Performance of precise marine positioning using future modernised global satellite positioning systems and a novel partial ambiguity resolution technique

The International Maritime Organisation (IMO) established a set of positioning requirements for future Global Navigation Satellite System (GNSS) constellations in IMO resolution A.915. It is important to be able to determine if these requirements can be met, and what shore infrastructure would be required. This thesis describes the collection of data in a marine environment and the analysis of these data with regards to the requirements. The data collection exercise was held at the beginning of May 2008 and saw THV Alert navigate into Harwich Harbour whilst Global Positioning System (GPS) observation data were recorded from onboard the vessel and from shore-based reference stations. Additional data were obtained from nearby Ordnance Survey reference stations, and two total stations were used to track the vessel’s passage to provide a truth model. Several modernised GPS satellites were tracked. The data were processed under different scenarios, using software developed at UCL, and the positioning performance was analysed in the context of the IMO requirements. Potential performance improvements from modernised GPS and Galileo were then discussed. Providing integrity through single-epoch real-time kinematic positioning, required to meet the strictest IMO requirements, is particularly difficult. The identification of phase observation outliers is not possible before the integer ambiguities are resolved, but an undetected outlier could prevent successful ambiguity resolution. It will not always be necessary to fix all the ambiguities to achieve the required positioning precision, particularly with a multi-GNSS constellation. This thesis introduces a new algorithm for partial ambiguity resolution in the presence of measurement bias. Although computationally intensive, this algorithm significantly improves the ambiguity resolution success rate, increasing the maximum baseline length over which the highest requirements are met with dual-frequency GPS from 1 km to 66 km

Dynamically turning off interactions in a two component condensate

We propose a mechanism to change the interaction strengths of a two component condensate. It is shown that the application of pi/2 pulses allows to alter the effective interspecies interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable once and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many body entangled states.Comment: 7 pages 5 figures, symbols changed, minor changes, to appear in Phys. Rev.

Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps

We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering amplitude for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single channel s-wave scattering of $^{23}$Na atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multi-channel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.Comment: 7 pages, 4 figures (PostScript), submitted to Physical Review

Simple method for excitation of a Bose-Einstein condensate

An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.Comment: 8 pages, 7 figures, version accepted for publication in Phys. Rev.

Resonant Generation of Topological Modes in Trapped Bose Gases

Trapped Bose atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.Comment: One reference modifie

Quantum feedback with weak measurements

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schr\"odinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere

Mechanical response functions of finite temperature Bose-Einstein Condensates

Using the Liouville space framework developed in nonlinear optics we calculate the linear response functions and susceptibilities of Bose-Einstein condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures of the dynamics of finite temperature BEC are obtained by solving the Hartree-Fock-Bogoliubov theory. Numerical simulations of the position dependent linear response functions of one dimensional trapped BEC in the time and the frequency domains are presented.Comment: 9 figures. Submitted to Phys. Rev.

Generalized coherent state representation of Bose-Einstein condensates

We show that the quantum many-body state of Bose-Einstein condensates (BEC) consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state (GCS). At zero temerature, the non-condensate density and the anomalous non-condensate correlation are not independent, allowing us to elimiate one of the three variables in the TDHFB.Comment: Submitted to Phys. Rev. A. No figures. Revised version fixes several minor typos, and adds to some discussions; no change to the conclusio

Performance of precise marine positioning using future modernised global satellite positioning systems and a novel partial ambiguity resolution technique.

The International Maritime Organisation (IMO) established a set of positioning requirements for future Global Navigation Satellite System (GNSS) constellations in IMO resolution A.915. It is important to be able to determine if these requirements can be met, and what shore infrastructure would be required. This thesis describes the collection of data in a marine environment and the analysis of these data with regards to the requirements. The data collection exercise was held at the beginning of May 2008 and saw THV Alert navigate into Harwich Harbour whilst Global Positioning System (GPS) observation data were recorded from onboard the vessel and from shore-based reference stations. Additional data were obtained from nearby Ordnance Survey reference stations, and two total stations were used to track the vessel’s passage to provide a truth model. Several modernised GPS satellites were tracked. The data were processed under different scenarios, using software developed at UCL, and the positioning performance was analysed in the context of the IMO requirements. Potential performance improvements from modernised GPS and Galileo were then discussed. Providing integrity through single-epoch real-time kinematic positioning, required to meet the strictest IMO requirements, is particularly difficult. The identification of phase observation outliers is not possible before the integer ambiguities are resolved, but an undetected outlier could prevent successful ambiguity resolution. It will not always be necessary to fix all the ambiguities to achieve the required positioning precision, particularly with a multi-GNSS constellation. This thesis introduces a new algorithm for partial ambiguity resolution in the presence of measurement bias. Although computationally intensive, this algorithm significantly improves the ambiguity resolution success rate, increasing the maximum baseline length over which the highest requirements are met with dual-frequency GPS from 1 km to 66 km.

The relationship between the angle of the trochlear groove and patella cartilage and bone morphology – a cross-sectional study of healthy adults

SummaryObjectivesAlthough the geometry of the trochlear groove is considered important in the pathogenesis of patellofemoral joint pathology it is unclear how the shape of the trochlear groove relates to patella morphology. This cross-sectional study investigated the relationship between the shape of the trochlear groove and patella cartilage and bone morphology in healthy adults.MethodsTwo hundred and ninety-seven healthy adults aged between 50 and 79 years with no clinical history of knee pain or pathology were examined using magnetic resonance imaging (MRI). From the magnetic resonance (MR) images, the bony angles formed at the distal and proximal trochlear groove were measured, together with patella cartilage and bone volumes and patella cartilage defects.ResultsAfter adjustment for potential confounders, there was an 8.70mm3 (95% confidence interval (CI) 2.15, 15.26) increase in patella cartilage volume (P=0.009), with no increased prevalence of cartilage defects (odds ratio=0.99 (95% CI 0.96, 1.02), P=0.35), for every 1° increase (i.e., as the angle became more flatter) at the distal trochlear groove. Moreover, there was a 53.86mm3 (95% CI −90.26, −17.46) reduction in patella bone volume for every 1° that the angle at the distal trochlear groove became more flattened (P=0.004). No significant association between the proximal trochlear groove angle and the patella cartilage or bone properties was observed.ConclusionA more flattened bony angle at the distal trochlear groove was associated with increased patella cartilage volume and reduced patella bone volume, but no increased prevalence of patella cartilage defects in adults with no history of knee pain or clinical disease. These cross-sectional findings suggest that a flattened distal trochlear groove may protect against degenerative patellofemoral conditions, such as osteoarthritis, but this will need to be confirmed in a longitudinal study