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The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use

The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable way to reconstruct the underlying function in one dimension. In particular, the PRM is shown to converge more quickly and to be more robust than current resampling techniques used in MRI, and is particularly amenable to highly irregular sampling patterns.
ContributorsGutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Viswanathan, Adityavikram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
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Finite element simulations modeling the hydrodynamic impact loads subjected to an elastomeric coating were performed to develop an understanding of the performance and failure mechanisms of protective coatings for cavitating environments.

In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical

Finite element simulations modeling the hydrodynamic impact loads subjected to an elastomeric coating were performed to develop an understanding of the performance and failure mechanisms of protective coatings for cavitating environments.

In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical simulations to allow conversion of measured distributions of pressure peaks in a cavitating flow to distributions of microscopic impact loadings modeling individual bubble collapse events, and 2) a finite strain, thermo-mechanical material model for polyurea-based elastomers was developed using a logarithmic rate formulation and implemented into an explicit finite element code.

Combining the distribution of microscopic impact loads and finite element modeling, a semi-quantitative predictive framework is created to calculate the energy dissipation within the coating which can further the understanding of temperature induced coating failures.

The influence of coating thickness and elastomer rheology on the dissipation of impact energies experienced in cavitating flows has also been explored.

The logarithmic formulation has many desired features for the polyurea constitutive model, such as objectivity, integrability, and additive decomposition compatibility.

A review and discussion on the kinematics in large deformation, including a comparison between Lagrangian and Eulerian descriptions, are presented to explain the issues in building rate-dependent constitutive models in finite strains.

When comparing the logarithmic rate with other conventional rates in test examples, the logarithmic rate shows a better conservation of objectivity and integrability.

The modeling framework was validated by comparing predictions against temperatures measured within coatings subjected to a cavitating jet.

Both the experiments and models show that the temperatures generated, even under mild flow conditions, raise the coating temperature by a significant amount, suggesting that the failure of these coatings under more aggressive flows is thermally induced.

The models show that thin polyurea coatings synthesized with shorter molecular weight soft segments dissipate significantly less energy per impact and conduct heat more efficiently.

This work represents an important step toward understanding thermally induced failure in elastomers subjected to cavitating flows, which provides a foundation for design and optimization of coatings with enhanced erosion resistance.
ContributorsLiao, Xiao (Author) / Oswald, Jay (Thesis advisor) / Liu, Yongming (Committee member) / Jiang, Hanqing (Committee member) / Rajan, Subramaniam D. (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2016