A study of the application of singular perturbation theory

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions

Impact of carbonates on the mineralisation of surface soil organic carbon in response to shift in tillage practice

The inorganic soil C pool is a major source of CO2 emission into the atmosphere along with the soil respiratory CO2 fluxes but is comparatively less studied than the organic C mineralisation processes. This study aims to understand how soil available carbonates influence the soil C dynamics under different tillage, mulching and temperature regimes. A 90-day incubation experiment was conducted by adding calcite nodules to soils (10% w/w) collected from an agricultural field maintained with or without 5 t ha−1 mulching under no-till (NT) or conventional tillage (CT) systems. Environmental Scanning Electron Microscope (ESEM) examination indicated greater morphological changes in the calcite nodules incubated with CT than NT soils. Soil samples incubated with calcite and mulching recorded 6.3% greater CO2 evolution than the un-mulched condition. Under the CT system, the overall CO2 emission rate was higher in the control treatment (43%), followed by a combined treatment of 5 t ha−1 mulch + CaCO3 (10% w/w) (29.2%), 5 t ha−1 mulch only treatment (27.9%), and 10% CaCO3 (w/w) (16.5%) treatment, with a rise in incubation temperature from 22 °C to 37 °C. Kinetic model calculations for CO2 emission indicated a greater half-life of easily mineralisable C pools in the NT system at 22 °C. Microbial biomass carbon (MBC) results further verified that the high temperature and disturbed soil conditions limit the availability of soil MBC under the CT systems, indicating a higher decomposition rate. Eventually, these results indicated that agricultural management practices, including tillage shift, explicitly influence the different functional components of soil organic matter (SOM)

Trapping of a random walk by diffusing traps

We present a systematic analytical approach to the trapping of a random walk by a finite density rho of diffusing traps in arbitrary dimension d. We confirm the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the survival probability, and compute the dimension dependent constant c_d to leading order within an eps=2-d expansion.Comment: 16 pages, to appear in J. Phys.

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Attitudes of Older Adults in a Group-Based Exercise Program Toward a Blended Intervention:A Focus-Group Study

Ageing is associated with a decline in daily functioning and mobility. A physically active life and physical exercise can minimize the decline of daily functioning and improve the physical-, psychological- and social functioning of older adults. Despite several advantages of group-based exercise programs, older adults participating in such interventions often do not meet the frequency, intensity or duration of exercises needed to gain health benefits. An exercise program that combines the advantages of group-based exercises led by an instructor with tailored home-based exercises can increase the effectiveness. Technology can assist in delivering a personalized program. The aim of the study was to determine the susceptibility of older adults currently participating in a nationwide group-based exercise program to such a blended exercise program. Eight focus-groups were held with adults of 55 years of age or older. Two researchers coded independently the remarks of the 30 participants that were included in the analysis according to the three key concepts of the Self Determination Theory: autonomy, competence and relatedness. The results show that maintaining self-reliance and keeping in touch with others were the main motives to participate in the weekly group-based exercises. Participants recognized benefits of doing additional home-based exercises, but had concerns regarding guidance, safety and motivation. Furthermore, some participants strongly rejected the idea to use technology to support them in doing exercises at home, but the majority was open to it. Insights are discussed how these findings can help design novel interventions that can increase the wellbeing of older adults and preserve an independent living.

Static charged perfect fluid spheres in general relativity

Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.Comment: 23 pages, Revtex (galley), journal version, to appear in Phys.Rev.