The instanton method and its numerical implementation in fluid mechanics

DOI10.1088/1751-8113/48/33/333001zbMath1327.76076arXiv1506.08745OpenAlexW3105123535WikidataQ62570025 ScholiaQ62570025MaRDI QIDQ3448391

Tobias Schäfer, Tobias Grafke, Rainer Grauer

Publication date: 23 October 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.08745

zbMATH Keywords

numerical methodsinstantonsturbulencefluid dynamics

Mathematics Subject Classification ID

Isotropic turbulence; homogeneous turbulence (76F05) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

Related Items (38)

Computing transition rates for the 1-D stochastic Ginzburg-Landau-Allen-Cahn equation for finite-amplitude noise with a rare event algorithm ⋮ Transient growth in stochastic Burgers flows ⋮ Ordered line integral methods for computing the quasi-potential ⋮ Instantons and fluctuations in a Lagrangian model of turbulence ⋮ Eddy-viscous modeling and the topology of extreme circulation events in three-dimensional turbulence ⋮ Parametric Resonance for Enhancing the Rate of Metastable Transition ⋮ WKB theory of large deviations in stochastic populations ⋮ Symmetries and zero modes in sample path large deviations ⋮ Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems ⋮ Computing non-equilibrium trajectories by a deep learning approach ⋮ Schrödinger equation driven by the square of a Gaussian field: instanton analysis in the large amplification limit ⋮ Numerical study of extreme mechanical force exerted by a turbulent flow on a bluff body by direct and rare-event sampling techniques ⋮ Metadynamics for Transition Paths in Irreversible Dynamics ⋮ Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise ⋮ Asymptotically Efficient Simulation of Elliptic Problems with Small Random Forcing ⋮ Instantons in a Lagrangian model of turbulence ⋮ Non-equivalence of dynamical ensembles and emergent non-ergodicity ⋮ Statistics of large currents in the Kipnis–Marchioro–Presutti model in a ring geometry ⋮ Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions ⋮ Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation ⋮ A dynamic-solver-consistent minimum action method: with an application to 2D Navier-Stokes equations ⋮ Study of the ground-state energies of some nuclei using hybrid model ⋮ Adaptive sampling of large deviations ⋮ Short time large deviations of the KPZ equation ⋮ Do extreme events trigger turbulence decay? – a numerical study of turbulence decay time in pipe flows ⋮ Finite-size effects in the short-time height distribution of the Kardar–Parisi–Zhang equation ⋮ First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions ⋮ Computing return times or return periods with rare event algorithms ⋮ Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation ⋮ Edge states in the climate system: exploring global instabilities and critical transitions ⋮ Instanton based importance sampling for rare events in stochastic PDEs ⋮ Numerical computation of rare events via large deviation theory ⋮ Rare transitions to thin-layer turbulent condensates ⋮ Metastable transitions in inertial Langevin systems: What can be different from the overdamped case? ⋮ Singularity formation in the deterministic and stochastic fractional Burgers equation ⋮ Parametric Hamilton’s equations for stochastic systems ⋮ A self-similarity principle for the computation of rare event probability ⋮ Gel’fand–Yaglom type equations for calculating fluctuations around instantons in stochastic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An adaptive high-order minimum action method
• Simulating rare events in dynamical processes
• Statistical behaviour of adaptive multilevel splitting algorithms in simple models
• Large deviations and asymptotic methods in finance
• Large deviations techniques and applications.
• Renormalization group analysis of turbulence. I: Basic theory
• Onsager's conjecture on the energy conservation for solutions of Euler's equation
• The path integral approach to financial modeling and options pricing
• Non-Gaussian error probability in optical soliton transmission
• Going forth and back in time: a fast and parsimonious algorithm for mixed initial/final-value problems
• A minimum action method for small random perturbations of two-dimensional parallel shear flows
• Fractional generalization of Kac integral
• Mathematical theory of Feynman path integrals. An introduction
• Genealogical particle analysis of rare events
• Combinatorial analysis of the adaptive last particle method
• STOCHASTIC RESONANCE IN A SIMPLE MODEL OF MAGNETIC REVERSALS
• Field Theory of Non-Equilibrium Systems
• The gentlest ascent dynamics
• Water waves, nonlinear Schrödinger equations and their solutions
• Condensed Matter Field Theory
• Onsager and the theory of hydrodynamic turbulence
• Dynamic Scaling of Growing Interfaces
• A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
• The geometric minimum action method: A least action principle on the space of curves
• Probability density functions in steady-state Burgers turbulence
• Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Supersymmetry in Disorder and Chaos
• Statistical theory for the stochastic Burgers equation in the inviscid limit
• Kicked Burgers turbulence
• Minimum action method for the study of rare events
• Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
• Financial Modelling with Jump Processes
• Instanton filtering for the stochastic Burgers equation
• Theory of Financial Risk and Derivative Pricing
• Arclength Parametrized Hamilton's Equations for the Calculation of Instantons
• Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing
• Some Applications and Methods of Large Deviations in Finance and Insurance
• Theory of Bound States in a Random Potential
• Steady-state Burgers turbulence with large-scale forcing
• The partial differential equation u_t + uu_x = μ_xx
• Fluctuations and Irreversible Processes
• Fluctuations and Irreversible Process. II. Systems with Kinetic Energy
• Brownian motion in a field of force and the diffusion model of chemical reactions
• Large deviations

This page was built for publication: The instanton method and its numerical implementation in fluid mechanics