at AmeriMech Symposium on Fluid Transport and Nonlinear Dynamics , Woods Hole Oceanographic Institution, USA
Publications
See also zbMATH, MathSciNet , arXiv ,
Publons , Scopus , GoogleScholar , ResearchGate , ORCiD , or my GitHub page
for my programming activities. - Preprints
- D. Karrasch, N. Schilling. Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains. submitted preprint
- G. Haller, D. Karrasch, and F. Kogelbauer. Barriers to the Transport of Diffusive Scalars in Compressible Flows. submitted preprint
- D. Karrasch, J. Keller. A geometric heat-flow theory of Lagrangian coherent structures. submitted preprint ,
Supplementary Material: advection movie of Lagrangian coherent structures in the rotating double gyre flow (video)
Supplementary Material: advection movie of Lagrangian coherent structures in the cylinder flow (video)
Supplementary Material: advection movie of Lagrangian coherent structures in the Bickley jet flow (video)
Supplementary Material: heat flow movie of heat localized within a coherent structure, based on the cylinder flow geometry (video)
Supplementary Material: heat flow movie of heat localized within the mixing region, based on the cylinder flow geometry (video)
- D. Karrasch, N. Schilling. Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains. submitted preprint
- Peer-reviewed articles
- G. Haller, D. Karrasch, and F. Kogelbauer. Material barriers to diffusive and stochastic transport.
Proceedings of the National Academy of Sciences, 2018. Journal link (open access)
- F. Hofherr, D. Karrasch. Lagrangian Transport Through Surfaces in Compressible Flows.
SIAM J Appl. Dyn. Sys. 17(1), 526–546, 2018. Journal link, postprint , BibTeX.
Find related code here
Supplementary Material: advection movie of particles in the crosschannel micromixer (video)
Supplementary Material: animation of evolution of donating regions in the crosschannel micromixer (video)
Supplementary Material: animation of evolution of donating regions in the crosschannel micromixer (video)
- A. Hadjighasem, D. Karrasch, H. Teramoto, G. Haller. A Spectral Clustering Approach to Lagrangian Vortex Detection.
Phys. Rev. E, 93(6), 063107, 2016. Journal link, postprint , BibTeX
Supplementary Material: advection movie of Lagrangian coherent vortices in the Bickley jet flow (mp4)
Supplementary Material: advection movie of Lagrangian coherent vortices in an ocean data set (mp4) - D. Karrasch. Lagrangian transport through surfaces in volume-preserving flows.
SIAM J. Appl. Math.76(3), 1178-1190, 2016. Journal link, postprint , BibTeX
- D. Karrasch. Attracting Lagrangian coherent structures on Riemannian manifolds.
Chaos, 25(8), 087411, 2015. Journal link, postprint , BibTeX
- D. Karrasch, M. Farazmand, G. Haller. Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures.
J. Computational Dynamics, 2(1), 83-93, 2015. Journal link, postprint , BibTeX
- D. Karrasch, F. Huhn, and G. Haller. Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows.
Proc. R. Soc. A, 471, 20140639, 2015. Journal link, postprint , BibTeX
- D. Karrasch, G. Haller. Do Finite-Size Lyapunov Exponents detect coherent structures?
Chaos, 23(4), 043126, 2013. Journal link, postprint , BibTeX
- D. Karrasch. Linearization of Hyperbolic Finite-time Processes.
J. Differential Equations, 254(1), 256-282, 2013. Journal link, postprint , BibTeX
- D. Karrasch. Comment on "A variational theory of hyperbolic Lagrangian Coherent Structures, Physica D 240 (2011) 574-598".
Physica D, 241(17), 1470-1473, 2012. Journal link, postprint , BibTeX
- T. S. Doan, D. Karrasch, N. T. Yet, and S. Siegmund. A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents.
J. Differential Equations, 252(10), 5535-5554, 2012. Journal link, postprint , BibTeX
- G. Haller, D. Karrasch, and F. Kogelbauer. Material barriers to diffusive and stochastic transport.
- Theses
- D. Karrasch: Hyperbolicity and Invariant Manifolds for Finite-Time Processes
Dissertation, TU Dresden, 2012. - D. Karrasch. On Generalized Models
Diploma Thesis, TU Dresden, 2009.
- D. Karrasch: Hyperbolicity and Invariant Manifolds for Finite-Time Processes
- Nonrefereed/Unpublished
- An Introduction to Grassmann Manifolds and their Matrix Representation: Some people have found this helpful: appendix B from my PhD thesis.
Teaching
| WS 2019/20: | Numerics of Dynamical Systems (TU München, TA) |
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| WS 2019/20: | Introduction to Nonlinear Dynamics (TU München, TA) | |
| SS 2019: | Dynamical Systems (TU München, Lecturer) |
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| WS 2018/19: | Einführung in die Numerische Lineare Algebra (MA 1304) (TU München, TA) |
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| WS 2018/19: | Einführung in die Programmierung (MA8003) (TU München, Lecturer) | |
| SS 2018: | Dynamical Systems (TU München, TA) | |
| WS 2017/18: | Geometric Continuum Mechanics (MA5339) (TU München, Lecturer) | |
| SS 2017: | Numerische Mathematik (EI) (TU München, TA) | |
| WS 2016/17: | Numerical Programming 1 CSE (TU München, TA) | |
| SS 2016: | Hauptseminar "Dynamical Systems and Graphs" (Co-organizer) | |
| SS 2016: | Linear Algebra (IT) (TU München, Tutor) | |
| WS 2015/16: | Analysis 3 (EI) (TU München, TA) | |
| SS 2015: | Nonlinear Dynamics and Chaos 1 (ETH Zürich, Lecturer) |
Supervision
- Current
- Alvaro de Diego, Tentative topic: Geometric and Stochastic Aspects of Lagrangian Coherent Structures (Ph.D. Applied Mathematics), 2018- (co-supervision with O. Junge)
- Nathanael Schiling, Tentative topic: Geometry of mixing (Ph.D. Applied Mathematics), 2018- (co-supervision with O. Junge)
- Past
- Phillip Rohrmüller, Topic: On numerical integration of the diffusion equation with time- and space-dependent diffusion coefficients (B.Sc. Mathematics), 2018-2019
- Bodi Yang, Tentative topics: Topics related to Lagrangian transport (research student from U Wisconsin Madison), 2018
- Andreas Kohl, Tentative topic: Efficient Computation of Derivatives of Flow Maps (M.Sc. Mathematics), 2017-2018
- Efdal Kalkan, Topic: On the simulation of turbulent flows (M.Sc. Mathematics), 2017-2018 (co-supervision with O. Junge)
- Irene Garnelo Abellanas, Topic: Applications of topological and geometrical data analysis to dynamical data sets (M.Sc. Mathematics), 2017. (now Data Scientist at Würth Elektronik)
- Bernd Huber, Topic: Geodesic Averaging of Diffusion Tensors (Research student), 2016
- Baykut Ayvaz, Topic: Computation of Coherent Sets by the Finite-Element Method (M.Sc. Mathematics), 2016-2017 (co-supervision with O. Junge)
- Florian Hofherr, Topic: Exact Quantification of Advective Mixing (B.Sc. Engineering Science), 2016. See our accepted preprint . (now M.Sc. Mathematics student at TUM)
- Sabrina Balzer, Topic: Dimensionsreduktion in der Moleküldynamik (B.Sc. Engineering Science), 2016 (co-supervision with O. Junge) (now M.Sc. Mathematics student at TUM)
Service
Reviewing Zentralblatt Mathematik, Mathematical Reviews (AMS) , and National Science Foundation (NSF) Refereeing Applied Math
Refereeing Fluid Physics
| Physical Review X | Physical Review E | Ocean Modelling |
| Physics of Fluids | Quarterly Journal of the Royal Meteorological Society | Environmental Fluid Mechanics |
