Doctor of Philosophy / Department of Physics / Vinod Kumarappan / In general, molecules in the gas phase are free to rotate, and measurements made on such samples are averaged over a randomly oriented distribution of molecules. Any orientation dependent information is lost in such measurements. The goal of the work presented here is to a) mitigate or completely do away with orientational averaging, and b) make fully resolved orientation dependent measurements. In pursuance of similar goals, over the past 50 years chemists and physicists have developed techniques to align molecules, or to measure their orientation and tag other quantities of interest with the orientation. We focus on laser induced alignment of asymmetric top molecules. The first major contribution of our work is the development of an effective method to align all molecular axes under field-free conditions. The method employs a sequence of nonresonant, impulsive laser pulses with varied ellipticities. The efficacy of the method is first demonstrated by solution of the time dependent Schr\"{o}dinger equation for iodobenzene, and then experimentally implemented to three dimensionally align 3,5 difluoroiodobenzene. Measurement from molecules aligned in this manner greatly reduces orientational averaging. The technique was developed via a thorough understanding and extensive computations of the dynamics of rotationally excited asymmetric top molecules. The second, and perhaps more important, contribution of our work is the development of a new measurement technique to extract the complete orientation dependence of a variety of molecular processes initiated by ultrashort laser pulses. The technique involves pump-probe measurements of the process of interest from a rotational wavepacket generated by impulsive excitation of asymmetric top molecules. We apply it to make the first measurement of the single ionization probability of an asymmetric top molecule in a strong field as a function of all relevant alignment angles. The measurement and associated calculations help identify the orbital from which the electron is ionized. We expect that this technique will be widely applicable to ultrafast-laser driven processes in molecules and provide unique insight into molecular physics and chemistry.

The spins of planetary bodies are not stagnant; they evolve in response to both external and internal forces. One way a planet's spin can change is through true polar wander. True polar wander is the reorientation of a planetary body with respect to its angular momentum vector, and occurs when mass is redistributed within the body, changing its principal axes of inertia. True polar wander can literally reshape a world, and has important implications for a variety of processes—from the long-term stability of polar volatiles in the permanently shadowed regions of airless worlds like the Moon and Mercury, to the global tectonic patterns of icy worlds like Pluto. In this dissertation, we investigate three specific instances of planetary true polar wander, and their associated consequences. In Chapter 2 we investigate the classic problem of the Moon's dynamical figure. By considering the effects of a fossil figure supported by an elastic lithosphere, and the contribution of impact basins to the figure, we find that the lunar figure is consistent with the Moon's lithosphere freezing in when the Moon was much closer to the Earth, on a low eccentricity synchronous orbit. The South Pole-Aitken impact basin is the single largest perturbation to the Moon’s figure and resulted in tens of degrees of true polar wander after its formation. In Chapter 3 we continue our analyses of the lunar figure in light of the discovery of a lunar ”volatile" paleopole, preserved in the distribution of hydrogen near the Moon's poles. We find that the formation and evolution of the Procellarum KREEP Terrain significantly altered the Moon’s orientation, implying that some fraction of the Moon’s polar volatiles are ancient—predating the geologic activity within the Procellarum region. In Chapter 4 we investigate how the formation of the giant, basin-filling glacier, Sputnik Planitia reoriented Pluto. This reorientation is recorded in both the present- day location of Sputnik Planitia (near the Pluto-Charon tidal axis), and the tectonic record of Pluto. This reorientation likely reflects a coupling between Pluto’s volatile cycles and rotational dynamics, and may be active on other worlds with comparably large, mobile volatile reservoirs. Finally, in Chapter 5 we consider the broader context of these studies, and touch on future investigations of true polar wander on Mercury, Venus, Mars, Vesta, Ceres, and other worlds in our solar system.

<p>The dynamical evolution of the spin axis direction due to gravitational and thermal factors is examined. It is found that the spin axis variations generally are regular and relatively small for the bodies in the asteroid main belt. There are also reasons to believe that this is the case for minor objects beyond the main belt. However, it is found that these regular variations are larger when the orbital inclination of the objects is increased. This effect may explain certain features in the spin vector distribution of the main belt asteroids, not possible to explain by collisional factors. The spin vector evolution of the asteroids in the inner solar system, including the Earth- and Mars-crossing objects, is often subjected to strong forces related to frequencies in the orbital evolution. The variations in the spin vector direction are then very large and often subjected to chaos. The larger frequency related obliquity zones of the Mars-crossers are usually regular while the zones of the Earth-Mars-crossers often are of a chaotic nature. The spin vector evolution of asteroids with comet-like orbits is often chaotic regardless of initial obliquity. For the inner solar system asteroids, it is often possible for an initial prograde spin to turn into a retrograde one, or vice versa, due to the frequency related phenomena. Though some spin vector directions seem to be more probable than other ones over time, there are no indications for an evolution towards a more prograde or a more retrograde spin vector distribution.</p><p>The effects on the spin vector evolution from the thermal Yarkovsky force are examined for objects with radii larger than 50 m. This force will affect the orbital evolution and thus indirectly affect the spin vector evolution. However, it is found that the studied effects are minor as compared to the gravitationally related ones. This is true both for the diurnal and the seasonal variants of the Yarkovsky force.</p>

The dynamical evolution of the spin axis direction due to gravitational and thermal factors is examined. It is found that the spin axis variations generally are regular and relatively small for the bodies in the asteroid main belt. There are also reasons to believe that this is the case for minor objects beyond the main belt. However, it is found that these regular variations are larger when the orbital inclination of the objects is increased. This effect may explain certain features in the spin vector distribution of the main belt asteroids, not possible to explain by collisional factors. The spin vector evolution of the asteroids in the inner solar system, including the Earth- and Mars-crossing objects, is often subjected to strong forces related to frequencies in the orbital evolution. The variations in the spin vector direction are then very large and often subjected to chaos. The larger frequency related obliquity zones of the Mars-crossers are usually regular while the zones of the Earth-Mars-crossers often are of a chaotic nature. The spin vector evolution of asteroids with comet-like orbits is often chaotic regardless of initial obliquity. For the inner solar system asteroids, it is often possible for an initial prograde spin to turn into a retrograde one, or vice versa, due to the frequency related phenomena. Though some spin vector directions seem to be more probable than other ones over time, there are no indications for an evolution towards a more prograde or a more retrograde spin vector distribution. The effects on the spin vector evolution from the thermal Yarkovsky force are examined for objects with radii larger than 50 m. This force will affect the orbital evolution and thus indirectly affect the spin vector evolution. However, it is found that the studied effects are minor as compared to the gravitationally related ones. This is true both for the diurnal and the seasonal variants of the Yarkovsky force.

This thesis explores the dynamics of a heteronuclear diatomic molecular ion, possessing a permanent electric dipole moment, µ, which is trapped in a linear Paul trap and can interact with an off-resonance laser field. To build our model we use the rigid-rotor approximation, where the dynamics of the molecular ion are limited to its translational and rotational motions of the center-of-mass. These dynamics are investigated by carrying out suitable numerical calculations. To introduce our numerical methods, we divide our research topic into two different subjects. First, we ignore the rotational dynamics of the ion by assuming µ = 0. By this assumption, the system resembles an atomic ion, which mainly exhibits translational motion for its center of the mass when exposed to an external trapping field. To study this translational behavior, we implement full-quantum numerical simulations, in which a wave function is attributed to the ion. Finally, we study the quantum dynamics of the mentioned wave packet and we compare our results with those obtained classically. In the latter case, we keep the permanent dipole moment of the ion and we study the probable effects of the interaction between the dipole moment and the trapping electric field, on both the translational and the rotational dynamics of the trapped molecular ion. In order to study these dynamics, we implement both classical and semi-classical numerical simulations. In the classical method, the rotational and the translational motions of the center of mass of the ion are obtained via classical equations of motion. On the other hand, in the semi-classical method, while the translational motion of the center-of-mass is still obtained classically, the rotation is treated full-quantum mechanically by considering the rotational wave function of the ion. In the semi-classical approach, we mainly study the probable couplings between the rotational states of the molecular ion, due to the interaction of the permanent dipole moment with the trapping electric field. In the end, we also present a semi-classical model, where the trapped molecular ion interacts with an off-resonance laser field.

Abstract The normal tibiotalar joint is a stable structure, where only a minor widening of the ankle mortise and rotation of the fibula is caused by normal flexion-extension movements and joint loading. The most common injury mechanism is excessive external rotation of the ankle, which may induce an ankle fracture or an injury of the syndesmosis ligaments, leading to instability of the joint. Subsequent surgical fixation can cause malreduction and dysfunction of the joint by restricting normal motion, which may lead to altered tibiotalar joint loading conditions and cause long-term complications, such as osteoarthritis. In order to correctly evaluate the potential post-traumatic conditions, clinicians must know the normal movements of the fibula in the distal tibiofibular joint and the talus in the upper ankle joint under weight-bearing conditions. Until now, the normal dynamics of the syndesmosis and upper ankle joint, as well as the changes in rotations have been unknown, and the aim was to answer these questions. In the first study, the distal tibiofibular syndesmosis was assessed on non-weight-bearing computed tomography (NWBCT) scans in order to provide standardized measures of the syndesmosis in cross-sectional imaging. Second, a distal tibiofibular syndesmosis was investigated in upright weight-bearing CT (WBCT) scans in the neutral standing position and under maximal internal and external rotational stress. Third, the normal anatomy and rotational dynamics of the upper ankle joint was observed. The first study demonstrated that in axial CT imaging of the syndesmosis, the location of the fibula was either anteriorly or centrally in the tibial incisura in 88–97% of patients in both the supine position with resting ankles, and in the neutral standing position. If the fibula lies posteriorly, malreduction should be considered. The second study demonstrated that when the ankle is maximally rotated, the fibula slides back and forth in the tibial incisura with 1.5 mm total movement and a rotation of 3°, but the distal tibiofibular joint is not widened. In internal rotation of the ankle, the talus is rotated externally, the fibula moves, and the fibula moves to the posterior part of the tibial incisura in 40% of subjects. In external rotation of the ankle, the talus is rotated internally, and the fibula moves concomitantly slightly anteriorly. The results of the third study show that the talus rotates in the ankle mortise 10°, with no change in the medial clear space (MCS) and no significant lateral widening in the joint space. Minimal intrasubject variation (less than 1 mm at all measurement points) was observed in the total rotational range of motion, while in some measurements the intersubject variation was large in both supine, neutral standing, and rotational stress images. Sex or age did not affect most of the measurements; only in maximal external rotation was a minor tilting of the talus seen in the older population. These findings suggest that the contralateral ankle can and probably should be used as a reference when possible malreduction of the syndesmosis or tibiotalar ankle joint instability is suspected. / Tiivistelmä Nilkkanivel on sääriluun, pohjeluun ja telaluun muodostama kokonaisuus, jota tiiviit nivelsiderakenteet vakauttavat. Normaalisti nivelen pääasiallinen liike tapahtuu ojennus-koukistussuuntaan ja kuormittumiseen liittyen tapahtuu vain hyvin vähäistä nivelhaarukan leviämistä, eikä telaluu pääse juurikaan kiertymään. Useimmat nilkkavammat taas syntyvät kiertoliikkeessä, joka voi johtaa nivelsidevammaan ja/tai nilkkamurtumaan, johon liittyen telaluu pääsee kiertymään normaalia enemmän ulkokiertoon ja nivelhaarukka leviämään, mikä johtaa nilkan epävakauteen ja poikkeaviin kuormitusolosuhteisiin. Vamman jälkeinen kirurginen hoito taas voi aiheuttaa luisten rakenteiden asettumiseen nivelen toiminnan kannalta epäanatomiseen asentoon ja estää nilkan normaalin liikkumisen. Sekä nivelen liiallinen väljyys että virheasentoon tehty kirurginen kiinnitys voivat aiheuttaa kipua, muuttaa nivelen kuormitusolosuhteita ja johtaa nivelen toimintahäiriöihin tai ennenaikaiseen kulumiseen. Jotta vamman jälkeisiä muutoksia pystyttäisiin arvioimaan sekä sääri- ja pohjeluun välisen sidekudossidoksen eli syndesmoosin alueella että ylemmässä nilkkanivelessä tulisi terveiden nivelten normaalit liikelaajuudet ja kuormituksen aiheuttamat dynaamiset muutokset pystyä mittaamaan luotettavasti. Tämän tutkimuksen tarkoituksena oli selvittää syndesmoosialueen ja ylemmän nilkkanivelen normaali anatomia sekä maaten kuvatuista tietokonetomografia- että seisten kuvatuista kartiokeilatietokonetomografia¬tutkimuksista arvioiden. Lisäksi mitattiin molempien nivelalueiden kiertorasituksessa todettavat normaalit liikelaajuudet seisten kuvatuista kartiokeilatietokonetomografiatutkimuksista. Ensimmäinen tutkimus osoitti, että normaalisti pohjeluu sijaitsee alemman pohjesääriluunivelen etuosassa tai nivelen keskellä 88–97 %:lla tutkituista potilaista. Jos taas pohjeluu on siirtynyt nivelen takaosaan, tulee epäillä virheasentoa. Toisen tutkimuksen tulokset osoittivat, että kiertorasituksissa pohjeluu liikkuu syndesmoosialueella edestakaisin 1.5 mm ja kiertyy 3 astetta, mutta nivel ei levene sivuttaissuuntaan. Telaluun sisäkierrossa pohjeluu liukuu 40 %:lla tutkituista vapaaehtoisista koehenkilöistä syndesmoosialueen takaosaan, ja ulkokierrossa taas nivelen etuosaan. Kolmas tutkimus osoitti, että telaluu kiertyy maksimaalisen ulko- ja sisäkierron välillä 10 astetta ilman merkittävää mediaalisen tai lateraalisen nivelraon leviämistä. Kaikissa tutkimuksissa todettiin, että mikäli koehenkilöitä verrataan keskenään, samojen mittauskohtien väliset erot ovat merkittäviä. Mikäli taas verrataan saman koehenkilön molempia nilkkoja keskenään, mittauksissa ei ole merkittävää puolieroa. Ainoa mittaustulos, johon iällä tai sukupuolella oli vaikutusta, oli vanhemmassa ikäryhmässä todettu telaluun vähäinen kallistuminen maksimaalisessa ulkokierrossa. Tutkimukset tuottivat tietoa alemman pohjesääriluunivelen ja ylemmän nilkkanivelen normaalista anatomiasta ja liikkuvuuksista kiertorasituksissa tietokonetomografiatutkimuksissa. Tutkimusten perusteella todetaan, että potilaan tervettä nilkkaa kannattaa käyttää normaalianatomian vertailukohtana sekä heti vamman jälkeen mahdollisen operatiivisen hoidon tarvetta arvioitaessa että hoidon tulosta arvioitaessa.

Submitted by Josué Cardoso dos Santos (josuesantosunesp@gmail.com) on 2018-09-10T18:36:37Z No. of bitstreams: 1 Tese_Final_Josue_Cardoso_Santos.pdf: 78449557 bytes, checksum: 4515b9cb7cc346753f7e9682b8e037de (MD5) / Approved for entry into archive by Pamella Benevides Gonçalves null (pamella@feg.unesp.br) on 2018-09-10T18:47:05Z (GMT) No. of bitstreams: 1 santos_jc_dr_guara.pdf: 78449557 bytes, checksum: 4515b9cb7cc346753f7e9682b8e037de (MD5) / Made available in DSpace on 2018-09-10T18:47:05Z (GMT). No. of bitstreams: 1 santos_jc_dr_guara.pdf: 78449557 bytes, checksum: 4515b9cb7cc346753f7e9682b8e037de (MD5) Previous issue date: 2018-07-04 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nowadays, despite the technological development experienced by science in general, a fact especially evident by the available powerful computer machines, the analytical and semi-analytical methods to study different space problems are still of great importance in the fields of astrodynamics and celestial mechanics. From the physical understanding of the motion of celestial bodies to the planing and designing of space missions, the use of mathematical models to deal with a very large number of contemporary problems plays a fundamental role in the progress of human knowledge. In this context, the present thesis presents the use of different mathematical techniques to deal with different various and current problems in astrodynamics and celestial mechanics. The studies developed throughout this work are applicable to both areas. The topics studied are the following ones: (1) The development of disturbing potentials using the double-averaging process, in order to be included in the Lagrange planetary which are numerically integrated to study features of orbits around Mercury and the Galilean moon Callisto; (2) The use of different perturbation integrals, techniques to identify and map different perturbations present in a planetary system, with focus on the analysis of systems of Giant planets with their massive moons; (3) The use of the concept of intermediary Hamiltonian and the use of a canonical transformation called elimination of the parallax, both to deal with binary systems in the context of the roto-orbital dynamics, this one as an approach of the fulltwo body problem; (4) An updated analysis of Gauss variational equations to study quasisatellite orbits around the Martian moon Phobos and with analytical predictions made after obtaining linear and averaged equations of motions. Therefore, this thesis intend not only to provide important analysis and results for each specific problem which it deals with along its pages, but also seeks to highlighting the merit and current relevance of different analytical and semi-analytical methods to be used in the fields of astrodynamics and celestial mechanics. Additionally, the author also hopes to offer an outcome of diverse interesting ideas and methods to be explored in future investigations in these research fields / Na atualidade, a despeito do desenvolvimento tecnológico experimentado pela ciência em geral, algo especialmente evidenciado por poderosas máquinas computacionais disponíveis, os métodos analíticos e semianalíticos para o estudo de diferentes problemas espaciais ainda são de grande importância nos campos de astrodinâmica e mecânica celeste. Desde a compreensão física do movimento de corpos celestes até ao planejamento e projeto de missões espaciais, o uso de modelos matemáticos para lidar com um grande número de problemas contemporâneos desempenha um papel fundamental no progresso do conhecimento humano. Neste contexto, a presente tese apresenta o uso de diferentes técnicas matemáticas para lidar com diversos e atuais problemas em astrodinâmica e mecânica celeste. Os estudos desenvolvidos ao longo deste trabalho são aplicáveis à ambas as áreas. Os tópicos estudados são os seguintes: (1) O desenvolvimento de potenciais perturbadores usando o processo de dupla média, de forma a serem incluídos nas equações planetárias de Lagrange que são integradas numericamente para estudar características de órbitas ao redor de Mercúrio e da lua galileana Calisto; (2) A utilização de diferentes integrais de perturbação, técnicas para identificar e mapear diferentes perturbações presentes em um sistema planetário, com foco na análise de sistemas de planetas gigantes com suas luas massivas; (3) A utilização do conceito de hamiltoniana intermediária e o uso de uma transformação canônica chamada eliminação da paralaxe, ambos para lidar com sistemas binários no contexto da dinâmica roto-orbital, essa sendo uma aproximação do problema completo de dois corpos; (3) Uma análise atualizada de equações variacionais de Gauss para o estudo de órbitas quasi-satélite ao redor da lua marciana Fobos e com predições analíticas realizadas após serem obtidas equações de movimento linearizadas e com média. Portanto, esta tese pretende não somente prover importantes análises e resultados para cada problema específico com os quais a mesma lida ao longo de suas páginas, mas também procura destacar o mérito e relevância atual de diferentes métodos analíticos e semianalíticos a serem utilizados nos campos de astrodinâmica e mecânica celeste. Adicionalmente, o autor também espera oferecer um produto de variadas ideias e métodos a serem explorados em futuras investigações nesses campos de pesquisa / 2013/26652-4 / 2015/18881-9

Here, we present a novel torsion balance with a torsional spring that can reach a resolution in the nano-Newton range while allowing for a total experimental weight of 2 kg. The balance uses an off-the-shelf electromagnetic actuator, which was calibrated. The oscillation of the balance is damped using an adaptable eddy-current brake to fine-tune the damping factor. Experiments and electronics are controlled and powered through four coaxial liquid contacts. The balance is shown to be highly linear between 0.01 and 300 μN. After an automated post-processing, the noise of a measurement was 1.0 nN, and an applied force of 10 nN had a calculated error of 11.9%.

Scannende MEMS-Mikrospiegel stellen eine vielversprechende technologische Entwicklung mit potentiellen Anwendungen im Bereich der miniaturisierten Bildprojektion und Umgebungssensierung dar. Im Regelfall oszilliert das Spiegelelement hierbei resonant um die horizontale Achse, während die vertikale Achse statisch ausgelenkt wird. Somit ergibt sich ein sogenannter Raster-Scan. Während eine resonante Aktuierung in MEMS-Technologie im Frequenzbereich mehrerer kHz effizient umgesetzt werden kann, stellt die Implementierung statischer Antriebe eine Herausforderung dar. In dieser Arbeit wird ein neuartiges Aktuierungskonzept vorgestellt, das effizientere quasi-statische Auslenkung ermöglicht. Hierfür wird der Drehimpuls, der durch die hochfrequente horizontale Schwingung erzeugt wird, durch eine weitere resonante Oszillation ähnlicher Frequenz gestört, wodurch sich ein für die quasi-statische Auslenkung nutzbares Drehmoment ergibt. Da gyroskopische Effekte ausgenutzt werden, die nicht in aktuellen auf Modalanalyse basierenden Simulationsmethoden berücksichtigt sind, werden Starrkörper- und transiente FEM-Modelle entwickelt, um die Realisierbarkeit des Antriebskonzepts simulatorisch zu verifizieren. Im Rahmen der durch den genutzten Prozess gegebenen Randbedingungen werden daraufhin Aktuierungselemente für die resonanten Achsen erarbeitet und mit diesen zwei Designvarianten eines 2D-Mikrospiegels erstellt. Nach modellbasierter Verifikation werden diese in einer MEMS-Fertigungslinie prozessiert. Mit den generierten Mustern wird dann eine vollständige experimentelle Charakterisierung unter Nutzung eines speziell erstellten FPGA-basierten Evaluations-Boards durchgeführt. Beide Design-Varianten zeigen hierbei voll funktionsfähige Sensierungs- und Aktuierungselemente. Es kann ein erfolgreicher Nachweis der Funktionsfähigkeit des neuartigen Antriebskonzepts vollbracht werden. Die dabei gezeigte 2D-Projektion erreicht Winkel von 12° x 1.8° / Scanning MEMS micromirrors are an emergent technology for compact form factor image projection and environment sensing applications. Commonly the mirror element oscillates resonantly along the horizontal axis, whereas it is deflected statically along the vertical axis, performing a so called raster scan. While resonant actuation can be implemented efficiently in MEMS, static deflection however remains challenging. In this thesis a novel actuation concept for 2D MEMS micromirrors is introduced that potentially enables efficient quasi-static actuation. Therefore the angular momentum that is generated by the high frequency resonant axis is disturbed by an orthogonal resonant oscillation of similar frequency, leading to a torque that can be utilized to achieve an indirect quasi-static deflection. As in this case gyroscopic effects are exploited that are usually not considered in state of the art modal finite element based MEMS simulation, in order to validate the feasibility of the actuation concept rigid body and transient finite element based models are developed and simulation studies conducted. Using an existing manufacturing process as a framework, actuation schemes for the resonant axes are introduced and two distinct micromirror designs are developed and verified by simulation. These are processed in a MEMS manufacturing line. A thorough characterization study is then carried out using a custom FPGA based evaluation board with closed loop control capabilities. Both design variants are functional with regard to all actuation and tilt angle detection elements. A successful implementation of the proposed actuation concept is shown achieving 2D projection of a laser beam with tilt angles of 12 ◦ × 1.8 ◦ in frequency and amplitude controlled operation.