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Mathematics Institute

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 2024/25:

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

  • 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)
  • J. E. Sprittles, J. Liu, D. A. Lockerby, T. Grafke, "Rogue nanowaves: A route to film rupture", Phys. Rev. Fluids 8 (2023), L092001 (link)
  • 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)
  • 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)
  • 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, 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)
  • 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)

Personal Homepage:
http://homepages.warwick.ac.uk/staff/T.Grafke/

Recent research grants:

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