In this thesis, we explore the use of stochastic Navier-Stokes equations through the Dynamically Orthogonal (DO) methodology developed at MIT in the Multidisciplinary Simulation, Estimation, and Assimilation Systems Group. Specifically, we examine the effects of the Reynolds number on stochastic fluid flows behind a square cylinder and evaluate computational schemes to do so. We review existing literature, examine our simulation results and validate the numerical solution. The thesis uses a novel open boundary condition formulation for DO stochastic Navier-Stokes equations, which allows the modeling of a wide range of random inlet boundary conditions with a single DO simulation of low stochastic dimensions, reducing computational costs by orders of magnitude. We first test the numerical convergence and validating the numerics. We then study the sensitivity of the results to several parameters, focusing for the dynamics on the sensitivity to the Reynolds number. For the method, we focus on the sensitivity to the: resolution of in the stochastic subspace, resolution in the physical space and number of open boundary conditions DO modes. Finally, we evaluate and study how key dynamical characteristics of the flow such as the recirculation length and the vortex shedding period vary with the Reynolds number.

Abstract: Decision-making under uncertainty is a thriving research area in artificial intelligence. It is increasingly common that agents must deal with uncertain action outcomes and system information. To model these problems, the partially observable Markov decision process (POMDP) model is a popular and powerful choice. When multiple decision makers are present, collaboration under uncertainty is another common and important problem. These problems can be modeled as decentralized POMDPs (Dec-POMDPs). Both of these models present difficult research challenges that must be overcome before large, realistic problems can be solved effectively. In this talk, I discuss some of our recent work on increasing the scalability of solution methods for these models including taking advantage of problem structure and domain assumptions as well as improved search and sampling methods for general problems.

James Cameron’s dive to the Challenger Deep in the Deepsea Challenger in March of 2012 marked the first time man had returned to the Mariana Trench since the Bathyscaphe Trieste’s 1960 dive. Currently little is known about the geological processes and ecosystems of the deep ocean. The Deepsea Challenger is equipped with a plethora of instrumentation to collect scientific data and samples. The development of the Deepsea Challenger has sparked a renewed interest in manned exploration of the deep ocean.
Due to the immense pressure at full ocean depth, a variety of advanced systems and materials are used on Cameron’s dive craft. This paper provides an overview of the many novel features of the Deepsea Challenger as well as related features of past vehicles that have reached the Challenger Deep. Four key areas of innovation are identified: buoyancy materials, pilot sphere construction/instrument housings, lighting, and battery power. An in depth review of technological development in these areas is provided, as well as a glimpse into future manned submersibles and their technologies of choice.