New Models to Characterize and Predict Rare Events in Complex Physical Systems 24-000006190
Abstract
The objective of this proposal is to assemble new mathematical tools and models tocharacterize and predict rare events in complex physical processes of interest to the United StatesNavy. The physical processes of interest include: (1) surface water waves, as generated by windand tidal forces in earth#s oceans, and as they affect the theatre of the US Navy#s operations; (2)thermal convection, as the driving force behind both atmospheric dynamics and the ocean#s largescalecirculation structure; (3) the earth#s magnetosphere, as generated by interior liquid-coredynamics, and as it underlies navigational systems. The rare events in these systems respectivelyinclude: (1) anomalous or rogue water waves; (2) large-scale circulation reversals in theatmosphere/ocean; (3) drifts and reversals of the Earth#s magnetic field.These topics will be approached from the unifying perspective of truncated dynamicalsystem analysis, which firmly connects simplified models to the known governing equations andpermits, where needed, parameterization of unresolved scales through stochastic or machinelearningmethodologies. The training of undergraduate research students, particularly those fromunderrepresented groups and disadvantaged backgrounds, is central to this proposal. The PI willclosely supervise research students asthey create a collection new models and algorithms toadvance the understanding of the above physical processes that are of fundamental importance tothe US Navy#s operations. In particular, the team will:1. Create a new class of parallelized algorithms to efficiently sample water-wave statistics fromthe governing Gibbs distribution and create a database to allow rapid assessment of conditionsunderlying rogue-wave occurrence.2. Create new generalizations of the PI#s reduced model for thermally-convective large-scalecirculation reversals. These generalizations will permit examination of three-dimensionalconvection under Coriolis effects, along with examination of small-scale turbulent fluctuations.3. Couple the thermal-convection model to magnetic-field evolution to examine dynamo actionand to determine combinations of velocity/magnetic fields leading to optimal dynamo growth.These tasks, along with new ideas that arise while the work is underway, will advance theUS Navy#s understanding of physical processes that influence its operations, and, at the same time,provide intensive training for several undergraduate students for careers in the mathematicalsciences. The unifying methodology of truncated-dynamical-system statistical analysis will ensurethat all findings are firmly connected to known underlying physical principles. This approach willavoid the shortcomings of heuristics or fitting procedures which often do not generalize tocircumstances lying outside of those in which they were created.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2024
- Source ID
- N000142412617
Entities
People
- Nicholas Moore
Organizations
- Colgate University
- Office of Naval Research
- United States Navy