Reduction of Poisson-Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with nondegenerate Nijenhuis tensor

We show how to reduce, under certain regularities conditions, a Poisson-Nijenhuis Lie algebroid to a symplectic-Nijenhuis Lie algebroid with nondegenerate Nijenhuis tensor. We generalize the work done by Magri and Morosi for the reduction of Poisson-Nijenhuis manifolds. The choice of the more general framework of Lie algebroids is motivated by the geometrical study of some reduced bi-Hamiltonian systems. An explicit example of reduction of a Poisson-Nijenhuis Lie algebroid is also provided.Comment: 35 pages, final version to appear in J. Phys. A: Math. Theo

2D Modeling of Forcespinning™ Nanofiber Formation with Experimental Study and Validation

A newly developed method of producing nanofibers, called Forcespinning™, has proven to be a viable alternative to mass produce nanofibers. Forcespinning™ utilizes centrifugal forces which allow for a host of new materials to be processed into nanofibers while also providing a significant increase in yield and ease of production. To improve and enhance the Forcespinning™ production method, a 2D computational Forcespinning™ fluid dynamics model is developed. Three computer models, namely time-independent and time-dependent inviscid models and a viscous model are obtained and the influences of various parameters on Forcespinning™ fiber formation are obtained. This work also presents a detailed explanation of this new fiber production method using high speed photography to capture the jet initiation process and to track the trajectories of the resulting jets. The effect that the controllable parameters have on the fiber trajectories and final fiber diameters are presented, and a comparison to theoretical calculations is made

Integration of electronic and optical techniques in the design and fabrication of pressure sensors

Since the introduction of micro-electro-mechanical systems fabrication methods, piezoresistive pressure sensors have become the more popular pressure transducers. They dominate pressure sensor commercialization due to their high performance, stability and repeatability. However, increasing demand for harsh environment sensing devices has made sensors based on Fabry-Perot interferometry the more promising optical pressure sensors due to their high degree of sensitivity, small size, high temperature performance, versatility, and improved immunity to environmental noise and interference. The work presented in this dissertation comprises the design, fabrication, and testing of sensors that fuse these two pressure sensing technologies into one integrated unit. A key innovation is introduction of a silicon diaphragm with a center rigid body (or boss), denoted as an embossed diaphragm, that acts as the sensing element for both the electronic and optical parts of the sensor. Physical principles of piezoresistivity and Fabry-Perot interferometry were applied in designing an integrated sensor and in determining analytic models for the respective electronic and optical outputs. Several test pressure sensors were produced and their performance was evaluated by collecting response and noise data. Diaphragm deflection under applied pressure was detected electronically using the principle of piezoresistivity and optically using Fabry-Perot interferometry. The electronic part of the sensor contained four p-type silicon piezoresistors that were set into the diaphragm. They were connected in a Wheatstone bridge configuration for detecting strain-dependent changes in resistance induced by diaphragm deflection. In the optical part of the sensor, an optical cavity was formed between the embossed surface of the diaphragm and the end face of a single mode optical fiber. An infrared laser operating at 1.55 was used for optical excitation. Deflection of the diaphragm, which causes the length of the optical cavity to change, was detected by Fabry-Perot interference in the reflected light. Data collected on several sensors fabricated for this dissertation were shown to validate the theoretical models. In particular, the principle of operation of a Fabry-Perot interferometer as a mechanism for pressure sensing was demonstrated. The physical characteristics and behavior of the embossed diaphragm facilitated the integration of the electronic and optical approaches because the embossed diaphragm remained flat under diaphragm deflection. Consequently, it made the electronic sensor respond more linearly to applied pressure. Further, it eliminated a fundamental deficiency of previous applications of Fabry-Perot methods, which suffered from non-parallelism between the two cavity surfaces (diaphragm and fiber), owing to diaphragm curvature after pressure was applied. It also permitted the sensor to be less sensitive to lateral misalignment during the fabrication process and considerably reduced back pressure, which otherwise reduced the sensitivity of the sensor. As an integrated sensor, it offered two independent outputs in one sensor and therefore the capability for measurements of: (a) static and dynamic pressures simultaneously, and (b) two different physical quantities such as temperature and pressure

Leibniz algebroid associated with a Nambu-Poisson structure

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds

Rural music teacher job satisfaction, retention, and music education's career ladder

2020 Spring.Includes bibliographical references.In order to provide an equitable music education to all students, rural schools need to retain experienced, job-satisfied music teachers. Teacher job satisfaction is determined by working conditions, student interactions, goal progress, and self-efficacy (Badri et al. 2006; Lent & Brown, 2006; Williams, 2015). Additionally, rural teacher satisfaction is concerned with community identity (Bumgartner, 2013; Huysman, 2007; McCoy-Wilson, 2011; Richardson, 2017), while music teachers emphasize a strong support system within the school (Howard, 2006; Siebert, 2008; Scheib, 2004). Music teachers and teachers in rural schools have different priorities in determining their job satisfaction, which suggests that rural music teachers have a unique set of values in job satisfaction. Job satisfaction is an important predictor of teacher retention (Stockard & Lehman, 2004; Thibodeaux, 2015; Williams 2015), along with years of experience and preparation for entering the teaching field (Darling-Hammond, 2003; Ingersoll, 2001; Stockard & Lehman, 2004; Strunk & Robinson, 2006). These predictors pose major concerns for rural schools who often employ young, inexperienced teachers (Monk, 2007). Music teachers are especially challenging for rural school districts to retain (Hancock, 2009), which has negative effects on student performance (Barnes, Crowe, & Schaefer, 2007; Kloss, 2012; Russell, 2012; Terry & Kristonis, 2008; Rockoff, 2004) and perpetuates a "rural to urban" career ladder for the music education profession (Bates, 2011; Brossette, 2015; Howard, 2006; Kuntzelman, 2016). This mixed-method study investigated how working conditions, school support systems, teacher characteristics, and community belonging relate to rural music teachers' senses of job satisfaction and the relationship that their job satisfaction has with their decision to retain or leave their current teaching assignment. Quantitative data were collected via questionnaire (Duffy & Lent, 2009) and qualitative data were gathered through multiple-case-study methodology (Stake, 2006) to illustrate both broad job satisfaction considerations across a population of rural music teachers in Colorado as well as specific context-dependent job satisfaction and retention considerations. Questionnaire respondents demonstrated strong relationships between positive affect as a teacher characteristic, organizational support, and perceived fit as a working condition and overall job satisfaction. Case study participants further color these findings by specifying autonomy, participation in a musical community, support from the school community, and by their own strides in making progress toward student-centered goals as factors that contribute positively to their job satisfaction. Detractors from job satisfaction include a low value of music in the school community, dissonance between professional goals and community values, and isolation as an impediment to student-centered goals