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Congratulations to Corbin Foucart on his graduation! Corbin received an SM from Mechanical Engineering for his research on “Efficient Matrix-Free Implementation and Automated Verification of Hybridizable Discontinuous Galerkin Finite Element Methods” with our MSEAS group at MIT.
Congratulations to Wael Hajj Ali on his graduation! Wael received an SM from Mechanical Engineering for his research on “Dynamically Orthogonal Equations for Stochastic Underwater Sound Propagation” with our MSEAS group at MIT.
Ali, W.H., 2019. Dynamically Orthogonal Equations for Stochastic Underwater Sound Propagation. SM Thesis, Massachusetts Institute of Technology, Mechanical Engineering, September 2019.
Grand challenges in ocean acoustic propagation are to accurately capture the dynamic environmental uncertainties and to predict the evolving probability density function of stochastic acoustic waves. This is due to the complex ocean physics and acoustics dynamics, nonlinearities, multiple scales, and large dimensions. There are several sources of uncertainty including: the initial and boundary conditions of the ocean physics and acoustic dynamics, the bathymetry and seabed fields; the models parameters; and, the models themselves. In the present work, we start addressing these challenges by deriving, implementing and verifying new optimally-reduced Dynamically Orthogonal (DO) differential equations that govern the propagation of stochastic acoustic waves for underwater sound propagation in an uncertain ocean environment. The developed methodology allows modeling environmental uncertainties in a rigorous probabilistic framework and predicting the uncertainties of acoustic fields, fully respecting the nonlinear governing equations and non-Gaussian statistics of the sound speed and acoustic state variables. The methodology is applied to the standard narrow-angle parabolic equation and is utilized to predict acoustic field uncertainties for three new stochastic idealized test cases: (1) an uncertain Pekeris waveguide with penetrable bottom, (2) an uncertain horizontal interface problem, and (3) an uncertain range-dependent sloping interface problem. For the first case, the solutions of the DO acoustic equations are validated against those obtained using standard Monte Carlo sampling. The second test case showcases results for predicting acoustic field probabilities due to uncertainties in the location of a sound speed channel. For the third test case, the advantages of the DO acoustic equations in predicting uncertainties in complex range-dependent environments are highlighted.
Aaron joined MSEAS in the fall of 2019, starting his masters in Computational Science & Engineering (CSE) with plans to pursue a PhD in MechE-CSE. Broadly, his interests span stochastic differential equations and signal processing. He has begun focusing on numerical solutions to the acoustic wave equation in the presence of uncertainty in addition to Bayesian inference for acoustic inverse problems (see DEEP-AI). Furthermore, he works on developing and improving reduced-order modeling techniques by incorporating differential geometry for applications in uncertainty quantification. Before coming to MIT, Aaron graduated with a Bachelor of Science from Brown University, double concentrating in applied mathematics and engineering, where he researched terahertz optics phenomena. Outside of academia, he enjoys running, water skiing, hiking, and low-level soccer.
Aditya completed his Bachelor’s in Mechanical Engineering at R.V. College of Engineering, Bangalore (2017) before moving to Purdue University to pursue his M.S in the same field. Upon graduating from Purdue in 2019, he joined MIT to pursue his Ph.D. in Mechanical Engineering. His previous work at Purdue focused on the development of numerical tools for investigating the self-similar propagation of low-Reynolds number gravity currents for geophysical applications. Presently his research interests lie in the areas of numerical methods and high-performance computing. Beyond research, Aditya enjoys reading, trekking, cycling, and would like to get involved in activities such as sailing, kayaking, and rowing.
