Difference Methods for Boundary Value Problems in Ordinary Differential Equations

A general theory of difference methods for problems of the form Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0, is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0 are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution

Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers

A model for sharp fronts in glassy polymers is derived and analyzed. The major effect of a diffusing penetrant on the polymer entanglement network is taken to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms via a relaxation parameter. This accounts for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state due to slow response to changing conditions. Both numerical and analytical perturbation studies of a boundary value problem for a dry glass polymer exposed to a penetrant solvent are completed. Concentration profiles in good agreement with observations are obtained

Shock Formation in a Multidimensional Viscoelastic Diffusive System

We examine a model for non-Fickian "sorption overshoot" behavior in diffusive polymer-penetrant systems. The equations of motion proposed by Cohen and White [SIAM J. Appl. Math., 51 (1991), pp. 472–483] are solved for two-dimensional problems using matched asymptotic expansions. The phenomenon of shock formation predicted by the model is examined and contrasted with similar behavior in classical reaction-diffusion systems. Mass uptake curves produced by the model are examined and shown to compare favorably with experimental observations

Testing and Concentration of a Low Grade Gold Ore from Marysville, Montana

The purpose of this thesis was to investigate and attempt to concentrate low grade cyanided tailings rejected from the old Montana Mining and milling Company\u27s mill situated 4 miles below the town of Marysville, Montana

Therapeutic Foster Care: Some Characteristics of Youth and Children in Out of Home Placements in the State of North Dakota

This study provides a description of the children and youth who are in out of home placements. The study population consists of an analysis of some characteristics of 146 children and youth to be used as a baseline analysis which can be utilized for agency program planning, policy development, and administration. The characteristics of the children and youth were obtained from individuals residing in therapeutic foster care in the state of North Dakota, supervised by the Professional Association of Treatment Home (PATH). An independent organization tabulated the raw data utilized in this study. The information was collection for a period of 18 months, beginning April 1, 1995. The analysis of the information collected will provide a partial profile of the children and youth served at PATH, differentiated by gender, psychiatric diagnosis, involvement with the judicial system, length of service, race, school problems, and family problems. The information concluded from this study will assist with future planning and program development for PATH of North Dakota. Recent political decisions and economic downsizing necessitate awareness of agency functioning and effectiveness. Ability to adapt and improve is the key to agency survival in order to maintain the commitment of quality service to the children and families served through PATH

The goldstone real-time connected element interferometer

Connected element interferometry (CEI) is a technique of observing a celestial radio source at two spatially separated antennas and then interfering the received signals to extract the relative phase of the signal at the two antennas. The high precision of the resulting phase delay data type can provide an accurate determination of the angular position of the radio source relative to the baseline vector between the two stations. This article describes a recently developed connected element interferometer on a 21-km baseline between two antennas at the Deep Space Network's Goldstone, California, tracking complex. Fiber-optic links are used to transmit the data to a common site for processing. The system incorporates a real-time correlator to process these data in real time. The architecture of the system is described, and observational data are presented to characterize the potential performance of such a system. The real-time processing capability offers potential advantages in terms of increased reliability and improved delivery of navigational data for time-critical operations. Angular accuracies of 50-100 nrad are achievable on this baseline

Transcriptional repression by ApiAP2 factors is central to chronic toxoplasmosis

Tachyzoite to bradyzoite development in Toxoplasma is marked by major changes in gene expression resulting in a parasite that expresses a new repertoire of surface antigens hidden inside a modified parasitophorous vacuole called the tissue cyst. The factors that control this important life cycle transition are not well understood. Here we describe an important transcriptional repressor mechanism controlling bradyzoite differentiation that operates in the tachyzoite stage. The ApiAP2 factor, AP2IV-4, is a nuclear factor dynamically expressed in late S phase through mitosis/cytokinesis of the tachyzoite cell cycle. Remarkably, deletion of the AP2IV-4 locus resulted in the expression of a subset of bradyzoite-specific proteins in replicating tachyzoites that included tissue cyst wall components BPK1, MCP4, CST1 and the surface antigen SRS9. In the murine animal model, the mis-timing of bradyzoite antigens in tachyzoites lacking AP2IV-4 caused a potent inflammatory monocyte immune response that effectively eliminated this parasite and prevented tissue cyst formation in mouse brain tissue. Altogether, these results indicate that suppression of bradyzoite antigens by AP2IV-4 during acute infection is required for Toxoplasma to successfully establish a chronic infection in the immune-competent host

SAFETY PATROL: UTILIZING TECHNOLOGY TO IMPROVE RESPONSE TIMES IN EMERGENCY EVENT SITUATIONS

Mass shootings have, tragically, been on the rise in recent years and, heartbreakingly, those incidents can and do take place on school grounds. Techniques are presented herein that support a Safety Patrol facility that accelerates emergency services response times and equips first responders with the critical information that is required to act quickly in an emergency situation. According to the presented techniques, after an emergency event (such as a gunshot, a fire alarm, etc.) is detected, a network may react to the notification of that event by automatically creating a new Wi-Fi service set identifier (SSID) named FirstResponders and generating a splash page for first responder login. After successfully logging in, the presented techniques provide an overview of a facility (through floor plan maps) and identify the locations of video cameras which may be selected to receive live video feeds. Additionally, according to the presented techniques detected events may be displayed on a floor plan along with timestamps to provide historical situational awareness and equip first responders with not just information regarding what occurred where, but also access to the live feeds depicting what is currently happening

Power balance in a helicon plasma source for space propulsion

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 107-109).Electric propulsion systems provide an attractive option for various spacecraft propulsion applications due to their high specific impulse. The power balance of an electric thruster based on a helicon plasma source is presented. The power balance is shown to be comprised of several variables, including the RF power supplied to the system, dissipative losses in transmission hardware, losses in the neutral confinement tube, uncoupled RF radiation, ionization power, and plume output power. A thermal model for the neutral confinement tube is presented whereby heat flux may be derived from thermal response data. Numerical simulation and experimental benchmarking are employed to validate this thermal model. A mapping of power consumption is presented. Comparison with experimental parameters indicates that 97% of the power supplied to the system is accounted for, suggesting that primary loss mechanisms have been identified. Avenues for improving the performance of the thruster, based on these data, are presented.by Daniel B. White, Jr.S.M