Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.

Halon 1301 (CF3Br), or bromotrifluoromethane, had been widely used as fire-extinguishing agent for many years before its production and consumption were severely regulated by the Montreal Protocol due to its hazardous depletion effect to the stratospheric ozone layer. It is therefore imperative to find an effective replacement fire-fighting agent before the mandated deadline of the complete phase out of CF3Br. Currently there are intensive efforts in searching for an environmentally acceptable fire suppression replacement. This, however, is hampered by a lack of fundamental understanding of how CF3Br suppresses the chemical reactions in a flame environment so effectively. Recent experimental evidence has shown that the addition of CF3Br significantly reduced the burning velocity of premixed H2/Air flames by depleting the important radical species that are important to sustain chemical reactions. Extending this finding to understand the suppression of more complicated diffusion flames and unsteady three dimension turbulent flames in the presence of Halon 1301, however, still faces enormous challenge because of the prohibitive requirement of the computational power. The present chemical reaction mechanism for even the simplest hydrocarbon fuel (CH4) combustion involves more than 300 elemental reactions and the addition of CF3Br adds approximately 70 more elemental reactions. This large number of reactions and the associated large number of reaction species, many of which still involve uncertain reaction coefficients and thermodynamics properties, present significant computing challenges for applications in multidimensional non-premixed flames that are often encountered in practice. Therefore, it is of interest to systematically reduce the full chemical mechanism to a few global reactions while still maintaining the accuracy of the original mechanism. The present research systematically reduced the complex H2/Air/CF3Br chemical reaction mechanism with 94 initial elemental reactions to 5 global reaction steps. The reduced mechanism results in dramatic savings in computer time and is capable of predicting the major species and important steady state species with high accuracy. Through detailed sensitivity and production rate analysis the present research was able to find the key elemental reactions that are responsible for the fire suppression behavior of CF3Br. Predicted maximum concentrations of H and OH were found to correlate closely with the existing laminar burning velocity data measured for the premixed H2/Air/CF3Br flames. Better agreement with the experimental data was found when two activation energies for the two most important elementary reactions from QRRK calculations were adopted. The reduced mechanism developed through this research can be used to assist in the calculation and the understanding of fire suppression of CF3Br for more practical multidimensional nonpremixed laminar and turbulent flames, and the effort in searching for other effective fire suppressing agents.

The need for low order models capable of performing damage identification has become apparent in many structural dynamics applications where structural health monitoring and damage prognosis programs are implemented. These programs require that damage identification routines have low computational requirements and be reliable with some quantifiable degree of accuracy. Response surface metamodels (RSMs) are proposed to fill this need. Popular in the fields of chemical and industrial engineering, RSMs have only recently been applied in the field of structural dynamics and to date there have been no studies which fully demonstrate the potential of these methods. In this thesis, several RSMs are developed in order to demonstrate the potential of the methodology. They are shown to be robust to noise (experimental variability) and have success in solving the damage identification problem, both locating and quantifying damage with some degree of accuracy, for both linear and nonlinear systems. A very important characteristic of the RSMs developed in this thesis is that they require very little information about the system in order to generate relationships between damage indicators and measureable system responses for both linear and nonlinear structures. As such, the potential of these methods for damage identification has been demonstrated and it is recommended that these methods be developed further. / Master of Science

The fundamental advantages of applying Isogeometric Analysis (IGA) to shell analysis have been extensively demonstrated across a wide range of problems and formulations. However, a phenomenon called numerical locking is still a major challenge in IGA shell analysis, which can lead to dramatically deteriorated analysis accuracy. Additionally, for complex thin-walled structures, a simple and robust coupling technique is desired to sew together models composed of multiple patches. This dissertation focuses on addressing these challenges of IGA shell analysis. First, an isogeometric dual mortar method is developed for multi-patch coupling. This method is based on Be ?zier extraction and projection and can be employed during the creation and editing of geometry through properly modified extraction operators. It is applicable to any spline space which has a representation in Be ?zier form. The error in the method can be adaptively controlled, in some cases recovering optimal higher-order rates of convergence, by leveraging the exact refineability of the proposed dual spline basis without introducing any additional degrees-of-freedom into the linear system. This method can be used not only for shell elements but also for heat transfer and solid elements, etc. Next, a mixed formulation for IGA shell analysis is proposed that addresses both shear and membrane locking and improves the quality of computed stresses. The starting point of the formulation is the modified Hellinger-Reissner variational principle with independent displacement, membrane, and shear strains as the unknown fields. To overcome locking, the strain variables are interpolated with lower-order spline bases while the variations of the strain variables are interpolated with the proposed dual spline bases. As a result, the strain variables can be condensed out of the system with only a slight increase in the bandwidth of the resulting linear system and the condensed approach preserves the accuracy of the non-condensed mixed approach but with fewer degrees-of-freedom. Finally, as an alternative, new quadrature rules are developed to release membrane and shear locking. These quadrature rules asymptotically only require one point for Reissner-Mindlin (RM) shell elements and two points for Kirchhoff-Love (KL) shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial order p of the elements. The quadrature points are Greville abscissae and the quadrature weights are calculated by solving a linear moment fitting problem in each parametric direction. These quadrature rules are free of spurious zero-energy modes and any spurious finite-energy modes in membrane stiffness can be easily stabilized by using a higher-order Greville rule.

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This thesis presents a review of the theory of evaporation of pure substances with respect to kinetic and mechanistic models. These concepts are applied to multi-component evaporation and a model for the evaporation of solute atoms from a solvent is postulated. The evaporation experiments were performed on Fe 1% Mn melts at a constant pressure of approximately 10 microns over a temperature range of 1320° to 1810°C. The correlation between the experimental results and the expected theoretical results is discussed thoroughly in terms of surface control and diffusion control. / Thesis / Master of Engineering (ME)

An investigation into the responses of microbeams to electric actuations is presented. Attention is focused mainly on the use of microbeams in two important MEMS-based devices: capacitive microswitches and resonant microsensors. Nonlinear models are developed to simulate the behavior of the microbeams in each device. The models account for mid-plane stretching, an applied axial load, a DC electrostatic force, and, for the case of resonant sensors, an AC harmonic force. Further, a novel method that uses a reduced-order model is introduced for simulating the behavior of microbeams under a DC electrostatic force. The presented method shows attractive features, like for example, a high stability near the pull-in and a low computational cost. Thus, it can be of significant benefit to the development of MEMS design software. The static behavior of microbeams under electrostatic forces is studied using two methods. One method employs a shooting technique for solving the boundary-value problem that governs the static behavior. The second method is based on solving an algebraic system of equations obtained from the reduced-order model. Further, the eigenvalue problem describing the vibrations of a microbeam around its statically deflected position is solved using a shooting method to obtain the microbeam mode shapes and natural frequencies. The dynamic behavior of resonant microbeams is also investigated. A perturbation method, the method of multiple scales, is used to obtain two first-order nonlinear ordinary-differential equations that describe the amplitude and phase of the response and its stability. The results show that an inaccurate representation of the system nonlinearities may lead to an erroneous prediction of the nonlinear resonance frequency of a microbeam. The case of three-to-one internal resonance between the lowest two modes is treated. Finally, the reduced-order model is used to study the dynamic behavior of the electrostatically actuated microbeams. The proposed models are validated by comparing their results with experimental results available in the literature. / Master of Science