The dynamics of a quantum system with a large number $N$ of identical bosonic particles interacting by means of weak two-body potentials can be simplified by using mean-field equations in which all interactions to any one body have been replaced with an average or effective interaction in the mean-field limit $N \rightarrow \infty$. In order to show these mean-field equations are accurate, one needs to show convergence of the quantum $N$-body dynamics to these equations in the mean-field limit. Previous results on convergence in the mean field limit have been derived for certain initial conditions in the case of one species of bosonic particles, but no results have yet been shown for multi-species. In this thesis, we look at a quantum bosonic system with two species of particles. For this system, we derive a formula for the rate of convergence in the mean-field limit in the case of an initial coherent state, and we also show convergence in the mean-field limit for the case of an initial factorized state. The analysis for two species can then be extended to multiple species.

The Moon displays weak magnetic fields resulting from areas of the lunar crust that are remanently magnetised. The origins of the magnetic fields that produced this remanent magnetisation are still under discussion, and theories include among several, an ancient lunar dynamo, or processes occurring on the Moon as a result of impacts. Lunar crustal fields have been mapped globally by the Magnetometer (MAG) and Electron Reflectometer (ER) on the satellite Lunar Prospector, providing vector magnetic field measurements at an average altitude of 30 km, and estimates of the total surface field. This thesis presents global and regional models of the magnitude and direction of lunar magnetisation within a layer, produced from both the MAG and ER data independently and jointly using several inversion methods. The inverse modelling techniques are based on those developed for terrestrial and Martian data sets, employing equivalent source dipoles as basis functions, and Green’s functions relating a magnetic field observation to a spatially continuous magnetisation distribution. A unique magnetisation solution is selected having the smallest rootmean- square (RMS) magnetisation for a given fit to the data, controlled by a damping parameter. The non-uniqueness in magnetisation distributions and the determination of source parameters is discussed with the use of forward models to assist the interpretation of the crustal magnetisation models. Suites of magnetisation models for layers with thicknesses between 10 and 50 km, and with different dipole depths, are able to reproduce both the ER and MAG data well. Inverse models utilising the scalar ER data have been developed successfully, resulting in a joint inversion of the ER and MAG data for one of the strongest magnetic anomalies on the Moon, Reiner Gamma. The largest concentrations of strongly magnetised crust are, like the crustal fields themselves, located antipodal to the youngest large impact basins, and in some isolated areas associated with the strongest crustal fields. The magnetisation distributions show robust magnitudes with different data sets and modelling techniques showing the extent of magnetised sources, but can not be used to infer the direction of the magnetising fields. Average magnetisation values in magnetised regions of 30-40 mA/m are similar to the measured magnetisations of the Apollo samples and significantly weaker than crustal magnetisations for Mars and the Earth. A global preference for a 30 km thick magnetised layer suggests that a dynamo field may be more consistent with these magnetisation models. The magnetisation models in this thesis are the first global magnetisation models for the Moon, and the first to combine the vector MAG and the scalar ER data. These magnetisation models can be used to predict the crustal contribution to the lunar magnetic field environment at a particular location, and in the absence of reliable sample returns, provide valuable information on the magnitude of lunar crustal magnetisation.

A passive wireless sensor is designed, fabricated and tested for the measurement of AC electric field in the vicinity of high voltage apparatus. This sensor is applicable in remote condition monitoring of high voltage apparatus where close distance measurements raises safety hazards for operators. The sensor is designed using a coaxial cavity resonator structure (in TEM mode) capacitively coupled to varactors. The resonance frequency of the sensor shifts corresponding to the capacitance variation of the varactors which in turn is perturbed by the external electric field. The electric field surrounding the apparatus induces a bias voltage over the terminals of the varactors. Therefore, the resonance frequency changes proportional to the inducing external electric field and correspondingly to the medium/high voltage. A printed circuit board on the top of the cavity provides coupling between the cavity and varactors and also between the varactors and the external field produced by the high voltage apparatus. The sensor structure is designed to resonate in the range of 2.4 GHz to 2.5 GHz of the industrial, scientific and medical (ISM) radio frequency band. A remote interrogation system identifies the instantaneous resonance frequency of the sensor by transmitting pulses of radio frequency (RF) signal and recording the ring back of the resonator. The ring back is down converted and analyzed to determine the resonance frequency of the sensor. Two possible applications of the sensor, i.e. voltage measurement and defect detection of insulators, are demonstrated by experimental results. / February 2017

This thesis investigates some inequalities and some relationships between function properties and integral properties.

No description available.

No description available.

In this report we study the Aizawa field by first computing a Taylor series expansion for the solution of an initial value problem. We then look for singularities (equilibrium points) of the field and plot the set of solutions which lie in the linear subspace spanned by the eigenvectors. Finally, we use the Parameterization Method to compute one and two dimensional stable and unstable manifolds of equilibria for the system. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

by Kenneth Y.P. Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 120-123.

Lau Kwok-kwong = 量子場在一維耗散性空腔中的特性 / 劉國光. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 82-83). / Text in English; abstracts in English and Chinese. / Lau Kwok-kwong = Liang zi chang zai yi wei hao san xing kong qiang zhong de te xing / Liu Guoguang. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Formalism of QNMs --- p.8 / Chapter 2.1 --- A Review of QNMs --- p.9 / Chapter 2.1.1 --- Projection for QNMs 一 Bilinear mapping --- p.11 / Chapter 2.1.2 --- Incoming field --- p.13 / Chapter 2.2 --- Physical examples of QNMs --- p.15 / Chapter 2.2.1 --- Dielectric rod --- p.15 / Chapter 2.2.2 --- Laser cavity --- p.16 / Chapter 2.3 --- Modes-of-the-universe approach --- p.17 / Chapter 3 --- Field Quantization --- p.21 / Chapter 3.1 --- Field operators and Commutation Relations --- p.22 / Chapter 3.2 --- Thermal Expectation Values --- p.23 / Chapter 3.2.1 --- "Quantum limit, T →0" --- p.25 / Chapter 3.2.2 --- "Classical limit, T→∞" --- p.26 / Chapter 3.3 --- Physical interpretation of QNM operators --- p.27 / Chapter 4 --- Discrete modes and background fields --- p.31 / Chapter 4.1 --- LSL Discrete modes --- p.32 / Chapter 4.2 --- Construction of discrete modes operators based on QNMs --- p.34 / Chapter 4.2.1 --- Commutation relations --- p.38 / Chapter 4.2.2 --- Equations of motion --- p.38 / Chapter 4.2.3 --- Input-Output relation of the discrete modes --- p.39 / Chapter 4.3 --- Properties of the background field --- p.40 / Chapter 4.3.1 --- Classical approach to understand the background field . --- p.41 / Chapter 5 --- Spontaneous Emission in a leaky cavity --- p.53 / Chapter 5.1 --- Spontaneous Emission: one qusaimode calculation --- p.54 / Chapter 5.2 --- Spontaneous Emission with background effect --- p.57 / Chapter 5.3 --- Difference between the rotating wave approximation and the background --- p.61 / Chapter 6 --- The connection between QNMs and System-Bath models --- p.66 / Chapter 6.1 --- Single-mode SBM --- p.68 / Chapter 6.1.1 --- Equation of motion --- p.68 / Chapter 6.1.2 --- Commutation relations --- p.70 / Chapter 6.1.3 --- Input-output relation --- p.72 / Chapter 6.2 --- N-modes SBM --- p.72 / Chapter 6.2.1 --- N = 2 case --- p.74 / Chapter 6.2.2 --- N >2 case --- p.76 / Chapter 7 --- Conclusion --- p.79 / Bibliography --- p.82 / Chapter A --- Correlation Function --- p.84 / Chapter B --- Relation between surface term and imaginary part of the frequency --- p.86 / Chapter C --- Green function approach --- p.88 / Chapter D --- Numerical results of SBM --- p.92

This thesis is in support of the Precision Personnel Locator (PPL) project being conducted by Worcester Polytechnic Institute (WPI). The overall goal of the PPL project is to locate firemen and other emergency personnel in buildings using Radio Frequency (RF) techniques. The aspiration is to prevent a tragedy similar to the Worcester Cold Storage fire of 1999. The Mantenna homing wand is a spinoff of the PPL system which uses the Near Field properties of Very Low Frequency (VLF band) waves. The Mantenna has been used to successfully demonstrate the ability to locate targets inside harsh RF environments and other radio opaque environments where normal radiation field based systems have degraded performance, such as commercial, industrial, and apartment buildings. This thesis builds upon the Mantenna rescue device by construction of a transmitter subsystem which is physically smaller than the previous version by redesign of the compact VLF antenna. Additionally, exploitation of the approach used by the Mantenna for homing purposes is explored for full location estimation. This work provides the theoretical background and proof of concept test of a Near Field based location system. Simulation and test results are compared for a minimal configuration involving a single receiver.