A research thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirement for the degree of Doctor of Philosophy. August 7, 2013. / In this thesis we consider the construction of exact solutions for models describing heat transfer through extended surfaces (fins). The interest in the solutions of the heat transfer in extended surfaces is never ending. Perhaps this is because of the vast application of these surfaces in engineering and industrial processes. Throughout this thesis, we assume that both thermal conductivity and heat transfer are temperature dependent. As such the resulting energy balance equations are nonlinear. We attempt to construct exact solutions for these nonlinear models using the theory of Lie symmetry analysis of differential equations. Firstly, we perform preliminary group classification of the steady state problem to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended by one element. Some reductions are performed and invariant solutions that satisfy the Dirichlet boundary condition at one end and the Neumann boundary condition at the other, are constructed. Secondly, we consider the transient state heat transfer in longitudinal rectangular fins. Here the imposed boundary conditions are the step change in the base temperature and the step change in base heat flow. We employ the local and nonlocal symmetry techniques to analyze the problem at hand. In one case the reduced equation transforms to the tractable Ermakov-Pinney equation. Nonlocal symmetries are admitted when some arbitrary constants appearing in the governing equations are specified. The exact steady state solutions which satisfy the prescribed boundary conditions are constructed. Since the obtained exact solutions for the transient state satisfy only the zero initial temperature and adiabatic boundary condition at the fin tip, we sought numerical solutions. Lastly, we considered the one dimensional steady state heat transfer in fins of different profiles. Some transformation linearizes the problem when the thermal conductivity is a differential consequence of the heat transfer coefficient, and exact solutions are determined. Classical Lie point symmetry methods are employed for the problem which is not linearizable. Some reductions are performed and invariant solutions are constructed. The effects of the thermo-geometric fin parameter and the power law exponent on temperature distribution are studied in all these problems. Furthermore, the fin efficiency and heat flux are analyzed.

Inertial measurement units, or IMUs, serve as effective tracking devices when used in sophisticated aerospace control and navigational systems. This tracking potential, coupled with ever advancing technology that permits IMUs to become smaller and more compact, is allowing IMUs to gain popularity in a many areas of research beyond the areas of aerospace. Using an IMU based on microelectromechanical (MEMS) technology, this document investigates an IMU’s ability to track complex, short range motions such as golf swings. To prepare the IMU, an accurate, yet quick, calibration procedure is proposed and illustrated to show the tools and equipment necessary for this approach. Once calibrated, experimental results from static and dynamic tests are compared to corresponding analytical results to help comprehend and confirm the IMU readings. The IMU is then applied to a series of short range motions for reliability and performance testing.

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The purpose of this thesis is to address the following research questions: 1) what is the current status of creativity research in a typical classroom, and 2) how does an instance of exemplary teaching serve to encourage creativity in a technology education setting? The first research question is focused on through a thorough review of published literature on creativity in order to frame the second research question. The second research question is addressed by understanding how Mr. Brad Thode, the technology teacher at Wood River Middle School in Hailey, Idaho, encourages his students to be creative. By investigating this one program, it will provide a greater understanding and deeper insight into how to promote creativity in students. Specifically, a phenomenological case study approach is used to investigate Mr. Thode and his nonlinear teaching style and to see how he fosters and promotes creativity in his classroom and among his students. Special attention is given to practices, methods, traits, etc. that have the potential to be replicated or modified for use in other classrooms. Findings are framed in the four generally accepted components of creativity: person, product, process, and press. Results indicate that creativity can be modeled and recommendations for promoting creativity in the classroom are outlined.

Experimental nonlinear dynamics is an important area of study in the modern engineering field, with engineering applications in structural dynamics, structural control, and structural health monitoring. As a result, the discipline has experienced a great influx of research efforts to develop a versatile and reliable experimental methodology. A technical challenge in many experimental studies is the procurement of a device that exhibits the desired nonlinear behavior. As a result, many researchers have longed for a versatile, but accurate, testing methodology that has complete freedom to simulate a wide range of nonlinearities and stochastic behaviors. The objective of this study is to develop a reconfigurable test setup as a tool to be used in a wide range of nonlinear dynamic studies. The main components include a moving mass whose restoring force can accurately be controlled and reprogrammed (with software) based upon measured displacement and velocity readings at each time step. The device offers control over nonlinear characteristics and the equation of dynamic motion. The advantage of having such an experimental setup is the ability to simulate various types of nonlinearities with the same test setup. As a result, the data collected can be used to help validate nonlinear modeling, system identification, and stochastic analysis studies. A physical test apparatus was developed, and various mechanical, electrical, and programming calibrations were performed for reliable experimental studies. To display potential uses for the reconfigurable approach, examples are presented where the device has been used to create physical data for use in change detection and deterioration studies. In addition, a demonstration is presented of the device’s ability to physically simulate a large-scale orifice viscous damper, commonly used in vibration mitigation in bridges and buildings. For a large-scale viscous damper, physical testing is required to ensure structural design properties. However, due to the large scale of the dampers, expensive dynamic loading tests can be carried out at a very iii limited number of facilities. Using the reconfigurable test setup, the dynamic signature of the large-scale viscous damper can accurately be simulated with pre-collected data. The development of a system capable of emulating the restoring force of a nonlinear device with software is a novel approach and requires further calibration for increased reliability and accuracy. A discussion regarding the challenges faced when developing the methodology is presented and possible solutions are recommended. The methodology introduced by this apparatus is very promising. The device is a valuable experimental tool for researchers and designers, allowing for physical data collection, modeling, analysis, and validation of a wide class of nonlinear phenomena that commonly occur in a wide variety of engineering applications.

The main purpose of this dissertation to investigate photophysical properties, third order nonlinearity and free carrier absorption and refraction in organic materials and semiconductors. Special emphasis of this dissertation is on characterization techniques of molecules with enhanced intersystem crossing rate and study of different approaches of increasing triplet quantum yield in organic molecules. Both linear and nonlinear characterization methods are described. Linear spectroscopic characterization includes absorption, fluorescence, quantum yield, anisotropy, and singletoxygen generation measurements. Nonlinear characterization, performed by picosecond and femtosecond laser systems (single and double pump-probe and Z-scan measurements), includes measurements of the triplet quantum yields, excited-state absorption, two-photon absorption, nonlinear refraction and singlet and triplet-state lifetimes. The double pump-probe technique is a variant of the standard pump-probe method but uses two pumps instead of one to create two sets of initial conditions for solving the rate equations allowing a unique determination of singlet- and triplet-state absorption parameters and transition rates. The advantages and limitations of the the double pump-probe technique are investigated theoretically and experimentally, and the influences of several experimental parameters on its accuracy are determined. The accuracy with which the double pump-probe technique determines the triplet-state parameters improves when the fraction of the population in the triplet state relative to the ground state is increased. Although increased accuracy is in iv principle achievable by increasing the pump fluence in the reverse saturable absorption range, it is shown that the DPP is optimized by working in the saturable absorption regime. Two different approaches to increase intersystem crossing rates in polymethine-like molecules are presented: traditional heavy atom substitution and molecular levels engineering. Linear and nonlinear optical properties of a series of polymethine dyes with Br- and Se- atoms substitution, and a series of new squaraine molecules, where one or two oxygen atoms in a squaraine bridge are replaced with sulfur atoms, are investigated. A consequence of the oxygento-sulfur substitution in squaraines is the inversion of their lowest lying ππ* and nπ* states leading to a significant reduction of singlet-triplet energy difference and opening of an additional intersystem channel of relaxation. Experimental studies show that triplet quantum yields for polymethine dyes with heavy-atom substitutions are small (not more than 10%), while for sulfurcontaining squaraines these values reach almost unity. Experimental results are in agreement with density functional theory calculations allowing determination of the energy positions, spinorbital coupling, and electronic configurations of the lowest electronic transitions. For three different semiconductors: GaAs, InP and InAsP two photon absorption, nonlinear refraction and free carrier absorption and refraction spectrums are measured using Zscan technique. Although two photon absorption spectrum agrees with the shape of theoretical prediction, values measured with picosecond system are off by the factor of two. Nonlinear refraction and free carrier nonlinearities are in relatively good agreement with theory. Theoretical values of the third order nonlinearities in GaAs are additionally confirmed with femtosecond Z-scan measurements. v Due to large spectral bandwidth of femtosecond laser, three photon absorption spectrum of GaAs was additionally measured using picosecond Z-scan. Again, spectral shape is in excellent agreement with theory however values of three photon absorption cross sections are larger than theory predicts.

This thesis describes the computational tools that allow the simulation of polymers made up of an arbitrary number of three-level systems, the study of such systems and comparisons to experimental nonlinear optical spectra. The three-level system generator (3LSG), is designed to automatically generate the operators that describe the system, whether it is a closed system or an open quantum system (OQS) in contact with a bath, with just a few input parameters. A user is free to specify each 3LS's energy levels and transition dipoles between said levels, site couplings between the different units of the polymer and in the case of open systems, the rates and couplings describing the different relaxation processes taking place in an OQS, using the Redfield formalism. In either cases, the 3LSG is then capable of generating the Hamiltonian 𝐻₀ describing the closed system or the Liouvillian 𝓛₀ describing the open system from the various inputs. The Ultrafast Spectroscopy Suite (UFSS) is an open-source software suite used to perform the nonlinear optical spectroscopies simulations. It contains 4 main modules, one of which is the Hamiltonian/Liouvillian Generator (HLG), a module previously designed to model simpler two-level systems. The 3LSG is a sub-module of the HLG. The three-level system generator is used to replicate a theoretical model describing a copolymer model made of many identical pairs of squaraine monomers, where each monomer is a three-level system interacting with its neighbouring sites and a surrounding bath. The system automatically generated by the 3LSG is used, along with other spectroscopic calculation tools, to simulate high-order transient absorption (TA) spectroscopies and study the long-time behaviour of the 3rd-order to 13th-order excited state absorption (ESA) peaks in the TA signals. The 3LSG is used in conjunction with spectroscopic calculations tools as it was originally intented, though it may also be used by itself to study Hamiltonians and Liouvillians of electronic three-level systems.

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