A new and more convenient technique using lasers has been developed to measure small vibrations of an object under observation. A mathematical analysis of the system is presented, which shows that it is possible to recover the information not only on the velocity or the position of the object, but also on its sense of direction. The instrument consists of a sophisticated Michelson interferometer, where the reference mirror is vibrated sinusoidally. The photodetector output signal contains components of the multiples of the mirror drive frequency modulated by the target vibration. A theoretical analysis shows that complete target information is available from this signal after suitable processing. Within certain limits, fluctuation of the intensity of the returned light does not affect this measurement and, therefore, the surface quality of the target is of secondary importance. The distance of the target from the laser, the permissible bandwidth of operation, and the accuracy of the instrument are discussed. Some consideration is given to various industrial applications of the technique, and it is compared to other methods where possible.

We provide different mathematical frameworks to describe singularities in General Relativity. The main idea is to regard singularities as obstructions to the dynamics of different matter models. The first part of the thesis initiates our examination of spacetime by probing spacetime with matter that can be modelled as a point-particle. In particular, we discuss the case of two-dimensional Lorentzian metrics. We give concrete applications of the framework in the case of the Minkowski spacetime (which is regular) and the Friedmann-Robertson-Walker spacetime (which is geodesically incomplete). In the second part of the thesis, we probe the geometry of spacetime with classical scalar fields. The general motivation is to redefine a singularity in spacetime not as an obstruction to geodesics or curves but as an obstruction to the dynamics of test fields. We discuss curve-integrable spacetimes, spacetimes with surface layers, impulsive gravitational waves and brane-world scenarios, and spacetimes that contain string-like singularities. In the third part of the thesis, we present the outline of a framework to analyse the geometry of the spacetime by probing it with quantum scalar fields. The main focus of this chapter is to describe what is meant by a quantisation in a spacetime with finite differentiability. The fourth part of the thesis presents future outlooks and some open problems.

Photoproduction events which have two or more jets with transverse energy ET > 4.5 GeV have been studied in the γp centre of mass energy range 158 GeV < W < 247 GeV with the H1 detector at HERA. The fraction f(Δη) of events with a rapidity gap between the two highest ET jets is measured as a function of the rapidity separation Δη between the jet axes. A gap is defined as the absence between the jets of any particle with energy E > 400 MeV. The gap fraction is observed to fall exponentially up to Δη < 3.5. An excess of events with a large rapidity gap, over what would be expected from standard photoproduction processes, is observed for Δη > 3.5. The excess can be interpreted as the result of the exchange of a strongly interacting colour singlet object. A new approach to the investigation of diffraction at high momentum transfer is presented in which the double dissociation process γp → XY is studied. The systems X and Y are separated by the largest rapidity gap in the event with all particles on the photon side of the gap ascribed to the system X. It is shown that a measurement of the cross section dσ/dx_p, where x_p = (M²ₓ - t)/W², allows a direct determination of the energy dependence of the diffractive process, and hence provides a stringent test of theories of high |t| diffraction. The double dissociation photoproduction cross section for the process γp → XY is measured for the first time at large 4-momentum transfer squared |t|. > 20GeV² using the H1 detector at HERA. Cross sections are measured differentially in x_p, for yp = (M²_y-t)/W² < 0.018 . In the range 0.0007 < x_p < 0.0040, the shape of the measured x_p distribution is compared to predictions for standard photoproduction processes and to a model based on the exchange of a strongly interacting colour singlet object at large |t|.

No description available.

Elastic wave scattering from randomly rough surfaces and a smooth surface are essentially different. For ultrasonic nondestructive evaluation (NDE) the scattering from defects with smooth surfaces has been extensively studied, providing fundamental building blocks for the current inspection techniques. However, all realistic surfaces are rough and the roughness exists in two dimensions. It is thus very important to understand the rough surface scattering mechanism, which would give insight for practical inspections. Knowledge of the stochastics of scattering for different rough surfaces would also allow the detectability of candidate rough defects to be anticipated. Hence the main motivation of this thesis is to model and study the effect of surface roughness on the scattering field, with focus on elastic waves. The main content of this thesis can be divided into three contributions. First of all, an accurate numerical method with high efficiency is developed in the time domain, for computing the scattered waves from obstacles with arbitrary shapes. It offers an exact solution which covers scenarios where approximation-based algorithms fail. The method is based on the hybrid idea to combine the finite element (FE) and boundary integral (BI) methods. The new method efficiently couples the FE equations and the boundary integral formulae for solving the transient scattering problems in both near and far fields, which is implemented completely in the time domain. Several numerical examples are demonstrated and sufficiently high accuracy is achieved with different defects. It enables the possibility for Monte Carlo simulations of the elastic wave scattering from randomly rough surfaces in both 2D and 3D. The second contribution relates to applying the developed numerical method to evaluate the widely used Kirchhoff approximation (KA) for rough surface scattering. KA is a high-frequency approximation which limits the use of the theory for certain ranges of roughness and incidence/scattering angles. The region of validity for elastic KA is carefully examined for both 1D and 2D random surfaces with Gaussian spectra. Monte Carlo simulations are run and the expected scattering intensity is compared with that calculated by the accurate numerical method. An empirical rule regarding surface parameters and angles is summarized to establish the valid region of both 2D and 3D KA. In addition, it is found that for 3D scattering problems, the rule of validity becomes stricter than that in 2D. After knowing the region of validity, KA is applied to investigate how the surface roughness affects the statistical properties of scattered waves. An elastodynamic Kirchhoff theory particularly for the statistics of the diffused field is developed with slope approximations for the first time. It provides an analytical expression to rapidly predict the expected angular distribution of the scattering intensity, or the scattering pattern, for different combinations of the incidence/scattering wave modes. The developed theory is verified by comparison with numerical Monte Carlo simulations, and further validated by the experiment with phased arrays. In particular the derived formulae are utilized to study the effects of the surface roughness on the mode conversion and the 2D roughness caused depolarization, which lead to unique scattering patterns for different wave modes.

No description available.

As an alternative to spherical harmonics, mass concentration (mascon) parameters have been successfully applied to the recovery of time-varying gravity (TVG) fields from the GRACE satellite mission. However, before meaningful mass anomalies can be estimated, the noise and errors inherent in the solutions needs to be quantified and appropriate procedures adopted for mitigation. The uniqueness of the mascon methodology is the capability to mitigate noise and errors using spatial and temporal constraints, which can be adapted and tailored to any geophysical signal of interest. Therefore, in the first instance, this work was motivated by the need to improve the accuracy of GRACE TVG fields by understanding the effect of noise and errors. This study then aims to validate mascons for recovery of basin scale inter-annual mass variability at a 10 day temporal resolution. Newcastle University’s orbit determination software, Faust, was modified to allow for estimation of mascon parameters including: modelling of accelerometer bias values; mascon parameterisation; and processing based on short-arc gravity field recovery and KBRR data. Accuracy assessments were undertaken using simulations in the presence of realistic noise facilitating the comparison of mascons and spherical harmonic coefficients, including an assessment of potential limitations associated with each technique. Comparisons with time-series derived from CSR RL05 Level-2 data validated the mascon TVG field recovery, before estimation of the mass change of Antarctica, Greenland and Alaska. Several hydrological basins, including the Amazon and Indus were also assessed before the GRACE trends resulting from the Sumatra earthquake of 2004 were investigated. While only provided for validation, these comparisons provide confidence in the mascon mass estimates. Between January 2003 and December 2013 a mass change of -83 ± 12 Gt/year and -242 ± 7 Gt/year were estimated for Antarctica and Greenland respectively by linear regression using mascons with a 10 day temporal resolution. Overall, the work undertaken in this thesis provides evidence of the improved accuracy achievable when using mascon parameters to estimating TVG fields from Level-1B GRACE data. ii As part of this work a processing methodology to estimate mascon parameters from Level-1B GRACE data using Newcastle University’s orbit determination software Faust has been established and documented. This leaves the University well placed to continue processing mascon solutions from Level-1B GRACE data and to estimate mascon solutions from the GRACE-FO mission. Through simulations, mascon parameters were found to offer advantages over spherical harmonics for the mitigation of noise and for improving the temporal and spatial recovery of the TVG field from GRACE. The mascon constraint matrix allowed more signal to be preserved up to degree ~35. Using basin constraints, simulation revealed that the constraint matric can be tuned to recovery the gravity changes resulting from any geophysical phenomena of interest. Basin constraints were found to optimise the signal recovery of GLDAS and a known mass change signal over Antarctica and Greenland. A novel way to create realistic noise and errors in the KBRR measurement was also documented. Generating monthly and 10 day mascon solutions using real data revealed that the noise and errors in mascon solutions is comparably lower than in CRS RL05 solution while also validating the mascon methodology established here. Comparison to published mass trends to those estimated using mascon parameters showed that the estimation of mascon parameters has application in the study of mass change in the cryosphere, hydrological applications and for the study of the co-seismic mass changes resulting from earthquakes.

Wet granulation, a common unit operation in multiple industries, involves the production of "granules" which are assemblies of primary particles held together by interparticle bonds. Depending on the application, granules with the required attributes such as enhanced strength, flowability, dissolution properties or uniform composition, can be manufactured. It is widely accepted in granulation research that the wet granulation process is comprised of several competing rate processes that dictate the granule growth behaviour and ultimately the granule attributes. In the micro-scale models developed for these rate processes (granule coalescence, consolidation and breakage) and further mapping studies to link formulation, processing and equipment variables to the granule growth behaviour, where the most significant of such work being the "Granulation growth regime map" (Iveson and Litster, 1998b; Iveson et al., 2001b), a fundamental parameter is the external stress exerted on the granules during granulation. The external stress is exerted by the main agitator in the granulator and subsequently transmitted via inter-granule or granule-wall collisions in the system. This thesis studies and characterises the external stress in a high shear granulator, more specifically the impeller blade-granule bed stress. The reserach was divided into the following main parts: A novel, custom-built telemetric impeller stress sensor in the studied granulator was first developed for direct measurements of the instantaneous blade-bed stress. With this system, the steady-state blade-bed stresses were studied for a range of parameters including bed load, granule sieve size and granule/particle density for dry beds and liquid addition for wet beds. The bed surface velocity, measured using high speed recording and analysed with Particle Imaging Velocimetry (PIV), was used to represent the characteristic velocity of the dynamic bed. A correction factor was applied to the theoretical blade-bed stress equation derived based on the imparted inertial stress on continuous bed, which accounted for the increasing bed 'fluidisation' with increasing impeller speed. This enabled much improved predictions of the time-averaged blade-bed stress for the studied parameters, especially at high impeller speeds. The blade-bed stress behaviour during the granulation process was also studied while looking at the evolution of granule attributes. Further characterisation of the steady-state blade-bed stress was carried out by simulating the dynamic dry particle beds in the high shear granulator using the Discrete Element Method (DEM), a widely used simulation method for granular systems. Following the validation of the DEM simulation with the experiments, additional impeller speeds, particle/particle bed properties, impeller geometries and granulator scales were studied from the simulations. A modified correction factor was also applied in the blade-bed stress equation to account for different granulator scales and blade widths. Additionally for the bed characteristic velocity, it was also shown that the bed surface velocity is not the dominant factor for the stress over-prediction from theory with increasing impeller speeds, i.e. the increasing bed 'fluidisation' is the dominant factor. Finally, the temporal values of the steady-state blade-bed stress, bed surface velocity and bed height were studied in terms of the variability/fluctuations, for the different parameters/conditions studied in the experiments and simulations as previously mentioned. More importantly, the results were also related to the identified flow regimes of the granule/particle bed when the impeller speed or Froude number was varied.

This thesis presents the study of a two-degree-of-freedom (2 DOF) nonlinear system consisting of two grounded linear oscillators coupled to two separate light weight nonlinear energy sinks of an essentially nonlinear stiffness. In this thesis, Targeted Energy Transfer (TET) and NES concept are introduced. Previous studies and research of Energy pumping and NES are presented. The characters in nonlinear energy pumping have been introduced at the start of the thesis. For the aim to design the application of a tremor reduction assessment device, the knowledge of tremor reduction has also been mentioned. Two main parties have been presented in the research: dynamical theoretic method of nonlinear energy pumping study and experiments of nonlinear vibration reduction model. In this thesis, nonlinear energy sink (NES) has been studied and used as a core attachment for the research. A new theoretic method of nonlinear vibration reduction which with two NESs has been attached to a primary system has been designed and tested with the technology of targeted energy transfer. Series connection and parallel connection structure systems have been designed to run the tests. Genetic algorithm has been used and presented in the thesis for searching the fit components. One more experiment has been tested with the final components. The results have been compared to find out most efficiency structure and components for the theoretic model. A tremor reduction experiment has been designed and presented in the thesis. The experiment is for designing an application for reducing human body tremor. By using the theoretic method earlier, the experiment has been designed and tested with a tremor reduction model. The experiment includes several tests, one single NES attached system and two NESs attached systems with different structures. The results of theoretic models and experiment models have been compared. The discussion has been made in the end. At the end of the thesis, some further work has been considered to designing the device of the tremor reduction.

No description available.