The Applied and Computational Analysis program develops and exploits methods in modern and classical mathematical analysis with emphasis on mathematical and computational models of physical phenomena. Naval interest in waves, flows, materials, structures, and information processing motivates research in the areas of:
- Multi-phase, multi-physics, multi-material problems
- Fluid transport and mixing
- Predictability of models for nonlinear dynamics
- Inverse problems arising from acoustic and electromagnetic wave propagation and scattering
Research Concentration Areas
- Multi-Scale/Multi-Physics Modeling: The goal is to develop novel analytical and computational tools to address problems whose description requires computing across many scales, both temporally and spatially. These problems may require multiple physics due to the complexity of the environment, for example, problems that involve taking into account hydrodynamics, salinity and thermodynamics, or multiple physics due to the presence of many scales, thus requiring combining atomistic and continuum modeling. Specific areas of interest to the Navy include analytically rigorous and computationally robust and efficient modeling of fatigue, fracture, dislocation, nucleation, shocks and contact lines.
- Dynamical Systems and Oceanic and Atmospheric Modeling: This aims to develop mathematical tools to understand the complex structure of the oceans and the atmosphere. It contains two sub-areas, one addressing the behavior of solutions of the governing partial differential equations of ocean and atmospheric dynamics. The second develops novel mathematical and computational tools for computing coherent structures for finite-time velocity fields that appear in oceans, especially those associated with coastal regions. Probabilistic and statistical tools, especially in the context of stochastic differential equations, are currently playing critical roles in this thrust.
- Inverse Methods: This area addresses the mathematical challenges facing the Navy in the area of inverse problems. Imaging targets in cluttered media, especially when the statistics of the medium are not known a priori, constitute an important area of application. Non-destructive evaluation in elastic-plastic media is another application area of emphasis. The mathematical challenges involve developing efficient and robust computational algorithms for the partial differential equations that arise in acoustics and electromagnetism.
Research Challenges and Opportunities
- Representation of multiple scales and multiple physics in reduced models of complex physical phenomena
- Development of analytical tools to study incomplete dynamical systems obtained from field measurements
- Development of fast computational tools to detect targets in cluttered media.
How to Submit
For detailed application and submission information for this research topic, please refer to our broad agency announcement (BAA) No. N0001425SB001.
Contracts: All white papers and full proposals for contracts must be submitted through FedConnect; instructions are included in the BAA.
Grants: All white papers for grants must be submitted through FedConnect, and full proposals for grants must be submitted through grants.gov; instructions are included in the BAA.