An analysis is presented of the linear and geometrically nonlinear static response of "thin" doubly-curved shells of revolution, under internal pressure loading. The analysis is based upon direct numerical integration of the governing differential equations, written in first-order state vector form. It is assumed that the loading and response of the shell are both axially symmetric; the governing equations are thus ordinary differential equations. The geometry of the shell is limited in the analysis by the assumptions of axisymmetry and constant thickness. The shell is allowed to have general composite laminate construction, elastic supports at the edges and internal ring stiffeners. In addition, the analysis allows for the possibility of circumferential line loads at discrete locations along the dome meridian. The problem is a numerically unstable two-point boundary value problem; integrations are performed using the technique of multiple shooting. A development of the multiple shooting technique known as stabilized marching is given. Results achieved by use of the multiple shooting technique are verified by comparison to results of finite element analysis using the finite element analysis codes STAGS and ABAQUS. Parametric studies are performed for ellipsoidal domes constructed of symmetric, 8-ply laminates. The parametric studies examine the effects of dome geometry for a quasi-isotropic laminate first, then examine whether material properties may be adjusted to create a "better" design. Conclusions and recommendations for future work follow. / Ph. D.

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Orientador: Lourdes de la Rosa Onuchic / Banca: Regina M.S.P. Tangredi / Banca: Romulo Campos Lins / Resumo: Este trabalho tem como tema central de investigação o ensino-aprendizagem das equações algébricas através da resolução de problemas. Nesta abordagem buscaram-se respostas para a questão de seu ensino no final do 3 ano do Ensino Médio. O estudo levou a um aprofundamento teórico de temas como: o ensino-aprendizagem da matemática, a matemática necessária para um trabalho com equações algébricas e uma metodologia de ensino-aprendizagem da matemática através de resolução de problemas. Na pesquisa de campo a coleta de dados utilizou-se de entrevistas, questionário, análise de documentos legais, análise de livros didáticos e não didáticos. Os tópicos de análise foram: a importância do ensino-aprendizagem das equações algébricas no final do terceiro ano do Ensino Médio, a utilização das equações algébricas em cursos universitários e como o ensino das equações algébricas no final do Ensino Médio é visto por alguns autores de livros didáticos e pesquisadores em Educação Matemática. Ainda, o tema equações algébricas assume o papel de enfeixar um programa de ensino de matemática ao longo de doze anos de estudo. A metodologia adotada neste trabalho foi a Metodologia de Romberg. / Abstract: This research has as central theme of investigation the teaching and learning of algebraic equations through problem solving. In this approach we have looked for answers to some questions about its teaching at the end of the third year of High School. The study took us to a theoretical deepening of themes like: the teaching and learning of mathematics, the necessary mathematics for a study with algebraic equations and a methodology of mathematics teaching and learning through problem solving. In the field research, we used interviews, questionnaires and analysis of legal documents and books. The topics of analysis were: the importance of teaching and learning of algebraic equations at the end of third year of High School, the use of algebraic equations in undergraduate courses and how the teaching of this topic at the end of High School is seen by some writers in mathematics education. So, the theme algebraic equations assumes the role of tying together the teaching of mathematics through twelve years of studying. As research methodology we adopted the Romberg's Methodology. / Mestre

This essay mirrors the structure found in my thesis film—a series of small vignettes—but does not emulate one for the other and vice versa. The essay is an experiment that seeks to allow rather than define and imagines a world already in place rather than built by the accumulation of reading and writing this text; the vignettes serve as a witness to this world rather than symbols building up a system of signs. I’m interested in expanding the conversation around political personhood towards a receptive stance; a politics of receptivity. This doesn’t serve as a counter to any narratives around a politics of action, activism and social justice, especially one that is needed now more than ever with the current political climate. Instead the text pays close attention to the daily, the individual, and the banal, not as an apathetic or reactionary stance, but as one charged with potential. In casting off an overarching relationship to narrative and resolve in the text, which does not deny narrativity found in the moments and individual vignettes, I posit a self of inconclusive gestures, pregnant moments and the feeling of something meaningful happening in a world of interviews, speculative text messages, portraits of binge watching tv, video essays, and case studies. The potential pitfalls and failures of a piece of this nature is to read each vignette as a simple projection of a stable self, that a stable I is seeing himself in all that is around. And while this writing encourages one to hold up a mirror and see oneself in a vignette it is also a piece that explores these affective limitations and symbolic acts of violence. There is the critique that non-narrative potential filled space creates a problematically uncomplicated relationship to the subject matter and viewer. This is a notion further developed in Maggie Nelson’s book, The Art of Cruelty that thinks through arts capability to enact change through often violent or problematic means. In discussing the work of artist Alfredo Jaar in which he rebukes Newsweek’s headlines with his own headlines about the Rwandan genocide, she writes, “since the artist has predetermined what it is, exactly, that we should have been looking at… what is the use of our looking at all?” (Nelson 26). By avoiding the possibility of critique or question to the piece by supplying the question and answer, Jaar’s work, she argues, becomes problematically tame. The receptive stance taken aims to keeps questions at the forefront rather than answer them. It is a writing that tries to keep the question, “What is left? What is still there after?” churning, full of potential and charged. It’s a piece that presumes a self always in the wake of, as Bergson writes with beautiful images of cones in his book Matter and Memory. It is a piece that also assumes a self that is always becoming, as Spinoza suggests with his famous line, “No one has determined what the body can do”. (Spinoza 87). Despite the contradiction of a self pulled to and from, past and future, this piece presumes that selfhood is formed on the basis of both simultaneously. Similar to how CA Conrad articulates his rituals creating space for himself, the text permits associations and cross readings in order to find some kind of residue to reside in. While this residual space from the accretion of texts rubbing up against each other is one in which I’m identifying a receptive selfhood, this space is one that also radically permits another. Kathleen Stewart articulates a similar position in her fantastic ethnographic study of coal mining communities in West Virginia, A Space on the Side of the Road. In it she writes, “In the effort to track something of the texture, density, and force of a local cultural real through its mediating forms and their social uses, it tears itself between evocation and representation, mimesis and interpretation.” It here could be both the text and an understanding of selfhood. This polemic of constructing a self through an affective refuge of experiences is one that is not a transaction. The vignettes, unless themselves an exchange, are complete onto themselves. They are curated and designed, but through their excess, unresolved nature and individuality they stand alone, while their impact secretes. I cannot say how the wake of the piece will be felt or what action comes from political passivity. But, as the Vipassana teacher Michele McDonald teaches, I know that in order to act first one has to understand where we are acting from. In this way the piece performs a similar purpose to Raymond William’s, Structures of Feelings that maps out affective terrains. This piece attempts to map, but never seeks to pin point or locate. There is no single source to find for one’s internal landscape, but there might be a way to witness where and how impact occurs in the radically passive personhood, the same way focusing on the breath allows one to witness when and how awareness shifts to thought, sensation or emotion; it’s about a continuous how, rarely about fixing a why. In lieu of the film one can think of the text as a bin system for video editing software. The folder in which this text is archived would be titled, potential. The text moves similarly to scrubbing through material. Then there is | |. I’m hesitant to pin down and strictly label the significance of | | but maybe thinking of it as a direction; | | is a whispered, “now,” or a pinched now, or a hand on the back with a warm now, but most importantly it is a continued now that respects critical/emotional distance. This sign is riddled throughout the text- in some moments performing an experience of time, time passing, or time severed, or performing the self addressing self through the correction of speech and grammar. At times it reveals an emotional temporal sense where the subjective experience extends or shrinks the actual.

Dynamical systems theory represents a prominent theoretical framework for the investigation of movement coordination and control in complex neurobiological systems. Central to this theory is the investigation of pattern formation in biological movement through application of tools from nonlinear dynamics. Movement patterns are regarded as attractors and changes in movement coordination can be described as phase transitions. Phase transitions typically exhibit certain key indicators like critical fluctuations, critical slowing down and hysteresis, which enable the formulation of hypotheses and experimental testing. An extensive body of literature exists which tested these characteristics and robustly supports the tenets of dynamical systems theory in the movement sciences. However, the majority of studies have tended to use a limited range of movement models for experimentation, mainly bimanual rhythmical movements, and at present it is not clear to what extent the results can be transferred to other domains such as discrete movements and/or multi-articular actions. The present work investigated coordination and control of discrete, multi-articular actions as exemplified by a movement model from the sports domain: the basketball hook shot. Accordingly, the aims of the research programme were three-fold. First, identification of an appropriate movement model. Second, development of an analytical apparatus to enable the application of dynamical systems theory to new movement models. Third, to relate key principles of dynamical systems theory to investigations of this new movement model. A summary of four related studies that were undertaken is as follows: 1. Based on a biomechanical analysis, the kinematics of the basketball hook shot in four participants of different skill levels were investigated. Participants were asked to throw from different shooting distances, which were varied in a systematic manner between 2m and 9m in two different conditions (with and without a defender present). There was a common significant trend for increasing throwing velocity paired with increasing wrist trajectory radii as shooting distance increased. Continuous angle kinematics showed high levels of inter- and intra-individual variability particularly related to throwing distance. Comparison of the kinematics when throwing with and without a defender present indicated differences for a novice performer, but not for more skilled individuals. In summary, the basketball hook shot is a suitable movement model for investigating the application of dynamical systems theory to a discrete, multi-articular movement model where throwing distance resembles a candidate control parameter. 2. Experimentation under the dynamical systems theoretical paradigm usually entails the systematic variation of a candidate control parameter in a scaling procedure. However there is no consensus regarding a suitable analysis procedure for discrete, multiarticular actions. Extending upon previous approaches, a cluster analysis method was developed which made the systematic identification of different movement patterns possible. The validity of the analysis method was demonstrated using distinct movement models: 1) bimanual, wrist movement, 2) three different basketball shots, 3) a basketball hook shot scaling experiment. In study 1, the results obtained from the cluster analysis approach matched results obtained by a traditional analysis using discrete relative phase. In study 2, the results from the method matched the a-priori known distinction into three different basketball techniques. Study 3 was designed specifically to facilitate a bimodal throwing pattern due to laboratory restrictions in throwing height. The cluster analysis again was able to identify the a-priori known distribution. Additionally, a hysteresis effect for throwing distance was identified further strengthening the validity of the chosen movement model. 3. Using eight participants, hook shot throwing distance was varied between 2m and 9m in both directions. Some distinct inter-individual differences were found in regards to movement patterning. For two subjects clear transitions between qualitatively distinct different patterns could be established. However, no qualitative differences were apparent for the remaining participants where it was suggested that a single movement pattern was continually scaled according to the throwing distance. The data supported the concept of degeneracy in that once additional movement degrees of freedom are made available these can be exploited by actors. The underlying attractor dynamics for the basketball hook shot were quite distinct from the bistable regime typically observed in rhythmical bimanual movement models. 4. To provide further evidence in support of the view that observed changes in movement patterning during a hook shot represented a phase transition, a perturbation experiment with five participants was performed. Throwing distance was once again varied in a scaling manner between 2m and 9m. The participants wore a wristband which could be attached to a weight which served as a mechanical perturbation to the throwing movement. Investigation of relaxation time-scales did not provide any evidence for critical slowing down. The movements showed high variation between all subsequent trials and no systematic variation in relation to either the mechanical perturbation or the successive jumps in throwing distance was indicated by the data. In summary, the results of the research programme highlighted some important differences between discrete multi-articular and bimanual rhythmical movement models. Based on these differences many of the findings ubiquitous in the domain of rhythmical movements may be specific to these and accordingly may not be readily generalized to movement models from other domains. This highlights the need for more research focussing on various movement models in order to broaden the scope of the dynamical systems framework and enhance further insight into movement coordination and control in complex neurobiological systems.

We consider here a class of mechanisms consisting of one or more compliant members, the manipulation of which relies on the deflection of those members. Compared with traditional rigid-body mechanisms, compliant mechanisms have the advantages of no relative moving parts and thus involve no wear, backlash, noises and lubrication. Motivated by the need in food processing industry, this paper presents the Global Coordinate Model (GCM) and the generalized shooting method (GSM) as a numerical solver for analyzing compliant mechanisms consisting of members that may be initially straight or curved. As the name suggests, the advantage of global coordinate model is that all the members share the same reference frame, and hence, greatly simplifies the formulation for multi-link and multi-axis compliant mechanisms. The GCM presents a systematic procedure with forward/inverse models for analyzing generic compliant mechanisms. Dynamic and static examples will be given and verified experimentally. We also develop the Generalized Shooting Method (GSM) to efficiently solve the equations given by the GCM. Unlike FD or FE methods that rely on fine discretization of beam members to improve its accuracy, the generalized SM that treats the boundary value problem (BVP) as an initial value problem can achieve higher-order accuracy relatively easily. Using the GCM, we also presents a formulation based on the Nonlinear Constrained Optimization (NCO) techniques to analyze contact problems of compliant grippers. For a planar problem it essentially reduces the domain of discretization by one dimension. Hence it requires simpler formulation and is computationally more efficient than other methods such as finite element analysis. An immediate application for this research is the automated live-bird transfer system developed at Georgia Tech. Success to this development is the design of compliant mechanisms that can accommodate different sizes of birds without damage to them. The feature to be monolithic also makes complaint mechanisms attracting in harsh environments such as food processing plants. Compliant mechanisms can also be easily miniaturized and show great promise in microelectromechanical systems (MEMS). It is expected that the model presented here will have a wide spectrum of applications and will effectively facilitate the process of design and optimization of compliant mechanisms.

Thesis (M.S.)--University of Wisconsin--Madison, 1982. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The carrying of concealed weapons for protection, specifically handguns, is a widely debated topic. This is especially true on college campuses following highly publicized mass shooting events. Researching students’ projected carrying behavior if legal on campus is important because it sheds light on the extent to which a concealed carry policy would be utilized in the university context, which has implications for public safety as well as student perceptions of safety. The scholarly literature indicates that White, Southern males who own guns are most likely to favor concealed carry policies. Donald Black’s theory of self-help (1983) and the collective security hypothesis (1987) frame this investigation by exploring whether students who feel that local law enforcement is ill equipped to protect them are more likely to say that they would utilize a concealed carry policy on campus as a measure of self-protection. Analyzing survey data from a Midwestern university In the Spring of 2009 with logistic regression, it is clear that the majority of students sampled are not in favor of a policy for carrying concealed firearms onto campus. As expected males and gun owners are significantly more likely to say they would carry concealed if legal. The interaction between gender and trust in law enforcement is also significant, indicating that males are more likely to say they would carry on campus relative to females as their level of confidence in law enforcement decreases. Overall, this research does not support Donald Black’s theory of self-help and the collective security hypothesis. In order to better test the theory of self-help and the collective security hypothesis, additional measures of the key variables are warranted in future research. In addition conducting a survey on projected carrying behavior with a nationally representative sample would aid understanding as to how the broader population of students in The United States would feel and behave if concealed carry were legal on their campus. Further investigation exploring why gender and law enforcement interact in predicting projected carry behavior is warranted.

abstract: Public mass shootings occur at a rate in the U.S. that is higher than any other developed country. These event initiate wide spread media attention. The media attention these events achieve have shown to impact the public behavior (e.g., increased firearm sales). However, the impact public mass shootings have on firearm storage and carry habits of the public is not well understood. Using data collected from the Transportation Security Administration, this study examines how mass shootings have led to moral panics occurring within the U.S. through the examination of the firearm carrying habits among the population immediately following mass shootings. The results indicate that loaded firearms with rounds in the chamber detected by the TSA have significantly increased since 2012. Further, firearms detected immediately following a public mass shooting had a higher proportion of firearms loaded with a round in the chamber relative to 7 days prior to the shooting. Moreover, the increase in proportions of firearms found loaded with a round in the chamber exponentially decays as days past the initial shooting, these events occur at a higher rate than the decay rate can normalize these occurrences. I conclude that in the wake of these shootings a moral panic ensues that is partially responsible for the change in the general public’s arming configuration habits. Further research is needed in to determine the impact on crime, and public health related issues due to this change in the public’s firearm carrying habits. / Dissertation/Thesis / Masters Thesis Criminology and Criminal Justice 2018

This thesis develops a study for the frequency warping introduced by time-domain methods. The work in this study focuses first on the time-domain methods used in the classical SPICE engine, that is the Backward Euler, the Trapezoidal Rule and the Gear's methods. Next, the thesis considers the newly developed high-order method based on the Obreshkov formula. This latter method was proved to have the A-stability and L-stability properties, and is therefore robust in circuit simulation. However, to the best of the author's knowledge, a mathematical study for the frequency warping introduced by this method has not been developed yet. The thesis therefore develops the mathematical derivation for the frequency warping of the Obreshkov-based method. The derivations produced reveal that those methods introduce much smaller warping errors than the traditional methods used by SPICE. In order to take advantage of the small warping error, the thesis develops a shooting method framework based on the Obreshkov-based method to compute the steady-state response of nonlinear circuits excited by periodical sources. The new method demonstrates that the steady-state response can be constructed with much smaller number of time points than what is typically required by the classical methods.