No description available.

No description available.

No description available.

<p>The protonation for several classes of weak bases has been studied by n.m.r. techniques and the structure of the conjugate acids determined. The rates of proton transfer and the activation energies for some of the processes have been calculated and in the cases of the methylbenzene-HSO₃F systems the mechanism of the proton transfer process has been elucidated.</p> <p>The acidity function (H₀) for the HSO₃F/SbF₅ system has been redetermined and extended to higher concentrations of SbF₅• The application of some n.m.r. methods to the measurement of H₀ is discussed.</p> <p>The behaviour of the n.m.r. spectra of sulphuric and fluorosulphuric acids upon the addition of electrolytes has been studied and the results interpreted.</p> / Thesis / Doctor of Philosophy (PhD)

Granular materials, such as sand, are systems consisting of huge numbers of particles that interact with each other through inter-particle contacts. Different from continuum materials, a granular material displays distinctive features due to the discrete nature of the microstructure, characterized by a spatial arrangement of inter-particle connection as well as a force-chain network. With a consideration of the contact force, the overall contact network is divided into a strong sub-network and a weak sub-network that carry contacts with normal contact forces larger and lower than the average normal contact force, respectively. Thus, the fabric anisotropy for different contact networks, are employed to characterize the microstructure of the granular material. In this research, the behavior of granular materials subjected to quasi-static shear was extensively investigated in terms of the fabric evolution including the magnitude and direction of anisotropy for different contact networks. Both statistical and micromechanical approaches were adopted to obtain the macroscopic properties, such as the fabric tensor, Cauchy stress tensor and the second-order work, in terms of the micro-scale variables. The discrete element method (DEM) was employed to simulate laboratory tests along fixed loading paths; for example, 2D tests along proportional strain paths, 2D simple shear tests and 3D tests along radial stress paths on the π-plane. Results demonstrated that the induced fabric anisotropy for the overall contact network can be related to the deviatoric stress ratio for both two-dimensional and three-dimensional conditions. The relation was found to be not unique, depending on the loading paths as well as the stress state. Nevertheless, a unique linear fabric-stress relation was presented between the stress tensor and fabric tensor for the strong sub-network. Specifically, the obliquity of this linear relation was found to be a function of the mean stress. This description held true for initially isotropic specimens subjected to proportional and non-proportional loading paths. On the other hand, for the initially anisotropic specimen, this correspondence only worked at the critical stress state. According to Nicot and Darve (2006), the macro second-order work cannot be interpreted as a summation of the local second-order work from the contact plane. The second-order work induced by the fabric evolution and the volumetric change must also be taken into account. The second-order work induced by the fabric evolution cannot be neglected in 2D analysis along proportional strain paths. Moreover, the vanishing of the second-order work is related to the fabric anisotropy in contact sub-networks that the decrease of fabric anisotropy for the weak sub-network or the degradation of weak sub-network was observed to be an indicator of deformation instability even though the strong sub-network dominants the shear resistance. The degradation of strong sub-network was a necessary but not a sufficient condition of instability. The direction of the fabric anisotropy for the strong sub-network was observed to be coaxial with the orientation of the principal stress. The principal direction of fabric anisotropy for the weak sub-network was always perpendicular to that of the strong sub-network, regardless of whether the principal stress rotated or not. For the overall contact network, however, the direction of the fabric anisotropy was not necessarily in line with the major principal stress direction, even for an initial isotropic granular assembly. Therefore, the finding by Radjaï et al.(1998) that the direction of the fabric anisotropy for the weak sub-network is perpendicular to that for the overall contact network only held true for the loadings in which the critical stress could be approached no matter if the principal stress orientation rotated or not. Under this circumstance, the fabric anisotropy for the overall contact network could be interpreted as a function of sub-networks’ anisotropy weighted by the ratio of contact number in each sub-network over the total number of contacts. At critical state, both the strong sub-network and the overall contact network developed high fabric anisotropy with the weak sub-network being mostly isotropic. When plotted on the π-plane, both the fabric anisotropy for the strong sub-network and the fabric anisotropy for the overall contact network depended on the stress paths but were independent of the mean stress level. The response surface of the former could be expressed as a Lade’s surface. The response envelope of the latter was an inverted Lade’s surface. / Dissertation / Doctor of Philosophy (PhD) / In civil engineering, granular materials are ubiquitous, such as sand, gravel, rock, and concrete. Due to the discrete nature of microstructure, this type of material usually displays exceedingly complicated behaviours under shear, for example, dilatancy, non-coaxiality, critical state, instability, and anisotropy. These mechanical responses are notoriously difficult to model and most existing models are phenomenological and lack a clear physical meaning. To provide a clear physical meaning for the constitutive model of granular material, the current study explored the evolution of the microstructure within the granular material subjected to quasi-static shear and the micromechanical origins of those macroscopic behaviours such as critical state, non-coaxiality, and instability. Both micromechanical analysis and discrete element method were applied. Results showed that the evolution of the whole microstructure depended on the loading condition. However, the evolution of the microstructure joined by the ‘strong contacts’ was independent of the loading path. At critical state, the microstructure was highly anisotropic, not unique and depended on the stress paths. The rearrangement of the microstructure helped to maintain the stability of a granular material. The instability of the granular material was triggered by the failure of the microstructure joined by the ‘weak contacts’.

Yes / A quantum system (n) with variables in Z(n), where n = Qpi (with pi prime numbers), is considered. The non-near-linear geometry G(n) of the phase space Z(n) × Z(n), is studied. The lines through the origin are factorized in terms of ‘prime factor lines’ in Z(pi)×Z(pi). Weak mutually unbiased bases (WMUB) which are products of the mutually unbiased bases in the ‘prime factor Hilbert spaces’ H(pi), are also considered. The factorization of both lines and WMUB is analogous to the factorization of integers in terms of prime numbers. The duality between lines and WMUB is discussed. It is shown that there is a partial order in the set of subgeometries of G(n), isomorphic to the partial order in the set of subsystems of (n).

Qweak will determine the weak charge of the proton, QpW, via an asymmetry measurement of parity-violating elastic electron-proton scattering at low four momentum transfer to a precision of 4%. QpW has firm Standard Model prediction and is related to the weak mixing angle, sin20W, a well-defined Standard Model parameter. Qweak will probe a subset of new physics to the TeV mass scale and test the Standard Model. The details of how this measurement was performed and the analysis of the 25% elastic dataset will be presented in this thesis. Also, an analysis of an auxiliary measurement of the parity-violating asymmetry in the N >> Δ transition is presented. It is used as a systematic inelastic background correction in the elastic analysis and to extract information about the hadronic parity violation through the low energy constant, dΔ. The elastic asymmetry at Q2 = 0:0252 ± 0:0007 GeV2 was measured to be Aep = -265 ± 40 ± 22 ± 68 ppb (stat., sys., and blinding). Extrapolated to Q2 = 0, the value of the proton's weak charge was measured to be QpW = 0:077 ± 0:019 (stat. and sys.) ±0:026 (blinding). This is within 1 o of the Standard Model prediction of QpW = 0:0705 ± 0:0008. The N >> Δ inelastic asymmetry at Q2 = 0:02078 ± 0:0005 GeV2 and W = 1205 MeV was measured to be Ainel = -3:03 ± 0:65 ± 0:73 ± 0:07 ppm (stat., sys., and blinding). This result constrains the low energy constant to be dΔ = 5:8 ± 22gπ, and, if the result of the G0 experiment is included, dΔ = 5:8 ± 17gπ. This result rules out suggested large values of dΔ motivated by radiative hyperon decays. The elastic measurement is the first direct measurement of the weak charge of the proton while the inelastic measurement is only the second measurement of the neutral current excitation of the Δ resonance. It is currently the best constraint for the low energy constant, dΔ. / Ph. D.

The Q_weak Experiment ran for two and a half years at the Thomas Jefferson National Accelerator Facility in pursuit of Q_w^p, the neutral weak analog to the electric charge of the proton. Qweak measured the parity-violating asymmetry in elastic electron-proton scattering at an extreme forward angle (Q² = 0.0249 (GeV/c)² ). From the data gathered via the 1.16 GeV 180 μA longitudinally polarized electron beam scattering off the unpolarized photons in the liquid hydrogen target, a value of Q_w^p (PVES) = 0.0719 ± 0.0045 was determined. The Standard Model has a definite prediction of Q_w^p (SM) = 0.0708 ± 0.0003, consistent with the value determined by Q_weak which sets a limit on possible new physics up to 7.5 TeV. The theory behind the main measurement of the Q_weak Experiment is described in this document, along with the apparatus that made the measurement possible. Understanding the kinematics of the apparatus was a vital component to Qweak 's final measurement. An in-depth explanation of the tracking system responsible for benchmarking the momentum transfer and scattering angle simulations is included. The unblinded analysis of Q_weak's final result is outlined, as are additional physics results related to the N→ ∆ transition. During April 2012, an opportunity was seized to take ancillary data on the inelastic N→ ∆ transition at a different beam energy(877 MeV) than the nominal Q_weak data. This data, combined with the inelastic data taken at nominal beam energy and a previous measurement, determined a constraint on d_∆ , a low energy constant related to hadronic parity violation, of (3.8 ± 14.7)g_π . It also resulted in a measurement of the beam-normal single-spin asymmetry of the N→ ∆ transition of 149 ± 3 (stat) ± 72 (syst) ppm. This document includes both the longitudinal and transverse analysis of the 877 MeV data. / Doctor of Philosophy / The Q_weak Experiment, run at the Thomas Jefferson National Accelerator Facility, measured the weak charge, the weak force analog of the electric charge of the electromagnetic force, of the proton. Unlike the well-know Large Hadron Collider, which operates on the energy-frontier and directly searches for new particles, Q_weak operates by precisely measuring the results of scattering electrons off of protons. This approach is referred to as the precision frontier and is used to test the Standard Model, which has a well-defined prediction for the weak charge of the proton. Deviations from the Standard Model would suggest that there was new physics beyond the Standard Model affecting the results. However, the Q_weak measured weak charge of the proton, Q_w^p (PVES) = 0.0719 ± 0.0045, is in good agreement with the Standard Model predicted value. This provides a new limit, 7.5 TeV, on possible new physics beyond the Standard Model. The theoretical background and apparatus of the Qweak experiment will be explained in this document. A vital component of the final result was understanding the path and energy of the electron as it passed through the apparatus. This was done via simulation but benchmarked by the tracking system. The tracking system will be explained in detail. The final analysis of the Q_weak measurement of the weak charge will also be explained. A secondary result discussed here focuses on data taken using the Q_weak apparatus but at a different beam energy than the nominal Q_weak data. For this data, the electron scatter inelastically off the proton. The lost kinetic energy of the electron causes the proton to be excited into the first resonance state, the ∆, which quickly decays away. This transition grants access to a low energy constant, d_∆, and a measurement linked to the spins of the electrons being polarized perpendicular to the direction of the beam, B_n. The extraction of these values is covered in detail.

Invention of silica based optical fiber not only led to revolution in communication but also provided fundamental basis for many research areas. One example area is distributed optical fiber sensing, which has been attracting research interests for decades. Optical fiber sensors are immune to electromagnetic interference, and resistant to corrosion and can endure harsh environment so they have found applications such as structural health monitoring, intrusion detection and oil downhole measurement. Significant research efforts have been paid to fiber sensing area, many techniques have been developed and some of them have been successfully demonstrated, however achieving both high-speed and long-range is still under intensive research. This dissertation proposes and demonstrates a technique with the capability of simultaneous long-range and high-speed sensing by employing serial ultra-weak fiber Bragg gratings (UW-FBGs) and dispersive components. Various factors which have influence on the system performance, including wavelength resolution, spatial resolution and sensing rate, are analyzed. Different types of light sources and dispersive units were designed and a sensing system was built. With this system, both static and dynamic response were measured, and a sensing link consisting of more than 2000 UW-FBGs was successfully measured at the speed of 20kHz. The noise sources of the system were also theoretically analyzed and experimentally measured. This demonstrated sensing technique can be applied to long range temperature and strain sensing. / Ph. D.

The concept of a weak sound radiating cell is proposed to reduce the low frequency radiated noise from structures. The cell consists of two coupled surfaces such that, when placed on a vibrating structure, the responses of the two surfaces are nearly out-of-phase and of equal strength over a wide frequency range. This structure response leads the cell to behave as an acoustic dipole and thus as a poor sound radiating source. The control of low frequency structurally radiated noise is then achieved by covering the structure with an array of these weak radiating cells, i.e. surface treatment. Thus, the surface treatment essentially transforms the response of the structure to that of a distributed array of dipoles yielding a low sound radiating structure. Theoretical models are developed to predict the performance of the cell. Experimental verification is performed for a single cell applied to a piston-like structure to demonstrate the concept on a simple radiating structure. The results demonstrated an overall sound power level reduction of 5.2 dB between 400-1600 Hz with maximum reductions over 30 dB at discrete frequencies. Finally, an array of weak radiating cells is experimentally applied to a more complex structure, a rectangular plate. The results of the plate experiments reveal an overall sound power level reduction of 10.2 dB between 100-1600 Hz with maximum reductions of 25 dB at discrete frequencies. These results demonstrate the potential of the weak radiating cell concept to reduce low frequency structurally radiated noise. / Master of Science