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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.

Proteins often carry an intrinsic electric dipole moment, which can interact with external electric fields and cause protein motion. Previous research has found that the orientation of small proteins in gas phase can be controlled in a static electric field. This effect is hoped to benefit applications such as single-particle imaging, and possibly other techniques involving proteins in electric fields. With the purpose of improving our understanding and modeling of protein orientation, this project investigated the scarcely explored quantum mechanical aspects of the process, namely the polarizability. Ground-state electronic structure simulations of three small model proteins, ubiquitin, Trp-cage and lysozyme, under the influence of electric fields were performed in vacuum. The electric dipole moments of the proteins were extracted from simulations with an applied electric field of strength 1 V/nm for varying angles, with respect to a body fixed reference frame. A Python program was written to analyze and visualize the results. The results point to a connection between the polarizability and the structure of the proteins, as well as size. Next a 3D rigid rotor model was developed using Mathematica in order to study the orientation dynamics classically in a simplified and time efficient way, with the possibility of including the previous quantum results. A comparison between a simulation of ubiquitin with and without polarizability concluded that the polarizability seems to have a damping effect on the orientation dynamics, at least for the initial conditions tested in this study. Further research is necessary to validate the model and perform statistical analysis of many simulations with varying initial conditions. / Proteiner bär ofta på ett inneboende elektriskt dipolmoment, som vid interaktion med externa elektriska fält och orsakar rörelse hos proteinerna. Tidigare studier har funnit att orienteringen av små proteiner i gasfas kan kontrolleras i ett statiskt elektriskt fält. Den effekten kan förhoppningsvis vara en fördel i tillämpningar såsom single-particle imaging, och eventuellt andra tekniker som innefattar proteiner i elektriska fält. I syftet att förbättra vår förståelse och modellering av protein-orientering, har detta projekt undersökt de föga utforskade kvantmekaniska aspekterna av processen, nämligen polariserbarheten. Kvant-baserade simuleringar av grundtillståndet av tre små proteiner, ubiquitin, Trp-cage och lysozym, under påverkan av elektriska fält utfördes i vakuum. Proteinernas elektriska dipolmoment extraherades från simuleringar med ett elektriskt fält med styrkan 1 V/nm för olika vinklar, med avseende på ett kroppsfixerat koordinatsystem. Ett Python-program skrevs för att analysera och visualisera resultaten. Resultaten tyder på att polariserbarheten beror på strukturen och storleken av proteinerna. Därefter utformades en stel-rotor-modell med hjälp av Mathematica för att studera prienteringen klassiskt på ett förenklat och tidseffektivt sätt, med möjligheten att inkludera de tidigare kvantmekaniska resultaten. En jämförelse mellan en simulering av ubiquitin med och utan polariserbarhet konstaterade att polariserbarheten verkar ha en dämpande effekt på orienteringen, åtminstone för begynnelsevillkoren som testades i denna studie. Vidare forskning krävs för att styrka modellen och utföra statistisk analys av många simuleringar med varierande begynnelsevillkor.

Rotordynamic instability can be disastrous for the operation of high speed turbomachinery in the industry. Most ??instabilities?? are due to de-stabilizing cross coupled forces from variable fluid dynamic pressure around a rotor component, acting in the direction of the forward whirl and causing subsynchronous orbiting of the rotor. However, all subsynchronous whirling is not unstable and methods to diagnose the potentially unstable kind are critical to the health of the rotor-bearing system. The objective of this thesis is to explore means of diagnosing whether subsynchronous vibrations are benign or have the potential to become unstable. Several methods will be detailed to draw lines of demarcation between the two. Considerable focus of the research has been on subharmonic vibrations induced from non-linear bearing stiffness and the study of vibration signals typical to such cases. An analytical model of a short-rigid rotor with stiffness non-linearity is used for numerical simulations and the results are verified with actual experiments. Orbits filtered at the subsynchronous frequency are shown as a diagnostic tool to indicate benign vibrations as well as ??frequency tracking?? and agreement of the frequency with known eigenvalues. Several test rigs are utilized to practically demonstrate the above conclusions. A remarkable finding has been the possibility of diagnosing instability using the synchronous phase angle. The synchronous phase angle ?? is the angle by which the unbalance vector leads the vibration vector. Experiments have proved that ?? changes appreciably when there is a de-stabilizing cross coupled force acting on the rotor as compared to when there is none. A special technique to calculate the change in ?? with cross-coupling is outlined along with empirical results to exemplify the case. Subsequently, a correlation between the synchronous phase angle and the phase angle measured with most industrial balancing instruments is derived so that the actual measurement of the true phase angle is not a necessity for diagnosis. Requirements of advanced signal analysis techniques have led to the development of an extremely powerful rotordynamic measurement teststand ?? ??LVTRC??. The software was developed in tandem with this thesis project. It is a stand-alone application that can be used for field measurements and analysis by turbomachinery companies.

Rotordynamic instability can be disastrous for the operation of high speed turbomachinery in the industry. Most ??instabilities?? are due to de-stabilizing cross coupled forces from variable fluid dynamic pressure around a rotor component, acting in the direction of the forward whirl and causing subsynchronous orbiting of the rotor. However, all subsynchronous whirling is not unstable and methods to diagnose the potentially unstable kind are critical to the health of the rotor-bearing system. The objective of this thesis is to explore means of diagnosing whether subsynchronous vibrations are benign or have the potential to become unstable. Several methods will be detailed to draw lines of demarcation between the two. Considerable focus of the research has been on subharmonic vibrations induced from non-linear bearing stiffness and the study of vibration signals typical to such cases. An analytical model of a short-rigid rotor with stiffness non-linearity is used for numerical simulations and the results are verified with actual experiments. Orbits filtered at the subsynchronous frequency are shown as a diagnostic tool to indicate benign vibrations as well as ??frequency tracking?? and agreement of the frequency with known eigenvalues. Several test rigs are utilized to practically demonstrate the above conclusions. A remarkable finding has been the possibility of diagnosing instability using the synchronous phase angle. The synchronous phase angle ?? is the angle by which the unbalance vector leads the vibration vector. Experiments have proved that ?? changes appreciably when there is a de-stabilizing cross coupled force acting on the rotor as compared to when there is none. A special technique to calculate the change in ?? with cross-coupling is outlined along with empirical results to exemplify the case. Subsequently, a correlation between the synchronous phase angle and the phase angle measured with most industrial balancing instruments is derived so that the actual measurement of the true phase angle is not a necessity for diagnosis. Requirements of advanced signal analysis techniques have led to the development of an extremely powerful rotordynamic measurement teststand ?? ??LVTRC??. The software was developed in tandem with this thesis project. It is a stand-alone application that can be used for field measurements and analysis by turbomachinery companies.

The presented diploma thesis deals with simulation of Laval rotor supported by nonlinear bearings. The first part of thesis deals with research, which is focused on description of Laval rotor and motion equations for case of rigid and flexible rotor, also on description and modeling of hydrodynamic and magnetic bearing, which is considered in thesis. The second part of thesis deals with simulation of rotor for different approaches to modeling hydrodynamic and magnetic bearings. Using simulations performer in time domain, the dynamic behavior of Laval rotor is evaluated and compared. Simulations are performer in MATLAB.