Time Evolution of Temperature and Entropy of Various Collapsing Domain Walls

We investigate the time evolution of the temperature and entropy of gravitationally collapsing domain walls as seen by an asymptotic observer. In particular, we seek to understand how topology and the addition of a cosmological constant affect the gravitational collapse. Previous work has shown that the entropy of a spherically symmetric collapsing domain approaches a constant. In this paper, we reproduce these results, using both a fully quantum and a semi-classical approach, then we repeat the process for a de Sitter Schwarzschild domain wall (spherical with cosmological constant) and a (3+1) BTZ domain wall (cylindrical). We do this by coupling a scalar field to the background of the domain wall and analyzing the spectrum of radiation as a function of time. We find that the spectrum is quasi-thermal, with the degree of thermality increasing as the domain wall approaches the horizon. The thermal distribution allows for the determination of the temperature as a function of time, and we find that the late time temperature is very close to the Hawking temperature and that it also exhibits the proper scaling with the mass. From the temperature we find the entropy. Since the collapsing domain wall is what forms a black hole, we can compare the results to those of the standard entropy-area relation. We find that the entropy does in fact approach a constant that is close to the Hawking entropy. However, both the de Sitter Schwarzschild domain wall and the (3+1) BTZ domain wall show periods of decreasing entropy, which suggests that spontaneous collapse may be prevented.Comment: This paper is a merging of two previously submitted papers: Time Evolution of Temperature and Entropy of a Gravitationally Collapsing Cylinder [arXiv:1106.2278]; Time Evolution of Temperature and Entropy of a Gravitationally Collapsing de Sitter Schwarzschild Domain Wal

Schrodinger formalism, black hole horizons and singularity behavior

The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstr\"om domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schrodinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schrodinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schrodinger equation becomes non-local, but the wave function describing the system is non-singular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.Comment: 10 pages; v2 added references and further comment on singularity behavior, version to appear in PR

Identification of dividing, determined sensory neuron precursors in the mammalian neural crest

Sensory and autonomic neurons of the vertebrate peripheral nervous system are derived from the neural crest. Here we use the expression of lineage-specific transcription factors as a means to identify neuronal subtypes that develop in rat neural crest cultures grown in a defined medium. Sensory neurons, identified by expression of the POU-domain transcription factor Brn-3.0, develop from dividing precursors that differentiate within 2 days following emigration from the neural tube. Most of these precursors generate sensory neurons even when challenged with BMP2, a factor that induces autonomic neurogenesis in many other cells in the explants. Moreover, BMP2 fails to prevent expression of the sensory-specific basic helix-loop-helix (bHLH) transcription factors neurogenin1, neurogenin2 and neuroD, although it induces expression of the autonomic-specific bHLH factor MASH1 and the paired homeodomain factor Phox2a in other cells. These data suggest that there are mitotically active precursors in the mammalian neural crest that can generate sensory neurons even in the presence of a strong autonomic-inducing cue. Further characterization of the neurons generated from such precursors indicates that, under these culture conditions, they exhibit a proprioceptive and/or mechanosensory, but not nociceptive, phenotype. Such precursors may therefore correspond to a lineally (Frank, E. and Sanes, J. (1991) Development 111, 895-908) and genetically (Ma, Q., Fode, C., Guillemot, F. and Anderson, D. J. (1999) Genes Dev. 13, in press) distinct subset of early-differentiating precursors of large-diameter sensory neurons identified in vivo

Payload deployment method and system

A method and apparatus for deploying the payload of space shuttle or the like is described. It is referred to as the Stabilized Payload Deployment System (SPDS). The payload is rotated about an axis outside of the payload but approximately longitudinally with the cargo bay of the shuttle craft. The payload may thus be rotated through ninety degrees. In this case, that is, in its rotated position, the payload may or may not have a small portion located within the cargo bay. Alternatively, the payload may be located completely outside of the bay. According to the apparatus two separable hinge-like devices connect at one longitudinal side or edge of the payload to respective ones of the payload trunnions at different longitudinally spaced locations along the length of the payload. Separation of the payload from the cargo bay is made by unlatching a latch and by the use of a repulsion spring at the position of each hinge-like device. Two four-link mechanisms allow movement between payload and bay. Such accommodative movement is required especially during launch when considerable vibration is encountered

Student perceptions regarding classroom environments for learning.

The classroom environment has a powerful influence on learning, and children\u27s perceptions of that environment influence their behavior. This study examines the perceptions of sixth grade students who are the most and least academically successful regarding how they perceive their classroom environment and those factors within it that enhance or inhibit learning. Data gathered in this research indicate that there are significant disparities in how the most and least successful students perceive their classroom learning environment. The most successful students perceived the classroom environment as more affiliative and task focused, perceived their teachers to be more trusting, caring, and supportive, and perceived that they had more choice in how they learned. In contrast, the least successful students perceived the class to be more teacher controlled and competitive. In spite of the differences in friendship and support perceived by study participants, both groups of students were able to provide clear examples of teaching approaches and classroom conditions that they perceived increased or inhibited their learning. This study also includes students\u27 suggestions for changes that would increase their learning. The findings in this study are consistent with the research and literature reviewed from the fields of education, psychology, and business regarding conditions that are likely to enhance learning. The major implications of this study are that teachers need to: (a) be able to form caring, supportive relationships with all students, (b) create safe, non-threatening environments where learning is less competitive and students are encouraged to form supportive relationships with one another, (c) provide students with interesting, challenging work that engages them, while supporting and encouraging students\u27 efforts, (d) develop a large repertoire of effective instructional approaches to meet the diverse learning needs of students, (e) keep current with the knowledge base, (f) ask, and listen to students to understand how they learn best, and (g) seek professional experiences that will help them reflect on how they can improve their practice. Finally, a number of recommendations are proposed for use by teachers, administrators, organizations that provide pre-service and in-service opportunities, educational policy makers, and other parties interested in assisting teachers and schools increase student learning