Applied and Computational Analysis Program

The Office of Naval Research (ONR) 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; and inverse problems arising from acoustic and electromagnetic wave propagation and scattering.

The Applied and Computational Analysis Program currently has three thrusts:

• Multi-Scale/Multi-Physics Modeling: The thrust's 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 thrust aims to develop mathematical tools to understand the complex structure of the oceans and the atmosphere. It contains two sub-thrusts, 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.

Proposal Submission Date: Ongoing

Note: Proposers are encouraged to contact the program officer to discuss their research interest prior to the submission of formal proposals.