We investigate a new perturbation technique introduced by E. Frieman to derive a kinetic equation from the equations of the BBGKY hierarchy. The orders of magnitude of the terms in the latter equations are calculated and Frieman's estimate is found incorrect. His derivation of the Landau's equation for a weakly coupled gas actually depends on the existence of the relaxation time rather than the much shorter mean free time as he expected. A physical interpretation of the Grad's theorem and Grad's original proof is given to justify the choice of the molecular chaos, conditions at the initial time. Two examples are given to clarify the applicability of the perturbation method. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Chiral perturbation theory allows us to probe the low energy properties of hadrons. In this thesis we have looked at the axial coupling constant (see chapter 4) and baryon number violation (see chapter 5).We calculated the axial coupling constant up to O(p^4) using the extended on mass shell renormalisation scheme in chiral perturbation theory. We also included the decuplet as an explicit degree of freedom. To fit the free parameters in our expression we used a combination of lattice and experimental data. We found that the fourth order corrections were quite large, and we struggled to produce an acceptable fit to the data. We also saw that the running of g_{A}^{pn} with M_\pi predicted by lattice QCD and ChPT at O(p^4) do not agree well. This is likely due to a combination of finite size effects impacting the low pion mass lattice data and the chiral perturbative series converging slowly. For our work on baryon number violation we looked at determining the values of two low-energy constants that appear in the baryon violating chiral Lagrangian. To do this, we matched our expression to lattice data. Previous determinations of the parameters had been done without calculating the effect of loops, ours was the first investigation to see what impact the loop diagrams would have. We found that our determinations of the parameters were in agreement with previous results, suggesting the effect of the loops is small. We also performed a chiral extrapolation, and found that our results were in agreement with previous results that did not account for loop corrections. This suggests that the impact of higher-order corrections is not significant for this baryon-number-violating process.

Given the rapid aging of the worldâ s population, improvements in technology for automation of patient care and documentation are badly needed. This project is based on previous research that demonstrated a â smartâ bed that can non-intrusively monitor a patient in bed and determine a patient's respiration, heart rate and movement without intrusive or restrictive medical measurements. The â smartâ bed is an application of spatially distributed integrating fiber optic sensors. The basic concept is that any patient movement that also moves an optical fiber within a specified area will produce a change in the optical signal. A statistical mode (STM) sensor and a high order mode excitation (HOME) sensor were previously investigated, based on which the author developed the present design including both modal modulation approaches. Development was made in both hardware and software for the combined STM/HOME sensor: a special lens system was installed allowing only the high order modes of the optical fiber to be excited and coupled into the sensor; computer-processing method was used for handling output from the dual STM-HOME sensor, which would offer comprehensive perturbation analysis for more reliable patient monitoring. Experimental results of simulating human body breathing and heartbeats by periodic mechanical perturbations are also presented, and the relative advantage and drawbacks of the two modal modulation approaches are discussed. / Master of Science

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The principal purpose of this thesis was to calculate certain mass differences of elementary particles in second order perturbation theory, within the framework of a gauge invariant theory of interactions. First we calculated the mass difference of the electron and the muon on the assumption that they have same bare mass and have different physical masses as a result of their interaction with a neutral vector meson field whose quantum is the phi meson. The previous attempts in this direction treated the muon and the electron unsymmetrically, which caused the ratio of the pion decay into (electron + electronic neutrino) to the pion decay into (muon + muonic neutrino) to have a value not permitted by the accuracy of the experimental results. Those calculations predicted also the value of the anomalous magnetic moment of the muon much higher than the experimental value. Our calculation, on the other hand, not only gives the mass difference of the muon and the electron in agreement with their experimental value but also does not run into any difficulty faced by the previous calculations. Secondly, generalizing the meaning of the electromagnetic interaction, we calculated the mass differences of the different members of every charge multiplet of the strongly interacting particles. Only with two adjustable parameters we have been able to predict the mass differences of the seven pairs of particles. Finally, we speculated on the origin of the masses of the phi and rho mesons. Using the coupling constants previously introduced, we calculated their masses in agreement with the experimental masses. We used the same cut-off parameter as was assumed for the electromagnetic mass splitting. / 2031-01-01

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Obesity is a major and growing health concern associated with an increased risk of falls. The majority of falls are thought to result from some kind of postural perturbation, yet the biomechanical mechanisms as to why obese individuals fall more often is unclear. Therefore, the goal of this study was to investigate the effects of obesity on balance recovery in response to small forward postural perturbations. Twenty male participants, including 10 lean (mean BMI ± SD: 21.9 ± 1.4) and 10 obese (BMI: 33.2 ± 2.3), were exposed to two types of postural perturbations (force impulses applied with a pendulum and angular displacements administered with a release mechanism). Participants attempted to recover balance with only an ankle strategy such that neither a step nor hip flexion was utilized. Quiet standing trials were also conducted for comparison with the literature. Obese individuals exhibited less center of mass (COM) displacement and a slower COM velocity compared to lean individuals when exposed to identical force perturbations. When exposed to the force perturbations relative to body weight, and when released from identical lean angles, no differences in COM performance were found. During quiet standing, no differences in center of pressure (COP) velocity were observed between obese and lean groups. In all tasks, the obese generated higher ankle torque than the lean. Overall, the obese participants exhibited no differences in movement or less/slower movement than the lean participants when recovering from small forward postural perturbations as well as during quiet standing. These results imply that obesity in young adult males did not impair balance recovery for the tasks investigated. / Master of Science

In this thesis we develop inverse scattering algorithms towards the ultimate goal of online diagnostic methods. The aim is to detect structural changes inside power transformers and other major power grid components, like generators, shunt reactors etc. Power grid components, such as large power transformers, are not readily available from the manufacturers as standard designs. They are generally optimized for specific functions at a specific position in the power grid. Their replacement is very costly and takes a long time. Online methods for the diagnostics of adverse changes of the mechanical structure and the integrity of the dielectric insulation in power transformers and other power grid components, are therefore essential for the continuous operation of a power grid. Efficient online diagnostic methods can provide a real-time monitoring of mechanical structures and dielectric insulation in the active parts of power grid components. Microwave scattering is a candidate that may detect these early adverse changes of the mechanical structure or the dielectric insulation. Upon early detection, proper actions to avoid failure or, if necessary, to prepare for the timely replacement of the damaged component can be taken. The existing diagnostic methods lack the ability to provide online reliable information about adverse changes inside the active parts. More details about the existing diagnostic methods, both online and offline, and their limitations can be found in the licentiate thesis preceding the present PhD thesis. We use microwave scattering together with the inverse scattering algorithms, developed in the present work, to reconstruct the shapes of adverse mechanical structure changes. We model the propagation environment as a waveguide, in which measurement data can be obtained only at two ends (ports). Since we want to detect the onset of some deformation, that only slightly alters the scattering situation (weak scattering), we have linearized the inverse problem with good results. We have calculated the scattering parameters of the waveguide in the first-order perturbation, where they have linear dependencies on the continuous deformation function. A linearized inverse problem with a weak scattering assumption typically results in an ill-conditioned linear equation system. This is handled using Tikhonov regularization, with the L-curve method for tuning regularization parameters. We show that localized one-dimensional and two-dimensional shape deformations, for rectangular and coaxial waveguide models, are efficiently reconstructed using the inverse scattering algorithms developed from the first principles, i.e. Maxwell’s theory of electromagnetism. An excellent agreement is obtained between the reconstructed and actual deformation shapes for a number of studied cases. These results show that it is possible to use the inverse algorithms, developed in the present thesis, as a theoretical basis for the design of a future diagnostic device. As a part of the future work, it remains to experimentally verify the results obtained so far, as well as to further study the theoretical limitations posed by linearization (first-order perturbation theory) and by the assumption of the continuity of the metallic waveguide boundaries and their deformations. / <p>QC 20160119</p>

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown that the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, it is shown that this amounts to a rigorous treatment of the radiation reaction.