Aeronautics and Astronautics - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7766
2015-03-05T22:33:00ZSimulation and design optimization of wave propagation in heterogeneous materials
http://hdl.handle.net/1721.1/95560
Simulation and design optimization of wave propagation in heterogeneous materials
SaĆ -Seoane, Joel
Propagation of waves through heterogeneous structured materials has been the focus of considerable research in recent years. These materials consist of quasi periodic geometries combining two or more piecewise homogeneous component media. The interest in these materials stems from the fact that when waves propagate through them one can observe phenomena, such as bandgaps, which cannot be obtained with any single homogeneous medium. The design of structured materials aims to identify patterns which have desirable features regarding wave propagation applications. The range of applications is very broad. In the context of electromagnetic waves, governed by Maxwell's equations, one may be interested in the design of low-loss waveguides, invisibility cloaks, superlenses or light frequency filters. For acoustic applications one may consider the design of passive noise filters or sound beams. The physics governing the propagation of waves is well understood and the existing mathematical models often provide excellent predictions. For this reason, the design of structured materials can greatly benefit from the use of numerical simulation and optimization techniques. Accurate numerical simulations can describe the propagation of waves through heterogeneous materials once the geometry and material properties are defined. Optimization methods can help determine arrangements of component materials and their properties in order to optimally accomplish a desired outcome. The work presented in this thesis includes a collection of multiscale high order accurate numerical simulation methods capable of simulating wave propagation in piecewise homogeneous media for two types of problems of interest: the source and the eigenvalue problems. In particular, we introduce the multiscale continuous Galerkin and multiscale hybridizable discontinuous Galerkin methods which exploit the inherent structure of the problem by reusing information from repeated subdomains. The efficiency that these approaches provide (reducing degrees of freedom by a factor of 20 to 100) allows for the numerical solution of large acoustic and electromagnetic wave problems, even in 3d, with a greatly reduced need for computational resources. Furthermore, a discrete topological optimization procedure enhanced with reduced basis approximations is developed in order to facilitate the automated design of these materials. The combination of both methods, simulation and optimization, yields enhanced capabilities for the design of optimal patterns for multiple applications. The design of invisibility cloaks and high transmission waveguide bends in 2d and 3d are considered.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 187-199).
2014-01-01T00:00:00ZFocused active inference
http://hdl.handle.net/1721.1/95559
Focused active inference
Levine, Daniel S., Ph. D. Massachusetts Institute of Technology
In resource-constrained inferential settings, uncertainty can be efficiently minimized with respect to a resource budget by incorporating the most informative subset of observations - a problem known as active inference. Yet despite the myriad recent advances in both understanding and streamlining inference through probabilistic graphical models, which represent the structural sparsity of distributions, the propagation of information measures in these graphs is less well understood. Furthermore, active inference is an NP-hard problem, thus motivating investigation of bounds on the suboptimality of heuristic observation selectors. Prior work in active inference has considered only the unfocused problem, which assumes all latent states are of inferential interest. Often one learns a sparse, high-dimensional model from data and reuses that model for new queries that may arise. As any particular query involves only a subset of relevant latent states, this thesis explicitly considers the focused problem where irrelevant states are called nuisance variables. Marginalization of nuisances is potentially computationally expensive and induces a graph with less sparsity; observation selectors that treat nuisances as notionally relevant may fixate on reducing uncertainty in irrelevant dimensions. This thesis addresses two primary issues arising from the retention of nuisances in the problem and representing a gap in the existing observation selection literature. The interposition of nuisances between observations and relevant latent states necessitates the derivation of nonlocal information measures. This thesis presents propagation algorithms for nonlocal mutual information (MI) on universally embedded paths in Gaussian graphical models, as well as algorithms for estimating MI on Gaussian graphs with cycles via embedded substructures, engendering a significant computational improvement over existing linear algebraic methods. The presence of nuisances also undermines application of a technical diminishing returns condition called submodularity, which is typically used to bound the performance of greedy selection. This thesis introduces the concept of submodular relaxations, which can be used to generate online-computable performance bounds, and analyzes the class of optimal submodular relaxations providing the tightest such bounds.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2014.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 91-99).
2014-01-01T00:00:00ZExperimental investigation of vortex rings and helicopter rotor wakes using a laser Doppler velocimeter,
http://hdl.handle.net/1721.1/92996
Experimental investigation of vortex rings and helicopter rotor wakes using a laser Doppler velocimeter,
Sullivan, J. P. (John Patrick)
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1973.; Vita.; Includes bibliographical references.
1973-01-01T00:00:00ZA study of differential equations possessing either time-varying coefficients or weak nonlinearities : application to an aerothermoelastic problem
http://hdl.handle.net/1721.1/91321
A study of differential equations possessing either time-varying coefficients or weak nonlinearities : application to an aerothermoelastic problem
Brunelle, Eugene J
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1962.; Vita.; Includes bibliographical references (leaves 216-223).
1962-01-01T00:00:00Z