A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

The non-promotion policy versus the social-promotion policy in the Boston public school system

Thesis (Ed.M.)--Boston Universit

Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of Schrodinger equations and provide explicit representation for three classes of such systems. We show also that there is an elegant relationship between these transformations and analytic complex matrix functions.Comment: 14 page

Ignition of mixtures of SiH sub 4, CH sub 4, O sub 2, and Ar or N sub 2 behind reflected shock waves

Ignition delay times in mixtures of methane, silane, and oxygen diluted with argon and nitrogen were measured behind reflected shock waves generated in the chemical kinetic shock tube at Langley Research Center. The delay times were inferred from the rapid increase in pressure that occurs at ignition, and the ignition of methane was verified from the emission of infrared radiation from carbon dioxide. Pressures of 1.25 atm and temperatures from 1100 K to 1300 K were generated behind the reflected shocks; these levels are representative of those occurring within a supersonic Ramjet combustor. Expressions for the ignition delay time as a function of temperature were obtained from least squares curve fits to the data for overall equivalence ratios of 0.7 and 1.0. The ignition delay times with argon as the diluent were longer than those with nitrogen as the diluent. The infrared wavelength observations at 4.38 microns for carbon dioxide indicated that silane and methane ignited simultaneously (i.e., within the time resolution of the measurement). A combined chemical kinetic mechanism for mixtures of silane, methane, oxygen, and argon or nitrogen was assembled from one mechanism that accurately predicted the ignition of methane and a second mechanism that accurately predicted silane hydrogen ignition. Comparisons between this combined mechanism and experiment indicated that additional reactions, possibly between silyl and methyl fragments, are needed to develop a good silane methane mechanism