2023

Schorlepp, Timo, Grafke, Tobias and Grauer, Rainer (2023) Symmetries and zero modes in sample path large deviations. Journal of Statistical Physics, 190 . 50. doi:10.1007/s10955-022-03051-w ISSN 0022-4715.

Grafke, Tobias and Laio, Alessandro (2023) Metadynamics for transition paths in irreversible dynamics. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal . ISSN 1540-3459. (In Press)

Sprittles, James E., Liu, Jingbang, Lockerby, Duncan A. and Grafke, Tobias (2023) Rogue nanowaves : a route to film rupture. Physical Review Fluids . ISSN 2469-990X. (In Press)

Grafke, Tobias, Schäfer, Tobias and Vanden‐Eijnden, Eric (2023) Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise. Communications on Pure and Applied Mathematics . doi:10.1002/cpa.22177 ISSN 0010-3640. (In Press)

2022

Frishman, Anna and Grafke, Tobias (2022) A mechanism for turbulence proliferation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2265). doi:10.1098/rspa.2022.0218 ISSN 1364-5021.

Alqahtani, Mnerh, Grigorio, Leonardo and Grafke, Tobias (2022) Extreme events and instantons in Lagrangian passive scalar turbulence models. Physical Review E, 106 (1). 015101. doi:10.1103/physreve.106.015101 ISSN 1539-3755.

Schorlepp, Timo, Grafke, Tobias, May, Sandra and Grauer, Rainer (2022) Symmetry breaking for extreme vorticity and strain in the 3D Navier-Stokes equations. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 380 (2226). doi:10.1098/rsta.2021.0051 ISSN 1364-503X.

Frishman, Anna and Grafke, Tobias (2022) Dynamical landscape of transitional pipe flow. Physical Review E, 105 (4). 045108. doi:10.1103/PhysRevE.105.045108 ISSN 2470-0045.

2021

Ferré, Grégoire and Grafke, Tobias (2021) Approximate optimal controls via instanton expansion for low temperature free energy computation. Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal, 19 (3). pp. 1310-1332. doi:10.1137/20M1385809 ISSN 1540-3459.

Margazoglou, Georgios, Grafke, Tobias, Laio, Alessandro and Lucarini, Valerio (2021) Dynamical landscape and multistability of a climate model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2250). 20210019. doi:10.1098/rspa.2021.0019 ISSN 1364-5021.

Bujorianu, Manuela L., MacKay, Robert S., Grafke, Tobias, Naik, Shibabrat and Boulougouris, Evangelos (2021) A new stochastic framework for ship capsizing. In: STAB&S 2021, the 1st International Conference on the Stability and Safety of Ships and Ocean Vehicles, Virtual conference [Galsgow], 7-11 Jun 2021. Published in: Proceedings of the 1st International Conference on the Stability and Safety of Ships and Ocean Vehicles (In Press)

Schorlepp, Timo, Grafke, Tobias and Grauer, Rainer (2021) Gel’fand-Yaglom type equations for calculating fluctuations around instantons in stochastic systems. Journal of Physics A: Mathematical and Theoretical, 54 (23). 235003. doi:10.1088/1751-8121/abfb26 ISSN 1751-8113.

Alqahtani, Mnerh and Grafke, Tobias (2021) Instantons for rare events in heavy-tailed distributions. Journal of Physics A: Mathematical and Theoretical, 54 (17). 175001. doi:10.1088/1751-8121/abe67b ISSN 1751-8113.

2019

Dematteis, Giovanni, Grafke, Tobias, Onorato, Miguel and Vanden-Eijnden, Eric (2019) Experimental evidence of hydrodynamic instantons : the universal route to rogue waves. Physical Review X, 9 (4). 041057. doi:10.1103/PhysRevX.9.041057 ISSN 2160-3308.

Dematteis, Giovanni, Grafke, Tobias and Vanden-Eijnden, Eric (2019) Extreme event quantification in dynamical systems with random components. SIAM/ASA Journal on Uncertainty Quantification, 7 (3). pp. 1029-1059. doi:10.1137/18M1211003 ISSN 2166-2525.

Grafke, Tobias and Vanden-Eijnden, Eric (2019) Numerical computation of rare events via large deviation theory. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (6). 063118 . doi:10.1063/1.5084025 ISSN 1054-1500.

Grafke, Tobias (2019) String method for generalized gradient flows : computation of rare events in reversible stochastic processes. Journal of Statistical Mechanics: Theory and Experiment, 2019 . 043206. doi:10.1088/1742-5468/ab11db ISSN 1742-5468.

2018

Dematteis, Giovanni, Grafke, Tobias and Vanden-Eijnden, Eric (2018) Rogue waves and large deviations in deep sea. Proceedings of the National Academy of Sciences of the United States of America, 115 (5). pp. 855-860. doi:10.1073/pnas.1710670115 ISSN 0027-8424.

2017

Grafke, Tobias, Cates, Michael E. and Vanden-Eijnden, Eric (2017) Spatiotemporal self-organization of fluctuating bacterial colonies. Physical Review Letters, 119 (18). 188003 . doi:10.1103/PhysRevLett.119.188003 ISSN 0031-9007.

Grafke, Tobias and Vanden-Eijnden, Eric (2017) Non-equilibrium transitions between metastable fixed-points in slow-fast systems with a bifurcating slow manifold. Journal of Statistical Mechanics : Theory and Experiment, 2017 . 093208. doi:10.1088/1742-5468/aa85cb ISSN 1742-5468.

2016

Bouchet, Freddy, Grafke, Tobias, Tangarife, Tomás and Vanden-Eijnden, Eric (2016) Large deviations in fast–slow systems. Journal of Statistical Physics, 162 (4). pp. 793-812. doi:10.1007/s10955-016-1449-4 ISSN 0022-4715.

2015

Grafke, Tobias, Grauer, Rainer and Schäfer, Tobias (2015) The instanton method and its numerical implementation in fluid mechanics. Journal of Physics A: Mathematical and Theoretical, 48 (33). 333001. doi:10.1088/1751-8113/48/33/333001 ISSN 1751-8113.

2014

Grafke, Tobias, Grauer, R., Schäfer, T. and Vanden-Eijnden, E. (2014) Arclength parametrized Hamilton's equations for the calculation of instantons. Multiscale Modeling & Simulation, 12 (2). pp. 566-580. doi:10.1137/130939158 ISSN 1540-3459.