La thèse concerne l’usinage à 5 axes de formes complexes. Le but est d’estimer le plus précisément possible les efforts induits par la coupe pour ajuster la vitesse d’avance et gagner en performance. Pour cela, il est nécessaire d’estimer les engagements radial et axial de la fraise à chaque instant. Ce calcul est rendu particulièrement complexe à cause de la forme de la pièce, de la forme du brut et de la complexité de la géométrie de l’outil. Les méthodes usuelles par Zbuffer sont particulièrement couteuses en temps de calcul. Dans ces travaux nous proposons une méthode de calcul rapide à partir d’une modélisation du contact dans toutes les situations envisageables. Différentes simulations et expérimentations ont permis de valider la précision expérimentalement. / This study presents a simple method to define the Cutter Workpiece Engagement (CWE) during sculptured surface machining in five-axis milling. The instantaneous CWE was defined by determining two engagement points, lowermost engagement (LE)-point and uppermost engagement (UE)-point. LE-point was calculated using a method called grazing method. Meanwhile the UE-point was calculated using a combination of discretization and analytical method. During rough milling and semi-finish milling, the workpiece surface was represented by vertical vector. The method called Toroidal–boundary was employed to obtain the UE-point when it was located on cutting tool at toroidal side. On the other hand, the method called Cylindrical-boundary was used to calculate the UE-point for flat-end cutter and cylindrical side of toroidal cutter. For a free-form workpiece surface, a hybrid method, which is a combination of analytical method and discrete method, was used. All the CWE models proposed in this study were verified and the results proved that the proposed method were accurate. The efficiency of the proposed model in generating CWE was also compared with Z-mapping method. The result confirmed that the proposed model was more efficient in term of computational time. The CWE model was also applied for supporting the method to predict cutting forces. The test results showed that the predicted cutting force has a good agreement with the cutting force generated from the experimental work.

The doctoral thesis is focused on research, design, implementation and testing of systems for the application of magnetic vector potential to biological materials. The main objective was to analyze and design systems which could generate magnetic vector potential without the presence of other unwanted fields or at least amplify its intensity. Moreover, the systems designed had to eliminate other foreign effects on the biological samples, especially the influence of waste heat from the coils. Toroidal coils were employed to generate the vector potential, because they confine the unwanted magnetic induction inside their core thanks to their shape. The thesis employed coils with two different outer diameters, specifically 102 and 600 mm. To excite the coils, four current pulse generators capable of delivering currents of up to 100 A were constructed. The systems’ generated fields were comprehensively analyzed with the help of finite-element simulations in ANSYS. To simplify the design phase, analytical equations for the calculation of vector potential intensity at an arbitrary point around the toroidal coils were also derived. A method employing electromagnetic shielding made of two different materials was developed to suppress the unwanted fields. To eliminate the influence of heat, the 102 mm system employed air cooling and the 600 mm system employed a closed water loop to equalize the temperatures of biological samples. The biological effects of both systems were tested on genetically modified bio-luminescent bacteria Escherichia coli K12 luxABCDEamp. The thesis was created in connection with the research project of The Ministry of Education, Youth and Sports of the Czech Republic named “Research into the effect of a combination of substances for targeted therapy and inhibitory action of the field pulse vector magnetic potential on oncogenous diseases”, No. 2B08063.

The ability to rapidly detect and identify hazardous analytes in the field has become increasingly important. One of the most important analytical detection methods in the field is gas chromatography-mass spectrometry (GC-MS). In this work, a hand-portable GC-MS system is described that contains a miniature toroidal ion trap mass analyzer and a low thermal mass GC. The system is self-contained within the dimensions of 47 x 36 x 18 cm and weighs less than 13 kg. Because the instrument has a small footprint, it was used as the detector for an automated near-real-time permeation testing system. In permeation testing, materials that are used to make individual protective equipment such as gloves, masks, boots, and suits are exposed to hazardous analytes to determine how long the equipment can be worn safely. The system described herein could test five samples simultaneously. A multi-position valve rotated among the various sample streams and delivered time aliquots into the MS for quantitation. Current field air sampling techniques suffer from long desorption times, high pressure drops, artifact formation and water retention. These disadvantages can be avoided by concentrating the analytes in short open tubular traps containing thick films. There are several advantages to using polymer coated capillaries as traps, including fast desorption, inertness and low flow restriction. An air sampling trap was constructed utilizing open tubular traps for the concentration of semi-volatile organic compounds. The system consisted of multiple capillary traps bundled together, providing high sample flow rates. The analytes were desorbed from the multi-capillary bundle and refocused in a secondary trap. The simultaneous focusing and separation effect of a trap subjected to a negative temperature gradient was also explored. In this configuration, analytes were focused because the front of the peak was at a lower temperature than the rear of the peak and, hence, moved slower. In addition to the focusing effect, analytes with different volatilities focused at different temperatures within the gradient, allowing for separation.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Optical elements are the fundamental components in photonic systems and are used to transform an input optical beam into a desired beam profile or to couple the input beam into waveguides, fibers, or other optical systems or devices. Macroscopic optical elements are easily fabricated using grinding and polishing techniques, but few methods exist for inexpensive fabrication of micro optical elements. In this work we present an innovative technique termed Additive Lithography that makes use of binary masks and controlled partial exposures to sculpt photoresist into the desired optical surface relief profile. We explore various masking schemes for fabricating a variety of optical elements with unprecedented flexibility and precision. These masking schemes used in conjunction with the additive lithographic method allows us to carefully control the photoresist exposure and reflow processes for fabricating complex aspheric lens elements, including aspheric elements whose fabrication often proves highly problematic. It will be demonstrated that employing additive lithography for volume sculpting followed by controlled reflow can also allow us to fabricate refractive beam shaping elements. Finally we will discuss the dry etching techniques used to transfer these optical elements into the glass substrate. Thus the additive lithography technique will be demonstrated as an inexpensive, high throughput and efficient process in the fabrication of micro optical elements.

The future fusion power plants that are based on magnetic confinement will deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come, for instance, from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite eigenmodes in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction of heating efficiency. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants. Two models have been developed to simulate the interaction between energetic ions and Alfvén eigenmodes. One is a bump-on-tail model, of which two versions have been developed: one fully nonlinear and one quasilinear. The quasilinear version has a lower dimensionality of particle phase space than the nonlinear one. Unlike previous similar studies, the bump-on-tail model contains a decorrelation of the wave-particle phase in order to model stochasticity of the system. When the characteristic time scale for macroscopic phase decorrelation is similar to or shorter than the time scale of nonlinear wave-particle dynamics, the nonlinear and the quasilinear descriptions quantitatively agree. A finite phase decorrelation changes the growth rate and the saturation amplitude of the wave mode in systems with an inverted energy distribution around the wave-particle resonance. Analytical expressions for the correction of the growth rate and the saturation amplitude have been derived, which agree well with numerical simulations. A relatively weak phase decorrelation also diminishes frequency chirping events of the eigenmode. The second model is called FOXTAIL, and it has a wider regime of validity than the bump-on-tail model. FOXTAIL is able to simulate systems with multiple eigenmodes, and it includes effects of different individual particle orbits relative to the wave fields. Simulations with FOXTAIL and the nonlinear bump-on-tail model have been compared in order to determine the regimes of validity of the bump-on-tail model quantitatively. Studies of two-mode scenarios confirmed the expected consequences of a fulfillment of the Chirikov criterion for resonance overlap. The influence of ICRH on the eigenmode-energetic ion system has also been studied, showing qualitatively similar effects as seen by the presence of phase decorrelation. Another model, describing the efficiency of fast wave current drive, has been developed in order to study the influence of passive components close to the antenna, in which currents can be induced by the antenna generated wave field. It was found that the directivity of the launched wave, averaged over model parameters, was lowered by the presence of passive components in general, except for low values of the single pass damping of the wave, where the directivity was slightly increased, but reversed in the toroidal direction. / De framtida fusionskraftverken baserade på magnetisk inneslutning kommer att hantera plasmor som oundvikligen innehåller energetiska (icke-termiska) partiklar. Dessa partiklar kommer exempelvis från fusionsreaktioner eller från externa uppvärmningsmekanismer av plasmat. Ensembler av energetiska joner kan excitera egenmoder i Alfvén-frekvensområdet i en sådan utsträckning att de resulterande vågfälten omfördelar de energetiska jonerna i rummet, och potentiellt slungar ut jonerna ur plasmat. Omfördelningen av joner kan orsaka en väsentligen minskad uppvärmningseffekt. Det är nödvändigt att förstå dynamiken hos denna typ av instabilitet för att kunna optimera verkningsgraden hos experiment och hos framtida fusionskraftverk. Två modeller har utvecklats för att simulera interaktionen mellan energetiska joner och Alfvén-egenmoder. Den första är en bump-on-tail-modell, av vilken två versioner har utvecklats: en fullt icke-linjär och en kvasi-linjär. I den kvasi-linjära versionen har partiklarnas fasrum en lägre dimensionalitet än i den icke-linjära versionen. Till skillnad från tidigare liknande studier innehåller denna bump-on-tail-modell en dekorrelation av våg-partikelfasen för att modellera stokasticitet hos systemet. När den karakteristiska tidsskalan för makroskopisk fasdekorrelation är ungefär samma som eller kortare än tidsskalan för icke-linjär våg-partikeldynamik så stämmer den icke-linjära och den kvasi-linjära beskrivningen överens kvantitativt. En ändlig fasdekorrelation förändrar vågmodens tillväxthastighet och satureringsamplitud i system med en inverterad energifördelning omkring våg-partikelresonansen. Analytiska uttryck för korrektionen av tillväxthastigheten och satureringsamplituden har härletts, vilka stämmer väl överens med numeriska simuleringar. En relativt svag fasdekorrelation försvagar även "frequency chirping events" (snabba frekvensskiftningar i korttids-Fourier-transformen av egenmodens amplitudutveckling) hos egenmoden. Den andra modellen, kallad FOXTAIL, har ett mycket bredare giltighetsområde än bump-on-tail-modellen. FOXTAIL kan simulera system med flera egenmoder, och den inkluderar effekter av olika enskilda partikelbanor relativt vågfälten. Simuleringar med FOXTAIL och med bump-on-tail-modellen har jämförts för att kvantitativt bestämma bump-on-tail-modellens giltighetsområde. Studier av scenarier med två egenmoder bekräftar de förväntade effekterna av när Chirikov-kriteriet för resonansöverlapp uppfylls. Även inflytandet av ICRH på dynamiken mellan egenmoder och energetiska joner har studerats, vilket har visat kvalitativt liknande effekter som har observerats i närvaron av fasdekorrelation. En annan modell, vilken beskriver effektiviteten hos "fast wave current drive" (strömdrivning med snabba magnetosoniska vågor), har utvecklats för att studera inflytandet av passiva komponenter nära antennen, i vilka strömmar kan induceras av vågfälten som genereras av antennen. Det visades att den utskickade vågens direktivitet, medelvärdesbildat över modellparametrar, generellt sett minskade vid närvaron av passiva komponenter, förutom vid låg "sinlge pass damping" (dämpning av vågen vid propagering genom hela plasmat), då direktiviteten istället ökade något, men bytte tecken i toroidal riktning. / <p>QC 20160927</p>

La description magnétohydrodynamique est utilisée pour étudier les plasmas de fusion par confinement magnétique dans deux configurations: tokamak et reversed field pinch. Une méthode de Fourier pseudo-spectrale et une technique de pénalisation en volume sont employées pour résoudre les équations. La méthode de pénalisation permet d’introduire des conditions aux limites de Dirichlet et donc de faire varier facilement la géométrie considérée. Les simulations dans des géométries toroïdales de type tokamak montrent l’apparition spontanée de vitesses. Une importante composante toroïdale se développe si le système est peu dissipatif. Il est aussi montré que la brisure de symétrie dans la forme de la section du tore fait apparaitre un moment angulaire toroïdal. Pour le Reversed Field Pinch on montre l’émergence de structures hélicoïdales. La forme de ces structures varie en fonction des coefficients de transport ainsi que du paramètre de pincement du champ magnétique imposé. Pour compléter l’étude on compare les résultats du tore aux calculs dans un cylindre périodique. Les différences dans la dynamique des deux cas sont mises en avant. Finalement les simulations sont confrontées à des expériences et un meilleur accord est observé entre simulation et expérience pour la géométrie toroïdale que pour la géométrie cylindrique. / A magnetohydrodynamic description is used to study magnetic fusion plasmas in two different configurations: tokamak and reversed field pinch. A Fourier pseudo-spectral method with a volume penalization technique are used to solve the system of equations. The penalization method is used to introduce Dirichlet boundary conditions and it al- lows to easily modify the consider geometry. The simulations of a tokamak configuration in a toroidal geometry show the spontaneous appearance of velocities. These velocities are dominated by their toroidal component if the system is little dissipative. It is also shown that the symmetry breaking of the cross section of the torus causes a toroidal angular momentum to develop. For the Reversed Field Pinch configuration we show the appearance of helical structures. The shape of these structures varies with the value of the transport coefficients and with the pinch ratio parameter of the imposed magnetic field. To complete the study, we compare the results of simulations obtained in toroidal and in periodic cylindrical geometries. The differences in the dynamics of these two cases are highlighted. Finally, simulations are compared to experimental data and a significant better agreement is observed between the simulation and the experiment for the toroidal geometry than for the cylindrical case.

Das Ziel dieser Arbeit ist die Berechnung der arithmetischen Volumina der Shimuravarietäten vom orthogonalen Typ und der natürlichen Höhen der speziellen Zykel auf diesen. Wir entwickeln, für den Fall guter Reduktion, eine allgemeine Theorie ganzzahliger Modelle von toroidalen Kompaktifizierungen der Shimuravarietäten vom Hodge Typ (sowie des Standardhauptfaserbündels darüber). Dies ermöglicht, unter Verwendung der Theorie der Borcherdsprodukte, das arithmetische Voluminen einer zu einem Gitter L der Diskriminante D assoziierten Shimuravarietät, bis auf log(p) Beiträge zu Primzahlen p mit p^2|4D, zu berechnen. Dies ist eine Verallgemeinerung einer Arbeit von Burgos, Bruinier und Kühn. Die Höhen der speziellen Zykel werden im Falle von Kodimension 1 bis auf log(p)-Beiträge mit p|2D berechnet, sowie unter leichten zusätzlichen Einschränkungen im Falle von Kodimension > 1. The resultierenden Grössen sind spezielle Ableitungswerte gewisser L-Reihen. Im Falle der speziellen Zykel stimmen diese mit speziellen Ableitungswerten gewisser normalisierter Eisensteinreihen überein (zusätzlich, bis auf Beiträge bei unendlich). Dies bestätigt Vermutungen von Bruinier-Kühn, Kudla und anderen. / The overall aim of this thesis is to compute arithmetic volumes of Shimura varieties of orthogonal type and natural heights of the special cycles on them. We develop a general theory of integral models of toroidal compactifications of Shimura varieties of Hodge type (and of its standard principal bundle) for the case of good reduction. This enables us, using the theory of Borcherds products, and generalizing work of Burgos, Bruinier and Kühn, to calculate the arithmetic volume of a Shimura variety associated with a lattice L of discriminant D, up to log(p)-contributions from primes p such that p^2|4D. The heights of the special cycles are calculated in the codimension 1 case up to log(p), p|2D, and with some additional restrictions in the codimension > 1 case. The values obtained are special derivatives of certain L-series. In the case of the special cycles they are equal to special derivatives of Fourier coefficients of certain normalized Eisenstein series (in addition, up to contributions from infinity) in accordance with conjectures of Bruinier-Kühn, Kudla, and others.

In dieser Dissertation entwickeln wir eine Schnittheorie von torischen bzw. toroidalen b-Divisoren auf torischen bzw. toroidalen Einbettungen. Motiviert wird dies durch das Ziel, eine arithmetische Schnittheorie auf gemischten Shimura- Varietäten von nicht-kompaktem Typ zu begründen. Die bisher zur Verfügung stehenden Werkzeuge definieren keine numerischen Invarianten, die birational invariant sind. Zuerst definieren wir torische b-Divisoren auf torischen Varietäten und einen Integrabilitätsbegriff für solche Divisoren. Wir zeigen, dass torische b-Divisoren unter geeigneten Annahmen an die Positivität integrierbar sind und dass ihr Grad als das Volumen einer konvexen Menge gegeben ist. Außerdem zeigen wir, dass die Dimension des Vektorraums der globalen Schnitte eines torischen b-Divisors, der nef ist, gleich der Anzahl der Gitterpunkte in besagter konvexer Menge ist und wir geben eine Hilbert–Samuel-Formel für das asymptotische Wachstum dieser Dimension. Dies verallgemeinert klassische Resultate für klassische torische Divisoren auf torischen Varietäten. Als ein zusätzliches Resultat setzen wir konvexe Mengen, die von torischen b-Divisoren kommen, mit Newton–Okounkov- Körpern in Beziehung. Anschließend definieren wir toroidale b-Divisoren auf toroidalen Varietäten und einen Integrierbarkeitsbegriff für solche Divisoren. Wir zeigen, dass unter geeigneten Positivitätsannahmen toroidale b-Divisoren integrierbar sind und ihr Grad als ein Integral bezüglich eines Grenzmaßes aufgefasst werden kann. Dieses Grenzmaß ist ein schwacher Grenzwert von diskreten Maßen, deren Gewichte über tropische Schnittheorie auf rationalen konischen polyedrischen Komplexen definiert sind, welche zu der toroidalen Varietät gehören. Wir setzen dieses Grenzmaß ebenfalls in Beziehung zum zu einem konvexen Körper assoziierten Flächeninhaltsmaß. Diese Beziehung erlaubt es uns, Integrale bezüglich des Grenzmaßes explizit auszurechnen. Zusätzlich erhalten wir eine kanonische Zerlegung der Differenz zweier konvexer Mengen und eine Beziehung zwischen das Volumen von den Teilen und tropische Schnittheoretische Mengen. Schließlich berechnen wir als Anwendung den Grad des b-Divisors von Jacobiformen vom Gewicht k und Index m bezüglich der Hauptkongruenzuntergruppe zum Level N >= 3 auf der verallgemeinerten universellen elliptischen Kurve und wir zeigen, dass der b-divisoriale Ansatz gegenüber lediglich einer kanonischen Kompaktifizierung Vorteile bietet. / In this thesis we develop an intersection theory of toric and toroidal b-divisors on toric and toroidal embeddings, respectively. Our motivation comes from wanting to establish an arithmetic intersection theory on mixed Shimura varieties of non- compact type. The tools available until now do not define numerical invariants which are birationally invariant. First, we define toric b-divisors on toric varieties and an integrability notion of such divisors. We show that under suitable positivity assumptions toric b- divisors are integrable and that their degree is given as the volume of a convex set. Moreover, we show that the dimension of the space of global sections of a nef toric b-divisor is equal to the number of lattice points in this convex set and we give a Hilbert-Samuel type formula for its asymptotic growth. This generalizes classical results for classical toric divisors on toric varieties. As a by-product, we relate convex sets arising from toric b-divisors with Newton-Okounkov bodies. Then, we define toroidal b-divisors on toroidal varieties and an integrability notion of such divisors. We show that under suitable positivity assumptions toroidal b-divisors are integrable and that their degree is given as an integral with respect to a limit measure, which is a weak limit of discrete measures whose weights are defined via tropical intersection theory on the rational con- ical polyhedral complex attached to the toroidal variety. We also relate this limit measure with the surface area measure associated to a convex body. This relation enables us to compute integrals with respect to these limit measures ex- plicitly. Additionally, we give a canonical decomposition of the difference of two convex sets and we relate the volume of the pieces to tropical top intersection numbers. Finally, as an application, we compute the degree of the b-divisor of Jacobi forms of weight k and index m with respect to the principal congruence subgroup of level N >= 3 on the generalized universal elliptic curve and we show that it is meaningful to consider the b-divisorial approach instead of just fixing one canonical compactification.

In this thesis we have focussed on two types of axially symmetric ion trap mass analysers viz., the quadrupole ion trap mass analyser and the toroidal ion trap mass analyser. We have undertaken three numerical studies in this thesis, one study is on the quadrupole ion trap mass analysers and two studies are on the toroidal ion trap mass analysers. The first study is related to improvement of the sensitivity of quadrupole ion trap mass analysers operated in the resonance ejection mode. In the second study we have discussed methods to determine the multipole coefficients in the toroidal ion trap mass analysers. The third study investigates the stability of ions in the toroidal ion trap mass analysers. The first study presents a technique to cause unidirectional ion ejection in a quadrupole ion trap mass spectrometer operated in the resonance ejection mode. In this technique a modified auxiliary dipolar excitation signal is applied to the endcap electrodes. This modified signal is a linear combination of two signals. The first signal is the nominal dipolar excitation signal which is applied across the endcap electrodes and the second signal is the second harmonic of the first signal, the amplitude of the second harmonic being larger than that of the fundamental. We have investigated the effect of the following parameters on achieving unidirectional ion ejection: primary signal amplitude, ratio of amplitude of second harmonic to that of primary signal amplitude, different operating points, different scan rates, different mass to charge ratios and different damping constants. In all these simulations unidirectional ejection of destabilized ions has been successfully achieved. The second study presents methods to determine multipole coefficients for describing the potential in toroidal ion trap mass analysers. Three different methods have been presented to compute the toroidal multipole coefficients. The first method uses a least square fit and is useful when we have ability to compute potential at a set of points in the trapping region. In the second method we use the Discrete Fourier Transform of potentials on a circle in the trapping region. The third method uses surface charge distribution obtained from the Boundary Element Method to compute these coefficients. Using these multipole coefficients we have presented (1) equations of ion motion in toroidal ion traps (2) the Mathieu parameters in terms of multipole coefficients and (3) the secular frequency of ion motion in these traps. It has been shown that the secular frequency obtained from our method has a good match with that obtained from numerical trajectory simulation. The third study presents stability of ions in practical toroidal ion trap mass analysers. Here we have taken up for investigation four geometries with apertures and truncation of electrodes. The stability is obtained in UDC-VRF plane and later this is converted into A-Q plane on the Mathieu stability plot. Though the plots in terms of Mathieu parameters for these structures are qualitatively similar to the corresponding plot of linear ion trap mass analysers, there is a significant difference. The stability plots of these have regions of nonlinear resonances where ion motion is unstable. These resonances have been briefly investigated and it is proposed that they occur on account of hexapole and octopole contributions to the field in these toroidal ion traps.