Thesis advisor: Joshua E. Greene / In this dissertation, we discuss cross sectional slices of embedded surfaces in the four-sphere, and give various constructive and obstructive results, in particular focusing on cross sectional slices of unknotted surfaces. One case of note is that of doubly slice Montesinos links, for which we give a partial classification. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Mon travail de thèse, débuté en septembre 2005, a été consacré au développement de l’émergente technique d’imagerie par spectrométrie de masse ToF-SIMS. Une première partie de ce travail a été orientée vers des aspects fondamentaux avec l’utilisation d’une source d’ions fullerènes comme faisceau d’ions primaires, mais aussi comme faisceau de pulvérisation. Le but était d’éprouver la possibilité de réaliser une imagerie 3D sur des échantillons biologiques par spectrométrie de masse ToF-SIMS. Une seconde partie de mon travail de thèse a été consacrée à l’utilisation de la technique proprement dite. Différents domaines d’application ont été étudiés, comme l’archéologie, avec l’analyse de la composition des patines recouvrant les statues rituelles de la tribu Dogon (Mali) ou l’étude de la dégradation de cheveux de momies chinoises. Un troisième projet a consisté à analyser in situ les surfactines, une famille de cyclodepsipeptides amphiphiles, sur des profils de colonisation de surface de Bacillus subtilis. Cette analyse qualitative par imagerie ToF-SIMS a été complétée par une analyse quantitative par spectrométrie de masse MALDI-TOF. Enfin, le dernier projet mis en œuvre durant ma thèse concerne la recherche de biomarqueurs lipidiques de la stéatose hépatique non alcoolique chez l’humain. Les résultats ont mis en évidence la complémentarité de l’imagerie par spectrométrie de masse avec d’autres techniques permettant la localisation de composés ciblés, comme la coloration histologique. Les résultats de cette thèse démontrent que l’imagerie par spectrométrie de masse ToF-SIMS peut être appliquée dans des domaines aussi divers que l’archéologie, la microbiologie ou la médecine. / My PhD’s work has been devoted to the development of the emergent technique ToF-SIMS imaging. The first part of my work was dedicated to fondamental aspects with the use of a fullerene ion source as a primary ion beam or sputtering ion beam. We expected to realize 3D imaging. The second part of my work consisted to applications of the mass spectrometry imaging. Several application fields were studied, as archeology as with the analysis of patina of the Dogon statuary or chinese mummy hair. A third project was dedicated to the in situ biomarker research from human liver biopsies. The goal of this study was to identify a potential lipid biomarker of the non-alcoholic fatty liver disease. The last part of this manuscript is devoted to the in situ qualitative and quantitative analysis of surfactins (a family of heptacyclodepsipeptides) on a Bacillus subtilis swarming community. We combined ToF-SIMS imaging for qualitative analysis and localization of surfactins within the swarming pattern and MALDI-TOF mass spectrometry for the quantification of these species. The results ot this PhD’s work show that ToF-SIMS imaging could be applied to various fields of research as archeology, microbiology and medicine.

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Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free non-degenerate SL_2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the set of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a proper reductive subgroup of G.

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The spatial response function (SRF) of the backscatter measurements for a radar scatterometer is often used in reconstruction. It has been found that in many cases the SRF can be approximated as a binary function that is 1 inside the - 6 dB contour of the SRF and 0 outside. This improves the computation speed of reconstruction. Computing the SRF contour can still be a lengthy computation, which can be simplified by precomputing and tabulating key SRF contours. The tabular parameterization for many spinning scatterometers, i.e., QuikSCAT, is straight-forward. For RapidSCAT, this estimation is more involved than other radars due to the irregular orbit of its host platform, the International Space Station (ISS). This thesis presents a process for parameterizing the slice contours for RapidSCAT that are acceptable for reconstruction purposes. This thesis develops a new process for parameterizing slice contours. First, RapidSCAT SRFs are calculated using XfactorRS3, and -6 dB slice contours are found using matplotlib. Then, a suitable filter is found for reducing noise present in slice contours due to quantization error and interpolation inaccuracies. Afterwards, the polygon comparison algorithm is used to determine a set of approximation points. With the approximation points selected, the 3-rd order linear approximation is calculated using parameters available in the L1B data files for RapidSCAT. Finally, analysis of the parameterization is performed. Overall, I developed a process that parameterizes RapidSCAT slice contours with an average root mean square (RMS) error of roughly 1.5 km. This is acceptable for the application of the slice parameterization algorithm and significantly reduces computation compared to fully computing the SRF.

The simulation of breaking wave has a computationally intensive application. In order to reduce the computation, this thesis presents a slice-based water simulation method for ocean breaking waves on natural simulation by generating the 2D simulations and then integrating these 2D simulation results into a 3D shape. We first simulate a 2D wave by a 2D Navier-Stokes solver to obtain the varying of ocean. Then, we combine VOF (Volume of fluid) with a new reconstruct free surface method that is a fast 2D simulation. We use linear interpolation with noise function to construct a complete 3D ocean simulation from these 2D simulations. By doing these, one can reduce the computation time and achieve better efficiency.

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The purpose of the headbox is to convert a flow of fiber suspension to a jet, with a thickness between 4 and 20mm and a width between 3 -8meters, depending on the paper machine model. To adjust the beam thickness, the lip adjustment arrangement is used. This master thesis was written to develop the headbox and the lip adjustment system, for paper machines with a width over 6 meters. In the beginning of the project much focus was layed on understanding the problem and develop the product and customer requirements of the Headbox. In order to utilize the entire idea space a number of idea generation methods were used. The evaluation of concepts were conducted with the method Analytic hierarchy process (AHP), which is a method for clarifying the decision pattern. From the evaluation of the concept, two concepts were chosen. A modification of the existing headbox and a new concept, which adjusts the slice opening with a number of elastic pockets and a wedge. To further evaluate the modified headbox concepts the Finite Element Method was used. During the simulations the elastic deformation was compared between the current and the modified solution. The second concept was developed by describing the new design and motivated the chosen material and structures.   Overall it can be said that the modification of the current headbox solves the main problem and maintains the current quality on the paper. The new and innovative solution enables a more exact adjustment of the lip opening and allows a larger potential of modularization. / Syftet med inloppslådan är att den ska transformera ett flöde av fibersuspension till en stråle som är mellan 4 och 20 mm tjock och 3-8 m bred, beroende på pappersmaskinsmodell. För att justera strålens tjocklek används läppjusteringsanordningen. Målet med detta arbete var att utveckla inloppslådan och dess läppöppningsarrangemang så att den kan användas till en pappersmaskin som är breddare än 6 meter. Projektet inleddes med att skapa en förståelse för problemet samt att undersöka vilka produkt- och kundkrav det finns på inloppslådan. För att utnyttja hela iderymden användes ett antal idegenereringsmetoder. Utvärdering av koncepten genomfördes med hjälp av en metod som heter Analytic hierarchy process (AHP) som är en metod som används för att tydliggöra beslutsvägen. Utifrån utvärdering med AHP valdes två koncept ut. En modifierad lösning av det nuvarande läppöppningsarrangemangen och ett nytt koncept vilket justerar läppöppningen med hjälp av ett antal trycksatta fickor och en vinge. För att ytterligare utveckla den modifierade inloppslådan användes Finita Elementmetoden. Under simuleringen jämfördes elastisk deformation i den nuvarande och den modifierade lösningen. Det nya konceptet utvecklades genom att den nya konstruktionen beskrevs utifrån struktur, materialval och tillverkningsmetoder. Sammantaget kan det sägas att den modifierade inloppslådan löser problemställning och bibehåller den nuvarande kvalitén på pappret. Den innovativa och nya lösningen möjliggör en mer exakt justering av läppöppningen och ökar möjligheten att modularisera inloppslådan.