104 citations · 129 across the 4 of their papers we have counts for
10 papers
Exponential time differencing for matrix-valued dynamical systems
Nayef Shkeir, Tobias Grafke
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or…
Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation
Sumeja Burekovic, Tobias Schaefer, Rainer Grauer
Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607 (2020)]. Here, we use ins…
The instanton method and its numerical implementation in fluid mechanics
Tobias Grafke, Rainer Grauer, Tobias Schäfer
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discus…
Relevance of instantons in Burgers turbulence
Tobias Grafke, Rainer Grauer, Tobias Schäfer +1
Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These re…
Arclength parametrized Hamilton's equations for the calculation of instantons
Tobias Grafke, Rainer Grauer, Tobias Schäfer +1
A method is presented to compute minimizers (instantons) of action functionals using arclength parametrization of Hamilton's equations. This method can be interpreted as a local va…
The space-fractional diffusion-advection equation: Analytical solutions and critical assessment of numerical solutions
Robin Stern, Frederic Effenberger, Horst Fichtner +1
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in vario…