DMS-EPSRC Sharp Large Deviation Estimates of Fluctuations in Stochastic Hydrodynamic Systems
Lead Research Organisation:
University of Warwick
Department Name: Mathematics
Abstract
Extreme events can be highly impactful. They are typically rare, which is fortunate if their consequences are negative on society, but also makes them difficult to predict. The scope of this project is to develop computational tools that can be applied to gain understanding of how extreme events occur in complex stochastic systems. Examples are models for the forecasting of extreme weather-related events like tropical storms and flooding as well as the spread of pollutants in case of ocean oil spills. Our tools will enable researchers to ask questions beyond of what is currently possible. This will lead to transformative improvement of current predictive models, which is essential for efficient management of natural and man made disasters. Further applications include the characterization of extreme events in stochastic models that behave similar to fluids, for example in the context of epidemics, traffic, and star formation.
People |
ORCID iD |
| Tobias Grafke (Principal Investigator) |
Publications
Sprittles J
(2023)
Rogue nanowaves: A route to film rupture
in Physical Review Fluids
Schorlepp T
(2023)
Scalable methods for computing sharp extreme event probabilities in infinite-dimensional stochastic systems
in Statistics and Computing
Schorlepp T
(2023)
Symmetries and Zero Modes in Sample Path Large Deviations
in Journal of Statistical Physics
Schorlepp T
(2021)
Gel'fand-Yaglom type equations for calculating fluctuations around instantons in stochastic systems
in Journal of Physics A: Mathematical and Theoretical
Schorlepp T
(2022)
Spontaneous symmetry breaking for extreme vorticity and strain in the three-dimensional Navier-Stokes equations.
in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Schorlepp T
(2022)
Symmetries and zero modes in sample path large deviations
Margazoglou G
(2021)
Dynamical landscape and multistability of a climate model.
in Proceedings. Mathematical, physical, and engineering sciences
Grafke T
(2024)
Metadynamics for Transition Paths in Irreversible Dynamics
in Multiscale Modeling & Simulation
| Description | The key finding of this award is the development of mathematical techniques for the computation of extremely small probabilities in complex dynamical systems. These tools are very helpful when trying to estimate the probability of scenarios that are at the same time extremely unlikely, but also very impactful, such as extreme weather events, stock market crashes, or tipping events in climate science. The developed method allows to compute precise limits of rare event probabilities in such systems, and develops algorithms to quantitatively compute them, by harnessing a results from the intersection of probability theory and quantum field theory. The major break-through lies in the fact that limiting probabilities can be sharply estimated by computing functional determinants around the so-called large deviation minimiser, intuitively accounting for fluctuations around the most likely scenario that exhibits a given rare event. |
| Exploitation Route | The developed method can be readily applied to a multitude of mathematical models describing real-world systems of impact, including the stability of ships on choppy sea, the stability of liquid thin films such as covering the eye, the development of turbulence in pipelines, or the breakdown of the Gulf stream in the north atlantic. All of these above examples have already been initiated over the course of the project and could be completed if taken forward. |
| Sectors | Environment Transport |
| Title | Raw data and figure scripts from Mechanism for turbulence proliferation in subcritical flows |
| Description | The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here, we propose the first-ever dynamical mechanism for puff proliferation-the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating the transition from a single puff to a two puff state, is introduced and its form is predicted. The role of fluctuations in the two stages of the transition, and how splits could be suppressed with increasing Reynolds number, are discussed. Using numerical simulations, the mechanism is validated within the stochastic Barkley model. Concrete predictions to test the proposed mechanism in pipe and other wall-bounded flows, and implications for the universality of the directed percolation picture, are discussed. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/Raw_data_and_figure_scripts_from_Mechanism_for_turbulence_p... |
| Title | Raw data and figure scripts from Mechanism for turbulence proliferation in subcritical flows |
| Description | The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here, we propose the first-ever dynamical mechanism for puff proliferation-the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating the transition from a single puff to a two puff state, is introduced and its form is predicted. The role of fluctuations in the two stages of the transition, and how splits could be suppressed with increasing Reynolds number, are discussed. Using numerical simulations, the mechanism is validated within the stochastic Barkley model. Concrete predictions to test the proposed mechanism in pipe and other wall-bounded flows, and implications for the universality of the directed percolation picture, are discussed. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/Raw_data_and_figure_scripts_from_Mechanism_for_turbulence_p... |
| Title | Supplementary Material (data): Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations from Spontaneous symmetry breaking for extreme vorticity and strain in the 3D Navier-Stokes equations |
| Description | In this supplemental material, we provide movies, raw data and python scripts to generate the figures of the paper. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/Supplementary_Material_data_Spontaneous_Symmetry_Breaking_f... |
| Title | Supplementary Material (data): Spontaneous Symmetry Breaking for Extreme Vorticity and Strain in the 3D Navier-Stokes Equations from Spontaneous symmetry breaking for extreme vorticity and strain in the 3D Navier-Stokes equations |
| Description | In this supplemental material, we provide movies, raw data and python scripts to generate the figures of the paper. |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| URL | https://rs.figshare.com/articles/dataset/Supplementary_Material_data_Spontaneous_Symmetry_Breaking_f... |
| Description | Interview Spektrum popular science magazine |
| Form Of Engagement Activity | A press release, press conference or response to a media enquiry/interview |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Public/other audiences |
| Results and Impact | Interview with the German popular science magazine 'Spektrum' about Large Deviations in Liquid Nanofilms. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://www.spektrum.de/news/nano-monsterwellen-in-hauchduennen-fluessigkeitsfilmen/2191872 |
| Description | Press release 'Going Rogue' - Warwick University |
| Form Of Engagement Activity | A press release, press conference or response to a media enquiry/interview |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Public/other audiences |
| Results and Impact | Press release by the University of Warwick concerning Rogue Nanowaves for thin liquid films. |
| Year(s) Of Engagement Activity | 2023 |
| URL | https://warwick.ac.uk/newsandevents/pressreleases/?newsItem=8a17841a8b3cb121018b4382282c1d5e |
| Description | Scientific American |
| Form Of Engagement Activity | A press release, press conference or response to a media enquiry/interview |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Public/other audiences |
| Results and Impact | Interview with Scientific American about the connection between Large Deviation Theory and Oceanic Rogue Waves |
| Year(s) Of Engagement Activity | 2022 |
| URL | https://www.nationalgeographic.com/premium/article/mathematicians-may-soon-be-able-to-predict-enormo... |