Journal publications

  1. Nayef Shkeir, Tobias Schäfer, Tobias Grafke, "Exponential time differencing for matrix-valued dynamical systems", ArXiv (2024) (link)
  2. J. Liu, J. E. Sprittles, T. Grafke, "Mean First Passage Times and Eyring-Kramers formula for Fluctuating Hydrodynamics", ArXiv (2024) (link)
  3. T. Grafke, T. Schäfer, and E. Vanden-Eijnden, "Sharp Asymptotic Estimates for Expectations, Probabilities, and Mean First Passage Times in Stochastic Systems with Small Noise", Communications on Pure and Applied Mathematics 77 (2024), 2268 (link)
  4. T. Grafke, A. Laio, "Metadynamics for transition paths in irreversible dynamics", SIAM Multiscale Modelling and Simulation 22 (2024), Iss. 1 (link)
  5. Jelle Soons, Tobias Grafke, Henk A. Dijkstra, "Optimal Transition Paths for AMOC Collapse and Recovery in a Stochastic Box Model", ArXiv (2023) (link)
  6. Reyk Börner, Ryan Deeley, Raphael Römer, Tobias Grafke, Valerio Lucarini, Ulrike Feudel, "Saddle avoidance of noise-induced transitions in multiscale systems", ArXiv (2023) (link)
  7. T. Schorlepp, S. Tong, T. Grafke, and G. Stadler, "Scalable Methods for Computing Sharp Extreme Event Probabilities in Infinite-Dimensional Stochastic Systems", Statistics and Computing 33 (2023), 137 (link)
  8. J. E. Sprittles, J. Liu, D. A. Lockerby, T. Grafke, "Rogue nanowaves: A route to film rupture", Phys. Rev. Fluids 8 (2023), L092001 (link)
  9. T. Schorlepp, T. Grafke, and R. Grauer, "Symmetries and Zero Modes in Sample Path Large Deviations", J Stat Phys 190 (2023), 50 (link)
  10. A. Frishman, and T. Grafke, "Mechanism for turbulence proliferation in subcritical flows", Proc. R. Soc. A 478 (2022), 2265 (link)
  11. M. Alqahtani, L. Grigorio, T. Grafke, "Extreme events and instantons in Lagrangian passive scalar turbulence models", Phys Rev E 106 (2022), 015101 (link)
  12. T. Schorlepp, T. Grafke, S. May, R. Grauer, "Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations", Phil Trans Roy Soc A 380 (2022), 2226 (link)
  13. A. Frishman, and T. Grafke, "Dynamical landscape of transitional pipe flow", Phys Rev E 105 (2022), 045108 (link)
  14. G. Margazoglou, T. Grafke, A. Laio, and V. Lucarini, "Dynamical Landscape and Multistability of a Climate Model", Proc. R. Soc. A 447 (2021), 2250 (link)
  15. T. Schorlepp, T. Grafke, and R. Grauer, "Gel'fand-Yaglom type equations for calculating fluctuations around Instantons in stochastic systems", J. Phys. A: Math. Theor. 54 (2021), 235003 (link)
  16. M.L. Bujorianu, R.S. MacKay, T. Grafke, S. Naik, E. Boulougouris, "A new stochastic framework for ship capsizing", ArXiv (2021) (link)
  17. T. Grafke, S. Scholtes, A. Wagner, M. Westdickenberg, "Numerics and analysis of Cahn-Hilliard critical points", ArXiv (2021) (link)
  18. M. Alqahtani, and T. Grafke, "Instantons for rare events in heavy-tailed distributions", J. Phys. A: Math. Theor. 54 (2021), 175001 (link)
  19. G. Ferré and T. Grafke, "Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation", SIAM Multiscale Model. Simul. 19(3) (2021), 1310 (link)
  20. G. Dematteis, T. Grafke, M. Onorato, and E. Vanden-Eijnden, "Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves", Phys. Rev. X 9 (2019), 041057 (link)
  21. G. Dematteis, T. Grafke, and E. Vanden-Eijnden, "Extreme event quantification in dynamical systems with random components", J. Uncertainty Quantification 7 (2019), 1029 (link)
  22. T. Grafke, and E. Vanden-Eijnden, "Numerical computation of rare events via large deviation theory", Chaos 29 (2019), 063118 (link)
  23. T. Grafke, "String Method for Generalized Gradient Flows: Computation of Rare Events in Reversible Stochastic Processes", J. Stat. Mech. 2019/4 (2019), 043206 (link)
  24. G. Dematteis, T. Grafke, and E. Vanden-Eijnden, "Rogue Waves and Large Deviations in Deep Sea", PNAS 115 (2018), 855-860 (link)
  25. T. Grafke, M. Cates, and E. Vanden-Eijnden, "Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies", Phys. Rev. Lett. 119 (2017), 188003 (link)
  26. T. Grafke and E. Vanden-Eijnden, "Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold", J. Stat. Mech. 2017/9 (2017), 093208 (link)
  27. T. Grafke, T. Schäfer, and E. Vanden-Eijnden, "Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools", Fields Institute Communications, In: Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science (Springer, New York, NY) (2017) (link)
  28. F. Bouchet, T. Grafke, T. Tangarife, and E. Vanden-Eijnden, "Large Deviations in Fast-Slow Systems", J. Stat. Phys. 162 (2016), 793 (link)
  29. T. Grafke, R. Grauer, and S. Schindel, "Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing", Commun. Comp. Phys. 18 (2015), 577 (link)
  30. T. Grafke, R. Grauer, and T. Schäfer, "The Instanton Method and its Numerical Implementation in Fluid Mechanics", J. Phys. A: Math. Theor. 48 (2015), 333001 (link)
  31. T. Grafke, A. Frishman, and G. Falkovich, "Time-irreversibility of the statistics of a single particle in a compressible turbulence", Phys. Rev. E 91 (2015), 043022 (link)
  32. T. Grafke, R. Grauer, T. Schaefer and E. Vanden-Eijnden, "Relevance of instantons in Burgers turbulence", EPL 109 (2015), 34003 (link)
  33. T. Grafke, R. Grauer, T. Schaefer and E. Vanden-Eijnden, "Arclength parametrized Hamilton's equations for the calculation of instantons", Multiscale Model. Simul. 12 (2014), 566 (link)
  34. T. Grafke and R. Grauer, "Lagrangian and geometric analysis of finite-time Euler singularities", Procedia IUTAM 9 (2013), 32 (link)
  35. T. Grafke, R. Grauer and T. Schaefer, "European Physics News Highlight: Instanton filtering for the stochastic Burgers equation", European Physics News 43 (2013) (link)
  36. T. Grafke, R. Grauer and T. Sideris, "Turbulence properties and global regularity of a modified Navier-Stokes equation", Physica D 254 (2013), 18 (link)
  37. T. Grafke, R. Grauer, and T. Schaefer, "Instanton filtering for the stochastic Burgers equation", J. Phys. A 46 (2013), 62002 (link)
  38. T. Grafke and R. Grauer, "Finite-Time Euler singularities: A Lagrangian perspective", Appl. Math. Letters 26 (2013), 500 (link)
  39. T. Grafke, H. Homann, J. Dreher and R. Grauer, "Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods", Physica D 237 (2008), 1932 (link)