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
- May 2020: My talk proposal for JuliaCon 2020
(virtual conference) was accepted.
- May 2020: I am mentoring Alexander Seiler's (Uni Basel, Siwtzerland) GSoC 2020 project on "General Improvements for LinearMaps.jl".
- April 2020: I was invited to join the github organization JuliaStats . Long live OSS!
- April 2020: Jointly with Nathanael Schilling, we have submitted our manuscript "A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit".
- April 2020: Our paper "A geometric heat-flow theory of Lagrangian coherent structures", jointly written with Johannes Keller, was (finally, finally) accepted for publication in Journal of Nonlinear Science. Thanks to the DEAL agreement our paper is going to be published open access.
- March 2020: Our paper "Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains ", jointly written with Nathanael Schilling, was accepted for publication in the free of charge, open-access SMAI Journal of Computational Mathematics .
- 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 linear 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
- July 2020: JuliaCon 2020 , online
- July 2020: ENOC 2020 , the 10th European Nonlinear Dynamics Conference, Lyon, France (postponed to 2021)
- January 2020: Invited participant of the workshop on Mathematical Aspects of Physical Oceanography , Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, Austria
- 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
Publications
See also zbMATH, MathSciNet , arXiv ,
Publons , Scopus , GoogleScholar , ResearchGate , ORCiD , or my GitHub page
for my programming activities. - Preprints
- D. Karrasch, N. Schilling. A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit.
Supplementary Material: animation of parameter study of a 2d turbulence simulation (video)
- D. Karrasch, N. Schilling. A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit.
- Peer-reviewed articles
- D. Karrasch, N. Schilling. Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains. SMAI Journal of Computational Mathematics postprint
Supplementary Material: animation of parameter study of a 2d turbulence simulation (video) - D. Karrasch, J. Keller. A geometric heat-flow theory of Lagrangian coherent structures. Journal of Nonlinear Science Journal link (open access) postprint ,
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) - G. Haller, D. Karrasch, and F. Kogelbauer. Barriers to the Transport of Diffusive Scalars in Compressible Flows.
SIAM J Appl. Dyn. Sys. 19(1), 85-123, 2020. Journal link, postprint
- 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
- D. Karrasch, N. Schilling. Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains. SMAI Journal of Computational Mathematics postprint
- 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, TopMath), 2018- (co-supervision with O. Junge)
- Past
- Nathanael Schilling, Topic: Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains (M.Sc. Mathematics, TopMath), 2019
- Phillip Rohrmüller, Topic: On numerical integration of the diffusion equation with time- and space-dependent diffusion coefficients (B.Sc. Mathematics), 2018-2019. (now M.Sc. Mathematics student at TUM)
- 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. (was Data Scientist at Würth Elektronik, now Ph.D. student at TUM)
- 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 |
