From the 1 of 9 linked papers with an AI index.
9 papers
Laminar gaps mirror turbulent puffs in pipe flow
Shai Kapon, Tobias Grafke, Anna Frishman
Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbule…
Escape over a saddle by coloured noise: theory and numerics
Jiayao Shao, Tobias Grafke, Robert S. MacKay
The paper develops new computational methods to study rare escape events over a saddle point in stochastic systems driven by coloured or degenerate noise, introducing a Hamiltonian…
Scalability of the second-order reliability method for stochastic differential equations with multiplicative noise
Timo Schorlepp, Tobias Grafke
We show how to efficiently compute asymptotically sharp estimates of extreme event probabilities in stochastic differential equations (SDEs) with small multiplicative Brownian nois…
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…
Self-Replication of Turbulent Puffs: On the edge between chaotic saddles
Anton Svirsky, Tobias Grafke, Anna Frishman
Pipe flow is a canonical example where turbulence first appears intermittently in space and time, taking the form of localized structures termed puffs. Turbulence spreads via puff…
Sampling conditioned diffusions via Pathspace Projected Monte Carlo
Tobias Grafke
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic…