An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer

Development of a remote digital augmentation system and application to a remotely piloted research vehicle

A cost-effective approach to flight testing advanced control concepts with remotely piloted vehicles is described. The approach utilizes a ground based digital computer coupled to the remotely piloted vehicle's motion sensors and control surface actuators through telemetry links to provide high bandwidth feedback control. The system was applied to the control of an unmanned 3/8-scale model of the F-15 airplane. The model was remotely augmented; that is, the F-15 mechanical and control augmentation flight control systems were simulated by the ground-based computer, rather than being in the vehicle itself. The results of flight tests of the model at high angles of attack are discussed

A remotely augmented vehicle approach to flight testing RPV control systems

A remotely augmented vehicle concept for flight testing advanced control systems was developed as an outgrowth of a remotely piloted research vehicle (RPV) program in which control laws are implemented through telemetry uplink and downlink data channels using a general purpose ground based digital computer which provides the control law computations. Some advantages of this approach are that the cost of one control system facility is spread over a number of RPV programs, and control laws can be changed quickly as required, without changing the flight hardware. The remotely augmented vehicle concept is described, and flight test results from a subscale F-15 program are discussed. Suggestions of how the concept could lead to more effective testing of RPV control system concepts, and how it is applicable to a military RPV reconnaissance mission are given

A selfconsistent theory of current-induced switching of magnetization

A selfconsistent theory of the current-induced switching of magnetization using nonequilibrium Keldysh formalism is developed for a junction of two ferromagnets separated by a nonmagnetic spacer. It is shown that the spin-transfer torques responsible for current-induced switching of magnetization can be calculated from first principles in a steady state when the magnetization of the switching magnet is stationary. The spin-transfer torque is expressed in terms of one-electron surface Green functions for the junction cut into two independent parts by a cleavage plane immediately to the left and right of the switching magnet. The surface Green functions are calculated using a tight-binding Hamiltonian with parameters determined from a fit to an {\it ab initio} band structure.This treatment yields the spin transfer torques taking into account rigorously contributions from all the parts of the junction. To calculate the hysteresis loops of resistance versus current, and hence to determine the critical current for switching, the microscopically calculated spin-transfer torques are used as an input into the phenomenological Landau-Lifshitz equation with Gilbert damping. The present calculations for Co/Cu/Co(111) show that the critical current for switching is $\approx 10^7A/cm^2$, which is in good agreement with experiment.Comment: 23 pages, 16 figure

Joint disease mapping using six cancers in the Yorkshire region of England

OBJECTIVES: The aims of this study were to model jointly the incidence rates of six smoking related cancers in the Yorkshire region of England, to explore the patterns of spatial correlation amongst them, and to estimate the relative weight of smoking and other shared risk factors for the relevant disease sites, both before and after adjustment for socioeconomic background (SEB). METHODS: Data on the incidence of oesophagus, stomach, pancreas, lung, kidney, and bladder cancers between 1983 and 2003 were extracted from the Northern & Yorkshire Cancer Registry database for the 532 electoral wards in the Yorkshire region. Using postcode of residence, each case was assigned an area-based measure of SEB using the Townsend index. Standardised incidence ratios (SIRs) were calculated for each cancer site and their correlations investigated. The joint analysis of the spatial variation in incidence used a Bayesian shared-component model. Three components were included to represent differences in smoking (for all six sites), bodyweight/obesity (for oesophagus, pancreas and kidney cancers) and diet/alcohol consumption (for oesophagus and stomach cancers). RESULTS: The incidence of cancers of the oesophagus, pancreas, kidney, and bladder was relatively evenly distributed across the region. The incidence of stomach and lung cancers was more clustered around the urban areas in the south of the region, and these two cancers were significantly associated with higher levels of area deprivation. The incidence of lung cancer was most impacted by adjustment for SEB, with the rural/urban split becoming less apparent. The component representing smoking had a larger effect on cancer incidence in the eastern part of the region. The effects of the other two components were small and disappeared after adjustment for SEB. CONCLUSIONS: This study demonstrates the feasibility of joint disease modelling using data from six cancer sites. Incidence estimates are more precise than those obtained without smoothing. This methodology may be an important tool to help authorities evaluate healthcare system performance and the impact of policies