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Dr Tobias Grafke


  Tobias Grafke

Tobias Grafke

Associate Professor

Office: C2.29
Phone: +44 (0)24 765 74309
Email: T dot Grafke at warwick dot ac dot uk


Teaching Responsibilities 2023/24:

Term 1: MA3J4 Mathematical Modelling with PDE
Term 2: MA2K4 Numerical Methods and Computing

Research Interests:

My research focuses on the development of numerical methods and mathematical tools to analyse stochastic systems. Applications include fluid dynamics and turbulence, atmosphere and ocean dynamics, and biological and chemical systems. My work concentrates on the prediction of pathways and rates of occurrence of rare and extreme events in realistic complex systems, to develop numerical methods for their simulation, and to quantify the effects of random perturbations on the system's long term behavior.

Keywords: Applied and computational mathematics - Rare events, fluid dynamics and turbulence, large deviation theory, metastability, non-equilibrium statistical mechanics, active matter

Most relevant recent publications:
For an up-to-date list of all publications, see my Personal Homepage

  • 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)
  • G. Dematteis, T. Grafke, and E. Vanden-Eijnden, "Extreme event quantification in dynamical systems with random components", J. Uncertainty Quantification 7 (2019), 1029 (link)
  • T. Grafke, "String Method for Generalized Gradient Flows: Computation of Rare Events in Reversible Stochastic Processes", J. Stat. Mech. 2019/4 (2019), 043206 (link)
  • G. Dematteis, T. Grafke, E. Vanden-Eijnden, "Rogue waves and large deviations in deep sea", PNAS, 115 (5) 855-860, 2018, (link)
  • T. Grafke, M. Cates, and E. Vanden-Eijnden, "Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies", Phys. Rev. Lett. 119 (2017), 188003 (link)
    • F. Bouchet, T. Grafke, T. Tangarife, and E. Vanden-Eijnden, "Large Deviations in Fast-Slow Systems", J. Stat. Phys. 162 (2016), 793 (link)
    • 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)
    • 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)
    • 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)

    Personal Homepage:

    Recent research grants:

    • 2020: DMS-EPSRC EP/V013319/1 (NSF/EPSRC joint grant)
    • 2020: EPSRC EP/T011866/1 (New Investigator grant)