Browsing by Subject "Dynamical systems theory"
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Item The co-emergence of Spanish as a second language and individual differences : a dynamical systems theory perspective(2012-05) Lyle, Cory Jackson; Koike, Dale April; Salaberry, Maximo; Nishida, Chiyo; Blyth, Carl; Streeck, JürgenDynamical Systems Theory (DST) (De Bot, Lowie, & Vespoor 2007; Larsen-Freeman 1997, 2007; Larsen-Freeman & Cameron 2008; Dörnyei 2009; and van Lier 2000) represents a scientific paradigm shift derived from the fields of physics, engineering and theoretical mathematics that attempts to solve real-world scenarios that do not respond to scientific reductionism, otherwise known as ‘analysis’. The purpose of this dissertation is to (re)frame foreign language learning/use as a dynamical process that that involves interplay among what Dörnyei (2009) terms the language, the agent and the environment. More specifically, this dissertation presents a quasi-experimental, psycholinguistic study that looks at the interface between language (in this case the talk that resulted from NS-NNS interactions) and agent (as defined by a set of personal traits, or Individual Differences [IDs], including motivation, attitudes, personality and aptitude) in order to answer the research question: Do IDs vary in conjunction with language learning/use, and if so, how? Eight tutored Spanish learners were followed over the course of 16 weeks during which time they participated in 8 chat sessions with a native Spanish-speaker. Their ID profiles were measured immediately before and after each session and sessions with significant pre- to post-session ID shifts were analyzed to determine to what extent such shifts correlated with certain types of talk and/or think-aloud sequences. Results indicated that all participants’ pre- and post-interactional ID profiles fluctuated measurably and significantly, even within the span of a single interaction. Moreover, those sessions with significantly positive ID shifts were qualitatively different in terms of language-related episodes (LREs), conversation management/pragmatic markers, and metacognition from those with significantly negative ID shifts. Other unexpected findings revealed, for example, that LREs (especially NS-initiated LREs) negatively impacted motivations and attitudes and, therefore, the language-learning process itself. Taken together, the results of this study indicate that the agent’s IDs and their (inter)language co-emerge; that is to say, they evolve simultaneously and in response to one another. Moreover, this study suggests that DST can indeed be quasi-experimentally applied to the study of SLA, thus necessitating further development in DST-oriented methodologies and research questions.Item A dynamical systems theory analysis of Coulomb spacecraft formations(2013-08) Jones, Drew Ryan; Ocampo, Cesar; Schaub, HanspeterCoulomb forces acting between close flying charged spacecraft provide near zero propellant relative motion control, albeit with added nonlinear coupling and limited controllability. This novel concept has numerous potential applications, but also many technical challenges. In this dissertation, two- and three-craft Coulomb formations near GEO are investigated, using a rotating Hill frame dynamical model, that includes Debye shielding and differential gravity. Aspects of dynamical systems theory and optimization are applied, for insights regarding stability, and how inherent nonlinear complexities may be beneficially exploited to maintain and maneuver these electrostatic formations. Periodic relative orbits of two spacecraft, enabled by open-loop charge functions, are derived for the first time. These represent a desired extension to more substantially studied, constant charge, static Coulomb formations. An integral of motion is derived for the Hill frame model, and then applied in eliminating otherwise plausible periodic solutions. Stability of orbit families are evaluated using Floquet theory, and asymptotic stability is shown unattainable analytically. Weak stability boundary dynamics arise upon adding Coulomb forces to the relative motion problem, and therefore invariant manifolds are considered, in part, to more efficiently realize formation shape changes. A methodology to formulate and solve two-craft static Coulomb formation reconfigurations, as parameter optimization problems with minimum inertial thrust, is demonstrated. Manifolds are sought to achieve discontinuous transfers, which are then differentially corrected using charge variations and impulsive thrusting. Two nonlinear programming algorithms, gradient and stochastic, are employed as solvers and their performances are compared. Necessary and sufficient existence criteria are derived for three-craft collinear Coulomb formations, and a stability analysis is performed for the resulting discrete equilibrium cases. Each specified configuration is enabled by non-unique charge values, and so a method to compute minimum power solutions is outlined. Certain equilibrium cases are proven maintainable using only charge control, and feedback stabilized simulations demonstrate this. Practical scenarios for extending the optimal reconfiguration method are also discussed. Lastly, particular Hill frame model trajectories are integrated in an inertial frame with primary perturbations and interpolated Debye length variations. This validates qualitative stability properties, reveals particular periodic solutions to exhibit nonlinear boundedness, and illustrates higher-fidelity solution accuracies.