Conformal Parametrization of Surfaces of Genus Zero and 3D Reconstruction of Nuclear Fusion Hotspots

The first part of this thesis is to study a modified version of mean curvature flow, the “conformalized mean curvature flow” (cMCF), developed by Kazhdan, Solomon, and Ben-Chen. The cMCF is a conformal mapping algorithm but it runs into numerical issues when it is applied on meshes with protrusions. We improve the cMCF with an initialization step which first maps the initial mesh onto a sphere. This initialization step is shown to improve the performance of cMCF such that it can be applied on meshes with long protrusions. More importantly, we give a new algorithm named “Sphericalized cMCF” to construct a homotopy from a degree one map to a homeomorphism from a unit sphere onto a unit sphere. The second part of this thesis focuses on my work in the limited view computer tomography at the Lawrence Livermore National Laboratory during a one year internship. This project is related to the inertial confinement fusion (ICF) experiments performed at the National Ignition Facility (NIF). Our work is to reconstruct the 3D x-ray emission distribution of the NIF-ICF hotspot from very limited number of 2D x-ray projection images. Such 3D x-ray reconstructions can help to characterize and compare the thermophysical states of the fusion plasma such its temperature. We apply and test the algebraic reconstruction technique (ART) to reconstruct the 3D x-ray emission distribution of the ICF hotspot. Subsequently, we infer the 3D hotspot electron temperature distribution from these 3D x-ray reconstructions in different energy channels.
Also submitted to the Office of Scientific and Technical Information OSTI. Release number LLNL-TH-818331

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