Physicshttp://hdl.handle.net/10523/982016-04-16T13:59:44Z2016-04-16T13:59:44ZInvestigation of first and second order correlation functions of ultra-cold atomic gasesToth, Emesehttp://hdl.handle.net/10523/62872016-03-21T00:16:09Z2016-03-18T03:16:47ZInvestigation of first and second order correlation functions of ultra-cold atomic gases
2016
Toth, Emese
In the first part of the thesis we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We describe the single particle evolution of the system during expansion and establish criteria for a far-field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including: Bogoliubov theory, mean-field decoupling, and particle-hole perturbative expantion about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on system correlations. We justify a Gaussian approximation from which we develop a general three-dimensional theoretical formalism for an inhomogeneous lattice system by comparison with the directly calculated correlation functions.
In the second part of the thesis we show how the conventional wisdom that increasing tem- perature means decreasing quantum coherence in system can be faulty. We explore a practical example that can be explored in optical lattice experiments. Using finite temperature perturbation theory and exact calculations we show that the short-range coherence of the Mott-insulating phase of bosons in an optical lattice can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near zero temperature coherence properties have been measured with high precision we expect these results to be verifiable in current experiments.
In the last part of the thesis we turn our attention to one dimensional Bose gases. We fo- cus on the moderate temperature weakly interacting regime namely the high temperature quasicondensate and quantum decoherent regimes, which we investigate using the stochas- tic projected Gross-Pitaevskii equation (SPGPE) formalism. Here we compare the SPGPE results against the Bethe ansatz and a mean-field formalism adapted to the quasicondensate regime. This theory covers a regime not addressed by other formalism.
2016-03-18T03:16:47ZMarkov Chain Monte Carlo Based Analysis of Bearing VibrationsLawrence, Hilary Janehttp://hdl.handle.net/10523/62142016-02-15T13:02:10Z2016-02-15T01:44:10ZMarkov Chain Monte Carlo Based Analysis of Bearing Vibrations
2016
Lawrence, Hilary Jane
The aim of the work in this thesis is to use bearing vibration data to infer the condition of bearings, in particular to detect the presence or absence of damage, and identify the location and cause of damage to parts of the bearing structure. Traditional methods of vibration analysis are evaluated and compared with Markov chain Monte Carlo (MCMC) methods.
The vibration datasets come from a selection of bearings that have been run from new. After running-in bearings, some are allowed to continue running for several hours. Others have seeded defects applied to balls or bearing races, and are then run for a short time. These data are used to evaluate the effectiveness of time-domain, frequency-domain and MCMC methods in the field of bearing vibration analysis.
Time-domain measures can detect the presence or absence of damage in most cases. Different defect types affect vibrations differently, and this can be seen in plots of vibration data. The conventional time-domain methods investigated take a discrete measure or measures over each data. They are simple to implement, but do not have the ability to detect these differences in vibrations, and therefore cannot detect the nature of damage.
Analysis in the frequency-domain is based on the fast Fourier transform (FFT) and filtering. It is successful in detecting the nature of some defects. Bearings with some defect types, or with low levels of damage, are difficult to distinguish from undamaged bearings, and each defect type is better detected using different filtering. These differences suggest that prominent vibrations occur at modes of flexural vibration of the outer race, and that the inner race can be approximated as a rigid body. A classification scheme is implemented using a mixture of time-domain and frequency-domain measures. This scheme can correctly classify data from many - but not all - bearings, but it gives no information on the certainty of classifications.
The findings from the time-domain and frequency-domain analysis have been well explored previously. In this thesis they are combined with Bayesian inference, using a correlation based measure of likelihood to infer bearing condition. MCMC methods are implemented using an adaptive Metropolis (AM) algorithm, existing models of bearing behaviour, and vibration data in the time-domain. MCMC outputs give estimations of the empirical marginal distribution of parameters, so that not only can parameter values - and therefore the underlying physical mechanism - be estimated, but uncertainties on these estimates can also be quantified.
An aims of this thesis is to see whether MCMC methods can be used to infer properties of bearing condition. This thesis shows this is possible, but there are difficulties to overcome. In particular, the use of the correlation based measure of likelihood results in the chain failing to converge in some cases. These states are identifiable, as the likelihood is lower than when convergence occurs. Possible solutions to this problem are discussed.
Analysis of MCMC outputs leads to model refinements to better measure bearing properties. Marginal distributions relating to vibration frequency have properties that allow the physical cause of vibration sources to be inferred. Using data in the time-domain has some advantages when separating the individual sources of these periodic vibrations. In the frequency domain some of these sources have harmonics or sidebands that coincide with predicted frequencies of other sources. In addition, some of these frequencies are not at their predicted values. This is not unexpected, as slippage and the effect of loads are known to alter these frequencies. The analysis of MCMC outputs allows the physical cause of discrepancies to be investigated. Vibrations during the normal operation of undamaged bearings have certain properties that differ from vibrations caused by bearing defects, and relevant parameters show these differences. Distributions of parameters relating to the amplitude and duration of vibrations caused by defects are shown to have a relationship to defect dimensions. Further development is required before defect dimensions can be directly inferred.
This thesis shows that traditional methods of vibration analysis can distinguish between damaged and undamaged bearings in most cases, and detect the nature of damage in some cases. MCMC methods have potential in the field of bearing vibration analysis, and can provide meaningful inference of the physical properties of bearings.
2016-02-15T01:44:10ZSequential Inference for Dynamical SystemsMorrison, Malcolm Erik Kinghttp://hdl.handle.net/10523/61832016-01-26T13:02:12Z2016-01-25T22:50:57ZSequential Inference for Dynamical Systems
2016
Morrison, Malcolm Erik King
Sequential inference methods have played a crucial role in many of the technological marvels that we use today, from GPS and navigation systems to machine learning. Most current methods, such as the unscented Kalman filter (UKF) make several, occasionally crippling assumptions which allow them to work efficiently and accurately for approximately linear dynamics. The problem with this is that the majority of systems are not linear. Inference methods fully representing the dynamics and probability distributions were considered infeasible in the early days of sequential inference. However, with the capabilities of modern computers this is no longer the case. In this thesis we propose a method to evolve a probability distribution on a dynamical system explicitly. This is done by using a finite volume partial differential equation solver to solve the continuity equation, combined with Bayesian observations. We present an example case of the simple pendulum and compare this with the UKF to examine several advantages.
2016-01-25T22:50:57ZPower Efficient, Telemetry-Enabled Position Sensor for Animal TrackingPanckhurst, Bradleyhttp://hdl.handle.net/10523/61372016-01-05T21:06:39Z2016-01-05T01:50:08ZPower Efficient, Telemetry-Enabled Position Sensor for Animal Tracking
2016
Panckhurst, Bradley
This thesis describes the design, development and characterisation of an animal position sensor system. It focuses on the implementation of a telemetry system capable of retrieving position data wirelessly.
The position sensor electronics weigh only 10 g and utilises the 868 MHz frequency band for telemetry. Implementing a solar energy harvesting system, the sensors demonstrated the potential for an indefinite deployable lifetime. With over 300,000 location acquisitions, the static position sensors were found to have a Circular Error Probable accuracy of < 4 m. The telemetry system showed reliable data transmission out to 1 km. However, it is capable of a range of 2.4 km with a clear line of sight.
All aspects of the position sensors were developed to be power efficient. The development included details of the hardware circuit design and the software for both the position sensor devices and the base station. Also included is a customised telemetry protocol centred around power efficient strategies. Characterisation and testing of the position sensor included the evaluation of three key factors. The factors investigated were location accuracy, power consumption and the telemetry transmission performance.
Finally, future revisions to the position sensor system are detailed, with exciting possibilities from the hardware layer up to the telemetry protocol.
2016-01-05T01:50:08ZC-Field Theory of Dynamics in One Dimensional Bose Gases: The Kibble-Zurek Mechanism and Bright Soliton ArrestMcDonald, Robhttp://hdl.handle.net/10523/58712015-09-08T14:02:10Z2015-09-08T03:56:11ZC-Field Theory of Dynamics in One Dimensional Bose Gases: The Kibble-Zurek Mechanism and Bright Soliton Arrest
2015
McDonald, Rob
A grand canonical C-field theory has been previously developed for modelling finite temperature Bose gases, the stochastic projected Gross-Pitaesvkii equation (SPGPE) [1]. Previous investigations have shown quantitative agreement between experiments and the SPGPE, with a fitted growth rate [2,3] or no fitted parameters at all [4]. These and other works [5,6] have used the number-damping SPGPE, a sub-theory of the SPGPE neglecting a scattering process between the coherent and incoherent regions that conserves the particle number of each region, known as energy-damping. The systems in these works were in quasi-equilibirium and as such a growth process, also known as number-damping, is thought to be dominant. Evidence suggests that energy-damping is significant when the system is far from equilibrium [7]; we may also postulate systems where energy-damping is the only allowed process. In this thesis we use the full SPGPE including the energy-damping reservoir interaction in systems where this process plays an important role in the dissipative evolution.
We model quenches of chemical potential across the Bose-Einstein condensation transition in a one dimensional Bose gas confined to a toroid. We use two different models; the full SPGPE and the number-damping SPGPE. The purpose of this is to test the results of our simulations against the predictions of the Kibble-Zurek mechanism (KZM), a theory of defect formation in second order phase transitions. We find that both models give results consistent with KZM, in that various measurable quantities obey a power law with respect to the quench time. The power law exponents are determined by critical exponents, which depend on the universality class of the phase transition. We find the number-damping SPGPE results are consistent with the critical exponents predicted by mean field theory. We are unable to find a universality class with critical exponents consistent with the results of the full theory, and in particular the dynamical critical exponent differs from that predicted by mean field theory.
We also use the SPGPE to simulate the motion of a bright soliton in a one dimensional attractive Bose gas confined to a toroid and in contact with a thermal cloud of a second component. The bright soliton is an analytical solution of the one-dimensional Gross-Pitaevskii equation for an attractive Bose-Einstein condensate, which can propagate in space without changing its functional form. We derive a stochastic differential equation for the soliton velocity, finding that the energy-damping reservoir interaction manifests as an Ornstein-Uhlenbeck process for velocity decay, affording a complete analytic solution for the damping and diffusion rates of the bright soliton. The results of simulating the bright soliton using the SPGPE are compared against the analytic solutions of the velocity stochastic differential equation, including the mean, variance, two-time correlations, and power spectra of the velocity. We find that the numerical and analytical solutions show excellent agreement for all these quantities, validating our procedure for obtaining the velocity equation of motion.
2015-09-08T03:56:11ZCavity Length Control System for the Investigation of Correlation Between two He-Ne Raman LasersMuir, Paulhttp://hdl.handle.net/10523/58302015-08-14T14:02:47Z2015-08-14T00:00:54ZCavity Length Control System for the Investigation of Correlation Between two He-Ne Raman Lasers
2015
Muir, Paul
A cavity length control scheme was developed in order to investigate correlation between the chaotic Raman lasing of two unidirectionally coupled Raman lasers for two Ne Raman lines, 603.0 (2p2 to 1s4) nm and 659.9 nm (2p2 to 1s1). The Raman lasers were standard internal mirror He-Ne lasers and were both pumped externally by 588.2 nm radiation from a single dye laser.
The cavity lengths of each He-Ne Raman laser were monitored via the beat frequencies between the modes in the standard 632.8 nm output and the 632.8 nm modes of a stabilised reference He-Ne laser. A software based PID feedback servomechanism actively controlled the cavity length by varying the current supplied to heating pads wrapped around each cavity, altering the thermal expansion/contraction.
2015-08-14T00:00:54ZSolar Powered Animal Tracking Tags with GSM TelemetryButler, Mark Davidhttp://hdl.handle.net/10523/56722015-05-19T22:26:13Z2015-05-19T22:25:05ZSolar Powered Animal Tracking Tags with GSM Telemetry
2015
Butler, Mark David
This thesis describes the development of a solar energy harvesting system for lightweight wildlife tracking tags that use GSM cellular communication for telemetry. An energy harvesting system was designed and implemented in combination with a replacement firmware solution that controls the whole tag at a minimised energy cost. The design was tested both in the lab, and during deployment on Northern Royal Albatross. The solar energy system and firmware significantly improved the tag lifetime allowing effectively indefinite deployment. This solution also allows a greater GPS fix frequency, enabling zoologists to obtain a more detailed understanding of a tagged animalsâ€™ behaviour.
2015-05-19T22:25:05ZFrom Disordered Bosons to Dipolar Fermions - Theoretical Studies in Ultracold AtomsTowers, Josephhttp://hdl.handle.net/10523/55862015-04-28T09:46:37Z2015-03-29T21:41:16ZFrom Disordered Bosons to Dipolar Fermions - Theoretical Studies in Ultracold Atoms
2015
Towers, Joseph
We use numerical simulation to study ultracold, quantum degenerate, atomic gases. In the first part of the thesis we study the effects of disorder, introduced via a bichromatic optical lattice, in one and two dimensional systems. We employ the Aubry-Andr\'{e} model and use time-dependent numerical simulations to investigate the disorder dependent transition to strong localisation present in the model. Weak s-wave interactions are added to the model and we observe the interaction between localisation and interaction induced self-trapping. We then add a tilted lattice potential to the model. In the homogeneous model this induces Bloch oscillations. While one might expect that a strong enough force will break the strong localisation or self-trapping, within the bounds of the single-band model, the trapping effect of the Bloch oscillations reinforces both of the other effects leading to increased confinement, albeit lacking the clear single frequency oscillation signature of pure Bloch oscillations.
Along with the two dimensional bichromatic optical lattice we add a term to the Hamiltonian equivalent to that of a uniform external magnetic field on charged particles. Since the experimental realisation of this model would employ neutral atoms, the magnetic field is synthetic, the equivalent effect being produced by an appropriate set of lasers and magnetic fields. We show that in the ballistic regime (weak bichromatic disorder) the system displays positive magnetoresistance. Conversely in the strong localisation regime the system exhibits negative magnetoresistance.
In the latter part of the thesis we use density functional theory to calculate the ground-state density of a harmonically trapped dipolar Fermi gas. We then use these to calculate the lowest energy collective mode oscillation frequencies under the hydrodynamic approximation. We find that increasing the strength of the dipoles has the effect of increasing the mode frequencies. The increase saturates for large dipole strengths. We verify this analytically and show that such is due to the local nature of the two dimensional energy functional and not dependent on the specific equation of state.
We employ an average density approximation to construct an energy functional for the inhomogeneous, 2D degenerate Fermi gas. The ground-state densities for a cylindrically symmetric harmonic trap are compared to the Kohn-Sham results, showing extremely good agreement in the tail region and good agreement with the exact ground-state energy. We then do the same for higher order polynomial traps and obtain improved agreement for higher degree.
2015-03-29T21:41:16Z