Numerical Methods and Closed Orbits in the Kepler-Heisenberg Problem

The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental solution to the sub-Laplacian. This system is known to admit closed orbits, which all lie within a fundamental integrable subsystem. Here, we develop a computer program which finds these closed orbits using Monte Carlo optimization with a shooting method, and applying a recently developed symplectic integrator for nonseparable Hamiltonians. Our main result is the discovery of a family of flower-like periodic orbits with previously unknown symmetry types. We encode these symmetry types as rational numbers and provide evidence that these periodic orbits densely populate a one-dimensional set of initial conditions parametrized by the orbit's angular momentum. We provide links to all code developed.Comment: 9 pages, 7 figures, completed in residence at MSRI; updated all images and some tex

Crossflow effects on steady and fluctuating pressures on an ogive-cylinder cone-frustum model in supersonic separated flow

Wind-tunnel tests were conducted on an ogive-cylinder model with two axisymmetric protuberances having cone frustum angles of cone = 23 deg and 45 deg that were used to generate detached shock waves and the resulting separated flow areas downstream of the shock. The tests were conducted in a 9 by 7 foot supersonic wind tunnel at a free-stream Mach number of 2.0 and at Reynolds numbers of 1.5 x 1 million and 3.9 x 1 million, based on body diameter. The model had an afterbody fineness ratio of 8.3, and the ogive nose had a fineness ratio of 3.0. Two characteristics of the fluctuating pressures in surface vortex flows that result from the crossflow component, (velocity along the tunnel longitudinal axis free stream angle of attack), in combination with changes in the longitudinal pressure gradient were measured: (1) the broadband, rms-pressure coefficients and (2) the power spectral densities. Measurements are presented for various flow regions on the model such as the attached turbulent boundary layer, the detached frustum shock wave, and separated flow areas. The results indicate that the pressure fluctuations around or in the neighborhood of the foci of the vortex flows had broadband intensities and power spectral densities nearly identical to the levels previously measured in separated-flow regions at angles of attack of 0 deg

Teacher Candidate Mental Health and Mental Health Literacy

Providing teacher candidates with a strong foundation in mental health literacy during their teacher education program is crucial in ensuring novice teachers are prepared to support the mental health needs of their students. In addition to responding to students, teacher candidates are typically at an age when mental health disorders are common and their personal mental health during the program also needs to be considered. In the current study, a survey was conducted with 375 teacher candidates in order to extend our understanding of the personal mental health and mental health literacy of pre-service teachers. Results showed that teacher candidate mental health was similar to the general population, with 77% reporting positive personal mental health. Teacher candidates did report high levels of stress. Teacher candidates had considerable personal and professional experience with mental health prior to starting the program and reported positive attitudes and moderate levels of knowledge about mental health disorders. Despite considerable experience and a positive perspective, teacher candidates did not feel ready or competent to support the mental health of students. Current teacher education programs should consider building on the knowledge and experience the teacher candidates bring, and enhancing their capacity to translate that knowledge into the classroom setting

Bringing Trauma to School: Sharing the Educational Experience of Three Youths

Experiencing a traumatic event can impact students’ well-being and jeopardize their academic achievement and social-emotional health. A quarter of all students will experience a traumatic life event before they graduate from high school (Costello, Erkanli, Fairbank, & Angold, 2002), necessitating an understanding of how trauma affects students in the school context. This paper brings the perspectives of three youths to the forefront and explores their educational experiences and their perception of the role schools play in supporting students who bring trauma to school. A qualitative case study design and personal interviews with the youth led to the findings reported here. The presentation and management of the trauma and resulting stress differed among participants, and overall school experiences ranged from very negative to very positive. Participants were more unified in their perceptions of what they wanted from schools and the role that school could play. Themes across cases emphasized the importance of teacher driven, supportive, caring relationships, and the need for schools to focus on student well-being as well as academic functioning. The protective nature of school connectedness, in increasing engagement and decreasing at-risk behaviours and emotional distress (Blum, 2005; Bond et al., 2007; Klem & Connell, 2004; McNeeley, Nonnemaker, & Blum, 2002), holds promise for students with traumatic stress

The conception of the nature of human personality in Plato's thought and in recent idealism

This item was digitized by the Internet Archive. Thesis (M.A.)--Boston Universit

Enhancing Understanding of the Nature of Supportive School-based Relationships for Youth who have Experienced Trauma

Student-teacher relationships play a critical role in supporting the learning and well-being of students with mental health problems. The purpose of this article was to draw from both current literature and previous qualitative interview research to understand the aspects of school-based relationships that are beneficial for students who have experienced trauma. The integration of theory with the first-person accounts of the youth led to the development of a model that describes the core needs created by experiencing trauma and the nature of student-teacher relationships that can meet these needs in the educational context.  The four aspects of student teacher relationships that supported trauma-related needs at school were relationships that were 1) teacher driven, 2) authentic caring, 3) attunement to students’ emotional states, and 4) individualized. Establishing caring connections with teachers was pivotal to student health and well-being and to meeting the core needs created by traumatic events (safety, control, trust, self-worth, self-expression, connections).  As youth with mental health problems spend considerable time each week in the classroom, a greater understanding of the nature of supportive school-based relationships can inform teachers in their efforts to teach and connect with students.   Keywords: mental health, trauma, student-teacher relationships, school connectednes

Effects of zirconium compounds on a bright glaze

The standard method for producing opacity and to some extend sic mattness in a glaze has always been the use of small amounts of tin oxide. This oxide, however, is very expensive and tends to fluccuate sic in price over a wide range due to world market conditions. The ceramic industry, therefore, has been searching for some substitutes for the tin oxide with some success. At the present time zinc oxide, antimony oxide, and zirconium oxide are used with varying degrees of success as opacifiers. Zirconium oxide and compounds are less soluble than the other oxides previously used. Therefore, it is greatly possible that zirconium compounds should produce crystalline structure in lower percentages than the other oxides. With this knowledge it is the object of this experiment to determine the possibilities of the uses of zirconium compounds at percentages capable for commercial use in producing the same effects as tin oxide --Introduction, page 1